Quaternary Science Reviews 20 (2001) 1475}1560
Terrestrial in situ cosmogenic nuclides: theory and application John C. Gosse *, Fred M. Phillips Department of Geology, 120 Lindley Hall, University of Kansas, Lawrence, KS 66045, USA Department of Earth & Environmental Science, New Mexico Tech, Socorro, NM 87801, USA
Abstract
The cosmogenic nuclide exposure history method is undergoing major developments in analytical, theoretical, and applied areas. The capability to routinely measure low concentrations of stable and radioactive cosmogenic nuclides has led to new methods for addressing long-standing geologic questions and has provided insights into rates and styles of sur"cial processes. The di!erent physical and chemical properties of the six most widely used nuclides: He, Be, C, Ne, Al, and Cl, make it possible to apply the surface exposure dating methods on rock surfaces of virtually any lithology at any latitude and altitude, for exposures ranging from 10 to 10 years. The terrestrial in situ cosmogenic nuclide method is beginning to revolutionize the manner in which we study landscape evolution. Single or multiple nuclides can be measured in a single rock surface to obtain erosion rates on boulder and bedrock surfaces, #uvial incision rates, denudation rates of individual landforms or entire drainage basins, burial histories of rock surfaces and sediment, scarp retreat, fault slip rates, paleoseismology, and paleoaltimetry. Ages of climatic variations recorded by moraine and alluvium sediments are being directly determined. Advances in our understanding of how cosmic radiation interacts with the geomagnetic "eld and atmosphere will improve numerical simulations of cosmic-ray interactions over any exposure duration and complement additional empirical measurements of nuclide production rates. The total uncertainty in the exposure ages is continually improving. This article presents the theory necessary for interpreting cosmogenic nuclide data, reviews estimates of parameters, describes strategies and practical considerations in "eld applications, and assesses sources of error in interpreting cosmogenic nuclide measurements. 2001 Elsevier Science Ltd. All rights reserved.
TABLE OF CONTENTS
1. Introduction ...... 1477
1.1. Development of the TCN methods ...... 1477 1.2. Applications of TCN Exposure methods ...... 1479 1.3. Previous reviews ...... 1480
2. Glossary ...... 1480
2.1. Terminology ...... 1480 2.2. Notation ...... 1482
3. Principles ...... 1485
3.1. Introduction ...... 1485 3.1.1. Source of the primary radiation ...... 1485 3.1.2. Ewects of the geomagnetic xeld on GCR ...... 1485 3.1.3. Trajectory models and models of secondary nuclide production rates ...... 1487 3.1.4. Recent numerical models of GCR particle production ...... 1489 3.1.5. Nuclide production from primary GCR ...... 1490 3.1.6. TCN production by energetic nucleons ...... 1491
* Corresponding author. Tel.: #1-785-864-4974; fax: #1-785-864-5276. E-mail address: [email protected] (J.C. Gosse).
0277-3791/01/$ - see front matter 2001 Elsevier Science Ltd. All rights reserved. PII: S 0 2 7 7 - 3 7 9 1 ( 0 0 ) 0 0 1 7 1 - 2 1476 J.C. Gosse, F.M. Phillips / Quaternary Science Reviews 20 (2001) 1475}1560
3.1.7. TCN production by low-energy neutron ...... 1491 3.1.8. TCN production by muons ...... 1492 3.1.9. Factors limiting TCN applications ...... 1493 3.2. Numerical simulation of low-energy neutron behavior ...... 1493 3.3. Analytical equations for TCN production ...... 1495 3.3.1. Fast neutron (Spallation) production ...... 1496 3.3.2. Production by epithermal neutrons ...... 1497 3.3.3. Production by thermal neutrons ...... 1498 3.3.4. Production by muons and muon-derived neutrons ...... 1499 3.3.5. Total nuclide production ...... 1502 3.4. Energetic neutron attenuation length...... 1502 3.5. Temporal variations in production rates ...... 1504 3.5.1. Variations in the primary GCR yux ...... 1506 3.5.2. Variations due to solar modulation of the magnetic xeld ...... 1507 3.5.3. Ewects of the geomagnetic xeld ...... 1507 3.5.4. Variations in atmospheric shielding ...... 1515 3.5.5. Other sources of temporal variations in production ...... 1515 3.6. Estimation of production rates ...... 1516 3.6.1. Helium-3 ...... 1516 3.6.2. Beryllium-10 ...... 1516 3.6.3. Carbon-14 ...... 1517 3.6.4. Neon-21 ...... 1517 3.6.5. Aluminum-26 ...... 1517 3.6.6. Chlorine-36 ...... 1518 3.7. Scaling and correction factors for production rates ...... 1518 3.7.1. Spatial scaling ...... 1518 3.7.2. Topographic shielding ...... 1520 3.7.3. Surface coverage ...... 1522 3.7.4. Sample thickness ...... 1522 3.7.5. Thermal neutron leakage ...... 1523 3.8. Exposure dating witha single TCN ...... 1523 3.9. Exposure dating withmultiple nuclides ...... 1527 3.10. Nuclide-speci"c considerations ...... 1531 3.10.1. Helium-3 ...... 1531 3.10.2. Beryllium-10 ...... 1531 3.10.3. Carbon-14 ...... 1532 3.10.4. Neon-21 ...... 1532 3.10.5. Aluminum-26 ...... 1532 3.10.6. Chlorine-36 ...... 1533 3.11. TCN dating of sediment ...... 1533
4. Sampling strategies ...... 1536 4.1. Field sampling considerations ...... 1536 4.1.1. Sample description ...... 1536 4.1.2. Sampling methodology ...... 1537 4.2. Other lithological considerations ...... 1538 4.3. How muchsample is needed? ...... 1538 4.4. Strategies for concentration-depthpro "les ...... 1539
5. Sample preparation and experimental data interpretation ...... 1540
5.1. TCN sample preparation ...... 1540 5.1.1. Preparation time ...... 1541 5.1.2. Physical and chemical pretreatment ...... 1541 5.1.3. Isotopic extraction ...... 1541 5.2. Experimental data interpretation ...... 1542
6. Uncertainty and sources of error ...... 1544 6.1. Sources of error ...... 1544 6.1.1. Sample characteristics ...... 1545 6.1.2. Sample preparation and elemental analyses ...... 1546 J.C. Gosse, F.M. Phillips / Quaternary Science Reviews 20 (2001) 1475}1560 1477
6.1.3. Mass spectrometry ...... 1546 6.1.4. Systematic errors ...... 1547 6.2. Reporting the uncertainty ...... 1548 6.2.1. Error propagation ...... 1549 6.2.2. Evaluating accuracy by intercomparison ...... 1549 6.2.3. Multiple sample measurements ...... 1550 6.2.4. Sensitivity analysis ...... 1550 7. Directions of future contributions ...... 1550 Acknowledgements ...... 1551 References ...... 1551
1. Introduction routine measurement of TCN, the annual numbers of publications applying TCN to earth-science problems For many years after its discovery in 1912 by Austrian has grown exponentially. However, we feel that one fac- physicist Victor Hess, cosmic radiation was studied tor still limiting the range and number of applications is mainly for the insights it could provide into fundamental the lack of readily available information on the theory particle physics. Since particle accelerators were not yet and practice of TCN techniques. Although several publi- invented, cosmic-rays provided a unique source of high- cations on TCN methods exist, there is no single refer- energy subatomic particles for physics experimentation. ence to refer for a complete overview. The objective of In 1934 A.V. Grosse suggested that cosmic radiation this review is to provide such a reference. It is intended could produce radioactive nuclides at the surface of the mainly for those potentially interested in the TCN earth and gave such (hypothetical) species the name `cos- methods, those starting to apply them, or for those who mic radio-elementsa. The realization by Libby in 1949 wishto evaluate TCN applications by others.We at- that cosmic radiation produced easily measurable tempt to provide su$cient detail on theory and para- amounts of C through interaction with the atmosphere meters to enable the reader to compute TCN ages and opened the new possibility of applications to the earth erosion rates, as well as practical advice on "eld strat- sciences. In 1955 Raymond Davis and Oliver Scha!er egies and sampling. We also analyze the sensitivity of the proposed that cosmogenic nuclides produced within TCN method to chemical, physical, and geological fac- minerals at the surface of the earth could be applied to tors which a!ect the interpretation of TCN data for geological problems. Starting in the 1950s, interactions of solving geologic problems. This paper does not attempt cosmic rays withrock materials was studied in meteor- to provide anything but cursory reviews of analytical ites, and in lunar samples since 1969 (Reedy et al., 1983), methods, previous earth-science applications, cosmic-ray but muchlower production rates inhibitedsimilar physics, or instructions for statistically treating the un- measurements in terrestrial rocks. A theoretical founda- certainty in interpretations of TCN data. References to tion for suchstudies was laid by Lal and Peters (1967). In other articles that treat these topics in detail are given. spite of these visionary early e!orts, terrestrial in situ We hope that this article will stimulate new ideas for cosmogenic nuclide applications languished until the applying and advancing TCN methods. mid-1980s because available analytical instrumentation was not capable of routinely measuring the exceedingly 1.1. Development of the TCN methods low concentrations of most cosmogenic nuclides produc- ed at earth-surface altitudes. The production rates in The development of the TCN exposure history sur"cial rocks are commonly several orders of magnitude methods can be summarized in four distinct phases: (1) less than average rates in the atmosphere. (In this paper the realization of the utility of TCN for determining we refer to cosmogenic nuclides produced within rocks or surface exposure ages; (2) the development of a means to minerals at, or close to, the surface of the earth as `terres- estimate the secondary cosmic-ray #ux at di!erent sites trial in situ cosmogenic nuclidesa (TCN), and describe of any latitude and elevation; (3) the development of nuclides produced in the atmosphere as `meteorica or AMS and highly sensitive noble-gas mass spectrometry; `atmospherica to distinguishthemfrom TCN.) and (4) the continuing re"nement of TCN techniques. As In the early-1980s two new types of geochemical in- described above, Raymond Davis and Oliver Schae!er strumentation were applied: accelerator mass spectro- (1955) were the "rst to attempt to apply TCN to geologi- metry (AMS) and highly sensitive conventional noble- cal problems. They measured the concentration of an in gas mass spectrometry. Withtheseanalytical advances situ cosmogenic nuclide (Cl) in a sample of ma"c rock the new earth-science investigation techniques proposed from below the limit of late Pleistocene glaciation in the by the early pioneers could become a reality. In the 15 Rocky Mountains using a screen-wall beta counter sim- years since the publication of the "rst papers demonstrat- ilar to that employed for radiocarbon dating by Libby in ing that these analytical methods were practical for 1949. Using an estimate of the half life of radioactive Cl 1478 J.C. Gosse, F.M. Phillips / Quaternary Science Reviews 20 (2001) 1475}1560 determined by the Chalk River Laboratory in Canada reactions of cosmic rays withatomic nuclei.) Although (tCl"3.01;10 yr), the thermal neutron cross additional veri"cation is needed over geological time section of chlorine (&32 barns), the neutron absorption scales (see below) the majority of TCN studies have used rate (derived by others) at sea level and mountain Lal's global star production model (most recently pre- (3000 m) elevations, and the absorption mean free path in sented in Lal, 1991) to normalize production rates. water (140 g cm\), they calculated an exposure age for The third phase of development of the TCN surface a pre-Wisconsinan surface on a phonolite from Cripple exposure dating method came 30 years after Davis and Creek, Colorado to be 24,000 years (witha 10% analyti- Schae!er's landmark work. Although the possibility of cal uncertainty), while the Cl activity of a Wisconsinan- using cosmic-ray-derived nuclides produced in rocks to ice-covered syenite surface near sea level in New Ham- date the exposure time was recognized, measurement of pshire was below the detection limits of the counter the rare radionuclides with su$ciently long half lives in (modern recalculation of the Cripple Creek sample gives most sur"cial rocks was not routinely practical with an age in excess of 200,000 years, due to a reduction in existing mass spectrometers or counting methods be- the value used for the neutron #ux). Despite the promis- cause of their extremely low concentrations. The devel- ing results of their experiments, exposure dating was not opment of AMS in the early 1980s and subsequent pursued by others because of the limitations of beta count- re"nements (Klein et al., 1982; Elmore and Phillips, 1987) ing (for example, even though the Cripple Creek phonolite rendered possible the measurement of isotopic ratios as had an exceptional Cl content of 3500 ppm, their analysis low as 10\, withtotal analytical reproducibility as low nevertheless required the extraction of 13 g of chlorine as (3%. Several groups were responsible for the reju- from more than 4 kg of rock) and the uncertainty of the venation of the TCN exposure dating method in the production rates of Cl and other TCN. Using high- mid-1980s. Originally concerned with Cl contributions sensitivity noble gas mass spectrometry 20 years later, to groundwater recharge from sur"cial production, Srinivasan (1976) determined that two Archean barite F. Phillips (New Mexico Tech) and D. Elmore and others samples contained spallogenic Xe produced from (University of Rochester, now at Purdue University) interactions withsecondary cosmic radiation. Srinivasan realized the production could be used for surface dating calculated a `surface residence timea of 270,000 to and used AMS to measure Cl concentrations from 120,000 years for the sedimentary barite sample from independently dated lava #ows (Phillips et al., 1986). The Fig Tree group of SouthAfrica. Thedi !erent ages second group (L. Brown at Carnegie Institution of Wash- resulted from the uncertainty in scaling the decrease in ington, and J. Klein and R. Middleton at University the cosmic-ray #ux with depth through the atmosphere. of Pennsylvania) accidentally arrived at the use of in situ The next milestone was marked by the contributions of products for exposure chronology during their pioneer- physicists in the late 1950s and early 1960s who attem- ing work on using atmospherically derived Be to trace pted to derive models describing the interaction between subducted sediments through magmatic arc volcanoes cosmic radiation and the complex geomagnetic "eld and (Brown et al., 1982). They postulated that a signi"cant atmosphere. The rate of in situ (and atmospheric) pro- component of Be measured in Columbia River basalt duction of cosmogenic nuclides increases withaltitude #ows was derived from in situ production. The Univer- and latitude (the reasons for this are discussed in Sections sity of Pennsylvania group subsequently sought to 3.1 and 3.7.1 below). Unfortunately, the scaling factors empirically determine the production rate of Be and for spatial and temporal variations in the particle #ux Al in quartz, together with K. Nishiizumi, Lal, and above the surface of the Earth are di$cult to derive. This Arnold (Nishiizumi et al., 1986). The "rst application of is because (i) the rate of change in cosmic-ray #ux (and terrestrial Be was to determine the surface exposure disintegration rate) with depth in the atmosphere is not history of Libyan Desert Glass from western Egypt constant with latitude, (ii) the atmosphere does not com- (Klein et al., 1986a). Concurrently withthe Be and Cl prise a homogeneous or simple layered shell, (iii) the developments, Kurz et al. (1985), (Kurz, 1986a, b), and Earth's geomagnetic "eld cannot always be considered then Craig and Poreda (1986), demonstrated that, due to a geocentric dipole, and (iv) high-altitude outermost neu- its relatively high cosmogenic production rate and trons may escape back to space before slowing. D. Lal nuclear stability, natural concentrations of cosmogenic (1958), Lal et al. (1958, 1960), and Lal and Peters (1967) He could be measured witha conventional mass spec- produced syntheses of data on nuclear disintegrations in trometer and could therefore also be useful for exposure the stratosphere and troposphere. This spatial model for dating. Subsequent investigations (cited below) improved star production rates in the atmosphere was veri"ed the sample strategies, sample processing and analysis, empirically by Lal et al. (1960) at high elevation at 513N and modeling aspects of TCN exposure dating, and the latitude and could be used to normalize production rates use of two additional in situ produced nuclides, Ne on the surface of the Earth (Lal and Peters, 1967). (Graf et al., 1991; Staudacher and AlleH gre, 1991; Poreda (`Starsa are multi-pronged tracks on photo emulsions and Cerling, 1992) and C (Jull et al., 1992, 1994a, b; that record the paths of several particles emitted during Lifton et al., submitted as two papers in 2000). Better J.C. Gosse, F.M. Phillips / Quaternary Science Reviews 20 (2001) 1475}1560 1479 isolation of the muonic contribution to TCN production Brown et al., 1998a; Van der Woerd et al., 1998; Zreda on and below earth's surface has been an important and Noller, 1998), and surface uplift rates, rock uplift recent development (e.g. Heisinger et al., 1997). Although rates, and incision rates (Brook et al., 1995a; Burbank more con"rmation is needed, their data support the prem- et al., 1996; Seidl et al., 1997; Small et al., 1997; Gosse ise that the muogenic production at the surface is less than et al., 1998; Leland et al., 1998; Gosse and Stone, submit- assumed by the most widely used scaling model for Be ted) (see Morris et al., submitted, for discussion). Several and Al, and provides a means to explain the discrepancy geologic anomalies have been dated by cosmogenic nucl- among production rate measurements at calibration sites ides, including a revealing exposeH of Libyan Glass (Klein withdi !erent altitudes (proposed by J. Stone, 1999). et al., 1986b) and the timing of the famous Canon Diablo We are just beginning the fourth major phase of TCN meteorite impact which excavated Meteor Crater at ap- development: the re"nement of cosmogenic nuclide pro- proximately 49,000 years ago (Nishiizumi et al., 1991c; duction scaling models that reliably incorporate second- Phillips et al., 1991). Because the concentration of order physical processes that in#uence in-situ production cosmogenic nuclides is sensitive to surface erosion and (e.g., work by Lifton et al., submitted; Stone, in press; depth below the surface, the in situ methods have made Masarik and Beer, 1999). These e!ects include the in#u- signi"cant breakthroughs in establishing the rates and ence of non-dipole components of the geomagnetic "eld, styles of local and large-scale erosion, soil development, temporal and spatial variations in the paleo-atmosphere and landscape evolution (Nishiizumi et al., 1986, 1991a; and surface elevation, and improvements in the mean Dockhorn et al., 1991; Albrecht et al., 1993; Bierman, absorption free pathof di !erent particles at and below 1994; Cerling and Craig, 1994b; Stone et al., 1994, 1998a; earth's surface at di!erent latitudes and altitudes. Al- Zreda et al., 1994; Bierman et al., 1995a; Bierman and though many of these e!ects have been individually mea- Turner, 1995; Brown et al., 1995b, 1998b; Gillespie and sured or predicted, it is clear that the development of Bierman, 1995; Wells et al., 1995; Granger et al., 1996, a single encompassing model will require the agglomer- 1997; Lal, 1996; Heimsathet al., 1997, 1999; Seidl et al., ation of resources from experts in many di!erent "elds. 1997; Small and Anderson, 1998; Ballantyne et al., 1998; Phillips et al., 1998; Small et al., 1997, 1999; Cerling et al., 1.2. Applications of TCN exposure methods 1999; Fleming et al., 1999). The method can be applied to study sur"cial processes over the full range of climate Published applications of TCN exposure history settings (Brook and Kurz, 1993; Brook et al., 1993; methods are already far too numerous to completely list. Brown et al., 1995a, b, 1998b), witha wide range of Instead, we list some prominent examples of various lithologies and mineralogy (quartz, plagioclase, pyro- applications based on our own reading. TCN methods xene, amphibole, olivine, and others, and whole rock have been used to reconstruct Quaternary ice volume analyses can be used for Cl). Depending on the surface #uctuations from continental (Nishiizumi et al., 1991a; preservation and exposure history, the dating technique Gosse et al., 1993; McCarroll and Nesje, 1993; Brook has an e!ective range from the Pliocene ('2.65 Ma) et al., 1995a, b, 1996a, b; Ivy-Ochs et al., 1995; Steig et al., (Nishiizumi et al., 1991a; Brook et al., 1995b; Ivy-Ochs 1998; Ackert et al., 1999; Bierman et al., 1999; Davis et al., et al., 1995; Schaefer et al., 1999) to the late Holocene (the 1999; Zreda et al., 1999; Marsella et al., in press) and Holocene is (10 ka) (Kurz et al., 1990; Cerling and mountain (Phillips et al., 1990; Gosse et al., 1995a, c; Craig, 1994a; Laughlin et al., 1994; Ballantyne et al., Phillips, 1996; Jackson et al., 1997; Briner and Swanson, 1998; Van der Woerd et al., 1998; Cerling et al., 1999). 1998; Moscariello et al., 1998; Ivy-Ochs et al., 1999) The rapid and wide acceptance of these techniques moraine and glacial erosion records. Several of these (utilizing He, Be, C, Ne, Al, and Cl) is not only have pushed the precision of the method to apparently due to their wide applicability to problems in sur"cial resolve short-lived events such as the Younger Dryas or geology but also to the reproducibility exhibited by many ice rafting events in the North Atlantic (Gosse et al., of the early results. The precision of multiple measure- 1995a; Phillips et al., 1996a; Ivy-Ochs et al., 1999). ments from a single landform (better than &5%, e.g. Neotectonic applications include the dating of volcanic Gosse et al., 1995a, c) has approached the limit of the events (Marti and Craig, 1987; Cerling, 1990; Kurz et al., analytical methods. Many valuable lessons have been 1990; Nishiizumi et al., 1990, 1994; Trull et al., 1991, 1995; learned over the past decade of technique development Anthony and Poths, 1992; Poreda and Cerling, 1992; and testing, including improvements in chemical Staudacher and AlleH gre, 1993; Zreda et al., 1993; Cerling methodologies (Kohl and Nishiizumi, 1992; Ochs and and Craig, 1994a; Laughlin et al., 1994; Phillips et al., Ivy-Ochs, 1997; Stone, 1998; Lifton et al., submitted) and 1994; Sheppard et al., 1995; Wells et al., 1995; Gosse et al., re"nements in the e!ective production rates of the indi- 1996c; Poths et al., 1996; Ackert et al., 1998; Cerling et al., vidual isotope-target systems (Cerling and Craig, 1994a; 1999; Licciardi et al., 1999), time control on paleoseismic Clark et al., 1995; Larsen et al., 1995; Gosse and Klein, events (Bierman and Gillespie, 1994; Gosse et al., 1996b; 1996; Phillips et al., 1996b; Stone et al., 1996, 1998b; Siame et al., 1997; Ayarbe et al., 1998; Bell et al., 1998; Kubik et al., 1998; Licciardi et al., 1999; Stone, 1999). 1480 J.C. Gosse, F.M. Phillips / Quaternary Science Reviews 20 (2001) 1475}1560
1.3. Previous reviews we "nd the recent book by Merrill et al. (1996) extremely helpful. We found other books useful for general cosmic- In addition to the articles describing detailed applica- ray theory and history (e.g. Wolfendale, 1963; Pom- tions above, there have been several comprehensive erantz, 1971; Friedlander, 1989). publications on the nature of TCN and utility of TCN methods to address geomorphic and geochronological questions. In his reviews of in-situ cosmogenic nuclides, 2. Glossary Lal (1988, 1991) summarized previous work by himself and others to provide fundamental data (including pro- 2.1. Terminology duction rate estimates, parameters for altitude and latit- ude production rate adjustments, and the relationship Allochthonous: describes rocks that have been trans- between geomagnetic "eld intensity and production rates ported from their place of origin (in the geomorphic on Earth's surface) and strategies for using single and sense) and subsequently deposited. Glacial erratics multiple nuclides to determine erosion rates. McHargue and clasts in alluvial fans, colluvium, geli#uction and Damon (1991) provided a thorough examination of lobes, alluvium, loess, and till are here considered the global Be cycle in which the natural sources and allochthonous. sinks of Be in the Earth's cryosphere, biosphere, hydro- Attenuation length (): the thickness of a slab of rock or sphere, and atmosphere were evaluated. Morris (1991) other mass (air, water, sediment, snow) required to at- reviewed the applications of both atmospheric and in situ tenuate the intensity of the energetic cosmic-ray #ux by Be as a chronometer, climate indicator, solar modula- a factor of e\ due to scattering and absorption processes tion monitor, and subduction zone tracer. Cerling and (absorption mean free pathor e-folding length). Units: Craig (1994b) provided an excellent review of prior TCN gcm\. Values for typically range from 121 to applications and caveats regarding the application of '170 g cm\ (45 to '65 cm in solid rock of bulk den- TCN exposure methods and showed how stable nuclides sity 2.7 g cm\; see Table 3). varies withaltitude and could be useful for chronologies of 10}10 yr. We highly latitude, mostly because geomagnetic "eld and atmo- recommend their review to anyone interested in the sphere e!ects change the energy spectrum (or &hardness') geomorphologic applications of terrestrial cosmogenic of the incident radiation. nuclides. Bierman (1994) and Bierman and Steig (1996) Autochthonous: rocks that have remained at or near summarized the basics of TCN calculations for certain their site of formation. Here, this term includes all bed- geomorphic applications, and o!ered ideas for applying rock and lava, tu!, authigenic vein "lling in soils, and TCN to obtain boundary conditions for landscape evolu- clasts in regolith or felsenmeer blocks which have not tion modeling. Gillespie and Bierman (1995) evaluated been signi"cantly translated or rotated. the precision and limitations of using single or multiple Cross section [elemental] (G): a measure of the prob- TCN measurements to determine surface erosion rate ability of a given incident particle (fast or slow neutron, and or exposure age. The issue of the di$culty in simulta- muon) interacting witha target atom of a particular neously solving erosion and exposure duration was dis- element. Cross section can be interpreted geometrically cussed later by Lal (1996). A workshop summary by by imagining a circle centered around the target nucleus Gosse et al. (1996a, d) provides a recent review of the with the radius proportional to the likelihood of interac- status of TCN production rates and compiled a list of tion. Cross sections are particular to eachparticle/target information that the meeting participants suggested interaction. Units: cm or barns (1 barn"10\ cm). should be included in publications involving the inter- Cross section [macroscopic] (): a measure of the prob- pretations of new TCN measurements. Morris et al. (sub- ability of a given incident particle interacting withany mitted) summarized the developments in subduction atom in a unit mass of rock or other material. The zone processes, paleomagnetism, and active tectonics macroscopic cross section is the sum of the cross sections withatmosphericand in situ cosmogenic Be. In addi- of all the atoms in the unit mass multiplied by tion, several reviews of the utility of AMS in earth science Avogadro's number and divided by the mean atomic have included worthwhile summaries of applications of weight. Units: cm g\. the TCN methods (e.g., Tuniz and Klein, 1989; Finkel Erosion: the dynamic processes of transportation and and Suter, 1993). A number of books published between removal of material from one site to another, regardless 1960 and 1990 are still fundamental resources on cos- of the mechanism. The rate and style of erosion of a rock mic-ray physics. Rossi's (1964) book is one of the most surface will in#uence the reliability of the TCN method useful from both a historical and cosmic ray physics used to determine its exposure duration. Weathered rock point of view. The book by Allkofer and Grieder (1984) surfaces tend to erode more readily than non-weathered includes more than 200 "gures and is the most complete surfaces. It is useful to specify the surface that is being single collection of cosmic-ray (primary and secondary) eroded to avoid ambiguity; i.e. a boulder on a moraine data available. For geomagnetism and paleomagnetism, and the moraine ridge can both erode. J.C. Gosse, F.M. Phillips / Quaternary Science Reviews 20 (2001) 1475}1560 1481
Galactic cosmic radiation (GCR): energetic particles and spontaneous "ssion of U in rocks can result in the (&0.1 to 10 GeV nucleon\), composed primarily of production of low-energy neutrons (indirectly, in the case protons (83%) and a small fraction of -particles (13%), of alpha decay) that can be absorbed by Cl to produce heavier nuclei(1%), and electrons(3%) (Smart and Shea, nucleogenic Cl. Nucleogenic contributions can poten- 1985). Most of the GCR responsible for TCN production tially form a signi"cant portion of the nuclide inventory is incident from outside the solar system and thought to for Ne, Cl, Ca and Al. mainly originate within our galaxy. Higher energy par- Nuclide: an atomic species that is characterized by a ticles (up to '10 eV), probably from extra-Milky Way unique combination of atomic number and neutron sources, have been detected but are less abundant (Gais- number (e.g., Be, consisting of four protons and six ser, 1990; Gaisser and Stanev, 1998). neutrons). Geomagnetic latitude: angular distance on the Earth's Production rate: the rate at which a speci"c nuclide is surface measured between the north and south geomag- produced from a speci"ed element or in a mineral. netic poles. It is analogous to geographic latitude, but Production rates may include separate terms for spal- witha coordinate system based on thegeomagnetic pole logenic, muonic, and thermal neutron capture inter- rather than rotational pole. actions. Production rates for all TCN vary spatially and Inheritance: refers to the retention of remnant cos- appear to have varied temporally. They are often re- mogenic nuclides from a previous episode of exposure. ported as normalized to sea level and high latitude. For example, a rock sampled on an alluvial fan surface Units: atoms (g target material)\ yr\ or atoms (mole may contain some residual TCN inherited from a time target material)\ yr\. that the rock was exposed on a cli! face prior to depos- Rigidity: The momentum of a particle per charge, or ition on the fan. the product BR of the radius of curvature R due to the Isobars: families of nuclides possessing a common mass de#ection of a charged particle through a magnetic "eld, number. B. Eachcosmic particle trajectory azimuthand zenith Isotopes: families of nuclides possessing a common angle has a cuto! rigidity (R), or threshold rigidity, which atomic number. is the minimum rigidity of an approaching particle of Momentum (p): Approximated by classical (Newtonian) a given charge required to penetrate the magnetic "eld mechanics as the (rest) mass m of a particle moving at and interact with upper atmosphere nuclei. The vertical velocity v,(p"mv), it is correctly de"ned relativistically cuto!s refer to the rigidity of vertically approaching as p"(m/(1!/c) v, where c is the speed of light in a particle trajectories. The &e!ective cuto! rigidity' (Shea vacuum. et al., 1965, 1987) considers that the trajectories that Muon [negative] (\): negative muons are short-lived project back to Earthare not allowed (protons and energetic lepton particles witha decay lifetime of about neutrons cannot penetrate through earth). At latitudes 10\ s. Due to their relatively weak propensity for inter- higher than about 583, the cuto! rigidity drops lower action with atoms, they can penetrate greater thicknesses than the minimum necessary momentum of the primaries of matter than strongly interacting particles such as required for in situ TCN (i.e. all particles withsu $cient protons, neutrons, and pions. Muonic production of energy to produce in situ TCN are permitted through the cosmogenic nuclides therefore decreases with depth more magnetic "eld so production rates do not vary with slowly than the other important production pathways magnetic "eld in#uences above this latitude). (e.g. by secondary neutrons). Secondary neutrons: here, cosmic-ray neutrons (mostly Muon capture reactions [negative]: negative muons 0.1(E(500 MeV, withaverage E"1MeV;(Yamashita may fall into the electron shells of atoms and then be et al., 1966; O'Brien et al., 1978; Lal, 1988) that are captured by the nucleus, resulting in the production of a products of the interaction of primary galactic cosmic cosmogenic nuclide. The probability that a muon radiation withatoms in theEarth 's atmosphere and captured by an atom will interact (captured by the nu- subsurface. cleus to form a TCN) depends on the cross section of the Spallation reactions: a nuclear reaction resulting from nucleus and the lifetime of the muon. Because muons (a the collision of a highly energetic nucleon (usually a sec- type of meson) are weakly attenuated relative to the ondary cosmic-ray neutron of energy '10 MeV in the nucleonic (e.g. protons and neutrons) component, the case of in situ TCN) witha target nucleus (Templeton, muon-capture component of TCN production becomes 1953). Spallation reactions di!er from "ssion reactions relatively more important at deeper rock depths (Kurz, because they typically release multiple particles (protons, 1986b; Fabryka-Martin, 1988). neutrons, and clusters of these nucleons) leaving a resid- Nucleogenic nuclides: nuclides that are produced in ual spallogenic nuclide with less mass than the original situ in earthmaterials as a result of nuclear reactions target nucleus. The mechanics of spallation involves two induced by daughter particles of the decay of non- steps: (1) shattering of the target nucleus resulting from cosmogenic radioactive elements within the material an initial collision, from which the primary particle (Reedy et al., 1994b, p. 338). For example, alpha decay may escape but withreduced momentum, and (2) an 1482 J.C. Gosse, F.M. Phillips / Quaternary Science Reviews 20 (2001) 1475}1560 immediate subsequent wave of nucleus disintegration D epithermal neutron di!usion coe$cient that continues until the nucleus energy falls below the (g cm\) [Eq. (3.16)] binding energy of individual nucleons. D thermal neutron di!usion coe$cient (g cm\) Standard atmosphere: To calculate the pressure vari- [Eq. (3.33)] ation in the atmosphere due to barometric e!ects (e.g. e> positron (Fig. 3.1b) adiabatic cooling), a model which describes the general e\ electron (Fig. 3.1b) decrease in air pressure withaltitude hasbeen used as E average long-term catchment erosion rate a standard to which cosmic ray and other pressure- (g cm\ yr\) dependent processes can be scaled. The present EI kinetic energy model, which is a static isothermal model for which f I fraction of stopped negative muons that are complete mixing is assumed, approximates the pressure captured by element k (`chemical compound in dry air up to about 11,000 m for mean annual factora) (unitless) [Eq. (3.41)] conditions in mid-latitude regions (CRC Handbook, f I fraction of stopped muons captured by ele- Lide, 1999}2000): It does not consider regional temper- ment k that are absorbed into the nucleus ature and pressure anomalies and may not apply well before decay (unitless) [Eq. (3.41)] to pressure regimes outside the mid-latitudes (Stone, f K fraction of epithermal neutron #ux absorbed in press). by elements that produce nuclide m (unitless) Terrestrial cosmogenic nuclide (TCN): a nuclide pro- [Eq. (3.12)] duced by the interaction of secondary cosmic radiation fG I abundance of the isotope of element k that withexposed target atoms in earth-surfacematerials. We produces nuclide m subsequent to slow muon use the term `TCNa to refer only to those cosmogenic capture (unitless) [Eq. (3.41)] nuclides that are produced in situ in minerals, not to those fL I K fraction of slow muon captures by ele- that are produced in the atmosphere and subsequently ment k that produce nuclide m (unitless) incorporated into sediment or rock (e.g., by absorption [Eq. (3.41)] from meteoric water into soils or by the inclusion of f K fraction of thermal neutron #ux absorbed by atmospherically derived nuclides in seawater into mag- elements that produce nuclide m (unitless) matic arc rocks) nor those produced in situ in minerals by [Eq. (3.29)] nuclear reactions arising from radioactive elements (see F cosmic-ray intensity (particles cm\ s\ sr\) `Nucleogenic nuclidesa). Although products of the cos- [Eq. (3.7)] mic-ray interactions yield a wide range of nuclides, here we F cosmic-ray intensity in the vertical direction use TCN primarily to refer to the six in situ-produced (particles cm\ s\ sr\) [Eq. (3.53)] nuclides that are commonly used in geological applica- (F)H parameter governing epithermal neutron #ux tions (He, Be, C, Ne, Al, and Cl). near the land/atmosphere interface Thermal neutron: neutrons characterized by energy [Eq. (3.25)] levels in the range imparted by thermal vibrations of the (I )H parameter governing thermal neutron #ux matrix (E+0.025 eV), here referring speci"cally to those near the land/atmosphere interface secondary neutrons produced in the atmosphere and [Eq. (3.36)] rock. Thermal neutrons are produced when fast secondary (I ) H parameter governing thermal neutron #ux neutrons collide repeatedly withatoms in theatmosphere near the land/atmosphere interface and rock and subsequently lose energy. Typically, tens to [Eq. (3.37)] hundreds of collisions are required to reduce neutron G acceleration due to gravity (9.80665 m s\) energies from the 1 MeV range to thermal energies. [Eq. (6.2)] Thermal neutron absorption: the capture of thermal H horizontal component of the geomagnetic neutrons by nuclei in rock, water, and air. Thermal neu- "eld (IGRF model or local measurement) tron absorption reactions are most important the top few I I dilute resonance integral for absorption of meters of the solid earth. epithermal neutrons by element k (barn"10\ cm\) 2.2. Notation I e!ective (macroscopic) resonance integral for absorption of epithermal neutrons (cm\ A mass number of a target nucleus g\) [Eq. (3.4)] A average atomic weight of atmosphere J production rate coe$cients (atoms g\ yr\) (14.5 g mol\) [Eq. (3.78)] AG average atomic mass of material i (g mol\) J/ production rate coe$cients corrected for [Eq. (3.18)] sample thickness (atoms g\ yr\) CI mass concentration of element k (g of [Eq. (3.87)] k (g rock)\) kaon (Fig. 1) J.C. Gosse, F.M. Phillips / Quaternary Science Reviews 20 (2001) 1475}1560 1483
¸ epithermal neutron di!usion length(g cm \) Q ratio of production rate integrated over the [Eq. (3.21)] thickness of a sample to the surface produc- ¸ thermal neutron di!usion length(g cm \) tion rate, due to epithermal neutron absorp- [Eq. (3.34)] tion (unitless) [Eq. (3.75)] m particle mass (g) Q ratio of production rate integrated over the m mean molar mass of air (g mol\) [Eq. (6.2)] thickness of a sample to the surface produc- m mass of carrier added to sample (g) tion rate, due to spallation (unitless) m mass of puri"ed sample (g) [Eq. (3.74)] M geomagnetic dipole moment Q ratio of production rate integrated over the M present-day geomagnetic dipole moment thickness of a sample to the surface produc- n neutron (Fig. 3.1b) tion rate, due to thermal neutron absorption N Avogadros number (unitless) [Eq. (3.76)] (6.02214;10 atoms mol\) QI ratio of production rate integrated over the N atomic concentration of element thickness of a sample to the surface produc- k (atoms g\) tion rate due, to muon absorption (unitless) NK concentration of nuclide m from contamina- [Eq. (3.77)] tion sources (atoms g\) R gas constant, 83.144 cm bar K\ mol\ or NK concentration of nuclide m inherited from 8.3144 J mol\ K or 287.05 J kg\ K\ exposure prior to the event of [Eq. (6.2)] interest(atoms g\) R ratio of epithermal neutron production in NK measured concentration of nuclide m subsurface to that in atmosphere (unitless) (atoms g\) [R "1] [Eq. (3.19)] NKL concentration of nuclide m accumulated from R ratio of thermal neutron production in sub- nucleogenic reactions (atoms g\) surface to that in atmosphere (unitless) NKR concentration of nuclide m accumulated [R "1] [Eq. (3.31)] during and since the geological event of inter- RKL ratio of the concentrations of nuclides m and est (atoms g\) n (unitless) [Eq. (3.98)] N*K concentration of nuclide m produced by RI ratio of muon production rate to epithermal radioactive decay reactions (atoms g\) neutron production rate (unitless) [Eq. (3.49)] P momentum (g cm s\); or proton (Fig. 3.1b) RI ratio of muon production rate to thermal P K production rate of nuclide m by epithermal neutron production rate (unitless) [Eq. (3.49)] neutron absorption reactions R present-day geomagnetic cuto! rigidity (atoms g\ yr\) [Eq. (3.11)] RH geomagnetic cuto! rigidity P production rate of epithermal neutrons (from S scaling factor for nucleonic production fast neutron #ux) in atmosphere (neu- as a function of elevation and latitude trons g\ yr\) [Eq. 3.9)] [Eq. (3.5)] PI K production rate of nuclide m by muon ab- S* scaling factor for excess di!usion of epither- sorption reactions (atoms g\ yr\) mal neutrons out of objects of irregular ge- [Eq. (3.40)] ometry (unitless) [Eq. (3.5)] PL I production rate by absorption of neutrons S* scaling factor for excess di!usion of thermal arising from photodisintegration reactions neutrons out of objects of irregular geometry induced by fast muons (atoms g\ yr\) (unitless) [Eq. (3.5)] [Eq. (3.40)] SI scaling factor for muonic production as PL production rate by absorption of neutrons a function of elevation and latitude (unitless) arising from slow muon capture reactions [Eq. (3.5)] (atoms g\ yr\) [Eq. (3.40)] S scaling factor for shielding of a sample surface P K production rate of nuclide m by spallation by snow, soil, or other material (unitless) reactions (atoms g\ yr\) [Eq. (3.5)] [Eq. (3.72)] P K production rate of nuclide m by thermal SR scaling factor for shielding of a horizontal neutron absorption reactions sample by surrounding topography (unitless) (atoms g\ yr\) [Eq. (3.67)] P K total production rate of nuclide S2 total scaling factor for shielding of a sample of m (atoms g\ yr\) [Eq. (3.5)] arbitrary orientation by surrounding top- p(E ) resonance escape probability of a neutron ography (unitless) [Eq. (3.70)] from the epithermal energy range (unitless) > average neutron yield per stopped negative [Eq. (3.3)] muon (n (stopped negative muon)\) 1484 J.C. Gosse, F.M. Phillips / Quaternary Science Reviews 20 (2001) 1475}1560
>I K total production coe$cient for nuclide cosmic-ray #ux received from entire unob- m from absorption of slow negative muons structed sky through a horizontal surface (atoms (stopped muon)\) [Eq. (3.41)] (particles cm\ yr\) [Eq. (3.9)] z linear distance (cm) H epithermal neutron #ux at land/atmosphere Z mass distance (g cm\) [Eq. (3.6)] interface that would be observed if interface Z sample thickness (g cm\) were not present (n cm\ yr\) [Eq. (3.22)] Z atomic number of a target nucleus H thermal neutron #ux at land/atmosphere that H di!erence in equilibrium epithermal neutron would be observed if interface were not pres- #uxes between atmosphere and subsurface ent (n cm\ yr\) [Eq. (3.35)] (n cm\ yr\) [Eq. (3.26)] muon [Eq. (3.2)] H di!erence in equilibrium thermal neutron neutrino [Eq. (3.2)] #uxes between atmosphere and subsurface bulk density of solid, liquid, or air (g cm\) (n cm\ yr\) [Eq. (3.38)] azimuthangle (deg) mass erosion rate (g cm\ yr\) strike of a sample surface (deg) ( ) angle between the normal to a surface and an azimuthof thenormal to a surface (deg) incoming cosmic-ray particle from any arbit- I elemental neutron scattering cross section for rary angle [Eq. (3.55)] element k (barn"10\ cm\) gamma ray or photon [Fig. 3.1b] I elemental thermal neutron absorption cross absorption rate of epithermal neutrons section for element k (barn"10\ cm\) (n g\ yr\) [Eq. (3.11)] macroscopic absorption and moderation absorption rate of thermal neutrons cross section for epithermal neutrons (n g\ yr\) [Eq. (3.28)] (cm g\) [Eq. (3.13)] geomagnetic latitude (deg) macroscopic neutron scattering cross section present-day geomagnetic latitude (deg) (cm g\) [Eq. (3.17)] paleo-geomagnetic latitude (deg) macroscopic thermal neutron absorption geographic latitude of past geomagnetic pole cross section (cm g\) [Eq. (3.1)] position (deg) I\ stopping rate of slow negative muons ((stop- decay constant for nuclide m (yr\) ped \)g\ yr\) geographic latitude of a sample site (deg) I production rate of nuclide m by spallation of attenuation lengthfor absorption and moder- element k (atoms (g target element) yr\) ation of epithermal neutron #ux (g cm\) dry air adiabatic lapse rate [Eq. (3.13)] I average log decrement of energy loss per colli- e!ective attenuation lengthfor cosmic-ray sion for element k (dimensionless) #ux through a surface of arbitrary orientation MG mean macroscopic log decrement of energy and shielding (g cm\) [Eq. (3.68)] loss per collision for element k in material particle attenuation lengthfor fast nucleonic i (dimensionless) particles (g cm\) [Eq. (3.7)] apparent attenuation lengthfor cosmic ray Subscripts #ux received from entire unobstructed sky through a horizontal surface (g cm\) * radiogenic [Eq. (3.59)] a atmosphere; or absorption attenuation lengthfor absorption of thermal c chemical; or carrier neutron #ux (g cm\) [Eq. (3.32)] inclination cont contaminated angle, measured from the vertical d decay slope of a sample surface, in the downward ee!ective direction (deg) el elevation-latitude inclination of the normal to a surface (deg) ethepithermal geographic longitude of past geomagnetic f fast pole position (deg) geo geomagnetic geographic longitude of a sample site i individual unit of material, a particle, or (deg) single event entity \ \ I$ fast muon #ux ( cm yr ) inhinherited epithermal neutron #ux [concentration] k element k (n cm\ yr\) m nuclide m thermal neutron #ux [concentration] n nucleogenic; or nuclide n (n cm\ yr\) meas measured J.C. Gosse, F.M. Phillips / Quaternary Science Reviews 20 (2001) 1475}1560 1485 o surface; or vertical; or present-day After spiraling through the interplanetary and terres- p, paleo past trial magnetic "elds, inelastic interactions of the pri- pd present day maries with nuclei of atoms in the atmosphere produce s slow; or spallation; or stopped; or site a cascade of particles and reactions, withnet energy sc neutron scattering being lost to the atmosphere and ultimately the materials ss subsurface of the Earth's surface (Fig. 1). The e!ects of the magnetic t time; or topography "eld on primary GCR are discussed in the next two T total sections. The particles produced from the initial interac- ththermal tions form what is traditionally referred to as &secondary tg target radiation'. Because collision cross section (probability for muon interaction of incident particle and target nuclei) is essen- tially independent of energy at the high energies ('100 MeV), the secondary nucleons (e.g. protons and 3. Principles neutrons) and mesons (e.g. kaons and muons) produced in the top of the atmosphere (above 100 g cm\) have 3.1. Introduction essentially the same properties as the primary (Fig. 1b). As a result, the particle #ux reaches a maximum at In a search for an analogy to teach his geomorphology a depthcorresponding to about one collision cross sec- class about terrestrial cosmogenic nuclide dating, profes- tion (&80}90 g cm\). This pile up is referred to as the sor Edward Evenson used the clever imagery of measur- Pfotzer Maximum after its discoverer in 1935 (Rossi, ing the degree of redness on a person's skin to estimate 1964, p. 167; Hayakawa, 1969, p. 8; Allkofer and Grieder, the duration of exposure to sunlight. Although the anal- 1984, p. 4). Below this depth, the hadron #ux (Fig. 1b) ogy is not direct, it is e!ective because many of the same declines as the hadronic cascade loses energy to success- principles, factors, and uncertainties that apply to the ive collisions (atmospheric depth corresponds to about suntan clock also apply to the TCN technique. Solar 13 collision lengths). The hadron #ux drops o! withthe radiation varies depending on elevation and latitude, and cumulative mass traversed by the cosmic-ray beam in temporally, and so does the secondary cosmic-ray #ux. a fashion analogous to the exponential decrease of light A tan will gradually wear away and cosmogenic radio- intensity withdepthinto an absorbing medium (suchas nuclides decay. Suntan lotion and hats will shield skin the atmosphere or rock), as described by Beer's Law. from solar radiation, while the atmosphere, snow, and Cascading causes the drop o! to be slower than uncol- mountains shield a landform from cosmic radiation. Not lided primaries attenuate, so the actual curve describing everybody tans to the same degree of redness and TCN the #ux is not exactly exponential. production rates vary in di!erent minerals. The change in the color of a sunburned epidermis after peeling may result 3.1.2. Ewects of the geomagnetic xeld on GCR in an overestimate or underestimate of the total sunlight Theoretical study of the in#uence of a dipole "eld on exposure time, while erosion may result in an overestimate charged particle trajectories had begun even before Hess' or underestimate of cosmic-ray exposure time. If return- discovery of cosmic rays. In his e!ort to explain ioniz- ing for a second day of tanning, the person will begin ation e!ects observed in aurorae, Norwegian geophysi- partially tanned from the previous exposure, just as cos- cist C. Stormer calculated the trajectories of suspected mogenic isotopes may be inherited from exposures prior solar particles through a geomagnetic dipole "eld. Ap- to the present duration. In the next section we provide an preciate that these complicated di!erential equations outline of how primary cosmic radiation initiate the were "rst numerically integrated by Stormer and his production of cosmogenic nuclides in rock on Earth. students without a computer, and early attempts re- quired over about 5000 hbetween 1904 and 1907 3.1.1. Source of the primary radiation (Stormer, 1935). Although subsequently found inad- The galactic cosmic radiation (GCR) of interest re- equate for auroral processes (cf. Rossi, 1964), Stormer's garding the production of terrestrial cosmogenic nuclides theories provide the basis to all subsequent models of is largely composed of high-energy nucleons, mostly pro- cosmic rays through a geomagnetic dipole "eld. Speci"- tons, which have su$cient energy (&1 GeV(E( cally, they provide a means to evaluate the minimum &10 GeV) to produce nuclear disintegrations in the momentum required of a particle to pass through the upper atmosphere. In this energy range, most of the geomagnetic (dipole) "eld of a given strength. primary cosmic radiation incident upon the Earth orig- Cosmic-ray intensity yux measurements. In 1927, using inates within the Milky Way galaxy, including the lower a ship-mounted ionization chamber, Dutch physicist energy particles from our sun (Lingenfelter and Flamm, J. Clay detected a slight decrease in cosmic-ray intensity 1964). A small component (withultrahighenergies up to around the Suez Canal enroute from Amsterdam to Java. 10 eV) originates from sources outside our galaxy. His results, among several unsuccessful contemporary 1486 J.C. Gosse, F.M. Phillips / Quaternary Science Reviews 20 (2001) 1475}1560
Fig. 1. Fate of a primary charged galactic cosmic ray particle &a'.In#uence on a proton trajectory of a geomagnetic dipole "eld that is tilted 223 from Earth's spin axis shown as the western half of the "eld in a meridian plane, compiled from Rossi (1964) and (Quenby and Wenk, 1962). &e.p.' is equatorial plane. According to Stormer theory (see text), outer shaded region is forbidden to particles of a given insu$cient rigidity. Trajectories 1, 2, and 3 of rigidity equivalent to the vertical threshold rigidity, arriving from in"nity, must pass through the jaws into inner allowed region and ultimately follow a dipole "eld line down the horn to atmosphere. Trajectory 4 is impossible due to the opacity of the earth. Distribution of allowed main cone &a', Stormer and shadow forbidden cones &f ', and the penumbra &p' are approximated from Pomerantz (1971) for a 10 GV positively charged particle at mid-latitude. (b). The major components of a cosmic-ray extensive air shower (cascade), showing secondary particle production in the atmosphere and rock (modi"ed from Allkofer and Grieder, 1984; Clay and Dawson, 1997). Particle symbols are given in the notation list. Numbers refer to examples of in situ cosmogenic nuclide interactions: (1) Cl(n , ) Cl; (2) O(n, 4p3n) Be; (3) Si(n,p2n) Al. Vertical scale not linear. J.C. Gosse, F.M. Phillips / Quaternary Science Reviews 20 (2001) 1475}1560 1487 attempts by others (particularly those at high latitudes), charge). Using the east}west asymmetry e!ect (the for- established that at least some primary cosmic rays were bidden Stormer cones will face east for positive particles, charged particles because their #ux was modulated by Fig. 1a), they and Rossi independently determined from the magnetic "eld. Withmore sophisticatedequipment, particle #ux measurements that the majority of particles the latitude shift (&knee' where the change in #ux was were positively charged. Notably, Stormer (1934) argued greatest) was later found to be between about 413 the Lemaitre and Vallarta (1933) calculations incorrectly (Millikan and Neher, 1936) and 253 in both hemispheres oversimpli"ed his trajectory models and lacked the pre- at sea level. It was later observed that the lowest cosmic- cision necessary to map the intensity distribution. ray intensity did not occur along a single latitude, but Subsequent papers revealed the inadequacy of a geo- varied longitudinally, indicating that the geomagnetic centric geomagnetic dipole "eld model to explain more "eld was more complicated than a simple dipole "eld re"ned geographic distributions of the cosmic-ray inten- model. Compton (1933) convincingly showed that the sity (Simpson et al., 1956; Pomerantz et al., 1960). The cosmic-ray #ux intensity variations were directly propor- intensity records had clear evidence of local magnetic tional to the horizontal component (H) of the geomag- "elds as well as possible external "elds (Quenby, 1966), netic "eld. and showed longitudinal patterns that were not consistent Subsequent measurements of the atmospheric distri- witha simple dipole model. To avoid unsolvable com- bution of bothfast proton and fast neutron #uxes and plexities in the integration of di!erential equations, mod- star production (e.g. Simpson et al., 1951, 1956; Simpson els incorporating non-dipole components of the magnetic and Fagot, 1953; Rose et al., 1956; Soberman, 1956; Lal, "eld must be relatively simple. An eccentric dipole-quad- 1958; McDonald and Webber, 1959; Light et al., 1973; rapole model that accommodates observed magnetic Merker et al., 1973) were made worldwide at di!erent "eld secular variations was employed (e.g. Gall, 1960). altitudes withshipmountedequipment and withairborne (balloon and jet) equipment to shallow depths in the 3.1.3. Trajectory models and models of secondary nuclide atmosphere. It takes a depth between 80 and 200 g cm\ production rates in the atmosphere (roughly 15,000 m asl, although this Cosmogenic nuclide dating requires a reliable means elevation is above of the e!ective limit of the Standard to determine the production rate at any given latitude, Atmosphere model) for the fast neutron #ux to reachits altitude, depthbelow theground surface, and time peri- maximum, because at shallower depths there are insu$- od. The goal is to produce a secondary cosmogenic cient targets to produce the secondary neutrons, because nuclide production model that (1) explains the modern the secondaries produced in the "rst cascade have prop- cosmic-ray #ux distribution at di!erent positions in the erties similar to the primaries, and because the secondary atmosphere or on land (e.g. Yamashita et al., 1966), (2) neutrons tend to di!use out of the atmosphere into space accommodates in#uences of secular changes in dipole (Fig. 1b). Toward the base of the atmosphere the #ux is intensity, dipole axis position, non-dipole e!ects, and attenuated rapidly withincreasing depthas it is con- distant changes due to the rotation of a tilted dipole sumed in interactions with the atmospheric nuclei through a highly ionized interplanetary gas (cf. Simpson (Fig. 1b). It was recognized that below 200 g cm\ the et al., 1956), and (3) can yield reliable results for any attenuation lengths of fast neutrons and protons were duration in the past (e.g. Lingenfelter, 1963). In this similar to the attenuation lengths for star producing section we begin witha discussion of thefundamental radiations (determined from emulsions) in air at di!erent aspects of these models and end with a review of modern latitudes and altitudes (Simpson et al., 1951; Treiman, transport codes of cosmic-ray #uxes. 1952). This suggested that the high-energy #ux below A charged GCR particle following a trajectory de#ec- 200 g cm\ was in approximate equilibrium withthe #ux ted toward earth through the interplanetary "elds will of secondary low-to-medium energy particles (cf. O'Brien begin feeling the e!ects of the dipole magnetic "eld long and Burke, 1973), and counts of star productions could before it reaches the atmosphere or is in#uenced by be used to describe spatial variability of the cosmic-ray second-order magnetic e!ects. As Rossi (1964) points out, intensity in the atmosphere (e.g. Lal and Peters, 1967). above 32 km there is less than 1% of the total atmo- Magnetic xeld ewects on incident GCR. Particle theory sphere, but even at 1600 km above earth the geomagnetic and cosmic-ray intensity measurements were soon com- "eld is at one half of its strength at sea level (see Section bined. Lemaitre and Vallarta (1933) used Stormer's the- 3.5.4 for atmospheric e!ects that must be simultaneously ory to reproduce the latitudinal variations in measured considered). The terrestrial geomagnetic "eld inhibits cosmic-ray intensities. They also proposed a means to low-energy, charged, primaries from penetrating the at- determine the sign of the charge by determining the mosphere near the equator and de#ects muchof the direction of incidence of the majority of the #ux (a radiation away from the earth. This is essentially because charged particle traversing a magnetic "eld will be de#ec- "eld lines are perpendicular to average incident cosmic- ted normal to both the direction of motion and the "eld, ray trajectories, which would cause the greatest de#ec- the direction of de#ection depending on sign of the tion. The net e!ect is that a harder (higher average 1488 J.C. Gosse, F.M. Phillips / Quaternary Science Reviews 20 (2001) 1475}1560 energy) #ux penetrates the upper atmosphere at the mag- Quenby and Webber (1959) derived Eq. (3.3) from netic equator, and that higher latitudes receive a wider Stormer theory and demonstrated that it was appropri- spectrum of energies. This is an oversimpli"cation which ate for latitudes above geomagnetic latitude 403. From will now be discussed in more detail. any position on the surface of Earth, a (Stormer) cone The de#ection of the trajectories of the incident cosmic containing the forbidden trajectories by positively rays can be studied by calculating the trajectory back- charged particles extends eastwards from the meridian wards from a position on earthusing Stormer 's equations plane (Fig. 1a). (The actual point of reference is not on the (which were designed to track particles from the sun). The surface of Earth, but approximately 5.5 km height into radius, R,ofthede#ection is proportional to the particle the atmosphere (Quenby and Wenk, 1962, p. 1461)). momentum, p, but inversely proportional to the magni- Cuto!s up to 60 GeV may be experienced by positively tude of the charge of the particle (Ze) and the magnitude charged particles approaching a dipole "eld from the east of the "eld intensity (B). So, along the equatorial plane. Considering only the dipole "eld e!ect, the trajectory of a particle at vertical cuto! pc "BR"R (3.1) rigidity would enter from in"nity an outer allowed zone Ze and be required to penetrate through a slit (&jaws' of the forbidden zone, Fig. 1a). The width of the jaws depends and the product BR is the magnetic rigidity, R,ofthe on the particle rigidity, latitude, and the dipole strength, particle. The proportional relation between particle kin- and can be estimated from the true (dipole and non- etic energy (eV) and rigidity (g cm) is approximately dipole) horizontal component of the "eld (Quenby and E "300R, as shown graphically by Rossi (1964, his I Webber, 1959; their Eq. (20)). Next, the particle would Fig. 5.3). perform tight loops in an inner allowed region inside the For any position on earth, a charged particle spiraling jaws, and ultimately closely follow dipole "eld lines into through a magnetic "eld will have allowed rigidities, the atmosphere (Fig. 1a). Also, depicted on Fig. 1a are the forbidden rigidities, and an intermediate penumbra in positions of allowed and forbidden regions (Stormer and which slight di!erences in trajectory may be allowed or shadow) for a 10 GV particle at mid-latitude (303N, zones forbidden (Fig. 1a). Models of particle trajectories can be approximated from Pomerantz, 1971, p. 73). run in reverse withincreasing momentum until they Below 403 latitude where the jaws of the forbidden escape the magnetic "eld. Any reverse approaches that zone are much closer to the atmosphere and non-dipole returned to earthwould be impossible. As determined by e!ects become important, the particles of near threshold the east}west e!ect, trajectories of protons withsu $cient rigidity do not follow the dipole "eld lines, and Eq. (3.3) momentum could arrive from any direction from the becomes invalid. The e!ect of the oversimpli"cation is west of vertical. However, easterly trajectories of posit- compounded by the increasing importance of o!-vertical ively charged particles were allowed only if the trajectory cuto!s with higher cuto! rigidities (equatorward). That extended up from the surface with a su$ciently vertical Eq. (3.3) is invalid at lower latitudes is important because angle and radius to avoid projection back to the opaque it is this equation that is that basis of several later articles, earth (see Rossi, 1964, his Fig. 5.8). This meant that the suchas Elsasser et al. (1956), whoattempted to express "nal portion of a predominantly easterly trajectory of the variation in C production in the atmosphere due to a proton must be able to curl and enter from the west or short-term variations in magnetic "eld intensity. For vertical. instance, below 203 a more appropriate expression for Earlier, Stormer showed that certain other trajectories vertical cuto! rigidity would include the non-dipole "eld below a certain threshold vertical (cuto!) rigidity were e!ects: impossible (&forbidden') to the particle because they would be bounded along dipole "eld lines or otherwise M " M M de#ected, according to R cos (3.4) 4R M 1!(1!sin cos with R" , (3.2) R sin cos H MM"M 1#0.6 , (3.5) where M is the dipole moment, R is the radius of earth, H" and is the geomagnetic latitude of the top of the atmosphere, and is the angle between the velocity where M is a modi"cation of the geomagnetic dipole vector of the particle and the meridian plane (plane latitude corrected for non-dipole-induced changes in in- containing the particle and the dipole). For vertical arri- clination, and H is the di!erence between the horizontal val, sin "0, Eq. (3.2) simpli"es to component of the dipole "eld H" and the horizontal component attributed to non-dipole (quadrapole) e!ects. M Between latitudes 20 and 403 some combination of the R" cos (GV). (3.3) 4R two equations was proposed (Quenby and Webber, 1959) J.C. Gosse, F.M. Phillips / Quaternary Science Reviews 20 (2001) 1475}1560 1489 and subsequent more rigid models have been computed Models of cosmic-ray distributions were also derived (Quenby and Wenk, 1962). The e!ects of non-dipole "eld by "tting star or neutron #ux data to model secondary distortions are increasingly important at lower latitudes, particle production at di!erent atmospheric altitudes and where the jaws (Fig. 1b) are narrower for a given rigidity. geomagnetic latitudes (Lal and Peters, 1967) and even For discussion of error of the use of trajectory mapping, di!erent times in the past (Lingenfelter, 1963). The model the reader is referred to Quenby and Webber (1958, developed by Lal (1991) has been the standard means of p. 103), and Stormer (1955). The in#uences of the non- scaling in situ TCN production rates for any given site dipole "eld on in situ production rates are speci"cally and depth, with an approximate uncertainty of '10% treated in Section 3.5.3. (D. Lal, personal communication). Dunai (2000) recently Eqs. (3.3) and (3.4) neglect the penumbral correction proposed that inclination could serve as a proxy for for forbidden trajectories which would intersect earth magnetic intensity at a given site, in lieu of latitude. The before arrival. Penumbral trajectories are completely for- proposed improvement was greater sensitivity to higher bidden below geomagnetic latitude 253 (dipole "eld) and pole e!ects (e.g. longitudinal e!ects due to non-dipole may amount to 1.5 GV in places, especially between 20 "eld components). However, these models were based and 303. Withincreasing latitude theregion is composed thermal neutron counting (or star production) data from of a decreasing ratio of forbidden : allowed rigidities, be- the atmosphere. The models are based on data in#uenced cause slight disturbances, such as non-dipole "eld by a magnetic "eld that incorporates short-term anomalies, can alter trajectory that would be otherwise ((10}10 yr) magnetic "eld anomalies due to non-axial forbidden in a dipole "eld. Quenby and Wenk (1962) position of the dipole and non-dipole "eld (Dunai, 2000). proposed a means to evaluate the non-dipole in#uences The applicability of these models is therefore limited by and the penumbral correction for given rigidities. With (1) the capacity of the magnetic "eld data upon which the aid of high-speed computers, understanding the they are based to represent the integrated "eld over geomagnetic e!ects on cosmic radiation was enhanced by arbitrary exposure durations; (2) the inability of geomag- making repeated trajectory traces to determine the max- netic latitude-based models to incorporate paleo-longitu- imum R3 (the rigidity value for the highest al- dinal anomalies (e.g. Lal, 1991); and (3) inconsistencies lowed/forbidden transition) and minimum R* (rigidity between site magnetic inclination from a degree '2 value for the lowest allowed/forbidden transition) harmonic geomagnetic reference "eld model and the ac- possible for a given latitude, longitude, altitude, zenith tual intensity "eld of the earth (Dunai, 2000). Lifton et al. angle, azimuthangle, and magnetic "eld model (Shea (submitted) are proposing a new approachfor in situ et al., 1987). Where the penumbra is transparent production that returns to the trajectory rigidity R!"R*, otherwise the di!erence between the two re- methods, with the advantage that the e!ective cuto! #ects the magnitude of the penumbra e!ect. They calcu- rigidity transport models are able to predict bothlongi- late an ewective cuto! rigidity to include the penumbra tudinal and latitudinal perturbations of cosmic-ray #ux e!ect. due to non-dipole and other e!ects. Using a Monte Carlo approach(cf. Armstrong et al., 3.1.4. Recent numerical models of GCR particle production 1973; Masarik and Reedy, 1996) to model the cosmic-ray Even withcomputers, it was considered impractical #ux through the atmosphere, Masarik and Beer (1999) (Shea et al., 1987) to model all of these variables for every have performed the most recent coupled cosmogenic position on earth, and only vertical cuto! values are nuclide production-transport simulations for the atmo- generally reported (but see Bland and Cioni (1968) for sphere. Unfortunately, they did not extend their model to non-vertical cuto!s). Advanced rigidity models and cas- include in situ production in rocks. Masarik and Reedy cade transport codes (e.g. Lingenfelter, 1963; Light et al., (1996) simulated production of speci"c atmospheric and 1973; Merker et al., 1973; O'Brien, 1979; Gaisser, 1990; in situ cosmogenic nuclides based on Monte Carlo codes Masarik and Reedy, 1996; Masarik and Beer, 1999) com- that predict particle production and transport according pare favorably withexperimental data (K. O 'Brien, pers. to the present understanding of relevant physical pro- comm., 2000). Many of the atmospheric transport codes cesses and conditions (e.g. nuclear cross sections). Their of cosmic radiation employ Monte Carlo simulations of results were generally consistent withempirical data the interactions of particles in a magnetic "eld that are (production rates, isotopic production ratios, attenuation governed by the Botzmann equation, which helps de- lengths). The next step logical would be to couple the scribe the production of particles of given energy consid- atmospheric and in situ transport codes to a variable ering the speed, direction, mean life, and collisional cross magnetic "eld model. sections (O'Brien et al., 1978; O'Brien, 1979). These mod- Most of these models use the Standard Atmosphere els account for higher-order "eld e!ects by calculating model to determine how the cosmic-ray #ux will travel the dipole strength that would give the actual cuto! through the atmosphere. Although a reasonable "rst- rigidity at a given location (see Quenby and Webber, order approximation, the Standard Atmosphere does 1959, p. 95; Quenby and Wenk, 1962, p. 1459). not incorporate signi"cant long-term second-order 1490 J.C. Gosse, F.M. Phillips / Quaternary Science Reviews 20 (2001) 1475}1560 anomalies that will contribute to the mis"t of the ob- atoms through spallation interactions. As energy is lost served cosmic-ray #ux data and geomagnetic "eld based due to successive reactions, down to the 1}5 MeV range, models. For instance, Stone (in press) points out that the neutrons are no longer capable of causing spallation persistent pressure deviations over Siberia and Iceland reactions and their remaining energy is dissipated mainly depart from the Standard Atmosphere by $4.4 hPa at by momentum transfer during elastic scattering o! inci- sea level, which would directly correspond to about dent nuclei. The neutrons pass through the epithermal a $3}4% change in TCN production rates (presently energy range (between &0.1 MeV and 0.5 eV) down to within the uncertainty of the nuclide production models the level dictated by the thermal energy of the gas or solid for any site). However, he points out that in situ produc- within which the neutron resides. Such neutrons are tion rates in Antarctica would be 25}30% higher than referred to as `thermal neutronsa and are characterized rates for the same latitude in the Arctic (Stone, in press). by a kinetic energy of approximately 0.025 eV per neu- Clearly, we are approaching a point in the development tron. In this state, their paths are described by Brownian of the TCN method when the secondary spatial (e.g. motion, due to random collisions withatomic nuclei in atmospheric, magnetic) variations must be accurately the medium. Ultimately these neutrons are absorbed by incorporated into the numerical scaling models of cosmic the nuclei of atoms they encounter, resulting in the ray #ux and TCN production. formation of `thermal-neutron-produced cosmogenic nuclidesa. By far, the most important of these is C, 3.1.5. Nuclide production from primary GCR produced in the atmosphere by thermal neutron absorp- As the cascade of reactions propagates down through tion into N (the reaction N(n,p)C). In minerals at the atmosphere and eventually the upper few meters of the Earth's surface, the most important thermal-neutron the Earth's crust, the composition of the nuclear particle produced cosmogenic nuclides are Cl (produced main- #ux tends to become dominated by neutrons (Fig. 1b). ly by the reaction Cl(n,)Cl) and Ca (produced by This is because they have a higher probability of being the reaction Ca(n,)Ca). Due to the di!erent types of emitted from stimulated nuclei, and because, being elec- cosmic-ray reactions involved, the pattern of TCN pro- trically neutral, they are not slowed by ionization energy duction withdepthby spallation reactions di !ers from losses to atoms they encounter. In addition to the sec- that of thermal-neutron-absorption reactions. This can ondary neutron radiation, a relatively smaller number of be illustrated by comparing the depth-dependence of the 3 and K3 mesons are produced (E&400 MeV), result- production of Be in a quartz arenite (Fig. 2a) and Cl ing in a #ux of short-lived muons which also contributes in a limestone (Fig. 2b). These reactions are discussed in to TCN production (cf. Section 3.1.8) (Fig. 1b). The sec- detail below. ondary fast nucleons (and minor mesonic #ux) continue All TCN exposure history methods are based on the to produce cosmogenic nuclides in the atmosphere, hy- production of rare nuclides from a small portion of drosphere, and lithosphere by breaking apart target the interactions between secondary cosmic radiation
Fig. 2. Variation of the production of TCN with depth in rock at high latitude and sea level: (a) Be in quartz arenite; (b) Cl in an ultrama"c rock. Average ultrama"c rock composition from Fabryka-Martin (1988) was used, but Cl concentration was reduced to 10 ppm. J.C. Gosse, F.M. Phillips / Quaternary Science Reviews 20 (2001) 1475}1560 1491 of di!erent energies and atoms in an exposed mineral. In tion rate by energetic cosmic radiation and hence follow the following sections, we do not distinguish between the exponential dependence of #ux withcumulative mass minerals in rocks and unconsolidated sediment because below the top of the atmosphere. However, the atmo- the major di!erences between rocks and unconsolidated sphere/land surface interface constitutes an abrupt dis- sediment is with regard to geomorphic processes, not the continuity in material properties that produces a fundamental principles of TCN methods. Speci"c treat- corresponding perturbation in the spatial distribution of ment of unconsolidated materials is discussed in Sections the low-energy neutron #uxes. The most important of 3.11, 4.4 and 5.2. these properties are the macroscopic thermal and epi- thermal neutron absorption cross sections ( and I ). 3.1.6. TCN production by energetic nucleons The macroscopic epithermal neutron absorption cross Most of the secondary high-energy ('&10 MeV) section is also referred to as the e!ective resonance inte- nucleonic radiation at mountaintop elevations is com- gral for absorption of epithermal neutrons. These para- posed of neutrons. A spallation reaction is a high-inci- meters describe the propensity of a heterogeneous (in dent energy process in which a neutron (or other terms of elemental composition) bulk material to absorb nucleon) collides witha target nucleus (e.g., a silicon neutrons through nuclear reaction. The macroscopic atom) and breaks from the target nucleus several (typi- thermal neutron absorption cross section is given by cally 3}10) lighter particles, leaving a lighter residual nucleus (e.g. Ne) (Templeton, 1953). Spallogenic reduc- " I NI, (3.6) tion of the nucleus mass occurs in two phases: (1) shatter- I ing of the target nucleus resulting from an initial where I is the elemental thermal neutron cross-section collision, from which the primary particle may escape but of the k element and NI is the concentration of withreduced momentum, and (2) a consequent spalling that element (in atoms g\ or mol g\). The elemental of individual or clusters of nucleons induced by the thermal neutron cross section is usually expressed in energy dissipation throughout the nucleus until the en- barns, where one barn is equal to 10\ cm (understood ergy falls below the binding energy of individual nuc- as per atom in this case). The macroscopic thermal leons. The product mass distribution is bimodal and neutron is therefore usually expressed in cm g\ or favors product masses that are either slightly less than barn mol g\. the target mass (the residual nucleus of the target atom) The macroscopic thermal neutron cross section of the or muchlighterparticles suchas protons and neutrons. atmosphere is 0.0602 cm g\, while that of common For example, when a Si is the target of a spallation types of rock ranges from about 0.004 to 0.008 cm g\ reaction, it is muchmore probable thatnuclides with (Fabryka-Martin, 1988; Liu et al., 1994). The approxim- masses of 27}25 and 1}3 will be produced than two ately one-order-of magnitude greater absorption by the nuclides with a mass of 14. This is partly why spallogenic atmosphere is due to the large thermal neutron cross Al has a greater production rate in quartz than Be section of nitrogen, 1.9 barns. As a result, the thermal does, even though Be can be produced from both Si neutron #ux in the atmosphere above the land surface and O. The spallogenic TCN concentration pro"les in is much less than in the solid earth below. The change the upper 2 m of rock are characterized approximately in thermal neutron #ux at the atmosphere/land interface by an exponential curve with e-folding lengththatis is not abrupt, however, because the gas-like properties similar to the attenuation pro"le of fast neutrons in of thermal neutrons allow net upward di!usion of air (Fig. 2a). However, a numerical simulation of neutrons thermalized in the solid earth (cf. O'Brien neutron #ux withdepthbelow a rock surface at sea et al., 1978). level and high latitudes by Reedy and Masarik (1995) The di!usive behavior of thermal neutrons therefore showed an initial #at region to a depthof 12 g cm \ produces a thermal neutron #ux pro"le that smoothly (roughly 4.4 cm) which was not seen with earlier trans- increases downward below the land surface to a depth of port models (e.g. O'Brien et al., 1978). The #attening was approximately 50 g cm\, then reverses and decreases also apparent in measured pro"les (Dep, 1995). If this with additional depth, a characteristic shape that we #attening is ignored (presently it is ignored), it would refer to as the thermal neutron `bulgea (Fig. 2b). This result in an underestimation of near surface production pro"le is in marked contrast to that of energetic cosmic rates by up to 3.7%. It suggests that a di!erent pro- radiation, which decreases exponentially with depth. This duction rate adjustment be made to shallow surface sam- divergence in the depth dependence of the production ples ((4 cm) for spallogenic or muogenic cosmogenic rates of thermal-neutron produced and spallation pro- nuclides. duced cosmogenic nuclides can be used to advantage in studies of sur"cial materials that may have had complex 3.1.7. TCN production by low-energy neutron exposure histories. However, such use requires the ability In general, the epithermal and thermal neutron #uxes to quantify the depth dependence of the thermal neutron are in equilibrium withthecosmogenic neutron produc- #ux. 1492 J.C. Gosse, F.M. Phillips / Quaternary Science Reviews 20 (2001) 1475}1560
3.1.8. TCN production by muons interesting dilemma has developed over the relative con- The sections above have described the production of tribution of muons to the total production of TCN in cosmogenic nuclides by reactions of terrestrial atoms rocks near the surface. Hampel et al. (1975) interpreted withneutrons, protons, and occasionally withheavier cosmogenic Al in silicate rock at &1.8 m depthas nuclear fragments. These particles, due to their strong being completely produced by muonic interactions. nuclear interactions and often high energies, are quite Measurements of Al at depths of 10 m below the rock reactive. Most of them are therefore absorbed in the surface by Middleton and Klein (1987) led them to pre- atmosphere and the top few meters of the solid earth. In dict that &10% of the surface production of TCN at sea sharp contrast, large numbers of very low-mass particles level was through muon capture by Si. Other evidence such as neutrinos can pass through the entire earth with suggests that 10% is too high and the value is probably so few reactions resulting that they are not useful for closer to 1}3% at the surface (Brown et al., 1992a, 1995a; geological applications. Muons occupy an intermediate Heisinger et al., 1997; Stone et al., 1998b). In the case of position. using cosmogenic Al and Be, it is not critical to know Primary cosmic-ray reactions in the upper atmosphere the exact muogenic component because fortunately the produce unstable 3 and K3 mesons. If they do not Al/Be muonic production ratio (7.0$0.4, Reedy et interact quickly with atmospheric nuclei these particles al. (1994a); 7.2$1.2, Heisinger et al. (1997)) is approxim- can decay to muons, with mass 207 times that of the ately the same as the Al/Be neutron spallogenic pro- electron, before reaching the land surface. At ground duction ratio (&6.0 in quartz, Nishiizumi et al. (1989), level approximately half the cosmic-ray #ux consists of and 7.1 in synthetic SiO targets, Reedy et al. (1994a)). energetic muons. Although muons decay rapidly (lifetime On the other hand, recent preliminary results of Kim et &10\ s), like other leptons they do not undergo strong al. (1999) show that the muon-dominated Al/Be less (nuclear force) reactions with other particles. Thus reac- than 4.4$0.1. This is lower than the neutron-dominated tivity is low, so the muons penetrate much deeper than Al/Be production ratio and is lower than the esti- the hadronic (i.e. meson and baryon particles that partici- mates from simulations and experiment. The magnitude pate in the strong interaction) component of the cosmic- of the muogenic production will a!ect boththespatial ray #ux. Suchmuons are lost due to eitherspontaneous scaling of production and the e!ects of erosion on the decay (to electrons and neutrinos) or due to slowing by rate of TCN buildup. ionization and capture (in the case of negative muons) by Muogenic nuclides are potentially very useful for positively charged nuclei. Muonic interactions producing a variety of earth-science applications. The sensitivity of TCN mainly involve the capture of slow negative muons nuclide concentrations to erosion rate decreases as the (\) by charged nuclei, although coulombic interactions attenuation lengthfor production increases (e.g., a nucl- of fast muons also contribute (Lal, 1988). Interactions ide produced mainly in the top few centimeters will be witha target of mass number A and atomic number `reseta by quite shallow erosion, whereas one whose Z induced by stopping slow negative muons to pro- production is spread over several meters of depthwill be duce TCN take on the general form muchless a !ected). The attenuation length for muon production (which does not adhere closely to an ex- \(A , Z )P(A !x, Z !1)#(x)n #v (3.7) G I ponential pro"le; Stone et al., 1998b) is about leading to a reduction of at least 1 in A (or in Z if, for 1500 g cm\ (Brown et al., 1995a), an order of magnitude example, x"0). Here n refers to neutrons and to longer than for neutron and proton production. The neutrinos. Reaction of the muon with a nuclear proton muon #ux actually decreases more slowly withdepth releases large amounts of energy and particles (including than an exponential relation would predict. Used in neutrinos) are ejected from the excited nucleus combination witha nuclide produced by a shorterat- (Charalambus, 1971). Negative muon reactions on vari- tenuation lengthreaction, muogenic nuclides o !er the ous target nuclei can produce Be, Al, Cl and other potential to determine boththeexposure age and erosion nuclides. They can also indirectly release neutrons, rate of rapidly eroding landforms (Stone et al., 1998b). through a variety of reactions, which can in turn generate Several deep pro"les of Cl (Kubik et al., 1984; Dock- nuclides suchas Cl through low-energy neutron ab- horn et al., 1991; Stone et al., 1998b), and Be and Al sorption (Stone et al., 1998b). Highly energetic muons (Nishiizumi et al., 1994; Brown et al., 1995a) that record can also interact spallogenically. muogenic production have been measured. In spite of It is di$cult to precisely isolate the contribution of these e!orts, and laboratory investigations of muon reac- muon capture mechanisms to TCN production at the tions as well, the systematics of muon reactions in geo- surface because neutron spallation reactions can also logical materials are poorly quanti"ed compared to the produce any muon-produced (&muogenic') product. major hadronic reactions. This is partially a result of the However, the muogenic component can be isolated complexity of muon reactions. Neutron and proton reac- from the fast nucleon component because muons have tions are essentially colligative, that is, they occur in the capacity to penetrate more deeply into rocks. An proportion to the abundance of the target element in the J.C. Gosse, F.M. Phillips / Quaternary Science Reviews 20 (2001) 1475}1560 1493 rock. Negative muons, however, "rst interact withthe other nuclides have not been used for one or a more of electron shells of the target atoms in a fashion analogous the following reasons: (i) the nuclide also exists naturally to electrons and thus the reaction parameters are depen- (from primordial or radiogenic sources) and the dent on the chemical properties of the rock. This addi- radiogenic contribution cannot be reliably determined tional complexity makes "eld calibration of the reaction (e.g., Li), (ii) the nuclide may decay too rapidly to be parameters a di$cult and involved task. These para- useful (e.g., Na, which has a half-life of 15 h), (iii) the meters have been established for muon production of cosmogenic production rate of the nuclide in rocks at the Cl in the relatively simple case of pure calcite by Stone surface of the earth may be too low to have concentra- et al. (1998b), but considerable additional work will be tions above the detection limits of existing analytical needed before muon production can be applied to geo- methods (e.g., TCN with A'56 are rarely produced logical problems involving other lithologies or nuclides. because of the low abundance of target elements), and (iv) In addition to the potential application of muogenic other isotopes of the element may exist naturally in rocks nuclides to deeply eroded landforms, their e!ects must in suchabundance as to make measurement of the also be considered in situations where materials covered abundance of the cosmogenic nuclide di$cult, even with to moderate depth are brought to the surface by either state-of-the-art accelerator mass spectrometry with iso- steady or episodic erosion. For example, Stone et al. topic ratio limits of 10\ (e.g., cosmogenic Ca in (1998b) have shown that in a limestone that has been plagioclase). rapidly eroding for a long period, up to 50% of the Cl at the surface can be a result of muon, rather than 3.2. Numerical simulation of low-energy neutron behavior spallation, production. Similarly, if a relatively stable limestone surface has in the recent past suddenly had Knowledge of the depth-distribution of TCN produc- several meters of rock removed by an event that is as- tion beneath the surface of the solid earth is necessary for sumed to have `reset the clocka for dating, a substantial surface exposure dating and erosion studies. As described background of muogenic Cl may be inherited from above, production due to spallation reactions, mainly production prior to the erosion event. These examples from energetic neutrons, follows a relatively simple ex- demonstrate the importance of quantifying muon pro- ponential distribution (see also Sections 3.3.1 and 3.4). duction. The distribution of low-energy neutrons, however, is more complex. (For the purposes of this paper, we con- 3.1.9. Factors limiting TCN applications sider `low-energy neutronsa to be those in the range At this point, it is important to make a distinction where TCN production by simple neutron absorption between meteoric cosmogenic nuclides, which are pro- reactions is signi"cant, &10 keV to 0.025 eV, corre- duced in the atmosphere, and terrestrial cosmogenic sponding to the epithermal and thermal energy regimes). nuclides that are produced in situ from nuclear transmu- This section and Section 3.3 describe approaches to tations in rock. The familiar radiocarbon dating method quantifying the low-energy neutron distributions. is based on the abundance of C, a cosmogenic nuclide Low-energy neutrons are produced as the result of produced in the atmosphere largely by thermal neutron a complex cascade of nuclear reactions propagated down absorption into N. Most of the commonly used TCN through the atmosphere and solid earth. The production are produced in the atmosphere as well as within rocks. distribution of cosmogenic nuclides depends on nuclear Some nuclides suchas Be are produced in the atmo- reactions at a wide range of energy levels within this sphere at a rate approximately 10 times greater than the cascade. The most satisfactory approach to simulating average rate of production in rocks on Earth, so it is the cosmogenic nuclide production is to comprehensively necessary to take rigorous steps in sample preparation to model the chain of reactions. Critically important early ensure that the atmospheric component does not con- e!orts in this direction were described by Lal and Peters taminate the terrestrial component (cf. Kohl and (1967). Later, O'Brien et al. (1978) focused on neutron Nishiizumi, 1992). Atmospherically produced TCN that #uxes, down to thermal energies, over a range of atmo- are highly reactive with mineral surfaces (e.g., Be) are sphere/surface interfaces. More recently, Dep (1995) has more of a problem than those that react little with rocks applied linked high- and low-energy neutron transport (e.g., He and Cl). codes to simulating neutron #ux distributions and result- Although there may be a very large number of nuclides ant Cl production rates at the atmosphere/land surface that can be produced from cosmic-ray interactions with interface. Dep et al. (1994a) compared the calculated target atoms in rock, only six TCN have been commonly thermal neutron #ux distribution withexperimental re- used for geologic applications: He, Be, C, Ne, sults and Dep et al. (1994c) compared the calculated Cl Al, and Cl (Table 1, see Lal, 1988 for others). In distribution withthatin a natural rock, bothwithvery addition, in situ produced cosmogenic Ar and Ca favorable results. have been investigated (Looosli, 1983; Middleton et al., A signi"cant proportion of the Cl is produced by 1989), but not applied to any signi"cant extent. Most absorption of epithermal neutrons (those with energies 1494 J.C. Gosse, F.M. Phillips / Quaternary Science Reviews 20 (2001) 1475}1560
Table 1 Important reactions and advantages and disadvantages due to physical and chemical attributes for common TCN
Nuclide Lifetime Reaction types Primary target Advantages Disadvantages and primary minerals targets
He stable Spallation on: O, Ol, Pyx, Hbl, Gnt He has the highest production rate He appears to di!use too rapidly from Mg, Si, Ca, Fe, Al of all TCN and low detection limit on quartz and "ne grained groundmass in Li(n,)HPHe a conventional mass spectrometer aphanitic rocks (Brook and Kurz, 1993). (blanks (50,000 atoms He, back- Correction for radiogenic /nucleogenic ground &20,000 atoms) so it can /magmatic He is necessary, particular on be used to date young surfaces rocks withold crystallization ages. Greater ((3000 kyr). Extremely long opportunity for inheritance of stable exposures can be investigated because cosmogenic He if the mineral grains have it is stable. Presently there is more ever been exposed previously. Interference known about production rate for He from HH molecules. than the other TCN noble gas Ne.
Be 2.2 Ma O(n,4p3n)Be Qtz, Ol, Mgnt, Simple, stoichiometric chemistry of Atmospheric Be is potentially Si(n, x)Be Plag? target mineral. Quartz is resistant to a signi"cant source of contamination. The O(\,pn)Be chemical weathering and is almost isobar Bisdi$cult to remove during Si(\,x) ubiquitous. Mostly produced through AMS analysis. Little work has been done BeLi(,p)Be spallation and muon reactions on O to determine the production rate of Be in Be(n,)Be and Si. Be samples can be prepared the olivine solid-solution series and other B(n,p)Be simultaneously with Al, C, and targets. Be has the lowest production C(n,)Be Ne in quartz. Olivine is fairly resistant rate in quartz of all TCN so young surfaces to weathering and may be a suitable require large samples or not possible. alternative where quartz is absent. Its long half life make it useful for long exposures. Not a gas, relatively immobile.
C 0.82 kyr O(n,2pn)C Qtz Excellent for recent exposure histories Short half life precludes investigation of Si(n, x)C because its short half life renders it long (' 30 kyr) exposure histories. O(\,2p)C insensitive to low erosion rates. Although whole rock analyses were N(n,p)C Inherited concentrations will likely attempted, quartz has been the only O(n,)C be minimal because of its fast decay. reliable target. Probability of B(,p)C Higher production rate than Be. contamination makes sample preparation and analysis di$cult and expensive.
Ne stable spallation: Mg, Na, Qtz, Ol, Gnt. Extremely long exposures can be Correction for radiogenic / nucleogenic Al, Fe, and Si Plag? investigated because it is stable. Ne Ne is necessary, particularly in old rocks O(,n)Ne does not di!use as rapidly through (worse if exposure time is short). Greater F(,pn)Ne quartz as He does (Brook and Kurz, opportunity for inheritance of stable Ne 1993; Brown et al., 1991; Staudacher if the mineral grains have ever been and Allegre, 1991). Higher production exposed previously. Interference for Ne > > rate than Be. isotopes from H O and Ar .
Al 1.0 Ma Si(n,p2n)Al Qtz Simple, stoichiometric chemistry of Mostly restricted to quartz. Mg is an Si(\,2n)Al target mineral, low stable Al isobar; AMS is required. Di$cult to Na(,n)Al abundances ((1%). Production rate measure low Al/Al in quartz withhigh of Al is higher than Be. Al contents.
Cl 430 kyr Ca(n,2n3p)Cl Spallation tgt: K- Has multiple production pathways Has multiple pathways on multiple \ K( ,p2n) Cl spar, Plag, Calcite (n, n , ) so it is possible to use just elements, so production rates from Ca(\,)Cl Thermal neutron Cl for erosion and burial investiga- individual pathways are currently di$cult Cl(n,)Cl activation tg: Cl tions. Atmospheric production is not to decipher. Exposures greater than K(n,)Cl in Chlorite, #uid as important as it is for Be, so & 1 Ma cannot be determined. inclusions in qtz whole rock chemistry is possible, and Complicated system unless pathways are therefore wide range of lithologies. isolated when erosion is slow but non zero. AMS sensitivity higher for Cl isotopic Thermal neutron leakage is signi"cant analysis than Be and Al. Production factor in variable moisture conditions, rate higher than Be. snow cover. Radiogenic and nucleogenic pathways limit low-level applications. AMS required for analysis. reactions: target(reacting particle, emitted particle)product; negative muon capture reactions also produce J.C. Gosse, F.M. Phillips / Quaternary Science Reviews 20 (2001) 1475}1560 1495 between approximately10 keV and 0.5 eV) and numerical adi!usive manner, similar to that of thermal neutrons. simulations can accurately model the transport of neu- However, epithermal neutrons can be `losta (i.e., drop trons in this energy range. In addition to a realistic out of the epithermal energy range) by energy loss due simulation of cosmic-ray physics, the numerical to kinetic energy transfer during collisions as well as modeling approachallows for theincorporation of com- due to absorption. Single-valued epithermal neutron plex boundary conditions into neutron-#ux computa- absorption cross sections (I ) are assumed to de- tions, for example, a high water-content soil over a layer scribe cosmogenic nuclide production in this range of non-porous rock. and the resonance escape probability (p(E )) is used to The main limitation of the numerical simulation ap- calculate the likelihood that a neutron will pass proach is the complexity and the relatively large com- through the epithermal energy range without being putational demands of the programs employed. Another absorbed in some nucleus. The resonance escape is the sensitivity of the results to small variations in input probability is given by parameters. An alternative to full-scale neutron transport I G simulation is to use simpli"ed analytical solutions. p(E )"exp ! , (3.8) I INI G I 3.3. Analytical equations for TCN production where I is the average log decrement of energy per collision for element k (dimensionless) and I is the Analytical expressions for neutron behavior o!er cross section of element k for scattering of neutrons, a simpler alternative approachto full-scale neutron and i identi"es the material for which the property is transport numerical modeling. In this approach, the en- calculated. If i"a, the atmosphere is indicated and ergy-dependent aspects of neutron transport are conden- i"ss indicates the subsurface. NI G is the atomic con- sed into a limited number of energy categories and the centration of element k in the atmosphere or subsur- transport properties are computed from bulk material face. I G is the e!ective resonance integral for composition. Although less #exible and comprehensive absorption of epithermal neutrons and is given by than "rst-principle transport codes, this approach has the advantage that solutions can be obtained in a few I G" I INI G, (3.9) minutes on standard personal computers. I For purposes of computing cosmogenic nuclide pro- where I I is the dilute resonance integral for element duction, we divide the equations governing neutron pro- k (commonly expressed in barns, where one barn duction and transport into three discrete energy ranges: equals10\ cm atom\). (Note that the `aa sub- script in I refers to `absorptiona, not `atmospherea). ** ++ I 1. High energy or fast range. This range extends from Values for these and other elemental constants used & maximum cosmic-ray energies ( TeV) to 10 MeV. below are provided in Table 2 (see Fabryka-Martin In this energy range, the cosmic-ray particles are as- (1988) and Phillips et al. (2000)for discussion). sumed to act as a beam. The cosmic-ray #ux is at- \ tenuated exponentially withmass depth(g cm ). Given the simpli"cations described above, the produc- Cosmogenic nuclides are assumed to be produced by tion of a particular cosmogenic nuclide, m, formed by spallation reactions, withtheproduction rate inde- nucleons in all three energy ranges and by muons, in pendent of the energy spectrum. a sample of "nite thickness at a speci"ed geographical 2. Thermal energy range. In the thermal energy range location is given by ((0.5 eV), the neutrons can be assumed to be moving in a Brownian fashion and hence a di!usion-equation PR K"SS2(QP #S* Q P #S* Q P ) approximation can be used to model their behavior. #S S Q P , (3.10) Similar approaches have long been employed in nu- I 2 I I I K clear reactor theory (Stephenson, 1954). In this range, where S is the scaling factor for the dependence of the cosmogenic nuclide production is assumed to be solely nucleonic component of the cosmic-ray #ux on elevation due to thermal neutron absorption. The production of and latitude, as described in Section 3.7.1 below and SI is thermal neutrons is assumed to be derived from the the same scaling factor for the muonic component. S2 is epithermal neutron #ux, less some fraction of neutrons the scaling factor for shielding of the nucleonic compon- absorbed in the epithermal energy range. Thermal ent of the cosmic radiation due to rock geometry and neutrons are, by de"nition, at the lowest energy pos- surrounding topography, described in Section 3.7.2 sible in their environment, and hence can be removed below, and S2 I is the same scaling factor for the from the thermal energy population only by absorp- muonic component. P K is the production rate of cos- tion into the nuclei of atoms with which they collide. mogenic nuclide m for the type of reaction q, where q"s 3. Epithermal energy range. In the epithermal range (be- indicates fast neutron (spallation) reactions, q"th tween &0.1 MeV and 0.5 eV) neutrons behave in indicates thermal neutron absorption reactions, q"eth 1496 J.C. Gosse, F.M. Phillips / Quaternary Science Reviews 20 (2001) 1475}1560
Table 2 Elemental values for low-energy neutron transport parameters, from Fabryka-Martin (1988). Parameters are de"ned in text and in Section 2.2
k A I (g mol\) (unitless) (10\ cm atom\) (10\ cm atom\) (10\ cm atom\)
O 16 0.12 3.76 0.0002 0.0004 H 1 1 20.5 0.33 0 C 12 0.158 4.74 0.0034 0.0016 Na 23 0.084 3.025 0.53 0.311 Mg 24.3 0.08 3.42 0.063 0.038 Al 27 0.072 1.41 0.23 0.17 Si 28.1 0.07 2.04 0.17 0.127 P 31 * 50.2* K 39.1 0.05 2.04 2.15 1 Ca 40.1 0.049 2.53 0.43 0.235 Ti 47.9 0.041 4.09 6.1 3.1 Mn 54.9 0.036 2.2 13.3 14 Fe 55.8 0.035 11.35 2.56 1.39 Cl 35.5 0.055 15.8 33.5 13.7 B 10.8 0.174 4.27 767 1722 Sm 150.4 0.013 38 9640 1400 Gd 157.3 0.013 172 41560 390
indicates epithermal neutron absorption reactions, q" length, and not on the atomic arrangement of those indicates muon reactions, and q"t indicates total pro- nucleons. In other words, the rate of interaction is pro- duction. S* is a scaling factor to account for the net portional to the density of the medium without regard to di!usion (`leakagea) of epithermal neutrons, in excess of the elemental composition. This property allows the at- the standard #at geometry, out of rocks that project into tenuation of the cosmic radiation with distance in any the air (Section 3.7.3), and S* is the same for thermal material to be characterized by a single constant, so long neutrons . Q accounts for the variation in the depth- as the path length is given in units of cumulative mass integrated production rate as a function of sample thick- traversed, or mass length, Z (g cm\): ness. It is the ratio of the average production over the X actual thickness of the sample to the production at the Z(z)" (z)dz, (3.11) surface. The method for calculating Q is given in Section 3.7.4. In general, for near-surface samples the muonic where z is ordinary linear distance (cm). Withdistance component of production is much smaller than the nuc- expressed in mass units, the rate of particle interception leonic and is often neglected. will simply be proportional to the #ux of particles pas- This section of paper derives in detail the equations sing through the medium: that describe the depth-dependence of TCN production for the various types of nuclear reactions. All of the dF" F , (3.12) material may not be of interest for all readers. For dZ N readers interested only in purely spallogenic nuclides where F is the cosmic-ray intensity (particles cm\ s\ (e.g., He and Ne) we recommend reading Sections from a single direction) and , the constant of propor- 3.3.1 and 3.3.5. For readers interested in Be, C, and tionality, is termed the particle attenuation length Al, we recommend Sections 3.3.1, 3.3.4 and 3.3.5. For (g cm\): the path length that is required to attenuate the readers interested in Cl and Ca we recommend all intensity by a factor of e\. This equation may be solved subsections of Section 3.3. for the boundary condition that F"F at some refer- ence point to yield: 3.3.1. Fast neutron (spallation) production The mechanics of spallation production have been Z F"F exp ! . (3.13) described above in Section 3.1.2. If only a small sector of N the sky area is considered, the cosmic radiation respon- To obtain the total cosmic-ray #ux, the intensity must sible for spallation reactions can be visualized as a linear be integrated over the entire sky. This produces the beam of high-velocity particles. It is an important prin- resulting analogous expression: ciple that the rate of reaction of cosmic-ray particles with the medium through which the beam passes depends on Z (Z)" (0)exp ! , (3.14) the number of nucleons in the medium, per unit path J.C. Gosse, F.M. Phillips / Quaternary Science Reviews 20 (2001) 1475}1560 1497 where is the annual cosmic-ray #ux integrated over directional transport in the usual sense of a #ux. G is the entire sky assuming a horizontal land surface and given by horizontal horizon (particles cm\2yr\), (0) is the \ \ integrated cosmic-ray #ux at zero depth(land surface), R" GI G# " . (3.18) and is the apparent attenuation length of the energetic G G cosmic-ray particles for the integrated #ux. The relation is a measure of the propensity of material i for between and is derived in Section 3.4. G N epithermal neutron absorption (the length of penetration The spallation production rate for nuclide m, of the epithermal neutrons decreases as the propensity P (atoms (g target material)\ yr\), is proportional to K for absorption grows). is the e!ective epithermal the cosmic-ray #ux, to the cross section of the target G loss (by bothabsorption and energy moderation) cross element for production of nuclide m, and to the abund- section (cm g\). M is the macroscopic (average) log ance of the target element in the target material. P is G K decrement energy loss per neutron collision: also a function of the cosmic-ray energy spectrum, be- cause reaction cross-sections depend on the incident par- I I INI G ticle energy. Because the energy spectrum does not vary MG" . (3.19) I INI G signi"cantly over the surface of the earth or with depth, the cross sections can be treated as constants. Inasmuch When neutrons have reached the epithermal energy as the target element cross sections are generally poorly regime, such that there is very little net directional trans- known and the production equation therefore empiric- fer of momentum, the spatial distribution of the epither- ally calibrated, the production equation is usually para- mal neutron #ux can be described by a di!usion equation meterized in terms of the product of the #ux and the cross (e.g., Glasstone, 1955) that balances the epithermal neu- section: K I(0), the production rate of species m by tron sources (moderation of energetic neutrons) and spallation of element k, per unit mass of k, at the reference sinks (moderation into the thermal range or absorption position (land surface (z"0), sea level, and high latitude) into atomic nuclei). The formulation that we present here (atoms (g target element)\ yr\): assumes that all epithermal neutrons are derived from moderated spallation and evaporation neutrons produc- " ! Z ed by high-energy cosmic-ray nucleons, and that other P K(Z) K I(0)CI exp , (3.15) sources of neutrons, suchas nucleogenic reactions (originating from radioactive decay), muon capture- where CI is the concentration of element k (g of k (g produced neutrons, and neutrons derived from photo- \ material) ). disintegration reactions, are neglected. The epithermal neutron #ux is assumed to be in temporal equilibrium 3.3.2. Production by epithermal neutrons with the high-energy #ux. Production of cosmogenic nuclides by epithermal neu- tron absorption is given by d G G D G " !R GP , (3.20) dZ G f K P K "f K " , (3.16) D is the epithermal neutron di!usion coe$cient G (g cm\), calculated according to where \ D G" 3 (1!2(3AG)\) , (3.21) NI I I G f K " (3.17) I where is the fraction of the total epithermal neutrons absorbed that are taken up by target element k (e.g., Cl or Ca) " I INI G (3.22) to produce nuclide m (e.g., Cl or Ca). In general, we G ` a will omit the material subscript (i.e., ss ) in production is the macroscopic neutron scattering cross section terms, since in this paper we are only concerned with in (cm g\) in material i. A is the average atomic weight of situ cosmogenic nuclide production. G material i. AG is given by is the total rate of epithermal neutron absorption (n g\ yr\). is the epithermal neutron #ux I AINI G (n cm\ yr\) and is the e!ective epithermal neutron AG" (3.23) NI G attenuation length(g cm \). Note that the epithermal I and thermal neutron #uxes are independent of the direc- where AI is the atomic mass of element k. For this tion of individual neutrons and are therefore the derivation the datum is the land surface; positive is equivalent of neutron concentration rather than a net downward and negative upward. 1498 J.C. Gosse, F.M. Phillips / Quaternary Science Reviews 20 (2001) 1475}1560
P is the production rate (n g\1yr\) of epithermal Eq. (3.25) can be expressed as neutrons from fast (i.e., energetic: &1}10 MeV) second- " " ary cosmogenic neutrons, given as a function of Z by "H ! Z # H ! Z G Gexp (F ) Gexp ¸ , Eq. (3.9) and P (0) is the production rate of epithermal G neutrons from fast neutrons in the atmosphere at the (3.27) land/atmosphere interface. R G dimensionless) is the normalization factor for the epithermal neutron where production rate and according to Dep et al. (1994b) is given by (D H/¸ H)H G!(D QQ/ )HH (F )H G" D /¸ !D /¸ AG G" , (3.24) (3.28) A and where A is the average atomic weight of the atmosphere, H "H !H , (3.29) equal to 14.5 g mol\. R is equal to unity. G H G As described in Phillips et al. (2000), coupled di!eren- D tial equations for atmosphere and for subsurface, of the HH "H ! H , (3.30) ? D form of Eq. (3.20), can be solved subject to the boundary conditions (Eq. (3.25)) below: where i is the environment of interest (a or ss) and j is the other environment (i.e., if i"a, then j"ss). Physically, (i) (R)"0 (the cosmic-ray #ux is completely at- * represents the epithermal neutron #ux tenuated at an in"nite depth) (n cm\2yr\) that would be observed at the position of R " (ii) ( ) (0) continuity of concentration the land surface if the atmosphere had the same epither- [commonly referred to as epithermal neutron #ux] mal neutron transport properties as the subsurface and across the atmosphere/subsurface boundary) * is the di!erence between the equilibrium epither- " (iii) D d (0)/dZ D d (0)/dZ (continu- mal neutron #uxes in a medium with the properties of the ity of [true] epithermal neutron #ux across the atmosphere and one with the properties of the subsur- boundary) face. (F) G represents the di!erence between the #ux (iv) that would be observed at Z"0 if only medium i were Z present and that actually observed in the presence of an (Z)"P (0) exp ! z;0 interface.
(at large distances above the boundary the epither- 3.3.3. Production by thermal neutrons mal neutron #ux is in spatial equilibrium withthe Production of cosmogenic nuclides by thermal neu- atmospheric energetic neutron #ux). tron absorption is given by The solutions for the subsurface and atmospheric epi- " "f thermal neutron #uxes are given by P f (Z), (3.31)
" H ! Z where G(Z) Gexp N f " I (3.32) " " (D /¸ )(H !H )! (H ! H ) # H H H G " ¸ ! ¸ D / D / is the fraction of thermal neutrons absorbed that are taken up by target element k to form the nuclide of " " ; Z interest, m. The distribution of the thermal neutron #ux exp ¸ , (3.25) G withdepthis assumed to be governed by an equation similar to that for epithermal neutrons, but with the ¸ where G is the epithermal neutron di!usion length epithermal neutron distribution as the source term, \ (g cm ), equal to (D G/ G) . The epithermal neu- rather than the fast neutron distribution: tron di!usion lengthis equal to approximately 0.4 times ! the net mean distance traveled by a neutron between d G G p(E ) H Z D G " !R G Gexp production and absorption. dZ G G !"Z" H " R G # H G P (0) . (3.26) (F ) Gexp ¸ , (3.33) G!D G/ G J.C. Gosse, F.M. Phillips / Quaternary Science Reviews 20 (2001) 1475}1560 1499 where Eqs. (3.27) and (3.37). These curves illustrate the e!ects of elemental composition on both the magnitude of the p(E )G neutron #uxes and the depth of its maximum. One im- R G" , (3.34) p(E ) portant advantage of the expanded derivations of Phil- \ lips et al. (2000) over the earlier ones of Liu et al. (1994) is G" , (3.35) that by deriving the source term for the thermal neutron G production from the epithermal neutron #ux, rather than \ directly from the fast neutron #ux, enables the depend- D G"3 (1!2(3A)\) . (3.36) ence of the epithermal and thermal neutron #uxes on G water content to be described. Figs. 3b and c show how Eq. (3.35) applies to both the atmosphere and the subsur- these #uxes vary in a shale as a function of water content. face, withthesubstitution of `aa and `ssa for `ia. These One signi"cant e!ect of the epithermal neutron pro- equations can be solved together, subject to the same duction is that it tends to counter the steep thermal boundary conditions listed under Eq. (3.24), except that neutron #ux gradient near the interface. The steep gradi- `tha is substituted for `etha. The solutions are of the form ent of thermal neutron #ux at the interface can make the inventory of thermal-neutron-produced nuclides at the ! !" " H Z H Z surface very sensitive to small amounts of erosion. Since G" Gexp #(I ) Gexp ¸ G the epithermal neutrons are also absorbed by the same target elements, the combined production varies less !"Z" steeply at the interface and hence is less sensitive to #(I ) H Gexp , (3.37) ¸ G erosion than thermal-neutron production alone. where 3.3.4. Production by muons and muon-derived neutrons p(E ) R H The calculation of cosmogenic nuclide production by H " G G , (3.38) muons di!ers considerably from the calculations for G ( !D /) G G G production by the nucleonic component, presented H above. This is because the mean transport length of the p(E )R G(F ) G (I )H G" , (3.39) lower-energy components of the nucleonic radiation are G( G!D G/¸ G) short enough that they can be assumed to be in quasi- (I ) H G"[D ( H \ !(I )H ¸\ ) equilibrium with the high-energy component. Muons are tertiary products of the high-energy component \ \ !D ( H #(I )H ¸ ) (produced by decay of secondary charged pions and K mesons, Fig. 1b) and are less reactive and hence have D # H H # H muchlonger mean transport lengths.As a consequence, ¸ ( G (I ) G) H the muon #ux is generally not in equilibrium with D D \ the local high-energy #ux and separate scaling factors, ; # . angular distributions, and attenuation lengths must ¸ ¸ (3.40) be used. Muons can produce TCN by a variety of mechanisms, H H The terms (I ) G and (I ) G quantify the devi- discussed in Section 3.1.8. Following Stone et al. (1998b), ations of the thermal neutron pro"le at the atmo- they can be summarized as follows: sphere/subsurface interface from one in the atmosphere only, due to, respectively, the shape of the parent epither- P I"SIS IQI(PI#P I#P I) (3.43) mal neutron pro"le and the subsequent di!usion of the where P is the total nuclide production by muons thermalized neutrons across the interface. The other I (atoms g\1yr\), P is direct production by capture of parameters in Eq. (3.40) are as follows: I slow negative muons (atoms g\1yr\), P I is produc- H H H tion by absorption of neutrons emitted following slow G" H! G, (3.41) negative muon capture (atoms g\1yr\), and P I is (I )H G"(I )H H!(I )H G. (3.42) production by absorption of neutrons emitted due to photodisintegration reactions initiated by fast muons. Phillips et al. (2000) compared the epithermal and The other terms are de"ned above. thermal neutron pro"les withdepthcomputed from Eqs. Of these reactions, slow negative muon capture is (3.27) and (3.37) withmeasurements performed within generally the most important. It is given by a concrete slab, withvery favorable results. Fig. 3a illus- trates epithermal and thermal neutron depth pro"les for PI K(Z)" I\(Z) f I fG I f I f I K">I KI\(z) (3.44) a variety of common rock types, calculated by means of I 1500 J.C. Gosse, F.M. Phillips / Quaternary Science Reviews 20 (2001) 1475}1560
Fig. 3. (a) Pro"les of the thermal and epithermal neutron #uxes withdepthin a variety of rock types. Rock compositions were taken from average values given by Fabryka-Martin (1988) and rocks were assumed to be at sea level, high latitude and to be dry. Heavy lines indicate thermal neutron #uxes and thin lines epithermal #uxes. (b) Epithermal neutron #ux as a function of depthand water content in an average shale(Fabryka-Martin, 1988). Shale was assumed to have 30% porosity. Numbers beside curves refer to volumetric water content. (c) Thermal neutron #ux as a function of depthand water content in same shale.
where k refers to all elements that may produce the capture (unitless), f I is the fraction of the captured nuclide of interest, m, by negative muon capture, I\(z)is negative muons that are absorbed by the nucleus of the muon stopping rate as a function of depth ((stopped element k before they decay (unitless), and fL I is the \)g\1yr\), fA I is the fraction of stopped negative probability that the nucleus of the particular isotope of muons that are captured by element k (unitless; known as element k will produce nuclide m after it has absorbed the the `chemical compound factora and dependent upon the negative muon (unitless). > is the (composition de- K chemistry of the material), fG I is the abundance of the pendent) total production constant for nuclide m from isotope that produces nuclide m after negative muon slow negative muon absorption reactions. J.C. Gosse, F.M. Phillips / Quaternary Science Reviews 20 (2001) 1475}1560 1501
Of the parameters in Eq. (3.44), some are fairly well neutrons by means of photodisintegration reactions in- determined (the scaling factors, I\(z), fG H, and f H). itiated by the deceleration of the fast component of the However, f H and f H are in most cases poorly known. muon #ux. As fast muons are slowed by collisions with The chemical compound factor, f H, in particular, is di$- atoms, bremsstrahlung (gamma rays, some highly cult to estimate. It can be crudely ($25%) calculated energetic) is produced. Absorption of the energetic brem- based on the Fermi}Teller Z-law (Charalambus, 1971): sstrahlung gammas by nuclei can cause photo-disintegra- tion reactions that result in the release of a neutron. NHzH Thermalization and absorption of these neutrons can f H" , (3.45) then produce TCN. The parameters governing the pro- NIzI I duction of bremsstrahlung and the release of photodisin- tegration neutrons are reasonably independent of rock z z j where H and I are the proton numbers of elements and type, and suchneutrons are only a minor source of k k , and refers to all elements in the material. This TCN production (except at great depth), therefore formulation is only approximate because it neglects in- Fabryka-Martin (1988) has presented a generalized for- teractions of the slow muons with the electron shells of mulation for neutron production from photodisintegra- the atoms comprising the material. The probability that tion reactions: the muon absorption will result in production of the nuclide of interest, f , can be obtained from muon ir- H PL I (Z)"8;10\ln(0.1Z) I3(Z), (3.47) radiation experiments, but withregard to reactions of signi"cance for TCN production, f H is fairly well known where I3(Z) is the fast muon (both positive and only for Ca(\,)Cl, for which it has a value of negative) #ux as a function of depth. This formulation 0.062$0.02 (Dockhorn et al., 1991), and for assumes that the average neutron yield per photodisin- O(\,pn)Be and Si(\,2n)Al for which the tegration is equal to unity. Due to the very long penetra- values are &0.704 and &0.296, respectively (Heisinger tion lengthof fast muons, thisproduction reaction tends et al., 1997). to become the dominant one at depths below 10}20 m of The slow negative muon stopping rate is always much rock. larger than the production rate of the nuclide of interest Total muon-induced neutron production is given by by direct muon capture (i.e., most of the slow muon combining the individual terms above: captures do not result in production of the nuclide of interest). Most of the muon captures, however, do result PI (Z)"> I\(Z)#8;10\ ln(0.1Z) I3(Z). (3.48) in the ejection of one or more neutrons from the nucleus. These `muogenic neutronsa are then thermalized and can Neither the slow muon stopping rate nor the fast muon produce Cl or Ca (or other TCN to a much lesser #ux follow an exponential distribution withdepth.Due extent) by thermal or epithermal neutron absorption to the nature of the reactions producing muons in the reactions. The production distribution of neutrons by atmosphere, the energy spectrum of the muon #ux has this reaction is given by a strong angular dependence, resulting in a decrease with depth that is slower than an exponential function. Stone P I(Z)"> I\(Z), (3.46) et al. (1998b) have presented polynomial formulas for these distributions. However, in the top &3000 g cm\ where > is the average neutron yield per stopped of rock (equal to &10 m linear depth), the slow muon negative muon. This parameter is dependent on the com- stopping rate does fairly closely follow an exponential position of the material (Fabryka-Martin, 1988) and is distribution withan attenuation length( I)of subject to a moderate degree of uncertainty. This formu- &1500 g cm\. The fast muon #ux decreases even more lation depends on the assumption that the muogenic slowly than the slow muon stopping rate, but the func- thermal neutron #ux is in equilibrium withthemuogenic tion ln(0.1Z) I3(Z) is also approximately proportional neutron production rate. Given the long attenuation to exp(!Z/1500 g cm\) in the upper 3000 g cm\. length for stopping muons, this should generally be Given these approximations, the total muon-induced valid, except near the atmosphere/subsurface interface, neutron production as a function of depthcan be given but there the muogenic thermal neutron #ux is small by compared to that derived from the nucleonic component. In the case of limestone close to sea level, Stone et al. Z P I"(>I#5.8;10\ I )exp ! (3.49) (1998b) found that the production rate from muogenic I neutron absorption was about one order of magnitude less than production by absorption of spallogenic where I is the slow negative muon stopping rate at the neutrons. land surface at high latitude and sea level, equal to In addition to direct emission of neutrons as a result of 175 cm\ yr\, and I is the fast muon #ux at land muon capture, muons also can indirectly produce surface at high latitude and sea level, equal to 1502 J.C. Gosse, F.M. Phillips / Quaternary Science Reviews 20 (2001) 1475}1560
7.9;10 cm\ yr\. The approximations above should Epithermal neutron production can be obtained by com- be adequate for typical surface exposure dating studies, bining Eqs (3.16), (3.25), and (3.50): and most erosion studies. However, studies of very deep pro"les, or samples from very rapidly eroding terrains "f (Z)" f H ! Z P exp ('10 mm/kyr\) should employ the full muon #ux for- mulations from Stone et al. (1998b) due to the possibility of signi"cant in#uence of production from Z #(1#RIR )(F )H exp ! '3000 g cm\ depth. ¸ Close to the land/atmosphere boundary the muon- induced neutron #ux cannot be assumed to be in equilib- Z #RIH exp ! , (3.54) rium withtheproduction rate because neutrons di !use in I proportion to the total neutron concentration, and at the interface the neutron concentration di!erence is domin- where f is the fraction of epithermal neutrons that are ated by the spallation-induced neutrons, as described absorbed by element k to produce cosmogenic nuclide m, above in this section and Section 3.3.1. We therefore and is given by Eq. (3.17). Similarly, thermal neutron assume that the muon-induced low-energy neutrons production is given by follow the same distribution as the spallation-induced f f Z neutrons at shallow subsurface depths. Given this " " H ! P exp assumption, the total subsurface epithermal and thermal neutron distributions are given by Z #(1#RIY )(I )H exp ! ¸ " H ! Z (Z) S exp Z #(1#RIY R )(I ) H exp ! H ¸ #(1#RIR )(F ) Z # Y H ! Z ;exp ! RI exp . (3.55) ¸ I Muon production, PI K, is given by Eq. (3.44). # H ! Z RI exp , (3.50) I 3.4. Energetic neutron attenuation length " H ! Z S exp Shielding measurements and calculations, describing the relative #ux of cosmic rays from varying incident angles, are made in the spherical coordinate system. Here # # Y H ! Z (1 RI)(I ) exp ¸ we choose a system consistent with the terrestrial physics convention, where the origin for the angle of inclination, , is vertically upward and the azimuth ( ) origin is north # # Y H ! Z (1 RIR )(I ) exp ¸ (Fig. 4a). The atmospheric depth through which incoming radi- ation must pass is thickest for rays that are close to # Y H ! Z RI exp , (3.51) horizontal and thinnest vertically overhead. The cosmic I radiation #ux is therefore greatest in the vertical and where decreases toward the horizon. The angular distribution of cosmic radiation is given by SIPI p(E ) RI" and RYI" RI. (3.52) F( )"F cosK , (3.56) SP (0)R p(E ) where F( ) is the intensity of the cosmic radiation in any 3.3.5. Total nuclide production particular direction, F is the maximum intensity (which The results from the sections above enable the produc- is in the vertical direction), is the inclination angle, and tion terms in Eq. (3.10) to be calculated. Spallation pro- commonly cited values of m vary from 2.3 (Lal, 1958) to duction is given by 3.5 (Heidbreder et al., 1971). The value m"2.3 is gener- ally used in cosmogenic nuclide applications (Nishiizumi Z et al., 1989). The e!ect of the di!erence is not large P (Z)" (0)C exp ! (3.53) (Fig. 5). J.C. Gosse, F.M. Phillips / Quaternary Science Reviews 20 (2001) 1475}1560 1503
Fig. 4. (a) Coordinate system for computations involving cosmic-ray distributions. The origin for the angle of inclination, , is toward the zenith and the origin for the azimuth, , is north. (b) Illustration of solid geometry used in integration of the cosmic-ray #ux.
where the sin term accounts for convergence of the spherical coordinate system toward the origin (Fig. 4b). However, the cosmic-ray #ux impinging on a horizon- tal surface from inclinations greater than zero (i.e., to- ward the horizon) will be distributed over a larger surface area as the inclination increases. When calculating the cosmic-ray #ux through a unit surface area, this `fore- shorteninga e!ect is proportional to cos , where ( )is the angle between the normal to the surface, N, and the incident ray, . ( , )" F( )sin cos ( )d d (3.58) F( D( , )isthe#ux of the energetic component of the cosmic radiation through the horizontal surface. For a horizontal surface, ( )" and, including the inclina- tion-dependence of the cosmic-ray #ux in Eq. (3.56), the expression for the cosmic-ray #ux through a unit surface area becomes
Fig. 5. Variation of the cosmic-ray intensity (F( )) withinclination angle ( ).The variation of the intensity is shown for both (, )" F cosK sin cos d d . (3.59) " " F( ) F cos and F( ) F cos . The fraction of the total #ux F ( passing through a surface rotated so as to be always normal to the #ux, the fraction of the total #ux passing through a horizontal surface, and Integration with "0 as the lower limit yields the cumulative fraction of the total #ux passing through a horizontal " 2F surface are also illustrated, based on F( ) F cos . (max)" . (3.60) m#1 The total incoming cosmic radiation will then be given by As shown in Section 3.3.1, the high-energy component of the cosmic radiation is generally considered to follow F" F( )sin d d , (3.57) an exponential decrease as a function of the cumulative F( mass penetrated perpendicular to the surface of the rock. 1504 J.C. Gosse, F.M. Phillips / Quaternary Science Reviews 20 (2001) 1475}1560
Because a large component of the incoming #ux arrives lecting rocks at discrete depths or from continuous rock at non-vertical angles, the attenuation depth of the integ- cores. Estimates of the fast nucleon range from 125 to rated #ux is generally shorter than the true particle 213 g cm\ in the atmosphere and 145}190 g cm\ in attenuation length. For a horizontal surface the vertical rock (Table 3). The di!erences in fast nucleon attenuation penetration depthof a particle, z, as a function of the data from rocks at the same latitude may be partly angle of incidence, , and the true particle attenuation attributed to di!erences in the contribution of muogenic length, , is given by production of di!erent nuclides. Attenuation lengths may also (i) increase withincreasing atomic weight(Brown z " cos . (3.61) et al., 1992a), (ii) be larger in solids than in air because The attenuation length that is usually cited is obtained pions will decay in air before interacting (Lal, 1991) and by "tting an exponential function to cosmogenic nuclide muons have a greater attenuation length in solids than in concentrations (e.g., Kurz, 1986b; Brown et al., 1992a or the atmosphere (Lal and Peters, 1967), but this is likely to neutron counts (e.g., Liu et al., 1994) measured beneath be (20% e!ect. However, because the muonic contri- horizontal, unshielded surfaces. These pro"les integrate bution relative to nucleonic contribution increases with production from all angles of exposure. The resulting depth, apparent attenuation lengths will appear to be parameter is commonly termed the apparent attenuation longer in deeper cores (i.e. for rock depthpro "les ap- length, and values range from 121 to '170 g cm\ proaching the cross over of the relative contribution to (Table 3, Fig. 6; see discussion in Dunai, 2000). The production, 800 g cm\ for Be in New Zealand, Kim apparent attenuation length, , can be calculated from et al., 1999). Attenuation lengths do not appear to the #ux-weighted integral of the average attenuation vary signi"cantly due to changes in solar modulation depth: (Lingenfelter, 1963; Merker et al., 1973). Despite these uncertainties and variations, values of 150)) " z( )cos sin d " cos sin d 170 g cm\ are presently used for fast nucleon attenu- cos sin d cos sin d ation coe$cients for rock samples within the upper 1 m 3.3 of Earth's surface. In general, variation within this range " . (3.62) has a small in#uence on the results of applied investiga- 4.3 tion of &surface' exposures. For subsurface samples, the If can be taken to be about 160 g cm\, then is uncertainty becomes more important. Within the next about 208 g cm\. In the atmosphere, the attenuation few years a better constrained value for the nucleon and lengthdecreases approximately withgeomagnetic latit- muon attenuation lengthin shallowrock worldwide will ude (Fig. 6) until latitude 603. At higher latitudes the undoubtedly be determined. secondary nucleon #ux is invariant withlatitude. The The attenuation of negative muons at sea level is e!ect at latitudes less than 603 results from the change in approximately exponential, similar to that of the high- the energy spectrum of the cosmic-ray secondaries. The energy neutron #ux. Muon production is di$cult to average spectrum is harder at lower latitudes (because distinguishfrom themuchlarger fast nucleonic produc- the vertical cuto! rigidity is higher), so the average at- tion near the Earth's surface, but the \ stopping rate tenuation lengthis greater (e.g. Lingenfelter, 1963). How- exceeds the fast neutron disintegration rate at depths of ever, at atmospheric depths below 600 g cm\, &200}300 g cm\ (Kurz, 1986b; Lal, 1987a; Brown (approximately 4400 m asl) the latitudinal dependence on et al., 1995a) at sea level, deeper at higher elevations. attenuation lengthmay be insigni "cant (Simpson and Estimates of I\ range from 800 to 1500 g cm\ Fagot, 1953). (Table 3). As described above, the attenuation coe$cient is gen- erally expressed in units of mass length(g cm \) because 3.5. Temporal variations in production rates the length depends on the total mass traversed. Length in units of cm can be determined for materials withconstant Like their atmospheric counterparts, all in situ produc- or known densities (e.g. for "160 g cm\, the depth tion rates vary over time. Early empirical production rate that the production rate will decrease by a factor of e\ is studies suggested evidence for temporal variations in the 61.5 cm in granite [ &2.6 g cm\], 64.0 cm in basalt time-integrated production rate of TCN in rocks over the [ &2.5 g cm\], 80 cm in soil or tu! [ &2gcm\], past 60 kyr (Kurz et al., 1990; Cerling and Craig, 1994a; 160 cm in water, and 640 cm in snow [ &0.25 g cm\]). Clark et al., 1995). Calculations employing estimates of Most attenuation lengths in air for fast nucleons have cosmic-ray intensities at di!erent sites based on dipole- been measured directly withneutron and proton moni- induced variations in geomagnetic paleolatitudes have tors during aircraft or balloon #ights (e.g. Merker et al., predicted that the integrated production rates may have 1973) or by measuring the abundance of TCN on rock varied more than 15% over that time period (Kurz et al., surfaces at di!erent elevations (e.g. Zreda et al., 1991). 1990; Bierman, 1996; Bierman et al., 1996; Clark et al., Attenuation lengths in rock have been measured by col- 1996). However, variation of terrestrial cosmogenic J.C. Gosse, F.M. Phillips / Quaternary Science Reviews 20 (2001) 1475}1560 1505
Table 3 Attenuation lengths Fast nucleon, thermal neutron, and muon attenuation lengths in stopping materials in the Earth's atmosphere, Earth rock, and Lunar rock. (Not an exhaustive list) Cosmogenic nuclide, material Reference (3)(gcm\)
Atmosphere (elevation in km or mb) Protons 50 150 (Conversi, 1950) Fast nucleons in 0}5000 m 0 160 compiled by Lal (1991) Fast nucleons in 0}5000 m 30 150 compiled by Lal (1991) Fast nucleons in 0}5000 m '60 140 compiled by Lal (1991) Fast neutrons between 200 and 700 mb 58 163$10 (Merker et al., 1973) Fast neutrons between 200 and 700 mb 57 172$13 (Merker et al., 1973) Fast neutrons between 200 and 700 mb 31.5 181$28 (Merker et al., 1973) Fast neutrons between 200 and 700 mb 17.3 215$15 (Merker et al., 1973) Fast Neutrons 0 212 (Lingenfelter, 1963) Fast Neutrons 10 213 (Lingenfelter, 1963) Fast Neutrons 20 205 (Lingenfelter, 1963) Fast Neutrons 30 196 (Lingenfelter, 1963) Fast Neutrons 40 182 (Lingenfelter, 1963) Fast Neutrons '60 164 (Lingenfelter, 1963) '35 MeV Neutrons, 1680}5960 m 0 149$2 (Dixit, 1955) '35 MeV Neutrons, 2630}5350 m 21 149$2 (Roederer, 1952) '35 MeV Neutrons, 150}3774 m 47}50 127$3 (Teucher, 1952) '8 MeV Neutrons, 0}3230 m 47}50 132$4 (Brown, 1954) (30 MeV Neutrons, 3000}4200 m 0 145$9 (Simpson and Fagot, 1953) (30 MeV Neutrons, 3400}4400 m 0 149$9 (Simpson et al., 1953) (30 MeV Neutrons, 260}4300 m 42}45 132$15 (Tongiorgi, 1949) (30 MeV Neutrons, 260 m 42 121$7 (Tongiorgi, 1949) (30 MeV Neutrons, 1900 m 44 140$2 (Lockwood and Yingst, 1956) (30 MeV Neutrons, 2500}5000 m 52 141$2 (Simpson and Fagot, 1953) (30 MeV Neutrons, 1000}7000 m 60}65 130 (Sandstrom, 1958) (30 MeV Neutrons, 4300}9000 m 60}65 138 (Sandstrom, 1958) Be 25 165 (Nakamura et al., 1972) Be 50 158 (Nakamura et al., 1972) Be 1.3}1.7 m 78 142 (Brown et al., 1991) Cl 280}4050 m 20 152 (Zreda et al., 1991) Thermal neutrons 0 220 (Lal and Peters, 1967) 1 eV neutrons 10.1 212 (Soberman, 1956) Thermal neutrons 39.5 165 (Boella et al., 1968) (0.5 eV neutrons, 1900 m 44 125 (Lockwood and Yingst, 1956) 1 eV neutrons 55.1 164 (Soberman, 1956) Thermal neutrons '60 150 (Lal and Peters, 1967) 1 eV neutrons 88.6 164 (Soberman, 1956) 247 (Lal et al., 1958); (Rossi, 1948) Earth rocks in deep saprolite 4 &800 (Brown et al., 1995) at depth '170 g cm\ in Hawaiian basalt 37 &1000 (Kurz, 1986a) at depth2650 g cm \ * 1500 (Middleton and Klein, 1987) Fast nucleons in SiO, CaO, and FO * 157}167 (Masarik and Reedy, 1995) He in Reunion basalt 21 159$10 (Sarda et al., 1993) He in Hawaiian basalt 37 164}170 (Kurz, 1986a) He in Antarctic sandstone 78 150, 227$14 (Brook et al., 1996b) Be to depth200 g cm \ saprolite 4 &150 (Brown et al., 1995) Be in laterite 12 190 (Bourle` s et al., 1992) Be in Bandelier Tu!, NM 36 172 (Olinger et al., 1992) Be in Bandelier Tu!, NM 36 159 (Nishiizumi et al., 1994) Be in Antarctic sandstone 78 145$7, 152$5 (Brook et al., 1996b; Brown et al., 1992) Ne in Reunion lava 21 165$6.2 (Sarda et al., 1993) Ne in Bandelier Tu!, NM 36 178 (Olinger et al., 1992) Al in Antarctica quartz sandstone 78 156$13, 152$5 (Brook et al., 1996b; Brown et al., 1992) Al in laterite 12 190 (Bourle` s et al., 1992) Al in Bandelier Tu!, NM 36 166 (Nishiizumi et al., 1994) Al in Bandelier Tu!, NM 36 173 (Olinger et al., 1992) Lunar rocks Be in Lunar basalt * 163 (Nishiizumi et al., 1984) Be in Lunar basalt * 120 (Middleton and Klein, 1987) Al in Lunar basalt * 165 (Nishiizumi et al., 1984) Al in Lunar basalt * 122 (Middleton and Klein, 1987) Cl in Lunar basalt * 180 (Nishiizumi et al., 1984)
Thermal neutron attenuation in the upper 200 g cm\ of rock cannot be described by a simple exponential function (Dep, 1995; Dep et al., 1997; Liu et al., 1994; O'Brien et al, 1978; Zreda et al., 1994). Atmospheric estimates are for equilibrium depths (below Pfotzer Maximum, i.e. '200 g cm\). For other estimates see discussion in Dunai (2000). The latitudes for some of these sites are geographic latitudes because we cannot assume the dipole was geocentric over the short time of TCN accumulation. 1506 J.C. Gosse, F.M. Phillips / Quaternary Science Reviews 20 (2001) 1475}1560
\ Fig. 6. Apparent attenuation length ) versus latitude ( ). Solid symbols are rock depthpro "les in upper 300 g cm , open symbols are from measurements in or at the bottom of the atmosphere. All other curves are linear "ts on withat least 3 measurements. Highlatitude sites are assigned to latitude 603, above which is invariant. Refer to Table 3. nuclide production withtime hasnot been unequivocally Oeschger cycles or multiple movements along a single documented and uncertainties in the chronological con- fault scarp), we need to establishthetemporal variations straints used in these early empirical studies may explain in order to reduce the uncertainty due to this second- the observed apparent temporal variations. More re- order source of systematic error (Section 6). cently, using 33 in situ Cl measurements for rocks with The #ux of cosmic radiation reaching the surface of the independent exposure ages ranging from 2.1 to 55 kyr, earth determines the rate at which cosmogenic nuclides Phillips et al. (1996a) found that incorporation of secular are produced in exposed rocks. The surface #ux varies variation of production, based on the paleointensity re- temporally according to (i) variations in the intensity of cord, did not improve the agreement of calculated ages the primary cosmic radiation; (ii) changes in the inter- with independently determined ages. Although this result planetary magnetic "eld and solar modulation of GCR; may be also in large part due to errors in the independent (iii) changes in the geomagnetic "eld e!ect on the GCR age constraints, it does indicate that the e!ects of and secondary radiation due to variations in dipole paleomagnetic intensity variations have not been intensity, dipole axis position (dipole wobble), and profound. Licciardi et al. (1999) also indicate that the variations in the presence and strength of non-dipole magnitude of the in#uence of paleointensity variations components of the geomagnetic "eld; (iv) variations in for mid-latitude sites is low (within 2 experimental atmospheric shielding; and (v) variations in the character uncertainty and error of the results) based on the con- of the landform surface over time. sistency of recent and recalculated published He production rates. More recently, Stone (1999) showed 3.5.1. Variations in the primary GCR yux that the Be production rate may not have varied more All applications of TCN have assumed that the pri- than the precision of the empirical production rate esti- mary GCR #ux has been constant over the exposure mates between 20 and 10 kyr. He re-scaled production durations of interest ((10 Myr). Vogt et al. (1990) and rates of Be to sea level at highlatitudewitha lower Ca!ee et al. (1988) provided summaries of the use of muonic component. However, because increased meteorites to determine the history of extra-terrestrial precision in TCN methods is allowing "ner resolution cosmogenic nuclide production, but more meteorites of geological events (e.g. correlation of Dansgaard} analyzed for radionuclides of appropriate half life are J.C. Gosse, F.M. Phillips / Quaternary Science Reviews 20 (2001) 1475}1560 1507 needed to substantiate this assumption. Lavielle et al. that creating the Maunder Minimum from 1645 to (1999) measured cosmogenic radionuclides in meteorites 1715 AD) is too short to be an in#uence on TCN produc- to determine the di!erence between recent ((10 Myr) tion integrated over 10}10 years. Direct measurements and long-term cosmic-ray #uxes (150}700 Myr). Using of #ux or production rates (e.g. from waterbed experi- a multiple-nuclide approach, they measured Be, Al, ments) need to be evaluated in terms of the speci"c time Cl, and the cosmogenic noble gases Ne, He, and Ar, of a solar cycle over which the data were collected, if they to select meteorites that were uncomplicated by erosion have not been averaged over multiple cycles (e.g. or other e!ects and to adjust for atmospheric shielding Nishiizumi et al., 1996). Although longer-period solar during residence on earth. They showed that the average cycles may exist, they are di$cult to isolate from signals cosmic-ray #ux for the last 10 Myr is 38% higher in prehistoric records that are also in#uenced by climate than the long-term average #ux based on published or the geomagnetic "eld. The solar modulation e!ect is K/K exposure ages of the same meteorites, in agree- thus assumed to integrate to a stationary mean value ment withprevious estimates (e.g. Hampel and Schae !er, over the periods of interest for geological applications. 1979). Until more is known about low-frequency solar modula- The growing cosmochemical database from meteorites tion of the GCR cosmic ray #ux, models for TCN dating and other sources have successfully limited the number of must perforce ignore this potential (probably minor) possible explanations for long-term changes in the pri- source of variation. mary GCR #ux to our solar system and earth. Hampel and Schae!er (1979) concluded that a decrease in the 3.5.3. Ewects of the geomagnetic xeld cosmic ray #ux in the inner solar system was the only The low latitude #ux is dominated by relatively par- explanation for Al/ Ne exposure ages of iron meteor- ticles that are relatively more energetic than those at high ites being two-thirds younger than K/ K exposure latitude (the low latitude #ux is said to be &harder'), as ages. They suggested that the recent decrease may have documented by empirical measurements. The incident been caused by a change in the galactic cosmic-ray inten- secondary #ux of particles generated in the atmosphere, sity, although solar modulations were also proposed (see and therefore production rates of TCN, will also increase Section 3.5.2). Alternatively, Earthcould pass through withgeomagnetic latitude. Themean absorption free di!erent static interstellar #uxes during its motion rela- pathwithdecrease withlatitude. Thisgeneralization is tive to nearby interstellar medium, although it can be true for long exposure durations because the time-aver- shown that Earth would not likely feel such variation in aged ('10 years) geomagnetic "eld is predominantly ' cosmic ray #ux over 10 yr periods (Jokipii, 1991). dipolar (Acton et al., 1996; McElhinny et al., 1996; Merrill Earth has also received GCR shock waves, e.g. from et al., 1996; McElhinny and McFadden, 1997). As shown a nearby supernova. The e!ect would be felt over short in Section 3.1 and Eq. (3.3) the geomagnetic cuto! rigid- ( time scales ( 10 yr). However, these are generally iso- ity is strongly latitude-dependent. To calculate the e!ect lated, non-recurring, short-lived events which would of a change in the magnetic dipole intensity on the cuto! have only a small e!ect on integrated TCN production rigidity of vertical particles at some time in the past, Eq. rates. Signi"cant variations in primaries result from (3.3) can be expressed as supernovae explosions and although such events are rare, they may be important for the time scales of 1 Myr " M (Reedy et al., 1983; Raisbeck et al., 1985; Lal, 1987a; R Ro cos ( ), (3.63) M Kocharov et al., 1989). where R is the present cuto! rigidity on the geomagnetic 3.5.2. Variations due to solar modulation of the magnetic equator, M/M is the ratio of the geomagnetic xeld paleodipole moment to its modern value, and is the Solar particles have only minor e!ects on atmospheric geomagnetic latitude of the site (Quenby and Webber, cosmogenic nuclide production and are inconsequential 1959; Quenby and Wenk, 1962; Shea et al., 1965, 1987; for TCN production at the surface of the earth (cf. Quenby, 1966; Lal and Peters, 1967; Bland and Cioni, Masarik and Reedy, 1995). On the other hand, solar 1968; Shea and Smart, 1983; Kocharov et al., 1989; modulation of the interplanetary magnetic "eld can in#u- Nishiizumi et al., 1989; Kurz et al., 1990; Lal, 1991). As ence TCN production rates. The interplanetary magnetic the dipole "eld lines become steeper near the magnetic "eld, generated mainly by the sun and transported by the poles, the permitted particle rigidity decreases and be- solar wind, serves to de#ect some portion of the primary comes less than the threshold energy required to produc- GCR. The resulting GCR-#ux variation with11- and ed cosmogenic nuclides at the surface of the earth. In this 22-year solar sun spot variations is well documented with region (geomagnetic latitudes above approximately 583 atmospheric cosmogenic nuclides (e.g. Be and C) and for the present dipole "eld, slightly lower for higher signi"cant in magnitude (Beer et al., 1991). However, elevations), the cosmogenic nuclide production rate is even the 200-year period of solar activity (for instance, insensitive to variations in the terrestrial magnetic "eld 1508 J.C. Gosse, F.M. Phillips / Quaternary Science Reviews 20 (2001) 1475}1560 strength(Lal, 1991; Lal and Peters, 1967). Below this (McHargue et al., 1995; Henken}Mellies et al., 1990; latitude, changes in M may result in a signi"cant change Morris et al., submitted; Raisbeck et al., 1985; Raisbeck in the cosmic-ray #ux to a site at a given time (depending et al., 1992). on the total exposure duration and the magnitude and Like atmospheric cosmogenic nuclide production duration of the intensity change). The following sections rates, in situ TCN production rates are controlled by examine how M may change over time at a given geo- variations in the geomagnetic dipole "eld strength. If the graphic latitude. history of the geomagnetic "eld intensity were known accurately, it would be possible to calculate the apparent 3.5.3.1. Paleointensity variations. Another way to ex- rigidities or geomagnetic latitudes by integrating press the relationship between geomagnetic "eld inten- Eqs. (3.62 and 3.63) over the exposure duration and then sity and cosmic-ray #ux above a site is that a change in adjusting the TCN production rate accordingly. Alterna- M will result in an apparent change in the e!ective tively, numerical simulations could be performed to as- geomagnetic latitude of a site relative to the present sess the time-integrated production rate change. geomagnetic latitude: Although paleointensity #uctuations have certainly had some in#uence on TCN production rates, the reader should be aware that the magnitude of the in#uence is " M cos cos , (3.64) still largely unknown and no agreement as to the amount M of production rate adjustment needed, if any, has been where is the present-day site geomagnetic latitude reached. Unlike the near-instantaneous in#uence that (Clark et al., 1995; Nishiizumi et al., 1989). Eq. (3.64) intensity #uctuations have on the production of atmo- allows us to predict the e!ect of dipole intensity changes spheric cosmogenic nuclides (which have short atmo- on production rate by calculating the apparent geomag- spheric residence times relative to their half lives), and netic latitude for any site (without considering the e!ects hence the necessity for independent calibration of or- on rigidity). This approximation is most appropriate for ganic radiocarbon dating, the in#uence on terrestrial latitudes above 303 because it does not consider the production is subdued because the e!ect is integrated accompanying variations in the higher-order "eld com- over the entire exposure time. Instantaneous in situ pro- ponents that will in#uence the e!ective cuto! rigidity for duction rates may change due to paleointensity-induced a given site. Furthermore, changes in dipole "eld strength changes in the cosmic-ray #ux, but when averaged over may cause changes in the size of allowed and forbidden the entire exposure duration the rates will approach trajectory cones (for more discussion see Lifton et al., a constant value, depending on the duration of exposure. submitted). Based on relative paleointensity records, over The "rst published attempts to show the relationship the past 200 kyr M/M has ranged between 0.35 and 2.0 between measured TCN production rates and an integ- (Guyodo and Valet, 1996). This range is probably a min- rated time-varying production rate modeled from esti- imum, as the true amplitudes of intensity variations may mates of paleointensity indicated that a small adjustment have been attenuated by the stacking of multiple relative may be useful (e.g. factor of 1.15 for a short &11 kyr paleointensity records withvariable age control in the exposure; Nishiizumi et al., 1989). Others indicated that Guyodo and Valet (1996) compilation record. the in#uence (assumed minor) of paleointensity vari- In addition to paleointensity records (discussed in ations may be recorded by He and Ne in lavas (Kurz more detail below), variations in magnetic "eld strength et al., 1990; Sarda et al., 1993; Cerling and Craig, 1994a, are also evident from the change in accumulation rate of b). However, they recognized that non-cosmogenic pro- atmospherically produced cosmogenic nuclides. The cha- duction and surface erosion and burial e!ects could also nges are apparent in measurements of Be, C, and cause anomalies in in situ TCN concentrations. The Cl accumulations in archives such as Barbados corals, necessity for calibration of the TCN timescales with polar ice cores, fossil rat urine, and marine and terrestrial other timescales, and the lack of highly reliable empirical sediments, although other factors such as climatically calibrations led to the use of &Be years' (analogous to induced disequilibrium among carbon reservoirs may C-years) to distinguishnon-calibrated exposure dates also play an important role in the temporal variation until a reliable calibration was attained (Gosse et al., of C (Elsasser et al., 1956; Lal et al., 1985; Beer et al., 1995a; Brown et al., 1998a). Others proposed re"nements 1988; Peng, 1989; Bard et al., 1990a,b; Mazaud et al., to the cosmogenic nuclide chronometers based on the 1991; Stuiver et al., 1995; Plummer et al., 1997; Kitagawa paleointensity records available and Eq. (3.64) (Bierman, and van der Plicht, 1998). It has been proposed that 1996; Bierman et al., 1996; Clark et al., 1996). More increases in the atmospheric production rates were recently, Lifton et al (submitted) have suggested that a result of a weaker geomagnetic "eld. Evidence for a trajectory modeling of particles at cuto! rigidities should strong correlation between the Earth's geomagnetic "eld be modeled using existing paleointensity data. intensity and atmospheric Be accumulation in marine Unfortunately, the geomagnetic paleointensity history sediments and polar ice has been repeatedly documented of the Quaternary was poorly known in the early to J.C. Gosse, F.M. Phillips / Quaternary Science Reviews 20 (2001) 1475}1560 1509 mid-1990s. Only a limited number of records were com- be coarser. (ii) We require that the paleointensity record piled (McElhinny and Senanayake, 1982; Meynadier has accurate temporal control to some uniform time- et al., 1992; Tric et al., 1992; Mankinen and Champion, scale. (iii) For exposure durations less than 30 kyr, the 1993; Tauxe, 1993; Valet and Meynadier, 1993; Roberts amplitudes of the paleointensity variations need to be et al., 1994), and estimates of the 1 uncertainty in the well constrained; older exposures are more forgiving, available combined relative and absolute paleointensity particularly if the paleointensity #uctuation is short lived records were approximately 25% (Gosse et al., 1996a, d). (see below). Since the mid-1990s, the paleomagnetism Accurate pre-historic absolute paleointensity records are community has made signi"cant progress in acquiring di$cult to attain for a variety of reasons. Paleointensity records that meet experimental criteria (King et al., 1983) curves based on direct measurements from volcanic for developing and testing a reliable paleointensity re- rocks and "red archeological materials commonly have cord for the late Quaternary (Stoner et al., 1995; large uncertainties due to non-ideal magnetic properties Yamazakia et al., 1995; Constable and Tauxe, 1996; (e.g., multidomain magnetizations), empirically irre- Guyodo and Valet, 1996; Kok and Tauxe, 1996a, b; producible cooling histories of lavas, and the discontinu- Kono and Hiroi, 1996; McClelland and Briden, 1996; ous nature of the record. The absolute records are Meynadier and Valet, 1996; Peck et al., 1996; Valet et al., produced by interpolating between paleointensities 1996; Verosub, 1996; Brassart et al., 1997; Channell et al., measured for single short time intervals which are often 1997; Lanci and Lowrie, 1997; Roberts et al., 1997; poorly dated and therefore are not truly continuous Guyodo and Valet, 1999). records and are often di$cult to correlate to other re- However, total uncertainties in recent absolute and cords because of dating uncertainties. Continuous relative paleointensity records are still too large to permit relative records from sedimentary paleointensity studies reliable adjustments of TCN production rates for shorter may be unreliable due to di$culties in dating and a ((10 kyr) exposures. For instance, 2 standard errors lack of a sound explanation for the acquisition of of the mean relative intensities from multiple records detrital remanence, considering the e!ects of inclination- often exceed 3;10 Am (40% of the present intensity), shallowing and other depositional and post-depositional and this does not account for systematic uncertainties in grain reorientation processes. Furthermore, it is extreme- the chronology or the attenuation of amplitudes that ly di$cult to remove the contribution of the non- results from the stacking of multiple records with di!er- dipole "elds from bothsedimentary } and volcanic/ ent chronology quality (Guyodo and Valet, 1996, 1999; archeological}based paleointensity records for the past Schneider and Mello, 1996; Roberts et al., 1997). The 15 kyr, until multiple sites withsu $cient geographic dis- present magnetic moment of the earth is approximately tribution can be correlated. Attempts to reconstruct 8;10 Am. Standard deviations about weighted high-resolution paleointensities from measurements of means of multiple measurements on single TRM events atmospherically produced cosmogenic nuclides such as for absolute paleointensities are also greater than C, Be, (which are produced predominantly from 2;10 Am (Brassart et al., 1997) especially magnetic N and O) and Cl (produced from Ar) in polar ice moments before 5 kyr BP (McElhinny and Senanayake, (Raisbeck et al., 1987; Raisbeck et al., 1992) and marine 1982). This standard deviation does not account for the and terrestrial sediments (Raisbeck et al., 1994; Robinson error in interpolating between dated events to construct et al., 1995; Frank et al., 1997) have also been made. The a continuous record or for non-dipole "eld e!ects due to results have generally been ambiguous because, unlike in the lack of su$cient geographic averaging of coeval mag- situ produced nuclides, the accumulation of these atmo- netic acquisitions. As the paleointensity record improves, spheric nuclides in ice or sediment can depend on envir- we can use accepted existing data to evaluate the poten- onmental conditions (e.g., temperature, precipitation, tial magnitude of the second-order in#uence of paleoin- circulation in the oceans and atmosphere), and because tensity on production rates. age constraints may have large uncertainties due to er- The Sint-200 relative paleointensity curve (Guyodo rors in snow accumulation, incorrect ice #ow models, or and Valet, 1996) arguably provided a reasonable estimate poorly known sedimentation rates. However, the coup- of the relative change in magnetic "eld strengthover the ling of Be with other records for deciphering paleoin- past 200 kyr (there is also a compiled record for the past tensity is becoming signi"cantly more useful (cf. Morris et 800 kyr (Guyodo and Valet, 1999). It is a low-resolution al., submitted). composite record of global relative paleointensity (Fig. 7) To make any reliable conclusion about the e!ects of based on paleomagnetic measurements from 18 marine paleointensity on the secondary cosmic-ray #ux, we need sediment cores withlow sedimentation rates, stacked and (i) a record withsu $cient resolution to capture the correlated using the SPECMAP O timescale (Martin- paleointensity variations that a!ect production rates son et al., 1987). Relative paleointensity data are interpo- over di!erent exposure durations; i.e. for the past 30 kyr lated linearly by increments of 1 kyr (Fig 5a of Guyodo we need to resolve paleointensity variations withperiods and Valet, 1996), withindication of standard deviation of 1 kyr, but for longer exposure times the resolution can and the number of cores involved in each successive time 1510 J.C. Gosse, F.M. Phillips / Quaternary Science Reviews 20 (2001) 1475}1560
ences of the volcanic data, ignored the anomalous paleointensities derived for transition periods (e.g. Las- champ excursion), and recalibrated radiocarbon dates based on Calib 3.0.3c (Bard et al., 1993; Stuiver and Reimer, 1993) and the recent varve chronology for radiocarbon ages greater than 18.4 ka (Kitagawa and van der Plicht, 1998). Using a Sint-200 scaling factor of 5.04;10 Am (amplitudes were not increased) the re- sulting dipole moment record is reasonably consistent withrecent absolute intensities of Brassart et al. (1997) and the original volcanic data used for scaling. However, the Holocene record of McElhinny and Senanayake (1982) shows higher amplitude variation than the Sint- 200 record, and the Holocene average paleointensity from the archeomagnetic data is less than the Sint-200 average. We attempted no further calibration to accom- modate this inconsistency because of the signi"cant dif- ferences in the nature of the two curves. Because there are no Sint-200 data for the last 2000 years, we extrapolated the Sint-200 curve through the absolute paleointensity Fig. 7. The Sint 200 record (dots and thin curve). The relative record was normalized for absolute mean VADM as discussed in text using the for 1200 cal. yr BP (500-year average from McElhinny absolute paleointensity data (open circles) from (Coe, 1978; Barbetti and Senanyake, 1982, age calibrated withClark (1975) to and Flude, 1979; Kovacheva, 1980, 1982; McElhinny and Senanayake, the present dipole moment of 8;10 Am (Fig. 7). Re- 1982; Chauvin et al., 1989, 1991; Brassart et al., 1997). Thick solid curve sults of modeling withtheSint-200 record were found to is the Holocene absolute paleointensity from McElhinny and be consistently within about 1.5% of the results modeled Senanayake (1982). The last 2000 yr is based on archeomagnetic data from McElhinny and Senanayake (1982) and a modern moment of only with the McElhinny and Senanayake (1982) record 8.0 Am. The error bars represent standard deviations. for the last 10 kyr. Recognizing the uncertainties associated with the paleointensity data we used and the manner in which we period. The curve has su$cient resolution for modeling calibrated the curve, we are not recommending any ad- the e!ects of paleointensity variations on exposure ages justments in TCN production rates. An assumption of between 50 and 200 kyr. However, higher resolution constant production rate is reasonable for middle and paleointensity records from sites with higher sedimentary high latitude sites ( '303) because the resulting (in- rates and less attenuation of the intensity variation are versely modeled) variations in integrated production rate necessary for exposure durations less than 50 kyr are less than the variation in production rates empirically (Meynadier et al., 1992; Tric et al., 1992; Stoner et al., measured for exposure periods ranging from 2 to 55 kyr 1995; Peck et al., 1996; Schneider and Mello, 1996; Chan- (e.g. Phillips et al., 1996b; Licciardi et al., 1999). Never- nell et al., 1997). Notwithstanding these shortcomings, theless, several observations can be made which may be because the Sint-200 composite record has been shown to important for sites at lower latitudes where there is be reasonably consistent withmore recent relative greater sensitivity to changes in geomagnetic intensity. (Channell et al., 1997; Roberts et al., 1997) and scaled The intensity of the "eld reached its maximum only 3 kyr absolute paleointensity records (Brassart et al., 1997) ago, so all TCN exposure applications will be in#uenced (withmost misalignments attributed to chronologydif- by this paleointensity maximum. Between 40 ka and 2 ka ferences), we will use it to analyze the in#uence of the "eld intensi"ed from approximately 3;10 Am to paleointensity on terrestrial production rates. 10.2;10 Am (even higher according to McElhinny To calibrate the Sint-200 curve to absolute paleoin- and Senanayake, 1982). The lower "eld strengthmay tensity, we assumed that the curve should have the same have permitted a higher cosmic-ray #ux and therefore mean dipole intensity when averaged over 30 kyr as vol- relatively higher production rates for the late Pleistocene canic data with reliable chronologies for the same time than in the Holocene. Between 200 and 50 ka, the mean period (Brassart et al., 1997). We selected the time period intensity was 5.0;10 Am (1.2;10 Am) but for between 10 and 40 kyr for our calibration interval be- the entire 200 to 2 ka record the mean is 5.2;10 Am cause (i) there are a large number of volcanic paleointens- (1.5 10 Am), indicating the past 50 kyr may have ex- ity data available for this time period; (ii) all 17 core perienced greater #uctuation. records used in the Sint-200 curve overlap during this If we assume that the geomagnetic "eld can be de- time; and (iii) it is the time in which much existing TCN scribed as an axial dipole (e.g. we ignore any paleosecular research has been conducted. We used the original refer- variation of the dipole axis and any non-dipole e!ects), J.C. Gosse, F.M. Phillips / Quaternary Science Reviews 20 (2001) 1475}1560 1511 we can examine the paleointensity-induced variation in 100 ka for 0}603 latitude (Fig. 8). The scaling factors of TCN production rate for a given geographic latitude. For Lal (1991, his Table 1) were used for 3 km elevation (the comparison, we assume under a geocentric dipole "eld variation is greater at higher elevations, Fig. 8 inset B). that the geographic latitude is equivalent to the geomag- The "rst-order trends indicate that the time-averaged netic latitude of the site under the current "eld strength production rates during the Holocene were signi"cantly (8;10 Am). During times of higher (or lower) paleoin- lower (for site geographic latitudes between 15 and 603) tensities, the geomagnetic latitude of the site will appear than during the late Pleistocene (Fig. 8). Sites above lower (or higher) than the current geomagnetic latitude. geographic latitude 353 have always been within 123 of We represent the e!ects of varying production rates as their geomagnetic latitude for the past 100 kyr. This may the ratio of the time-averaged production rates inte- explain why Phillips et al. (1996a) did not see a signi"cant grated over the exposure duration, P(t), to the production variation attributable to paleointensity variations in Cl rate for the present geographic latitude assuming a geo- production rates over 2.1}55 kyr time period, considering centric dipole "eld and the present dipole moment, all except one of the 33 rock samples they analyzed were P(geog). We consider the e!ects of a non-geocentric collected at or above 353 geographic latitude. Production dipole "eld below. rate variation is greatest for latitude 203 (see Fig. 8 inset We have calculated the time-averaged production A), which may explain why Kurz et al. (1990) observed rates over the range of exposure times between 0.1 and the e!ects of paleointensity variation from Holocene He
Fig. 8. E!ects of paleointensity on TCN production rates at di!erent latitudes and altitudes, using the Sint-200 relative paleointensity record (Fig. 7) to estimate dipole moment. The e!ect is expressed as the ratio of time-averaged production rate, P(t), to the present production rate at the geographic site latitudes (0 to 603) at 2000 m elevation. Inset A shows the standard deviation in time-averaged production rates over the past 200 kyr, one way of showing that the greatest variability is felt at 203 latitude (negative latitude represents south). Inset B shows the e!ect of paleointensity variation at di!erent elevations (sea level, 1, 2 and 3 km) at 203 latitude. All spatial scaling was done using Table 1 in Lal (1991). 1512 J.C. Gosse, F.M. Phillips / Quaternary Science Reviews 20 (2001) 1475}1560 calibration samples collected at Hawaii (although we show in the following section that wobble of the dipole axis will decrease this e!ect at Hawaii). Sites at geo- graphic latitude above 603 have not experienced an ap- parent geomagnetic latitude of less than 573 during the past 200 kyr, even if modeled withpaleointensities from McElhinny and Senanayake (1982), so these sites are invariant withpaleointensity variations because theyre- mained above the cuto! rigidity.
3.5.3.2. Ewects of reversals and excursions. When aver- aged over long exposure periods ('5;10 yr) even large amplitude paleointensity variations associated with transition events such as the Brunhes}Matuyama rever- sal 780 kyr ago (Baski et al., 1992) do not signi"cantly in#uence the time-averaged TCN production rates (cf. O'Brien, 1979). This is true even considering that Fig. 9. Impact of a short-lived high amplitude geomagnetic intensity although it may take only 5 kyr for the directional change on TCN production rates. The thick solid line shows the e!ect change (Merrill et al., 1996) intensity #uctuations last on production rates if the magnetic "eld was constant except during the more than three times that duration (Raisbeck et al., Brunhes}Matuyama transition. The curve show the e!ect of decreasing a intensity to 20% of the modern intensity between 790 and 770 kyr. 1985; Valet and Meynadier, 1993). Using Eq. (3.64) and The e!ect reaches 3% for exposures that began within a few 100 kyr paleointensity data from Valet and Meynadier (1993) before the reversal. The upper dashed curve is the P(t)/P(today) based which show a '10; increase in relative intensity im- on Valet and Meynadier (1993) paleointensity for exposure times be- mediately after the low intensity associated with the tween 1000 and 600 kyr. For comparison, the thin dashed line is the reversal, time-averaged production rates for exposures same data, but relative to an average production rate (today's magnetic "eld appears to be almost 1.5 times stronger than the average intensity beginning during the reversal would be at most 3% over the past 1 Myr). higher than the lowest production rates after the reversal (for a site withtheworst-case scenario, at 20 3 latitude, 3 km elevation, Fig. 9). The actual a!ect is di$cult to symmetric about the Earth's spin axis: (1) variations in determine from the Valet and Meynadier (1993) paleoin- the position of the dipole moment axis; and (2) signi"cant tensity because the duration of the reversal is di$cult to contributions of (asymmetric) non-dipole "eld compo- deduce. However, if a simpli"ed model is used by assum- nents over long time periods (discussed below). It has ing a constant paleointensity interrupted between 790 been shown that the axial dipole component of the and 770 kyr withan intensity of only 20% of theconstant geomagnetic "eld can be considered approximately geo- strength, the production rate for this worse-case site centric when averaged over the last 780 kyr (Negrini averaged at 791 kyr would be approximately 3% higher et al., 1987; Acton et al., 1996; Constable and Tauxe, than at 769 kyr, and exposures much longer than 1996). Gubbins and Kelly (1993) have shown that for the 1000 kyr would be required to return to the normal rate past 2.5 Myr there is a strong resemblance of the mor- (Fig. 9). The simulation overestimates the actual e!ect phology of the paleomagnetic and modern "eld and that because the actual paleointensity appears to have in- paleosecular variation of the magnetic "eld has been creased immediately before and after the transition (Rais- similarly intense as today. Virtual geomagnetic poles beck et al., 1985; Valet and Meynadier, 1993), which (VGP), the position of the equivalent geomagnetic pole reduces the a!ect of the reversal on production rates. It is calculated for an instant in time from multiple geographi- clear that even in the worst-case scenario, TCN produc- cally spaced concurrent readings of the paleomagnetic tion rates for long ('10 kyr) exposures are essentially "eld, have been calculated with the greatest reliability for indistinguishable from a constant long-term integrated the past 10,000 years by Ohno and Hamano (1992) and production rate for the same period, a point made earlier Merrill and McElhinny (1983) from archeomagnetic and by Sarda et al. (1993). sediment paleomagnetic data. The reader is directed to recent discussion regarding the selection criteria of 3.5.3.3. Secular variations in the dipole axis position. In paleomagnetic data for VGPs over the past 5 Myr addition to changes in the geomagnetic paleointensity (Quidelleur et al., 1994; Johnson and Constable, 1995; variations discussed above, the e!ective geomagnetic lat- McElhinny and McFadden, 1997). The mean position of itude of a sample site may also vary withsecular changes the geomagnetic pole over the past 10,000 years is in the geomagnetic "eld geometry over short (i.e. 88.23N, 84.63E, withapproximately 1 3 uncertainty (Ohno (10 yr) exposure durations. There are two ways that and Hamano, 1992). When averaged over 5 Myr, the the averaged geomagnetic "eld geometry may not be dipole position is not exactly geocentric but lies at J.C. Gosse, F.M. Phillips / Quaternary Science Reviews 20 (2001) 1475}1560 1513 approximately 873N 1443E(&13), depending on the method (e.g. average including far-sided e!ect or com- mon-site longitude) and dataset used to calculate it (Merrill et al., 1996, p. 220). However, for most TCN applications this is su$ciently geocentric that time-integ- rated pre-Holocene production rates will not be a!ected. For shorter timescales the VGP are not consistent with the geographic north pole. Single VGP (excluding transition periods) have been measured below 803N latit- ude (e.g. the modern geomagnetic north pole, and for around 2.8 kyr ago (Ohno and Hamano, 1992)). Withtheexception of Sternberg(1996), Klein and Gosse (1996), and Licciardi et al. (1999) the e!ects of dipole wobble on TCN production rates have not been considered. Does the variation in the position of the dipole axis signi"cantly a!ect TCN production rates? Klein and Gosse (1996) showed that for geomagnetic latitudes above 203, dipole axis position variation may Fig. 10. Comparison of the e!ects on geomagnetic latitude of variation contribute a greater in#uence on production rates than in intensity (long dashes) and dipole axis position (thick solid curve). paleointensity variations, although their estimate of pos- Upper curves for the Wind River Range, United States (geographic sible pole position changes (203) is double the average latitude 433N). Lower curves for Southern Alps, New Zealand (geo- deviations for the Holocene. Using the 500-year averaged graphic latitude 443S). Paleointensity e!ects based on Sint-200 curve (Figs. 5 and 6). Dipole wobble e!ects modeled from VGPs of Ohno and Holocene VGP positions ( , ) of Ohno and Hamano Hamano (1992). Fine dashed line is geographic latitude. (1992), we recalculated the site geomagnetic paleolatitude for sites speci"ed by means of geographic position ( , ) by subtracting the paleocolatitude ( ) from 903, model is based on relative magnetic records from sedi- where ment at up to 11 sites, but only one site had an ar- chaeomagnetic record close enough to allow correction " # ! cos sin sin cos cos cos( ). of the core timescale (e.g. due to #uctuating sedimenta- (3.65) tion rates and marine reservoir e!ects), adjustments for inclination shallowing, and calibration of the relative The production rate scaling factors for the geomag- declinations to absolution values. They were forced to netic paleolatitudes were then integrated over the expo- construct a second-degree spherical harmonic global ex- sure time (as done previously for paleointensity e!ects) to pansion anchored with only six suitable archaeomag- calculate the time-averaged production rates for di!erent netic records. We cannot evaluate the uncertainty of the locations. Note that because the longitude of the VGP pole positions because their global geomagnetic "eld has also varied with time, geographic site locations will variation model was insu$ciently constrained (Merrill have lower or higher magnetic "elds depending on et al., 1996), and because the pole positions for sites older whether the longitude of the VGP is far-sided or near- than 7 kyr are based on only half the number of sites used sided. to constrain the past 2 kyr record. Nevertheless, Fig. 10 Based on the Ohno and Hamano (1992) record, it (c.f. also Fig. 11) shows that for exposures greater than appears the variation in geomagnetic latitude induced by 7 kyr, the e!ect of polar wobble is less important on an secular variation in the dipole axis position is of a similar integrated production rate, but that the consequent magnitude to the paleointensity-induced variations for changes in geomagnetic latitudes for the late Holocene low latitude sites (Fig. 10). It was shown in Fig. 8 that can have large ('15%) in#uences at certain sites. The geocentric dipole paleointensity variations would not true e!ects of dipole axis wobble (and non-dipole "eld in#uence sites withgeographiclatitude above 60 3. How- e!ects discussed below) will become increasingly impor- ever, if we consider the Holocene history of the dipole tant issues to resolve as the analytical and chemical axis position, some high latitude sites (again, depending precisions improve to allow "ner (10 yr) resolution of on longitude) dropped below the cuto! rigidity for TCN late Holocene exposure histories. production. Their record for polar motion over the past 2 kyr is consistent witharchaeomagneticallyderived pole 3.5.3.4. Non-axial dipole xeld. Despite early recognition positions (Merrill and McElhinny, 1983). Unfortunately, of the in#uence of the non-axial dipole "eld components the Ohno and Hamano (1992) data may not be su$- on atmospheric secondary nucleon production rates ciently reliable to warrant corrections of the integrated (Section 3.1.2), they have been largely ignored at ground TCN production rate for the rest of the Holocene. Their level (however, see O'Brien (1996; Dunai, 2000; Lifton 1514 J.C. Gosse, F.M. Phillips / Quaternary Science Reviews 20 (2001) 1475}1560
Fig. 11. E!ects of variations in the geomagnetic "eld on TCN production rates, expressed as relative production rate. Dashed line is the change in time averaged production rate due to paleointensity variation according to the Sint-200 data (Fig. 7). Thin solid line is the e!ect on production rate due to secular variations in the dipole axis position. Thick line is the net geomagnetic "eld e!ect, calculated as described in the text. All graphs are for 1 km elevation for comparison. (A) Wind River Range, Wyoming, USA, 433N, 2513E. (B) Echo Lake, Sierra Nevada, California, USA (39.73N, 2863E). (C) Hawaii, Paci"c Ocean (213N, 2093E). (D) Prescott Island, Central Arctic, Canada (743N, 2633E). (E). Southern Alps, New Zealand (443S, 1693E). (F) Gobi Desert, China (413N, 1133E). et al., submitted). Using deviations in Holocene archeo- tween 120 and 114 ka BP. Thus, the general thinking was magnetic intensity data, McElhinny and Senanayake that because most of the magnetic "eld e!ects on TCN (1982) showed that the variation in magnetic moments production rates can be attributed to an axial dipole "eld due to the non-axial dipole "eld contributions (plus ex- (and essentially all of it after 20 kyr) any e!ects of non- perimental errors) account for about 20% of the total axial dipole components would be relatively small, if not "eld, and that this proportion has been relatively consis- negligible, over exposure periods greater than a few thou- tent throughout the Holocene. Acton et al. (1996) have sand years. shown that over 90% of the paleomagnetic "eld can be More investigation of these non-axial dipole "eld ef- explained withan axial dipole "eld ("tted to be geocen- fects is clearly needed for a more complete appreciation tric) witha quadrapole "eld approximately 6.2$4.7% of of the in#uences of the magnetic "eld on TCN produc- the dipole "eld when averaged over 780 kyr. Their "eld tion rates. geometry, constrained by means of skewness tests on global magnetic data for a ubiquitous magnetic anomaly 3.5.3.5. Net geomagnetic ewects. The e!ects of vari- (Central marine magnetic anomaly after the B/M rever- ations in dipole axis position cannot be evaluated for sal) is consistent withotherpredictions of dipolar geo- exposures greater than 10 ka until better estimates of the centricity (Kono and Hiroi, 1996). More recently, Fang location of the geomagnetic north pole are established. et al. (1997) obtained antipodal VGP data in loess above For exposures greater than 100 ka, it is likely that the and below the Blake Event, leading them to suggest that "eld is geocentric, so the net geomagnetic e!ect would be the "eld was dipolar and approximately geocentric be- the production rate variation due only to paleointensity J.C. Gosse, F.M. Phillips / Quaternary Science Reviews 20 (2001) 1475}1560 1515 variations, and we have demonstrated the low sensitivity of TCN production rates to paleointensity variation over suchlong exposure durations. Thenet geomagnetic e !ect for the Holocene should be modeled for any geographic site by "rst calculating the variations in geomagnetic latitude due to secular variation of the dipole axis posi- tion, then recalculating the e!ects of paleointensity vari- ations on these geomagnetic latitudes, and integrating the production rate scaling factors over the exposure time (i.e., the net e!ect is not simply determined by taking the sum of the deviations in the magnetic latitudes from bothpaleomagnetic and paleosecular variation e !ects). Net changes in production rates are site speci"c (latit- ude, longitude, and altitude, Fig. 11). As an example, we have modeled the Sierra Nevada Be production rates of Nishiizumi et al. (1989)and Nishiizumi et al. (1996) for the geographic site location 383N, 2413E, 3.32 km elevation, assuming 13 kyr of exposure (Clark and Gilles- pie, 1997), and using the Sint-200 paleointensity record, Fig. 12. Comparison of spallogenic production rates on a stationary correcting the last 10 kyr for dipolar wobble and assum- surface in the central Arctic with those on surfaces that have been ing geocentric dipole before 10 ka BP to provide an isostatically rebounding at an exponential rate (emergence rate from estimate of the net geomagnetic e!ect. The time-averaged Dyke et al. (1991) based on 40 calibrated radiocarbon dated driftwood production rate over 13 kyr of exposure at the geo- fragments on beaches around Prince of Wales island, with emergence \ \ history adjusted for eustatic sea level rise estimated from Fairbanks, graphic location is 52.4 atoms g SiO yr , corre- 1989). sponding to a high latitude sea level production rate of approximately 5.6 atoms g\ SiO yr\ (muonic and spallogenic components scaled in the same manner as only a 1% di!erence. However, in the case of tectonic Lal, 1991). Scaled today, the production rate would be surface uplift that occurs over longer time periods (Brook 54.2 atoms g\ SiO yr\ at the geographic site and et al., 1995a), the e!ect can be signi"cant. 5.8 atoms g\ SiO yr\ at high latitude and sea level. Production rate variations may also result from chan- We also scaled the Sierra Nevada production rate for ges in atmospheric &thickness' via the migration of per- longer time periods (50}1000 kyr), assuming no change in sistent density anomalies due to climate change, although position due to tectonic or isostatic e!ects, and using this is still speculative and has not been documented. Valet and Meynadier (1993) data for the "rst 800 kyr. At Relatively "xed pressure deviations from the Standard the geographic site, the long time-averaged production Atmosphere have been proposed by Stone (in press) to rate is 61.6 atoms g\ SiO yr\ ("1.2, range" o!set production rates as muchas 30% over Antarctica, 58.4}65.5 atoms g\ SiO yr\). At high latitudes and less than 5% elsewhere, from production rates scaled sea level, the long time-averaged production rate is with Lal (1991) and other published scaling models. To 6.6 atoms g\ SiO yr\ ("0.13, range" calculate this, it was necessary to assume that the an- 6.3}7.0 atoms g\ SiO yr\). nually averaged pressure anomalies were static over the Holocene. A model of sea surface and land paleotem- 3.5.4. Variations in atmospheric shielding peratures and adiabatic lapse rates could help verify the Changes in e!ective atmospheric depth can a!ect pro- e!ects of Holocene climate change. Also, barometric cha- duction rates over 10}10 year periods. For example, nges due to #uctuations in sea level will need to be atmospheric depth changes can result from changes in considered (albeit this is probably a third-order e!ect). the crustal altitude of a sample by isostatic rebound. For longer durations, the magnitude and location of the Fig. 12 shows e!ect on integrated production rate and anomalies may have been signi"cantly di!erent (e.g. ages of beaches on an emergent shoreline in the central shifting and enlarging of the intertropical convergence Arctic. The emergence is due to isostatic rebound since zone). about 10 kyr ago. The marine limit around Prescott Island is approximately 130 m. The emergence curve was 3.5.5. Other sources of temporal variations in production determined withradiocarbon-dated driftwood around The above sources of variation deal with physical on Prince of Wales Island and Be-dated boulders on the primary and secondary cosmic-ray #ux before they beaches on Prescott Island. The "gure expresses the reachthesurface. Additional temporal variation can be di!erence in an calculated age that ignore the e!ect of expected with the changes in the surface exposure his- uplift and the corrected age. In less than 10 kyr there is tory. Although it is impractical to evaluate the potential 1516 J.C. Gosse, F.M. Phillips / Quaternary Science Reviews 20 (2001) 1475}1560 magnitude of the e!ect of suchchanges,we suggest a few (1991) normalization method may not apply to all common examples: (i) periodic snow cover (e.g. Gosse regions (e.g. Antarctica due to atmospheric a!ects et al., 1995a), (ii) episodic loess cover, (iii) gradual erosion (Stone, in press) or tropical regions due to magnetic and of a sediment (e.g. till) cover exposing a bedrock surface atmospheric deviations) it provides a uniform means of with little or no evidence of the cover, (iv) changes in comparing production rates. All of the production rates vegetation shielding (should be a small e!ect, determined reported below have been normalized (by the original or by the total mass of the organic molecules per area above subsequent authors) to production at high latitude sea the ground, but extremely dense forest may reduce the level withLal 's scaling model. cosmic ray #ux by up to 4% (Cerling and Craig, 1994b) and may also enhance thermalization of cosmic-ray neu- 3.6.1. Helium-3 trons), and (v) paleoaltimetry change (Brook et al., 1995a; Empirically derived production rates of the noble gas Schaefer et al., 1999). He have been mostly reported for olivine and pyroxene, although other phases have been attempted, including 3.6. Estimation of production rates quartz (Hudson et al., 1991; Brook and Kurz, 1993). Although there was an apparent discrepancy among He Production rates have been determined by three gen- production rate estimates recently Licciardi et al. (1999), eral methods: (i) with geological calibration, by measur- recalibrated the independent lava ages and normalized ing the concentration of the nuclide in a natural rock the previously published production rates including their surface witha known simple exposure history(stable, no own for He data from Oregon basalts. At mid-latitudes erosion, no shielding) that has been exposed for an inde- (393}463 N), Cerling and Craig (1994a) measured an aver- pendently determined duration. In essence, this method age production rate of about 114$2 atoms g\ yr\ is calibrating a particular nuclide time scale to another over the past 17,500 years (calibrated), for olivine and time scale, suchas radiocarbon-, U }Th-, or dendro-years. pyroxene at sea level high latitude. This is slightly lower A variant on this approach is to perform calibration than earlier measurements on Hawaiian lava by Kurz measurements on stable surfaces that are known to have et al. (1990) (approximately 125$3 atoms g\ yr\ at been exposed for long enoughto reachsaturation (at- sea level high latitude according to Licciadi et al., 1999). tained secular equilibrium without erosion), either from The average normalized production rate reported by independent geological data or through measurement of Licciardi et al. is 119$1 atoms g\ yr\ based on 44 a longer-lived TCN (e.g., Nishiizumi et al., 1990; Jull measurements that span from about 600}17,500 yr. The et al., 1992; Brook et al., 1995b). (ii) Production rates can precision and consistency of these measurements make be determined experimentally, by laboratory measure- the He system the best calibrated, and also suggests than ments of the nuclide concentration in slabs of known any dipole or non-dipole "eld e!ects were not signi"cant. composition that were placed in a nuclear accelerator However, because the low latitude Kurz et al. (1990) beam line of particles withenergy thatcan be extrapo- production rates have a large range (55$9}231$ lated to the secondary radiation #ux on the Earth or by 101 atoms g\ yr\) over the Holocene and are higher, it exposing target materials to actual cosmic radiation at is possible that there was a magnetic (dipole or non- high altitudes for periods of years (e.g. Nishiizumi et al., dipole) or surface e!ect on these data. Other recent esti- 1996); and (iii) by numerical simulation of the nuclear mates of He in pyroxene (Schaefer et al., 1999) agree interactions and other physical processes that would be withtheLicciardi (1999) results. responsible for the product nuclides (e.g. Masarik and Reedy, 1995). Although all three have been useful, spal- 3.6.2. Beryllium-10 logenic production rates used in most TCN applications Considering that Be is largely produced by only one have been derived from geological calibration. Table kind of nuclear reaction (spallation), the discrepancies in 4 gives a current list of production rate estimates for the calculated production rates are large. Published values six commonly used TCN. Where earlier estimates of for production in quartz, based on empirical measure- a nuclide production rate has been revised by the same ments range from 4.74 atoms g\ yr\ (Clark et al., 1995) authors we only provide the latest estimate. to 6.4 atoms g\ yr\ (Brown et al., 1991), a range of We emphasize that it is important for the reader to nearly 40%. The discrepancies between the numerous consult the original source of these rates in order to Be production rate estimates may derive partially from evaluate, for example, the suitability of the sample sites, uncertainties in the assumed exposure times of the calib- the reliability of the time scale being calibrated against, ration sites or unrecognized shielding by snow or the manner in which it was normalized to high latitude sediment, and partially from temporal variations in and sea level, or the accuracy of the transport code. production rate due magnetic and atmospheric e!ects. Fortunately, most of the production rates measured this The standard Be production rate study was (and prob- decade have used the scaling model by Lal (1991) even if ably will continue to be) the measurements by Nishiizumi they report results of other scaling models. Even if Lal's et al. (1989) on surfaces assumed to be 11,000 years old. J.C. Gosse, F.M. Phillips / Quaternary Science Reviews 20 (2001) 1475}1560 1517
When scaled to sea level at high latitudes, the surfaces 3.6.3. Carbon-14 yielded an average rate of 6.03 atoms g\ yr\ (neutron Although production rates for in situ C have been and muon contribution combined, but scaled separately estimated withnumerical simulations (most recently and according to Lal, 1991). When the 11,000 C yr BP age withvery comparable results, by Masarik and Reedy, was calibrated to 11.5 cal kyr BP, the corresponding rate 1995), a few production rates have been determined em- is 5.96 atoms g\ yr\. pirically. Establishing the production rate of Chas However, in 1995 two studies led to the conclusion lagged behind the other isotopes (with the arguable ex- that these earlier production rate estimates were too high ception of Ne) mainly because of the di$culty in the (Clark et al., 1995, 1996; Bierman et al., 1996). One study extraction of cosmogenic C witha low isotopic back- provided an improved glacial history for the Sierra ground. Recent improvements in the extraction proced- Nevada (Clark and Gillespie, 1997) and indicated that ure of C from limestone (Handwerger et al., 1999) and the surfaces sampled by Nishiizumi et al. (1989) were quartz (Lifton et al., submitted) have demonstrated that exposed for at least 13.0 cal kyr BP and probably longer the isotope can now be reliably measured routinely in for some of the surfaces. This resulted in much lower Be these phases. The earliest empirical estimates of in situ production rates (4.74 atoms g\ yr\ or lower, depend- C production rate were derived from whole rock sam- ing on scaling). Concurrently, Clark et al. (1995) reported ples (similar to Cl, Section 3.6.6). From measurements the results of empirical measurements from the terminal on basalts (that had not reached saturation) from Taber- moraines of the Laurentide Ice Sheet in New Jersey nacle Hill, Utahat approximately 1500 m asl, Jull et al. which supported lower production rates (maximum of (1994a) calculated a whole rock production rate correc- 4.76 atoms g\ yr\). They also proposed that geomag- ted to SiO composition of 55$10 and 51$9. When netic paleointensity could a!ect the production rates of scaled to high latitude sea level using the approach of Lal Be, and could be invoked to explain a possible discrep- (1991), the rate was 20$2 atoms g\ yr\. This value ancy between Be ages and TL ages of Meteor Crater. agreed well with their earlier estimates based on whole Yet subsequent estimates of Be production rate in rock samples that were assumed to have attained satura- quartz yielded high production rates (Gosse and Klein, tion (Donahue et al., 1990; Jull et al., 1992). Lifton et al. 1996; Nishiizumi et al., 1996; Kubik et al., 1998) equiva- (submitted) recently determined with a much higher pre- lent to the Nishiizumi et al. (1989) value. Additionally, it cision the production rate of C in quartz to be was recognized that the published Nishiizumi et al. (1989) 15.0$0.5 atoms g\ yr\ (using Lal (1991) to scale to production rate needed to be adjusted for an approxim- high latitude sea level). Handwerger et al. (1999) "nd ately geocentric dipole "eld, which returned the produc- a similar production rate of 18$3 atoms CO per tion rate to its original high value, even assuming the g CaCO from limestone at the same latitude, altitude, longer exposure duration of Clark and Gillespie (1997). and exposure age (Provo Shoreline, scaled with Lal, The dilemma resulted in a loss of con"dence in the 1991). applicability of TCN methods for high-resolution dating (e.g. Clark et al., 1995, p. 367). 3.6.4. Neon-21 Fortunately, Stone et al. (1998a) and Stone (1999) Neon-21 is a noble gas that has often been measured found an explanation for the discrepancy between the in the same samples as He. Production rates of Ne published production rates. They recognized that pro- from Mg and Al are 196 atoms g\ yr\ and duction rates derived from low elevation sites (e.g. Clark 55 atoms g\ yr\ respectively (Schaefer et al., 1999), and et al., 1995; Stone et al., 1998a) yielded lower normalized 169 atoms g\1yr\ in olivine (Sarda et al., 1993). How- production rates relative to high elevation sites (e.g. ever there has been a number of measurements of Ne in Nishiizumi et al., 1989; Gosse and Klein, 1996; Kubik quartz, showing that unlike the more di!usive He, neon et al., 1998). If the muonic component of the total pro- appears to be well contained in quartz (at least in the duction at sea level and high latitudes is assumed to be samples reported). The production rate in quartz has 0}5% (cf. Strack et al., 1994; Brown et al., 1995a; Heisin- been determined to be approximately 21 atoms g\ yr\ ger et al., 1997) instead of the 15.6% or higher used by (Niedermann et al., 1994). Reviews of the production Nishiizumi et al. (1989) and Lal (1991), then the scaled systematics, including non-cosmogenic components have high production rates would accordingly be signi"cantly been included elsewhere (Marti and Craig, 1987; Graf reduced. By assuming a 3% contribution of muons to the et al., 1991, 1995; Poreda and Cerling, 1992; Niedermann production of Be at sea level, the scaled production et al., 1993; Phillips et al., 1998). rates from the di!erent sites worldwide converge to ap- proximately 5.1$0.3 Be atoms g\ yr\ (Stone, 1999). 3.6.5. Aluminum-26 Therefore, by modifying the way the site measurements The production of Al in quartz has been closely tied were normalized to production at sea level and high withtheproduction rate of Be (Section 3.6.2). The latitudes, the discrepancy production rate of Be can be two are commonly measured in the same sample because eliminated and the dilemma is probably resolved. the extraction chemistry is similar and can be done 1518 J.C. Gosse, F.M. Phillips / Quaternary Science Reviews 20 (2001) 1475}1560 simultaneously. The measured Al/Be production ra- of potassium also necessarily decreased since the calib- tio is approximately 6.0 to 6.1 (Nishiizumi et al., 1989; ration "xed the production ratios from these two ele- Bierman et al., 1996), although it has been reported as ments. The 40% increase in P (0) is almost entirely due to high as 6.5 (Brown et al., 1991; Kubik et al., 1998). The the new epithermal/thermal neutron equation. AMS measurement of the Al/Al remains di$cult relative to Be/Be and the other radionuclides, so a 3.7. Scaling and correction factors for production rates signi"cant part of the discrepancy among Al pro- duction rate estimates may be attributed to analytical The reference condition for the production of cos- uncertainty. mogenic nuclides is a horizontal surface on a #at plain at high latitude and sea level. However, TCN samples may 3.6.6. Chlorine-36 be collected at any latitude and elevation, and may be on The di!erence in the estimates of production rates for sloping surfaces that have partially obstructed horizons. three pathways of Cl from di!erent groups is large Some surfaces may be covered, perhaps temporarily, by (Table 4). At least a part of the di!erence may be ex- snow or sand. These deviations from the standard refer- plained by the methods used in determining the rates. ence situation can be addressed quantitatively by means Stone et al. (1994, 1996, 1998b) worked withmineral of scaling factors and modi"ed attenuation lengths. separates (plagioclase and microcline) in di!erent envi- ronments to isolate individual pathways and maximize 3.7.1. Spatial scaling target element abundance and Ca/Cl and K/Cl, and used Recent models of the altitude and latitude variation in high altitude sites for the spallation reactions and deep the global #ux of secondary radiation (Section 3.1.4) have subsurface sites for muon reactions. They scaled spal- been based on experimental measurements of (i) slow and logenic and muonic reactions separately. Phillips et al. fast neutrons in the atmosphere, (ii) nuclear disintegra- (1996b) based their latest estimate on the measurement of tions (star production) in nuclear emulsions and cloud Cl in 33 whole-rock samples. In addition to production chambers, (iii) energy spectra of protons and the second- rates for the spallation of Ca and K, they indirectly ary component in the atmosphere, (iv) energy spectra of determined the rate of Cl production via the thermal various charged particles at production in nuclear disin- neutron component by quantifying all other pertinent tegrations at mountain latitudes (e.g. Lal et al., 1960; (Liu et al., 1994) chemical and physical parameters for Yokoyama et al., 1977), and (v) physical processes con- each sample, then solving the age equation while maxi- trolling the #ux and interactions. These measurements mizing the weighted function for the three unknowns. have been extrapolated in order to estimate the global They demonstrated that accounting for temporal vari- distributions of the cosmic-ray #ux of secondary thermal ations in geomagnetic paleointensity #uctuations did not neutrons, muons, and fast nucleons responsible for TCN improve the weighted function. They grouped the (Lal, 1958, 1991; Lal et al., 1960; Lal and Peters, 1967). muonic component withthespallogenic component and The normalized spatial variation in rates of production ignored the di!erent altitude-scaling of muons by using from thermal neutrons and fast nucleons with predominantly low altitude sites (the majority at E(400 MeV is identical (Lal et al., 1958) which simpli"- 1300}1700 m asl), and calibrated against three di!erent es the scaling models. These scaling models are tem- clocks: calibrated C, K/Ar, and thermoluminescence. porally invariant, use a simple model for spatial Swanson (1996) estimated the contribution of the three variations in atmospheric density, and do not account for Cl production pathways in 64 radiocarbon-age-con- non-dipole and other second-order a!ects on the cos- strained glacierized rock surfaces near sea level at high mic-ray #ux. latitude. The causes of the di!erences in the results of the The most widely used scaling model is that by Lal three groups are not yet explained and are an area of (1991). It is di$cult to evaluate the uncertainty in the Lal active investigation. The most likely candidates are (1991) scaling factors (Fig. 13), although Lal suggests the methodological di!erences (most likely in sample prep- total uncertainty is approximately 10}20%. The altitude aration) or problems withtheindependent age control. scaling seems reasonably robust for mid- to high-latitude The new formulation of epithermal neutron #uxes that sites. Measurements of cosmogenic Cl in independently was presented by Phillips et al. (2000) also requires that dated Hawaiian lava #ows and moraines over a range in the production parameters be recalibrated. Phillips et al. elevations from 120 to 4090 m (Zreda et al., 1991) and (2000) used the same data set as Phillips et al. (1996) for measurements of He over similar altitude and latitude the recalibration, but in addition to the new epithermal range (Cerling and Craig, 1994a; Licciardi et al., 1999) neutron equations, they also included muon production suggest at least the altitude scaling of the 1991 model is (Table 3). This recalibration resulted in a production rate a reasonable "rst order approximation. However, as dis- by calcium spallation lower by about 10%. This is largely cussed above (Section 3.6.2), the 1991 model scales from a result of including production due to slow muon ab- a 15.6% muonic contribution of the total production of sorption by calcium. The production rate from spallation Be at sea level, which may be too large (Stone et al., J.C. Gosse, F.M. Phillips / Quaternary Science Reviews 20 (2001) 1475}1560 1519
Table 4 Production rates at the rock surface, (normalized where necessary by the authors using Lal, 1991) for production at sea level and high latitude
Path}target}nuclide Exposure time Rate Reference (ca sideral) (atom g\ target a\) P 1- He Calculated 75 (Lal, 1991) P 1- He Calculated 124 (Masarik and Reedy, 1995) P -" He Calculated 64 (Lal, 1991) P -" He Calculated 105 (Masarik and Reedy, 1995) P -" He Calculated 115 (Yokoyama et al., 1977) P -" He 0.6}13.5 ka 47}50 (Kurz, 1986b; Kurz et al., 1990) $ P -" He 2}17.5 ka 115 4 (Cerling and Craig, 1994a) $ P -" He 2}7 ka 116 3 (Licciardi et al., 1999) ( " P .%$ He 11 ka P -" He (Laughlin et al., 1994) $ P 1- Be 4 solar cycles 5.32 0.27 (Nishiizumi et al., 1996) & $ P 1- Be 21.5 ka 5.17 0.15 (Bierman et al., 1996; Clark et al., 1995) P 1- Be 14.0 ka 4.74 (Clark et al., 1995) P 1- Be Calculated 5.97 (Masarik and Reedy, 1995) P 1- Be Calculated 6.5 (Lal and Peters, 1967) P 1- Be 2.5 Ma 6.4 (Brown et al., 1991) P 1- Be 7 Ma 6.13 (Nishiizumi et al., 1991a) P 1- Be 12.2 ka 6.03 (Ivy-Ochs, 1996; Nishiizumi et al., 1989) $ P 1- Be 12.9 ka 5.5 0.7 (Gosse and Klein, 1996) $ P 1- Be 17.6 ka 5.4 0.6 (Gosse and Klein, 1996) $ P 1- Be 10.0 ka 5.75 0.24 (Kubik et al., 1998) P -" Be Calculated 5.25 (Nishiizumi et al., 1990) P Be Calculated 1.83 (Yokoyama et al., 1977) (using Lal, 1991) P C 17.8 ka 20 $ 4 (Jull et al., 1994; Jull et al., 1992) 1- P 1- C Calculated 18.6 (Masarik and Reedy, 1995) P 1- Ne Arti"cial target 19.3 (Graf et al., 1996) P 1- Ne Calculated 8 (Lal, 1991) P 1- Ne Calculated 18.4 (Masarik and Reedy, 1995) & P 1- Ne 11 ka 21 (Niedermann et al., 1994) P -" Ne Calculated 32 (Lal, 1991) P -" Ne Calculated 38.7 (Masarik and Reedy, 1995) P -" Ne 17.8 ka 45 (Poreda and Cerling, 1992) P 1- Al 14.0 ka 28.9 (Clark et al., 1995) P 1- Al 12.2 ka 36.8 (Nishiizumi et al., 1989) P 1- Al 7 Ma 37 (Nishiizumi et al., 1991a) $ P 1- Al 10.0 ka 37.4 1.9 (Kubik et al., 1998) P 1- Al Calculated 27.5 (Lal, 1991) P 1- Al Calculated 36.1 (Masarik and Reedy, 1995) P -" Al Calculated 15.4 (Nishiizumi et al., 1990) P Al Calculated 40.6 (Yokoyama et al., 1977) (using Lal, 1991) $ P ! Cl Calculated 99 20 (Yokoyama et al., 1977) P ! Cl Calculated 64.6 (Masarik and Reedy, 1995) $ P ! Cl 2.1 to 55 ka 73.6 5.0 (Phillips et al., 1996b) $ P ! Cl 15.2 ka 44.2 1.4 (Swanson, 1996) $ P ! Cl 11 to 17 ka 48.8 3.4 (Stone et al., 1996) $ P ! Cl 2.1 to 55 ka 66.8 6.8 (Phillips et al., 2000) $ P ) Cl Calculated 321 64 (Yokoyama et al., 1977) $ P ) Cl 2.1 to 55 ka 154 10 (Phillips et al., 1996b) $ P ) Cl 15.2 ka 73.8 5.0 (Swanson, 1996) $ P ) Cl 11 to 17 ka 185 15 (Stone et al., 1996) $ P ) Cl 11 to 17 ka 235 10 (Stone et al., 1996) $ P ) Cl 2.1 to 55 ka 137 60 (Phillips et al., 2000) $ P ! 11 to 17 ka 4.8 0.5 (Stone et al., 1996) $ P Cl 2.1 to 55 ka 597 83 (Phillips et al., 1996b) $ P Cl 2.1 to 55 ka 626 105 (Phillips et al., 2000) This value of the production rate of fast secondary neutrons per gram of air above the air-rock interface per year is used (Liu et al., 1994; Phillips et al., 1996b) in lieu of the more complicated parameterization of the thermal neutron capture component of Cl by determining the thermal neutron absorption rate per gram of rock per year. Earlier published production rates by the same group are not included if a more recent interpretation of the same data is provided. The calculated values are based on numerical simulations and models with di!erent assumptions, nuclear cross sections, and reliability. At the time of publication of this manuscript, J. Stone has proposed that a di!erent scaling function be used to normalize production rates to sea level, high latitude by assuming a 3$1% muon capture instead of 15.6% (the latter has been estimated by earlier work and used extensively through Lal's (1991) scaling equations). This proposed scaling will bring the majority of Be production rates in quartz to 5.06$0.29 Be atoms g\ yr\, and explains most of the apparent discrepancy. Scaling with a lower muonic component will a!ect the production rates of other nuclides that have been scaled with the Lal (1991) model. Licciardi et al. (1999) have recently improved the independent chronology of sites used in earlier He production rate determinations by recalibrating and re-dating some of the sites. For mid-latitude sites they calculate a (normalized) production rate of 115 atoms g\ olivine yr\. 1520 J.C. Gosse, F.M. Phillips / Quaternary Science Reviews 20 (2001) 1475}1560
radiation #ux through the surface to the #ux that would be present if the entire horizon were horizontal. It is given by the following relation: +( ( F ( , ) F F cos sin cos d d SR" " , (max) (max) (3.66)
where is the inclination of the surface itself (equal to 903 in all directions for a horizontal surface) and ( )is the inclination angle in direction dictated by the sur- rounding topography. In general, as illustrated in Fig. 5, the e!ect of typical topographic obstructions is small because the incoming Fig. 13. Scaling factor for variation of production rates withelevation cosmic radiation is strongly concentrated near the verti- and latitude (S) based on Lal (1991). Contours are elevation in km. cal. For example, a #at surface on the bottom of a conical pit with45 3 walls would still receive 80% of the radiation incident upon an unobstructed surface. However, the 1998a). Reducing the muon contribution most strongly shielding e!ect may be accentuated if the sampled surface a!ects the altitude scaling at low altitudes. Previously is sloped toward a major topographic obstruction. published dates on surfaces above 2500 m elevation based on the Nishiizumi et al. (1989) production rate and 3.7.2.2. Shielding of sloping surface. When the surface Lal (1991) scaling model will not change signi"cantly. sampled is sloped, several factors act to increase the Other attempts are now being made to measure depth e!ective shielding. One is that, since the preponderance pro"les to resolve the muonic contribution to production of the cosmic radiation is from close to the vertical, the at di!erent elevations and di!erent rock types. For in- foreshortening e!ect will tend to reduce the radiation stance, initial results of Kim et al. (1999) show the #ux. A second is that the e!ective surface area in the transition from neutron-induced to muon-induced pro- direction parallel to the axis of rotation will also be duction of Be and Al at 800 g cm\ and show that the foreshortened (e.g., a surface on a vertical cli! face will muon-dominated Al/Be less than 4.4$0.1. receive no radiation from any inclination along the azi- The horizontal scaling may not be so robust. Pre- muthparallel to thecli ! face). Finally, the portion of the viously described atmospheric and longitudinal e!ects slope above the sample point will topographically block are not accounted for in the Lal (1991) model. Ongoing incoming radiation (e.g., the upper portions of a vertical investigations (e.g. Graham, 1996) are attempting to cli! will block one-half of the radiation potentially reach- more precisely evaluate Lal's scaling for latitude by ing a sample site in the middle of the cli! face). In this measurements in natural and arti"cial samples at di!er- case, the angle between the normal to the surface, N, and ent latitudes in the Southern Hemisphere. the incident ray, , is a function of both and , i.e. ( , ) (Fig. 14). The normal to the sample surface is de"ned by 3.7.2. Topographic shielding an inclination and an azimuth , in the spherical The standard model for calculating cosmogenic nucl- ide production assumes that the production is taking place below a horizontal planar surface. In actuality, many samples are collected from sloping surfaces, and many samples are in the vicinity of topographic irregu- larities that may block part of the otherwise incident cosmic radiation. The e!ects of these factors are usually termed `shieldinga. In this section we describe ap- proaches to calculating the appropriate correction fac- tors for topographic shielding. Our approach is derived somewhat di!erently, but yields results similar to the equations presented by Dunne et al. (1999).
3.7.2.1. Shielding of horizontal surface. The e!ect of topographic obstructions on the cosmic-ray #ux through horizontal surfaces is accounted for by means of a scaling Fig. 14. Illustration of geometrical quantities used in derivation of the factor, SR,. This scaling factor is the ratio of the actual shielding factor for sloping surfaces. J.C. Gosse, F.M. Phillips / Quaternary Science Reviews 20 (2001) 1475}1560 1521 coordinate system (Figs. 4a and b). Geological surface measurements however, are usually taken as strike ( , the azimuth of the intersection of the surface with a hori- zontal plane) and dip ( , downward slope of the surface below the horizontal). Given these conventions, L" and " $903, using `#a if the dip is reported north to east and `!a if it is reported southto west, if the normal geological convention of reporting strike only in the northern half of the compass is followed (Compton, 1962). In order to avoid ambiguity, for cosmogenic nucl- ide measurements it is generally preferable to report `direction of dipa rather than strike, where the direction of dip is equal to . Given a description of the orienta- tion of the normal to the surface, the required cosine of ( , ) (again, the angle between the normal and an arbit- rary spherical orientation) can be derived using the spherical law of cosines " # ! Fig. 15. Total topographic scaling (S2) as a function of surface dip cos ( ( , )) cos cos sin sin cos ( ). angle and topographic shielding. Degree labels on curves refer to the (3.67) angle of shielding by surrounding, axially symmetric, topographic fea- tures. For a "eld sample, the lower limit on the inclination of exposure, for a particular azimuth, may be limited either by a topographic obstruction, ( ), or by the projection dipping one, the surface production rate, PR K(0) of the slope of the sampled surface. For a sloping surface, \ \ (atoms g 1yr ), will be slightly greater for the dipping that projection, ( ), is given by surface because, as indicated by the shorter e!ective ( )"903#tan\ (cos( ! ) tan ). (3.68) attenuation length, the same amount of production is concentrated in a shorter thickness (measured perpen- The equation describing the #ux of the energetic com- dicular to the surface). This can be accounted for by ponent of the cosmic radiation through the surface thus equating the vertically integrated production beneath becomes a horizontal surface to the production integrated perpen- ( F dicular to a dipping surface ( , )" ( F Z F cos sin ! " ! F ( S2 P exp d S P exp dZ, D C D ;cos ( ( , )) d d . (3.69) (3.72) The scaling factor for a sloping surface surrounded by where l is the perpendicular to the dipping surface and irregular topography is then given by S2 is the complete (total) scaling factor for topographic
+( F ( F # ! F cos sin (cos L cos sin L sin cos( L )) d d S " F , (3.70) R (max) where (max) is obtained from Eq. (3.60). obstructions, dipping surfaces, and changes in e!ective Increasing the obliquity of the angle between incident attenuation length. Integration yields the scaling factor radiation and the sample surface has another e!ect be- for changes in e!ective attenuation length. sides altering the attenuation length (Fig. 15b). A more oblique angle creates a longer path-length through the S2" S "SSR. (3.73) sample, thereby slightly increasing production over a given depth, Z (this e!ect in fact exactly counteracts the foreshortening e!ect previously described so that, in The total shielding, as a function of slope of surface, for some formulations of the production equations (e.g., varying topographical geometry is shown in Fig. 15. Dunne et al., 1999), bothterms may be neglected). Thus, even for the case in which the cosmic-ray #ux through 3.7.2.3. Ewects of shielding and slope on attenuation a horizontal surface is the same as through a steeply length. For a surface penetrated by cosmic rays from 1522 J.C. Gosse, F.M. Phillips / Quaternary Science Reviews 20 (2001) 1475}1560 a range of incidence angles, an e!ective attenuation equation length, , can be de"ned from the weighted average of " e \8" , (3.75) all penetration depths. This attenuation length, like that " for a horizontal surface, is de"ned as being perpendicular where Z" is the mass of cover per unit area over the to the rock surface. The e!ective attenuation length, , rock sampled. The correction for the cover must also is calculated by combining Eq. (3.66) and (3.54) include any temporal variation in depth. For instance, +( snow survey data of average snow depthand average ( F " F Fcos sin cos( ( , )) d d snow water content can be used to construct distribution +( . ( F F F cos sin d d curves (as a function of time of the year) of snow water (3.74) content overhead at various heights above the surface. The temporal distribution of snow water shielding is Although the apparent attenuation length, , is often needed because the relationship between water content treated as a constant, it approximates suchonly for and shielding is not linear. Using these water content horizontal, unshielded surfaces. A dipping surface will curves and Eq. (3.70), the shielding at di!erent heights as have a shorter e!ective attenuation lengthbecause more a function of time of the year can be computed. Finally, of the particles will enter at oblique angles and a strongly these can be averaged over the year and divided by the shielded horizontal surface will have a longer e!ective computed #ux without snow cover to yield curves of attenuation lengthbecause fewer of theparticles will be annual snow shielding (S#) as a function of height of entering from oblique angles. Fig. 16 illustrates the vari- the sampling point above the land surface. A typical ation of the e!ective attenuation lengthwithsurface dip annual snow shielding formulations is given in Eq. (3.76), and topographic shielding. using monthly snow depths as an example. 1 3.7.3. Surface coverage S " e\ X# G\X M# G , (3.76) # 12 One relatively common type of shielding is that due to G cover by winter snow, or possibly sand, soil, or peat. where z# is the monthly average snow height (cm) Snow is the most common cause for surface coverage above the land surface, # G is the average monthly corrections and the discussion below will be framed in snow density, and z is the height (cm) of the boulder terms of snow corrections. However, the equations and or other sampling point above the land surface. In this principles are applicable to coverage by any other mater- case, monthly intervals were used because snow depth ial, withsuitable modi "cations for density and timing data is the most commonly available in monthly of the coverage. At any time when snow is present on means. However, the e!ect could be integrated over the surface the energetic component f the cosmic radi- di!erent time periods appropriate for the cover. This ation is reduced according to the exponential attenuation type of analysis can be generalized by computing curves of S# as a function of height above land surface (i.e., as a function of z) so that snow cover can quickly be estimated for a number of boulders of varying height. Typical corrections for 4 months of shielding by snow of di!erent depths and densities are shown for a spal- logenic nuclide in Fig. 17 (cf. Gosse et al., 1995a; Licciardi et al., 1999). Onuchin and Burenina (1996) used a database of 2456 snow density observations in northern Eurasia to show a relationship between snow density variation and three other parameters: snow thickness, air temperature, and snow cover period. The range of densit- ies they measured was 0.16}0.48 g cm\ while the aver- age range was 0.16}0.33 g cm. Their model may be useful for estimating snow densities where historical records of the other parameters are available.
3.7.4. Sample thickness Cosmogenic nuclide production rates are speci"ed at the rock surface. However, the production pro"le varies Fig. 16. E!ective attenuation length( ) as a function of surface dip angle and topographic shielding. Degree labels on curves refer to the continuously withdepthand samples are collected over angle of shielding by surrounding, radially symmetric, topographic "nite depth intervals. The production rate must therefore features. be integrated over the actual sample thickness and J.C. Gosse, F.M. Phillips / Quaternary Science Reviews 20 (2001) 1475}1560 1523
Z QRF" H 1!exp ! #(1#RI)(I )H ¸ Z ; 1!exp ! ¸ #(1#RIR )(I ) H ¸ Z ; 1!exp ! ¸
# H ! !Z R I I 1 exp I ;+Z[ H #(1#RI)((I )H #(I ) H )#RIH ],\, (3.80) Fig. 17. E!ects of shielding by snow of common densities and thick- I[1!exp(!Z/I)] nesses. Calculated for a spallogenic nuclide, assuming an otherwise QI" . (3.81) simple exposure, withsnow shieldinginstantaneously applied for Z 4 months each year. This is a multiplicative e!ect so the deviation can The e!ect of sample thickness on the correction factor for apply to any exposure age. Cl produced in a quartz arenite is shown in Fig. 18a. In general, the sensitivity of calculated ages to normal errors divided by the surface production to yield the thickness in estimation of sample thickness or bulk density is small, correction factor QG on the order of 1 or 2%, as illustrated in Fig. 18b.
PG K 8PG K dZ 3.7.5. Thermal neutron leakage QG K" " , (3.77) PG K(0) ZPG K(0) Eq. (3.10) contains correction terms for epithermal and thermal neutron leakage. This refers to the enhanced where QG K refers to the ithreaction producing the mth di!usion (due to greater surface area) of low-energy neu- nuclide and Z is the thickness of the sample (assuming trons out of the corners and edges of objects that project that the top of the sample is the surface). The production into the air, relative to the `standarda di!usion out of #at terms in the numerator and denominator of Eq. (3.77) surfaces. This e!ect has unfortunately never been ad- cancel and hence the correction factor depends only on equately quanti"ed, although it is probably generally the type of reaction and not on the nuclide produced. small. For a very unfavorable geometry (the top of a thin, Substituting Eqs. (3.53)}(3.55), and (3.48) into Eq. (3.77) spine-like basalt pressure ridge) Zreda et al. (1993) esti- and solving yields mated a minimum value for the thermal neutron leakage scaling factor of 0.7. The e!ect will be largest for sample Z sites withsigni "cant three-dimensional geometry (e.g., Q" 1!exp ! , (3.78) Z the top of an acute-angle pyramid), less for a more regular three-dimensional point such as the corner of ZQ a cube, and less yet for a two-dimensional geometry such Q " H 1!exp - as the edge of a cube. Epithermal and thermal neutron di!usion lengths are such that the low-energy neutron #(1#RIR )(F )H ¸ #uxes typically return to near-equilibrium values within &25 cm below the rock surface. Given these character- Z istics, the simplest method of dealing with the neutron ; 1!exp ! ¸ leakage problem is to sample #at surfaces at least 30 cm back from the edges of boulders, and to avoid sample Z sites consisting of acute vertices. #RIH I 1!exp ! I 3.8. Exposure dating with a single TCN ;[Z(H #(1#RI)(F )H Eqs. (3.10), (3.47) and (3.53)}(3.55) can be combined to #R H )]\ , (3.79) obtain the total cosmogenic nuclide production rate (by I spallation reactions, epithermal and thermal neutron 1524 J.C. Gosse, F.M. Phillips / Quaternary Science Reviews 20 (2001) 1475}1560
Fig. 18. (a) Variation of sample thickness scaling factor with sample thickness for spallation scaling factor (Q), thermal neutron scaling factor (Q ), and epithermal scaling factor (Q ). Calculations are for an average low-Ca granite (Fabryka-Martin, 1988) with1% volumetric water content and bulk density of 2.7 g cm\. (b) Variation in apparent age as a function of assumed rock density and sample thickness. Rock was a quartz arenite with actual density of 2.7 g cm\ and actual sample thickness of 5 cm. absorption, and production from muons) as a function of where Z is the depth of the sample at the time the depth sample material was "rst exposed (t"0). The dependence of the cosmogenic nuclide concentra- Z Z tion in the rock, N (atoms g\), on time is given by PR K"SS2S J exp ! #J exp ! K ¸ dNK "PR K(Z)! KNK. (3.89) # ! Z # ! Z dt J exp ¸ J exp , (3.82) I Substituting Eqs. (3.82) and (3.88) into Eq. (3.89) and where solving for the initial condition NK"0att"0 yields J Z !t J " (0)C #S (1!p(E )) " O ! K I I * NK(Z, t, ) SS2S ¸ # exp ¸ I O /(A )O K (A )O ;f \ H #S \ H (3.83) Z * !exp ! t! , (3.90) K (A¸) J "(F )H [(1!p(E ))S* O ; \ where q refers to the production reaction and (AL) to the f (1#RIR ) O attenuation lengthpertaining to it, as follows: # \ # S* f (1 R I)] (3.84) (q, (AL)O)"(f, ), (eth, L ), (th, L ), (, I). Frequently cosmogenic nuclide samples (of "nite J "S (1#R R )(I)H \ (3.85) * I thickness) are collected from the land surface position " ! \ H JI S* RI(1 p(E )) f (Z"0). In this case Z"t and, if the thickness correc- tions are included, Eq. (3.90) becomes S #S R f \ H # I > \(0) (3.86) * I S I K I J/ I N (t,)"S S S O K CJ 2 Q A¸ # If the land surface is not stable, but rather is eroding at O /( )O K a constant rate, then the sample depth will be a function ; ! ! # of time: 1 exp K t , (3.91) (A¸)O dZ "!, (3.87) where dt where is the erosion rate (g cm\2yr\). Eq. (3.87) can be JD/"QQ K I(0)CI#Q S* (1!p(E )) integrated to yield I Z"Z!t, (3.88) ;f \ H #Q S* \ H (3.92) J.C. Gosse, F.M. Phillips / Quaternary Science Reviews 20 (2001) 1475}1560 1525
J/ "(I )H [Q (1#RIR )(1!p(E )) In general, applications of single nuclides are limited by the pervasiveness of erosion, inasmuch as both age ;S f \ R #Q S f \ (1#R )], * * I and erosion rate cannot be obtained by a single nuclide (3.93) measurement. As discussed above, a spallogenic cos- mogenic nuclide concentration (e.g. all except for Cl, / " # H \ J Q S* (1 R IR )(I ) , (3.94) see (iv) below) will provide a minimum age estimate of the total exposure duration of a surface that has been eroding. JI/"Q S* RI(1!p(E ))f \ H However, under some circumstances a single nuclide \ H #Q S* R If (3.95) can provide adequate information. Those circumstances include the following: Two special cases allow simpli"cation of Eq. (3.91). One is the case where the surface has been exposed for a very (i) Geological evidence of negligible erosion. In some long time so that the cosmogenic nuclide pro"le has cases surface textures provide strong evidence that reached equilibrium with the erosion rate. In this case the surfaces considered for dating have not su!ered sig- surface nuclide concentration will be given by ni"cant erosion since the event intended to be dated. J/ Examples include the preservation of glacial polish N "S S S O K( ) 2 ¸ # . (3.96) (Nishiizumi et al., 1989; Clark et al., 1995), #uvially O /(A )O K smoothed textures (Burbank et al., 1996), and diag- " The second is the case where the surface is stable ( 0): nostic textures on the surfaces of lava #ows (Ander- son et al., 1994; Cerling, 1990; Phillips et al., 1996b). NK(t)"SS2S K\ J/O [1!exp(! Kt)]. (3.97) (ii) Reasonable inference of negligible erosion.Thee!ect O of erosion on cosmogenic nuclide accumulation does Eqs. (3.96) and (3.97) can be further simpli"ed for several not depend on the erosion rate, but rather on the additional special considerations. If the nuclide of inter- total erosion depth. As illustrated in Fig. 19, high est is produced only by spallation, its abundance as rates of erosion have little e!ect on nuclide concen- a function of time and erosion will be given by trations until the exposure time is long enough for signi"cant erosion to have occurred, but relatively " N (t, ) SS2SQ low erosion rates can have signi"cant e!ects on the ! ! #\ cosmogenic inventory as secular equilibrium is ap- I I K(0)CI(1 exp( ( K )t)) ; . proached. Signi"cant erosion can be de"ned as an K#\ appreciable fraction of the apparent attenuation (3.98) length, on the order of 15 or 20 cm rock depth. In many cases, it may be possible to argue that total After a time that is large compared to #\, K R erosion depths are relatively shallow, even in the Eq. (3.98) will further simplify to
SS2SQP K NK Q()" , (3.99) K#\R where P K is the total spallation production rate (usually expressed per unit mass for a particular mineral). This is often refereed to as the `steady-state erosion modela for a spallogenic nuclide. If a large age can be justi"ed and constant erosion assumed, the erosion rate may be dir- ectly obtained. A further simpli"cation of Eq. (3.99) is possible if the cosmogenic nuclide is stable (i.e., the half-life is in"nite), since bothof thecommonly used stable nuclides ( He and Ne) are produced by spallation reactions. In this case, Eq. (3.99) reduces to
NK Q(t,)"SS2SQR \P K[1!exp(!\R t)]. (3.100) If the surface is also stable, the accumulation rate for a stable cosmogenic nuclide becomes linear withtime Fig. 19. Chlorine-36 concentration in Fabryka-Martin (1988) average low-Ca granite at sea level and high latitude as a function of surface NK (t)"SS2SQPK t. (3.101) exposure age and surface erosion rate. 1526 J.C. Gosse, F.M. Phillips / Quaternary Science Reviews 20 (2001) 1475}1560
absence of direct evidence suchas preserved diagno- stic surface textures. A variety of bothconventional and cosmogenic nuclide studies on denudation rates (Bierman, 1994; Summer"eld and Hulton, 1994; Brown et al., 1995b, 1998b; Bierman and Steig, 1996; Gosse et al., 1997; Fleming et al., 1999; Summer"eld et al., 1999) indicates that total bare-rock surface loss rates typically lie in the range of (1to 20 mm kyr\, except in basins withunusually steep topography or dominated by hillslope processes or areas withincompetent rock. For carefully selected samples that are of relatively resistant lithology, this range is likely reduced to (1}5 mm kyr\ (Phillips et al., 1997b). Even for erosion rates at the high end of this range, about 30 kyr will be required to e!ect signi"cant erosion. Reasonable argument can there- fore be made that single nuclides and assumptions of negligible erosion are probably generally adequate for surface-exposure dating studies in the late Quat- Fig. 20. Variation of apparent surface exposure age witherosion rate for di!erent proportions of spallation and low-energy neutron ernary age range (provided, of course, that signi"cant production. The spallation-only curve would approximate the e!ects inheritance a complex exposure histories can also be for He, Be, C, Ne, and Al for shallow samples or low erosion considered unlikely). rates where muonic contributions were not signi"cant. Hypothetical (iii) Reasonable inference of great age. Conversely to the sample was Fabryka-Martin (1988) average low-Ca granite at sea case in (ii) above, in many cases it may be possible to level and high latitude. Chlorine concentration and Cl concentration were varied to maintain constant zero-erosion age while changing argue that the rock surface being investigated has proportions of production reactions. 54% spallation production cor- been exposed for a time that is long compared to the responds to 200 ppm Cl, the actual average value from Fabryka-Martin nuclide half-life, and that erosion is relatively in- (1998). cremental and steady. Examples include the famous inselbergs and bornhardts of Australia (Bierman and Turner, 1995), summit #ats in mountain ranges of the western United States (Small et al., 1997), and di!erent proportions of spallation versus thermal nunataks and surfaces in the dry valleys of Antarc- and epithermal neutron production. For the case of tica (Nishiizumi et al., 1991a; Brook et al., spallation production only, apparent ages increase 1995a; Bruno et al., 1997; Schaefer et al., 1999). In consistently withincreasing assumed erosion rate. this case, the cosmogenic nuclide inventory can reas- (As the assumed erosion rate increases, the time- onably be inferred to be in secular equilibrium with integrated production rate decreases, hence a longer the erosion rate, and the erosion rate calculated time is required to accumulate the measured amount using Eq. (3.99). In cases where the surface sampled of the cosmogenic nuclide.) In contrast, thermal neu- can neither be inferred to be of great age, nor to have tron production increases withdepth,down to about had a negligible total depth of erosion, useful chro- 50 g cm\, and if the low-energy neutron production nological estimates can still be obtained by placing is su$ciently large the apparent age may decrease for reasonable constraints on the rock erosion rates. low erosion rates. As discussed above, numerous studies are available to help bound the range of reasonable erosion rates, The counteracting trends with depth of spallation and based on lithology, climate, and topography. Appar- low-energy neutron production can be an advantage in ent ages can be calculated through this range and the some studies where only a single cosmogenic nuclide is extreme ages selected as chronological references (cf. measured. If the rate of change of the high- and low- Phillips et al., 1997b). This approach can provide energy production reactions withdepthare approxim- useful results so long as the erosion rates are not ately equal (as for the 70% spallation case, Fig. 20) then high, nor the surface ages too old. the total production rate will vary little with depth and (iv) It is worthwhile to note that production of Cl by the apparent age will be relatively insensitive to erosion. thermal neutron reactions, in addition to spallation On the other hand, if production is strongly dominated reactions, can cause erosion to have e!ects on sur- by low-energy neutron absorption, the depth-depend- face exposure dating that are markedly di!erent than ence of the production will be even greater than for for spallation alone. In Fig. 20 apparent Cl age is spallation alone and the apparent age will be very sensi- illustrated as a function of assumed erosion rate for tive to erosion (Bierman et al., 1995a). J.C. Gosse, F.M. Phillips / Quaternary Science Reviews 20 (2001) 1475}1560 1527
3.9. Exposure dating with multiple nuclides
Under the favorable circumstances listed in Section 3.8 a single nuclide may su$ce to de"ne the exposure age or erosion rate of a surface (see Gillespie and Bierman (1995) for discussion of precision). If an upper limit on erosion rate can be speci"ed, a range of possible exposure ages can be determined. However, in the general case, the observed cosmogenic nuclide concentration in a sample will be a function of at least two independent variables, exposure age and erosion rate, and in order to uniquely determine both of them the concentrations of at least two nuclides must be measured. For example, a nuclide with the shorter half life such as C (Lifton et al., submitted) provides an estimate for the erosion rate of the surface because it reaches secular equilibrium (saturation) in about 25 kyr (even earlier for higher erosion rates). We must assume that the erosion rate was constant, continu- Fig. 21. Why use two isotopes? A single TCN measurement will at best ous, and gradual (reasoning discussed below). Once the provide a minimum estimate of an exposure age, because in most cases shorter half-life has been used to constrain the erosion erosion reduces the concentration. After 30 kyr of exposure, in situ " \ \ rate , a stable nuclide (or a radionuclide withlong C at sea level high latitude (P! 8 20 atoms g yr ) is within half-life, e.g. Be, Fig. 21) can be used to determine the 97% of the secular equilibrium concentration (1.65;10 atoms g\,at " \ " \ exposure age of the surface by compensating for any 0mmkyr ). For higher erosion rates ( 1, 3, and 10 mm k yr ) the C saturation concentration is lower (respectively illustrated as e!ects of erosion. Explicitly, Eq. (3.91) can be used to long dash, dash-dot, and dot) and equilibrium is attained earlier. On solve for exposure time as a function of . a surface known to predate the last glacial maximum, a measurement of In the absence of an isotope system that has reached &C'"1.59;10 atoms g\ would indicate that the erosion rate of the equilibrium witherosion ( C is not yet routinely surface was 3 mm kyr\. Once the erosion rate is known it is possible to measured in quartz), two nuclides can still be used use a stable or longer-lived isotope (which has not reached saturation) to determine the actual exposure age. In this example, the measured to estimate total exposure duration, minimum total " ) \ \ " concentration of Be (P 8 5.5 atoms g yr )is&Be' duration of burial, erosion rate, and style of erosion. 5.05;10 atoms g\, which at "3 mm kyr\ corresponds to an expo- Based on Eq. (3.91), the variation of the ratio of two sure age of 127 kyr (assuming ideal conditions as described in text). spallation-produced radionuclides, m and n, withtime will be given by N (t) Other spallogenic nuclides with su$cient half-life di!er- R (t)" K " ences can be used, and we describe below the additional KL N (t) L advantages of using the ratio of a thermal-neutron- P (0) ( #/ ) +1!exp[1!exp(! #/ )t], derived nuclide witha spallogenic one. K L K . PL(0) ( K#/ ) +1!exp[1!exp(! L#/ )t], The exposure/erosion history of a sample can be infer- red from the position relative to the `steady-state erosion (3.102) islanda (Lal, 1991), as described in the caption of Fig. 23. Note that the expressions for the two nuclides di!er This approach was "rst implemented by Klein et al. only in the half-life and production terms, and thus in (1986b) and its advantages have been well illustrated, order to be used for this purpose the two nuclides must among others, by the work of Nishiizumi et al. (1991a) on exhibit some signi"cant di!erence in either half-life or glacially exposed rocks in Antarctica. A sample can plot production pro"le (e.g., the ratio of two stable, spal- in four "elds (Fig. 22b) which yield di!erent information logenic, noble gas nuclides will not vary witherosion rate about the age, erosion style and rate, and or history of or time). surface burial. The two-nuclide approach was "rst proposed by Lal and Arnold (1985). They proposed application of the (i) Samples with Al/Be greater than the initial pro- Al/Be pair, since bothcan be readily measured in duction ratio (plot above the steady-state erosion a single mineral separate (e.g. quartz), bothhavesimilar island) cannot be explained by any combination of geochemical behavior, and they have half-lives that di!er erosion, burial, exposure, or inheritance, and thus by a factor of two (Fig. 22a). The ratio Al/Be is indicate sample preparation or measurement prob- customarily plotted against the log of measured Be lems. (Another possible, although unlikely, explana- concentration (scaled to production at sea level and high tion is nucleogenic production of bothspecies.) Most latitude) to evaluate age and erosion e!ects (Fig. 22b). existing studies in which the Al/Be was measured 1528 J.C. Gosse, F.M. Phillips / Quaternary Science Reviews 20 (2001) 1475}1560
\ \ " Fig. 22. TCN ratio diagram for Al and Be. (a) Production curves for Al (P 8 33.6 atoms g yr ) and Be (P 8 5.5 \ \ ( atoms g yr ), withproduction ratio of 6.1 (theseproduction rates will vary withsites above sea level or K 603). Additional curves for erosion rates of "1, 3, and 10 mm kyr\ as in Fig. 21. The change in Al/Be also shown for "0, 1, 3 and 10 mm kyr\. (b) As in (a), Al/Be shown for "0, 1, 3, and 10 mm kyr\, but plotted (traditionally) against log Be concentration (normalized for production at sea level and high latitude). Samples with ratios plotting on the upper curve can be interpreted at have no erosion, and total exposure duration corresponds to distance along the "0 ratio curve. Samples plotting on or between erosion curves have experienced the modeled erosion rate (assumed continuous, constant, and gradual), and the total exposure time corresponds to the distance along the erosion trajectory.
in a continuously exposed surface withnegligible terpreted as ages separately, the shorter half-lived erosion simply assume that the initial production isotope will yield a younger age, and the disparity ratio is about 6.1. However, more reliable determina- increases withexposure duration. tions of the production ratios of these and other (iv) Samples plotting below the steady-state erosion is- isotopes are urgently needed (see Section 7 and Bier- land (under the curve that connects all of the man et al., 1999). Although the ratios cannot plot end points of the erosion production ratio curves) above the production curve, a ratio can plot to the have traditionally been interpreted as indicating right of the curve if the assumed production rate (at that the exposure of the surface was interrupted by its present location) is lower than the actual produc- a shielding event (e.g. Granger et al., 1997; Bierman tion rate that the surface recorded (e.g. in the case of et al., 1999) (Fig. 23a). When a surface is completely subsidence or movement downslope). or partially buried (e.g. by snow, sediment, glaciers, (ii) Samples which plot on the production ratio curve or water), the ratio will change due to the di!erences probably have never been buried or eroded during in the radioactive decay rates of the two isotopes. the current exposure duration, and inheritance from If the longer-lived or stable isotope is the denomin- an earlier exposure is unlikely. The distance along ator, the ratio will decrease during burial. Graphi- the production ratio curve corresponds to the cally, the pathway of the buried sample is vertical if exposure age of the sample. The Be or Al the TCN denominator is stable, or slightly toward concentration can be interpreted directly as an ex- the origin if the TCN denominator is radioactive. posure age. Bothisotopes will yield thesame expo- The length of the path (or the distance below the sure age. steady-state erosion island) is proportional to (iii) Samples plotting within the steady-state erosion is- the burial duration. Once the burial period is com- land have traditionally been interpreted to represent plete and the surface becomes exposed again, the some combination of erosion and exposure. ratio will increase (on a exponential pathway A unique production ratio curve for a constant, toward the production ratio curve). Therefore, ratios gradual, and continuous erosion rate can be "t plotting below the island have been interpreted to through the sample, so the sample's erosion rate and have undergone complicated exposure histories, age (distance along that erosion curve) can be cal- where the surface was shielded from cosmic rays at culated simultaneously. If the two nuclides were in- least once. J.C. Gosse, F.M. Phillips / Quaternary Science Reviews 20 (2001) 1475}1560 1529
Fig. 23. TCN ratio diagrams. (a) Al/Be, as in Fig. 22b. Samples plotting below the steady state erosion island must have had experienced complicated exposure history (partial or complete shielding or plucking). The measured ratio could be explained by an in"nite number of trajectories involving exposure, subaerial erosion, burial, or plucking. An example of complete shielding is given. If geological observations can decipher which sur"cial processes are likely, then the pathways illustrated can provide constraints on the minimum exposure age, minimum complete burial duration, and average plucking depth. Low ratios in allochthonous sediment also implies inheritance, so multiple nuclides are useful in depth pro"le studies. (b) C/Be plot showing how the ratio behaves in the case of cli! retreat by block falls (i.e. erosion, not burial, caused the low ratios). If a cli! face was episodically retreating over the last 40 kyr, the ratios at any given time for the "nal surface are shown by the lowest curve (#). In this scenario, the cli! was exposed for 19 ka, then a 50 cm thick block fell, then the cli! was exposed for another 9 ka, then a 20 ka block fell, then another 10 ka, and "nally another 50 cm block fell very recently (e.g. the block can be seen below the cli!, and the surface is very fresh). The average erosion rate is 120 cm over 38 kyr or "3.16 cm kyr\. In reality, we do not know this retreat history of the cli!. We can, however, provide an estimate of the minimum possible erosion rate to achieve the measured ratio. The dashed curves are calculated for the scenario that the cli! only underwent one block fall just before the sample was collected. The curves therefore provide the minimum possible erosion rate that could explain the measured ratio (considering 1 uncertainty"8%, AMS and ICP.OES measurements only, see Sections 6.1). In this case, the dashed curves bracket the minimum average erosion, "2.33}2.36 cm kyr\.
From the buried sample alone, there is no way to There is a variant interpretation of ratios which plot determine how many episodes of burial or the total below the island. The traditional interpretation described duration of burial that a surface may have experienced, above considers that an unattached material is covering and without independent information there is no way to the surface, such as a glacier over a bedrock surface. determine how long a surface was exposed since burial A ratio will also plot below the steady-state erosion (e.g. Bierman et al., 1999). However, where a bracketing island if the surface has experienced episodic erosion in age can provide useful insight, estimates of the minimum which thick layers of material are removed rapidly, such exposure duration and minimum burial duration can be as during subglacial plucking or block erosion of a re- inversely modeled. The minimum exposure duration is treating vertical cli! face. For instance, a surface on determined by "rst assuming that the surface became a high tor that has recently lost a thick cap (say 60 cm) instantaneously uncovered seconds before it was sam- due to frost shattering or mass wasting will have a ratio pled. (If the actual post-emergence exposure duration is that plots below a steady-state erosion island. With the known independently, it could be modeled so that the exception of Macciaroli et al. (1994) and Gosse et al. ratio is returned (lowered) to the pre-exhumation value (1995b), this possibility has not been widely considered, (Gosse et al., 1993; Granger et al., 1996)). The distance and may have resulted in misinterpretations of TCN along the burial pathway corresponds to the minimum ratios in glaciated regions. The distance that the zero- burial duration, and the distance along the zero-erosion erosion production curve is displaced to the left is production curve to the intersection with the burial path- proportional to the thickness of the block removed way is the minimum duration of exposure before the (Fig. 23b). In this sense, we can use the ratio of two single burial event. The three durations combined (pre- isotopes to help constrain the style and maximum rate of exposure, burial duration, and post-emergence exposure) erosion on a surface that was not likely buried by another provide the minimum total exposure duration. material (other than self-shielding). 1530 J.C. Gosse, F.M. Phillips / Quaternary Science Reviews 20 (2001) 1475}1560
Unfortunately, considering the uncertainty in the measurements involved and the non-unique causes for changes in the ratios, it is easy to make interpretations of multiple TCN measurements that are misleading, incom- plete, or constitute over-interpretation. Here are some caveats to keep in mind when interpreting multiple ratios: 1. Analytical uncertainties are greatly enhanced when ratios of nuclides are considered. For example, even for optimal analyses the uncertainty is generally at least 7% for the Al/Be ratio (1 ICP.AES and AMS experi- mental uncertainties only) (cf. Granger et al., 1996). Be- cause of the shape of the island, this uncertainty will have signi"cant implications for younger samples ((10 kyr) because the 1 range will cross a wider range of erosion production ratio curves and therefore a scenario of zero erosion cannot be distinguished from a scenario of very high erosion. On the other hand, samples with longer ' exposure durations ( 10 kyr) that plot along the sub- Fig. 24. Ratio diagram, Cl/Be vs. Cl (log concentration, nor- vertical portion of the production ratio curve will have malized, as in previous "gures) for boulder samples from moraines in 1 uncertainties which cross only very low erosion rate the Wind River Range, Wyoming (from Phillips et al.,1997). Position of production ratio curves. It is therefore important to min- samples indicates generally very low erosion rates for boulder surfaces. imize the consequences of measurement uncertainties and optimize the resolution of the erosion curves by selecting isotope pairs that provide the shape of island tron absorption. The di!erence in production pro"les for that is optimal for the speci"c study at hand. See below the high- and low-energy reactions will accentuate the for the utility of using isotopic ratios that do not have the di!erence in behavior on the plot. same production mechanisms. This e!ect is illustrated using Cl and Be data from 2. The interpretation of low isotopic ratios (long-lived boulders on moraines in the Wind River Range, Wyom- or stable denominator) is non-unique (multiple burial ing, from Phillips et al. (1997b) (Fig. 24). Due to the and exposure events are possible) and ambiguous * low component of thermal neutron production in these sam- ratios could be due to either burial or episodic rapid ples (approximately 50%), the width of the erosion island erosion unless there is an independent means to indicate is greatly increased, relative to the analytical accuracy of burial (striae or till indicates at least partial shielding by the ratio. The position of most of the data pairs on the ice) or lack of shielding (e.g., on top of a pedestal in plot indicates that surface erosion rates are very low. a non-glaciated region, or on a high vertical face). In In principle, it should be possible to tailor nuclide pairs glaciated terrains, it will be di$cult to resolve whether for various speci"c applications. For example, the combi- the resulting low ratio is due to ice shielding, plucking, or nation of Ne and Be should be very suitable to some combination of both. Depending on the question determining boththeexposure age and erosion rate of being addressed, in many cases it may not matter which very old ('1 Ma) surfaces. However, the same pair process caused the low ratio. For example, Gosse et al. would prove less informative for surfaces younger than (1995b) argued that both plucking and shielding require 300 kyr because there would be insu$cient time for decay that a glacier was present in a controversial area where of the Be and thus the sensitivity to erosion would be geomorphic and biologic evidence has been adduced for low. Here, the Be/Cl pair would prove more e!ective. the complete absence of any late Quaternary ice cover. For young surfaces ((100 kyr), C paired witha lon- Although this approach to elucidating geomorphic ger-lived nuclide would be optimal. Furthermore, such histories of samples has proved to be powerful, it is paired applications need not even involve two di!erent limited by the precision of the nuclide analyses. The nuclides. If one nuclide is produced by bothspallation typical analytical uncertainty in the Al/Be ratio is and low-energy neutron reactions, as is Cl, then min- similar to the height of the steady-state erosion island, eral separates in which one or the other reaction pre- o!ering limited resolution of the erosion/exposure para- dominates (e.g., a potassium feldspar separate in which meters. The narrow shape of the island is determined by spallation production o! potassium predominates, the magnitude of the di!erence in half-lives, since Al paired with a quartz separate in which thermal neutron and Be share the same spallogenic production pro"le. production from Cl predominates) can be used in Liu et al. (1994) suggested that the resolution of the a similar fashion (Vogt et al., 1996). The main advantage approachcould be improved by combining a spallogenic of this approach is that it can greatly simplify the sample nuclide with one that is also produced by thermal neu- preparation and analysis. J.C. Gosse, F.M. Phillips / Quaternary Science Reviews 20 (2001) 1475}1560 1531
3.10. Nuclide-specixc considerations ponent can be identi"ed by analyzing the He isotopic composition of gas released upon crushing and during The selection of the appropriate nuclide is controlled step heating (the inherited magmatic component, pre- by the estimated exposure duration of the surface being dominantly in melt and #uid inclusions, should be re- investigated, the elevation of the surface, and the nature leased "rst, whereas the cosmogenic He is mostly held of the study. Conversely, the choice of lithologies can inside the olivine lattice). The inherited He compon- restrict the nuclides used. ent is determined (Kurz, 1986a, b) using the He/He The e!ective ranges of the various TCN depend on released during crushing, and the total He2 measured: their half-lives and production rates, and spectrometry detection limits. If a surface has been continually exposed " He He He2 . (3.103) and negligibly eroded, it is possible to date pre-Quater- He! nary landforms withstable and long-lived TCN ( He, Be, Ne, Al). For instance, well-preserved rock sur- Additional non-magmatic nucleogenic or radiogenic He faces in the Dry Valleys of Antarctica have yielded min- accumulates in the olivine after crystallization. This will imum exposure dates of '2.0 Myr, witherosion rates of be important for old lavas withrecent exposure ages, (1mm\ kyr (Brown et al., 1991; Nishiizumi et al., because the non-cosmogenic He will overwhelm the 1991a; Brook et al., 1993, 1995a; Ivy-Ochs et al., 1995; cosmogenic He. By measuring He in the same rock but Schaefer et al., 1999), although these ages may have at completely shielded depths it is possible to evaluate considerable uncertainty due to an Antarctic atmosphere this di$culty (Cerling, 1990). The method clearly works anomaly (Stone, in press). Rock surfaces in other climate best on rocks withyoung crystallization ages. regimes may undergo higher erosion rates, so the upper Retention of He is a more serious problem. Helium-3 limit is truly geomorphic process. The shorter-lived nucl- is quantitatively retained in olivine, pyroxene, and dia- ides C and Cl will reachsaturation after 20 kyr and mond (Kurz, 1986a, b; Lal, 1987b; Lal et al., 1989; 1 Myr, respectively, so can provide minimum age esti- Cerling, 1990). Retention of He in quartz is poor when mates and valuable information regarding erosion (Sec- ambient temperatures are elevated (Cerling, 1990; Trull tions 3.8 and 3.9). et al., 1991) and grain sizes are "ne, although success at The lower limit of exposure dating is controlled mainly using He in cold regions has been reported (e.g. Brook by the combination of production rate and analytical and Kurz, 1993). detection limit (i.e. it is a function of nuclide and site location). For instance, He is ideal for dating young 3.10.2. Beryllium-10 lavas because it has the highest relative production rate In the last "ve years especially, cosmogenic Be has (P&116 atoms g\ olivine yr\) and nucleogenic He been used in a wider number of applications than any has not become signi"cant (Kurz, 1986a; Cerling and other TCN. This is partly due to the relatively well- Craig, 1994a). Even Be (P &6 atoms g\ constrained production rates (only He is better con- quartz yr\) has been used successfully to date late Holo- strained) and partly due to the ability to measure Al in cene cirque moraines (Gosse, 1994) at high elevations the same sample. (Although Al can provide a valuable (P at 3500 m &60 atoms g\ quartz yr\). Shorter- internal check on the Be measurement, see above (Sec- lived TCN suchas CandCl will also have a shorter tion 3.9) for a discussion on the perceived use of the retention of inherited concentrations which may be advant- Al/Be method). In situ production systematics have ageous for rocks expected to have been previously exposed. been discussed throughout Section 3. The most impor- tant of the non-cosmogenic (nucleogenic) Be reactions 3.10.1. Helium-3 is from low-energy -particle interactions with Li. How- The selection of the He method over others requires ever, except in materials containing unusually high con- two considerations: (i) like Ne, it can have a signi"cant centrations of Li, U, and Th, the nucleonic production magmatic component that is contained mostly within rates are generally too low to produce signi"cant back- melt and #uid inclusions; and (ii) because it is a gas, it can ground concentrations (Brown et al., 1991). Cosmogenic di!use out of the target mineral. The (non-cosmogenic) Be is abundantly produced in the atmosphere by spal- magmatic (or trapped) He can either be primordial or lation of oxygen and nitrogen and thence deposited on from nucleogenic or radiogenic production after crystal- the land surface or in marine sediments (Brown et al., lization. Non-cosmogenic He may be produced from 1989, 1992b). Meteoric Be derived from recycling of beta decay of H; indirectly from -induced n- and p- marine sediment through subduction zones may be interactions (particularly radiogenic thermal neutrons on found in some island-arc volcanic rocks at signi"cant Li) and low-energy -particles on B (Morrison and levels (Brown et al., 1982; Morris, 1991). Meteoric Pine, 1955; Lal, 1987b, 1988); from primordial He (Craig Be can also in"ltrate even dense rocks and adsorbs and Poreda, 1986; Kurz, 1986a; Lal, 1987b; Cerling and strongly to the surfaces of mineral grains. During sample Craig, 1994a); and atmospheric He. The magmatic com- preparation, mineral separates must undergo rigorous, 1532 J.C. Gosse, F.M. Phillips / Quaternary Science Reviews 20 (2001) 1475}1560 repeated partial dissolutions in HF in order to remove Because of its short half-life, the use of in situ this meteoric component, which is often much larger C decays quickly and therefore attains saturation faster than the cosmogenic component (Kohl and Nishiizumi, than the other TCNs. This renders it useful to character- 1992; Klein et al., 1997). Stepped leaching experiments ize average erosion rates for the short term, and o!ers the have been conducted to determine the amount of leach- ability to e!ectively use TCN ratios for short exposure ing required to remove the atmospheric Be (Brown et histories (Section 3.9). al., 1991; Kohl and Nishiizumi, 1992). Attempts have been made to measure in situ Be in 3.10.4. Neon-21 whole rock, or mineral phases other than quartz and The in situ cosmogenic Ne production has been olivine for Be measurement, but the results have not discussed earlier (Sections 3.3.1 and 3.6.4). Its uses are been encouraging. Klein et al. (1997) showed with in- similar to the other noble gas He, but its relatively lower cremental leaching of whole rock that granites, dissolved di!usivity in quartz provides a signi"cant advantage. to the extent that more than 35% of the original When electing the use of Ne, its three non-cosmogenic mass was lost, still contained more than 3 times the sources should be considered: a component from the concentration of Be measured in thoroughly treated atmosphere and undegassed mantle (Niedermann et al., pure quartz from the same rocks. Even after 90% leach- 1993; Sarda et al., 1993; Phillips et al., 1998); a primordial ing, the concentration of one rock never stabilized (a MORB-like component (Staudacher and AlleH gre, 1991, plateau was seldom obtained in whole rock basalts or 1993; Niedermann et al., 1993; Sarda et al., 1993); and tu!s, although based on comparative ages rocks with nucleogenic reactions on oxygen, sodium, and magne- a signi"cant desert varnishcoating contained less me- sium, especially in minerals withhighU concentrations. teoric Be). This experiment indicated that unless there Like He, even at common levels of U and Thconcentra- is signi"cant varnishcover thatprotects rocks susceptible tion, su$cient nucleogenic Ne can accumulate over to weathering, many felsic and ma"c rocks can never be periods of millions of years to create major background su$ciently cleaned of atmospheric Be. Ivy-Ochs et al. problems in relatively old rocks even withshortexposure (1998) attempted to isolate in situ Be from pyroxene, histories (Niedermann et al., 1993, 1994). Neon-21 is but were unable to reliably remove the meteoric compon- therefore best suited for application to relatively young ent. At least three non-quartz phases have been analyzed: volcanic rocks, which have not had time to accumulate olivine (Nishiizumi et al., 1990; Kong et al., 1999), one large amounts of nucleogenic Ne (e.g. Poreda and known instance of Be in feldspar (Graham, R., pers. Cerling, 1992), or in rocks withvery low U and Th comm.), and magnetite (Lal, D., pers. comm.). concentrations, suchas ultrama "c volcanics (Staudacher and AlleH gre, 1991). Neon-21 does not appear to share 3.10.3. Carbon-14 with He the problem of rapid di!usive loss from most The ability to precisely extract in situ C from min- minerals and Ne is retained well by quartz (cf. Phillips erals has only recently been demonstrated (Handwerger et al., 1998). It also has the advantage that ratios of the et al., 1999; Lifton et al., submitted) although extraction three isotopes measured on sequential-heating steps can from ice was made earlier (Jull et al., 1994b). In addition be combined on a single plot to help separate cosmogenic to the previously discussed in situ cosmogenic produc- Ne from the non-cosmogenic contributions (Graf et al., tion, nucleogenic C can be produced from radiogenic 1991; Niedermann et al., 1994). neutrons interacting with Ni and O in rocks and from radiogenic -particles on B (Barker et al., 1985; 3.10.5. Aluminum-26 Lal, 1987a), and radiogenic C has been detected from The major sample-related problem with Al is the the U decay series (Barker et al., 1985). Nucleogenic stable element background. Aluminum has only one production in rock, and hence subsurface background, of stable isotope (Al) which is abundant in most types of C is generally very low. However, C is produced at rock, swamping the Al/Al ratio to unmeasurably low a very high rate in the atmosphere from neutron absorp- levels unless the Al can be separated from virtually tion by nitrogen (Libby et al., 1949). This meteoric Al-free mineral separates. In situ Al is typically mea- C has proved very di$cult to reliably isolate from sured in tandem with Be in quartz because of the high mineral samples and this problem had inhibited routine native Al content in most other common silicates except measurement of in situ C (cf. Jull et al., 1994a). Muchof olivine (Kong et al., 1999). Aluminum-26 has appreciably this contaminating meteoric C may be introduced dur- higher typical nucleogenic production rates than Be, ing sample processing, rather than contained within the especially due to reactions on sodium (Sharma and sample. Initial applications of C were done in whole Middleton, 1989). This may create background problems rock samples from lava (Section 3.6.3) but due to chem- for young (in terms of surface exposure age) samples with istry and production rate considerations, ongoing devel- high U and Th. In contrast, meteoric Al production opment of this method is focused on quartz (Lifton et al., rates are quite low, due to lack of target elements in the submitted) and carbonate rocks (Handwerger et al., 1999). atmosphere, and Al thus does not share the severe J.C. Gosse, F.M. Phillips / Quaternary Science Reviews 20 (2001) 1475}1560 1533 potential meteoric contamination problem of Be. This ashof known age (Gosse, 1994; Klein et al., 1995; Ander- may make it the isotope of choice for measurements in son et al., 1996; Repka et al., 1997; Hancock et al., 1999; quartz of very young exposure ages or deep rocks. Zentmire et al., 1999). (2) Alluvial fans in semiarid and arid environments are too dry for radiocarbon-datable 3.10.6. Chlorine-36 material and too coarse for routine application of many Chlorine-36 is produced at moderate levels by nuc- other methods (Bierman et al., 1995b; Trull et al., 1995; leogenic neutron absorption by Cl, and also from Siame et al., 1997; Ayarbe et al., 1998; Brown et al., 1998a; -particle interaction with S and from nucleogenic Phillips et al., 1998). Since then, TCN experiments on neutrons with K (e.g., Bierman et al., 1995a; Fabryka- hillslope deposits (Kubik et al., 1998; Small et al., 1999), Martin, 1988). Cosmogenic production rates are much beachsediments (Trull et al., 1995; Gosse et al., 1998) and higher than other TCN (except He), so background soils (Heimsathet al., 1997, 1999) havebeen interpreted levels are usually a problem only for very young samples. to have variable success. It has been demonstrated that Nucleogenic Cl should routinely be accounted for in desert pavement clasts provide exposure ages that are calculation of surface exposure ages, and the approach of statistically similar to independent estimates of the land- Fabryka-Martin (1988) is usually followed for this pur- form age (see noteworthy paper by Wells et al. (1995), in pose. Chlorine-36 is also abundantly produced in the which pavements on lava #ows yielded ages similar to the atmosphere by spallation on argon. Fortunately, such Ar/Ar age of the lava #ow). Moraines are also alloch- meteoric Cl is strongly hydrophilic and can be re- thonous landforms, but because they typically show little moved from rock samples by simple grinding and water inheritance, and because large boulders are not subject to leaching (Zreda et al., 1991). This hydrophilic nature may mixing processes (see discussion below), they are in prac- possibly create problems by mobilizing Cl during tice more similar to bedrock outcrops. weathering. No evidence of such mobilization has been Exposure models for surface clasts on depositional found (Zreda et al., 1994), but further systematic invest- landforms are similar to models for bedrock surfaces if igation would be desirable. the sediment has not been vertically mixed. However, TCN measured in undisturbed subsurface sediments pro- 3.11. TCN dating of sediment vide much more information about the exposure history of the sediments and can signi"cantly improve the accu- A rapidly increasing number of studies are being pub- racy of the sediment chronology by minimizing the lished on use of TCN as a means of `calibratinga e!ects of surface processes (turbation, overturning, clast geomorphic process studies (e.g. Burbank et al., 1996; erosion) and inheritance. Gosse (1994) and Klein et al. Small et al., 1997; Fleming et al., 1999). In many cases, the (1995) used one or two subsurface samples composed of measurements are being made on sediments, not bedrock one to ten cobbles to date glacial outwashin theWind surfaces. These include application to geomorphic redis- River Range. Ages for the oldest terrace (Sacagewea tribution within soils (Anderson et al., 1996; Repka et al., Ridge Glaciation) were concordant withtheexposure age 1997), relationships between rates of soil formation and of the Sacagewea Ridge moraine. However, a large con- morphology of landscapes (Heimsath et al., 1997, 1999; centration was inherited from previous exposure and Small et al., 1999), rates of landscape denudation and resulted in ages that were too old for the ultimate quanti"cation of erosion and deposition within drainage (Pinedale) glaciation. Anderson et al. (1996) proposed basins (Brown et al., 1995b, 1998b; Granger et al., 1996), a means of using more than two subsurface samples: and ages of fans, terraces, and beachsediment (Gosse, concentration-depthpro "les. Later they (Repka et al., 1994; Bierman et al., 1995b; Trull et al., 1995; Siame et al., 1997) showed numerically that at least 20 clasts per 1997; Ayarbe et al., 1998; Brown et al., 1998a; Gosse sample were needed to reduce the e!ects of inheritance. et al., 1998; Hancock et al., 1999). The work by Granger Concentration-depthpro "les are based on the predict- et al. (1997) using multiple nuclides in cave sediment to able decrease in TCN concentration withdepthdue to determine the duration that the sediment became shiel- attenuation of secondary fast and thermal neutrons. ded from cosmic rays (&burial age') was discussed in Muogenic production has been ignored unless depths Section 3.9. approachabout 800 g cm \ where muogenic production There has been a growing trend since the early-1990s begins to dominate (Kim et al., 1999). The concentrations to use TCN to date alluvial deposits and other alloch- can be modeled to show the individual or combined thonous landforms. Originally there were two fascina- in#uence of erosion, burial, hiatuses in sedimentation, tions that drove this application. (1) Fluvial and changes in bulk density over time and depth (Fig. 25), glacio#uvial records in alpine environments older than and other factors for any Quaternary deposit (terraces, the limits of radiocarbon dating lack anything but rela- fans, beaches, colluvium, moraine). Curves can also be "t tive chronology with the rare exception of U-series to more complicated pro"le models involving thermal travertine ages, luminescence dates on samples that were neutron and muon production (Fig. 2a and b) (Ayarbe not completely reset, or some tenuous relationship with et al., 1998). 1534 J.C. Gosse, F.M. Phillips / Quaternary Science Reviews 20 (2001) 1475}1560
which deposited 200 cm of sediment 18 kyr ago. Multiple signi"cant episodic depositional events may therefore be identi"ed in the pro"le record where normal exponential decrease in concentration is punctuated. Field evidence (suchas buried soils our distinct "ning upward units) should be sought to support an interpretation of separate depositional events within a single section. With the exception of constant erosion, each of these histories produce curves that are distinguishably di!erent. Not shown is the uniform curve (Phillips et al., 1996c Type III) representing complete mixing of the sediments in a highly bioturbated or cryoturbated setting (but these areas can generally be recognized in the "eld and avoid- ed, Section 4.4). Combinations of these processes will clearly complicate the depth pro"le. A detailed soil and sediment stratigraphic examination, higher TCN samp- ling frequency, additional independent ages, and Monte Carlo simulations of the possible models can help pro- vide constraints for the interpretation of a compound scenario. Fig. 25. Depthpro "les for spallogenic Be showing the model concen- The work of Ayarbe et al. (1998)on eroding fault scarps tration for exposure scenarios described in the text. provides an example of the advantages of the depth- pro"le approach. The scarp is located close to Socorro, New Mexico. It showed 3.5 m of o!set and was about 15 m in width. Erosion and bioturbation had clearly Accompanied withdetailed interpretation of thesoils disturbed the surface in many areas, so subsurface samp- and sediment stratigraphy, the concentration-depth pro- ling was necessary. They measured Cl pro"les down to "le method is a powerful means documenting the depos- 3.5 m depthfrom a medial position on a fault scarp (the itional history of an allochthonous landform (Fig. 25). pro"le was sampled from the footwall of the fault, about Curve A (Fig. 25) is for the concentration of a spallogenic 1 m above the scarp itself). A pro"le was also measured at nuclide that is assumed to decrease exponentially (#at- a point about 30 m above the position of the fault on the tening in upper 20 g cm\ is ignored (Section 3.1.6) in an upthrown side, referred to as the `control pro"lea. At this ideal deposit that has not experienced signi"cant erosion location, the topography was relatively #at and soil data or aggradation and that has been exposed during a single indicated very little erosion. The samples were obtained exposure event 18 kyr ago (Phillips et al., 1996c Type I). If by collecting several kilograms of sediment (consisting of the sediments had inherited concentrations of TCN from coarse, poorly-sorted debris #ow material) and amalga- previous exposures (Sections 4.4 and 5.2), the concentra- mating '150 individual clasts in the 1.5}0.5 cm size tions would be higher (curve would be displaced to the range. Two samples were collected as geological blanks right of a curve representing sediment of the same deposit from the deepest position on the control pro"le and were without inheritance) and would not de"ne a simple ex- processed identically. ponential equation unless the amount of inheritance was Several characteristics of their results are noteworthy uniform with depth. Curve B is the model case where an (Fig. 26). First, the smoothness of the pro"les indicates 18 kyr old deposit was gradually eroded at a fast and that a su$cient number of clasts have been homogenized constant rate (5 cm/kyr\), although non-constant epi- to yield a consistent average inheritance for the deposit. sodic erosion can also be modeled (Section 3.9). The net This inference is strongly supported by the near-identical e!ect of erosion is that the concentration will be propor- values for the replicate process samples from the deepest tionately lower at all depths. Curve C represents a de- position on the control pro"le. Second, bothpro "les posit whose surface was continuously aggrading at a rate converge withdepthto a consistent `baselinea, which is of 50 cm/kyr\ beginning 18 kyr ago (Phillips et al., the inherited component, equal in this case to 10 atoms 1996c Type II). The progressively more recent sediments of Cl g\. This inheritance is quite substantial, equiva- on top are younger than the sediments below, and the lent to that which would accumulate from about 30 kyr linear depthpro "le is characteristic of a rapid constant of surface exposure. The control pro"le has a larger aggradation rate. Below 9 m depth, the pro"le would inventory of Cl and a smoothly exponential shape. again decrease exponentially. Curve D represents the Accounting for the inheritance, the exposure age for the situation where a fan was deposited 35 kyr ago, followed terrace surface is 175 kyr. The footwall pro"le shows by 17 kyr of stability, then a rapid aggradation event consistently lower inventories of Cl, as would be J.C. Gosse, F.M. Phillips / Quaternary Science Reviews 20 (2001) 1475}1560 1535
area;5 m (plus the surface area of reworked older alluv- ial fans;5 m). In steady-state cases, it is possible to predict the actual average concentration of inheritance. Where sedimentation rate (or hillslope erosion rate) is approximately constant over the duration of interest, the concentration of the inherited nuclides is simply propor- tional to the long term average catchment erosion rate (E), regardless of whether or not the regolith on the bedrock is being turbated, and regardless of the total exposure time after the steady state has been attained (Lal, 1991; Granger et al., 1996):
P N" . (3.104) E
Unfortunately, in many circumstances stripping events are episodic over climate timescales of 20 kyr, so this simpli"cation does not hold. For inheritance resulting from prior exposure on an old sedimentary surface before reworking, the sediment storage time may be too long Fig. 26. Depthpro "les of Cl concentration measured at two loca- (</E); and the total volume of stored sediment is too tions close to the Socorro Canyon Fault scarp. The control pro"le was large. Because there is no simple model for a non-steady- sampled topographically above the scarp, in a location with little state system, the signi"cance of inheritance must be erosion. Continuous curve illustrates calculated Cl concentration evaluated empirically by measuring the average TCN after 140 ka of exposure. Star indicates average Cl inheritance of clasts in deposit. Footwall pro"le was sampled 1 m above fault plane, in concentration integrated over the entire catchment basin location of maximum erosion. The e!ect of the erosion is seen in the (an expensive project) or by isolating the inheritance lower Cl concentrations in this pro"le. The Cl accumulation under from in situ production in the deposits eroded from the the eroding surface, shown by the dashed curve, was modeled using catchment basin. a topographic di!usion-equation approach. It may be possible to predict which sediment may carry high inherited components by studying the geomorphic processes prior to "nal deposition. For in- stance, catchment basin size, geometry, hypsometry, rock expected in an eroding position. It is matched fairly well type and fracture density, weathering rate and style, and by a pro"le calculated assuming a steady 6 mm/kyr duration and frequency of precipitation events will in#u- erosion rate. This model is not strictly accurate, ence sediment production on the hillslope. Zentmire et al. inasmuchas geological evidence indicates multiple (1999) showed that modern outwash from the rupture episodes on the fault, but it clearly illustrates Matanuska glacier, Alaska, had no inheritance in "ve the sensitivity of depth pro"les to erosion. The study cobbles (all were indistinguishable from their chemical demonstrates that with appropriate sample processing, blank). This led them to suggest that it is favorable to TCN depthpro "les can overcome the inheritance prob- sample sediment from glaciated catchments when pos- lem and can yield information about geomorphic history sible, or at least seek to maximize the glaciogenic the and processes that would otherwise be very di$cult to component when sampling a bajada or terrace with mul- obtain. tiple source basins. Their rationale was that because In addition to the advantage of avoiding problems glaciers shield their substrate and are e$cient at eroding suchas turbation whicha !ects surface clasts, subsurface their beds, glaciogenic sediment will have on average pro"le sampling o!ers a powerful means of identifying a lower probability of pre-exposure than most non-gla- and quantifying inheritance. Exposure of sediment prior ciogenic sediment in adjacent catchments. The observa- to and during transportation will result in excess concen- tion that of more than 80 boulder measurements on tration of all TCNs proportional to the duration of moraines in the Wind River Range only two had indica- pre-exposure on the hillslope or, in the case of a steady- tions of inheritance (Gosse, 1994) supports their con- state system, the rate of long-term hillslope erosion. As clusion. Furthermore, the variability of multiple TCN described above, fast neutrons and muons can penetrate ages on alluvial surfaces withglaciogenic contributions regolithand bedrock on a hillslopeand produce measur- appears to be lower when a signi"cant portion of the able TCN to depths of 5 m (deeper for the less signi"cant alluvium is glacigenic (e.g. Bierman et al., 1995b) and muon #ux). The total sediment volume containing in- higher where no glacigenic component is present (e.g. herited concentrations is essentially the catchment Trull et al., 1995). 1536 J.C. Gosse, F.M. Phillips / Quaternary Science Reviews 20 (2001) 1475}1560
4. Sampling strategies 1995b, 1998b; Heimsathet al., 1997, 1999; Phillipset al., 1998; Small et al., 1997, 1999; Summer"eld et al., 1999)). The maxim that numerical ages are only as good as the Depending on the nuclide used, many sur"cial processes samples upon which they are based holds particularly can a!ect the TCN concentration during exposure (some true for TCN studies. When stringent sampling strategies nuclides are not as sensitive as others to certain pro- are invoked, fewer production rate adjustments and geo- cesses) (Section 5.2). Many boulders may exist on the metrical measurements will be necessary, and the result- crest of a moraine, but only a few may have been continu- ing decrease in random errors will signi"cantly improve ously exposed and never buried since the initial depos- the total precisions of the ages (Section 6, Fig. 27). The ition of the moraine. In addition to di!erent exposure objective of sampling is to collect and describe the at- histories of surface on a single landform, Gosse et al. tributes of a sample that precisely represents the expo- (1995c) demonstrated that on a single alpine moraine the sure history of a given landform (even if the landform is TCN ages may re#ect the timing of deposition. Boulders simply a narrow gully for which an erosion rate is on the front of the crest of the Pinedale (22 kyr) terminal sought). The following sections describe sampling strat- moraine were deposited almost 6 kyr before the boulders egies that are used in many TCN studies. Because the on the up-ice edge of the ridge. That trend shows that the sample strategy used depends on the nuclide-target se- age of a moraine may depend on the position of the lected (e.g. Ne in quartz) a fundamental knowledge of sample relative to the leading edge of the moraine. Di!er- the principles of each of the six TCN is also useful ent strategies will be used when attempting to determine (Section 3.10). &when the ice margin arrived at the moraine',or&the average moraine age' or &the timing of initial retreat'. This 4.1. Field sampling considerations sample-speci"c nature of TCN stands in contrast with many types of dating (e.g. the position of a sample within Sample relevance: TCN studies typically seek to relate an unaltered basalt #ow should minimally a!ect its K}Ar cosmogenic nuclide concentrations to the timing of some age). Careful posing of the geological problem studied geological event (e.g., a glacial advance (Gosse et al., and consideration of the geomorphic processes are im- 1995a; Phillips, 1996), mass wasting (Kubik et al., 1998; perative to selecting relevant samples. Potential sample- Cerling et al., 1999), #ooding (Cerling, 1990) or to some to-sample variability provides a strong argument for geomorphological process rate (e.g., denudation rate or collecting multiple samples (Section 6.2.3). soil formation rate (Albrecht et al., 1993; Brown et al., Surface geometry: The ideal geometry of a rock or landform surface for TCN exposure sampling is one that can be characterized as su$ciently extensive, #at, and horizontal. Su$ciently extensive means that a sample can be collected at least 50 cm from an edge or second face. Edge e!ects are most signi"cant for TCN that are produced in part through thermal neutron capture (such as Cl and Ca). Flatness is desired because complic- ated geometries require adjustments for self-shielding or changes in the e!ective cosmic ray #ux (Section 3.7). Modeling the cosmic-ray #ux on a horizontal surface is straightforward whereas dipping surfaces require adjust- ments for foreshortening e!ects because the total ray #ux (particles m\) is less than that on a horizontal surface (Section 3.7.2). Eachof theseadjustments require addi- tional measurements and calculations which have in- herent uncertainties. The e!ort involved in "nding an ideal surface geometry on a landform will be compen- sated by fewer required measurements and a greater precision and accuracy. Variance among multiple sam- Fig. 27. TCN precision based on multiple ages on a single landform. Filled circles are Be measurements on freshgranitic boulders with ples can help validate surface geometry corrections. heights above ground '1.2 m on a single moraine at 3200 m asl; coe$cient of variation is 4.8% (Gosse et al., 1995a). Open circles are 4.1.1. Sample description Be measurements on granodioritic boulders (H'2 m) withvarying In addition to the considerations related to the history degrees of weathering, on tightly nested recessional moraines of the of a particular sample, cosmogenic nuclide results will Half Moon Lake Lobe near Pinedale, Wyoming, 2300 m asl; coe$cient of variation is 4.6% (Gosse et al., 1995b). Measurements were done over also depend strongly on observations related to the two years withdi !erent but low chemical blanks (Be/Be averaged setting of the sample, inasmuch as the cosmic-ray (2;10\), at the University of Pennsylvania. `dosea depends on the sample geometry and surrounding J.C. Gosse, F.M. Phillips / Quaternary Science Reviews 20 (2001) 1475}1560 1537 topography. Unless accurate observations of these para- (7) Shielding geometry: To record sample shielding meters are made the interpretation of the "nal results will above the 2 horizon, set up a table (or circle) with be, at best, ambiguous. At a minimum, we suggest record- azimuthal intervals (e.g., 230}2903) of major features on ing the following: the skyline and the corresponding angle ($33) above the horizontal to the skyline. Alternatively, J. Klein has used (1) Rationale for sample selection: Why was this particu- a camera equipped witha "sheye lens can be leveled (so lar piece of rock selected? What is its postulated connec- that it is pointing vertically upwards) and the resulting tion to the event or process of interest? What evidence image digitized and processed to yield a very detailed indicates that it is superior to alternative samples? What shielding pro"le. In general, shielding of less than 53 is of items raise doubts about its utility? How does it compare negligible importance. Also describe vegetation canopy to other samples collected at the same site? (Section 3.5.5). (2) Description of object sampled: Size, shape, color, (8) Subsurface proxle samples: In the case of depth other distinguishing or possibly signi"cant character- pro"le sampling, describe the thickness of the layer sam- istics. Note the height of the sample above surrounding pled, the depth from the surface to the top of the layer, ground level; this is important when shielding by snow or average bulk density above eachsample (or integrated sediment is evaluated, and recent exhumation may ex- over multiple point measurements), average clast size and plain why a surface has a lower-than-expected exposure number of clasts sampled in eachlayer (agglomerates of age. Photographs and labeled sketches are useful when pea-sized samples are favorable), average rooting depth, attempting to revisit a site and in interpreting the "nal amplitude of relief by tree throw disturbance, sedimen- results. tary structures that allowed you to deduce that the sedi- (3) Description of sample material: Sur"cial texture (e.g., ment sampled was not turbated, soil characteristics that presence or absence of glacial polish, #uvial rounding, imply erosion, hiatuses, or burial (by eolian or #uvial projection of weathering-resistant inhomogeneities, dis- processes), and estimate the possibility of periodic snow solution features suchas gnammas and rillen, granular or loess cover. disintegration or `case hardeninga of the surface) is often an important clue to the history and stability of the 4.1.2. Sampling methodology sample. Note degree of weathering and lithology/min- Samples for TCN studies on rock surfaces are usually eralogy. Surface area covered by lichen may also be collected with a hammer and chisel (see below for samp- indicative of rate and style of erosion. ling strategies in alluvium). The hammer and chisel has (4) Location of sample: Both the location within the advantages of portability, simplicity, and reliability. The geomorphic setting (e.g., `just below the crest of a slightly main disadvantage is that some desirable sampling sites raised bed of gravel 20 m west of the bank of the paleo- on rock surfaces may not be amenable to this method #ood channela) and accurate geographic coordinates (in (quartzite, in particular). The portable drill and cuto! addition to latitude ($0.013) and altitude ($3 m), saw can sample in nearly any location on any rock. We longitude ($0.013) are also needed for exposures within have successfully used an airless jackhammer on quar- the last 10 kyr to adjust for dipole wobble and non-dipole tzites, which is an alternative to motorized equipment e!ects (Section 3.5.3) and to revisit the surface. Standard that requires fuel or lubricant. Unfortunately, the geographical latitude is used in calculating the geo- optimum least-weathered sites are often also the most graphical scaling factors (S and SI) for pre-Holocene di$cult ones to sample! exposures (longitude/latitude is thus the most convenient Given the choice, samples with no shielding have high- system of coordinates to use (Section 3.7.1). Longi- er priority over samples with shielding (topographic or tude/latitude in decimal degrees is more convenient for otherwise). The likelihood of blockage of the cosmic calculations than deg/min/s. Accuracy in elevation is radiation at some time in the past, even if the surface is muchmore important for calculation of production rates bare at present, also should be considered (Section 3.7.3). than is accuracy in `x}ya coordinates. In some cases, suchas snow cover, reasonable estimates (5) Orientation of sample: Dip and dip direction can can be made of the degree of shielding over the long term. be measured ($5) witha standard geological hand In general, sites that are located above the surrounding transit. topography, such as the tops of high boulders, are more (6) Sample thickness: In order to maximize the concen- likely to have been wind swept and less likely to have tration of the TCN and minimize the uncertainty due to experienced coverage than those in depressions. integrating the cosmic ray #ux through thick samples, Even after a particular location (e.g., boulder, outcrop, most TCN strategies use samples collected within the slab) has been chosen, the speci"c point of sampling must upper 2 cm of the surface. Note the sample thickness still be carefully considered. If possible, sites near edges ($1 cm) and whether it is variable or if it needs to be or corners of outcrops or boulders should be avoided trimmed in the laboratory. An exception is when depth because of complications due to cosmic-ray penetration pro"ling is conducted. from multiple directions and, in the case of Cl and 1538 J.C. Gosse, F.M. Phillips / Quaternary Science Reviews 20 (2001) 1475}1560
Ca, possible thermal neutron leakage (Section 3.7.5). Other considerations include di!erences in rock weather- ing from point to point and the sampler's evaluation of the distribution of surface erosion processes over the rock surface, suchas granular disintegration, spalling, and formation of dissolution pits. If possible, sample the rock as small chips rather than large chucks to avoid trimming and possible contamination in the laboratory.
4.2. Other lithological considerations
In addition to restrictions of lithology that the characteristics of a particular TCN may impose, the competency of the lithology must be considered when determining exposure ages. This is particularly true on surfaces expected to be exposed longer than about 50,000 years, on which even modest erosion rates of 1 mm kyr\ will begin to signi"cantly a!ect precision (Gillespie and Bierman, 1995). Interpretation of the TCN will be more Fig. 28. Possible e!ects of lithology on exposure dating. Measurements reliable if the e!ects of erosion can be minimized. With of Be and Al on 13 boulders (H'2 m) on the crests of broad Bull only a few exceptions, any rock type can have variable Lake-age moraine ridges of the Fremont Lake Lobe, Wind River competency withrespect to erosion, even in thesame Range, Wyoming. Lithology numbers are ranked in order of increasing outcrop. For example, granites may be very resistant or resistance to erosion and di$culty in sampling [(1) weathered plagioc- lase porphyroblastic granodiorite; (2) plagioclase porphyroblastic nearly saprolitized, depending on hydrothermal activity, granodiorite; (3) weathered granite; (4) fresh, unweathered granite]. climatic regime, history of glaciation, slope, and other These Bull Lake moraines are believed to approximately coincide with regional and local factors. Typically, the least erodable Oxygen Isotope Stage 6 glaciation. The correlations are weak, but the rocks tend to be more siliceous endmembers (e.g., aplites positive trends in the Al and Be ages indicate that the more and quartzites, but not diorites) and "ner grained. Grain resistant lithologies tend to erode less. The measured Al/ Be also decrease withdecreasing resistance to erosion. Withtheexception of size is perhaps more important than lithology. All at- inheritance, other geological factors that may cause variability should tempts should be made to collect from the same resistant be constant. Although samples were collected from di!erent recessional rock type unless other systematic uncertainties may arise moraines of the same glaciation, there is no correlation between age and (for example, the e!ects of inheritance may be reduced if stratigraphic position. multiple lithologies are used). The e!ects of slightly di!er- ent lithologies on TCN exposure ages of 13 boulders on enable measurement at the desired level of con"dence. ca. 150 kyr-old moraines in the Wind River Range, The minimum amount of sample required is not "xed Wyoming were shown by Gosse (1994) to be minor but and varies depending on TCN used, exposure duration, distinguishable (Fig. 28). Although other factors in- site e!ective production rate, proportion of the mineral cluding stratigraphic position and inheritance may phases sought, and nature of the analysis. A detailed contribute to the observed scatter, there is a clear but review of the latter is beyond the scope of this paper. The statistically weak trend. Due to the potential for variable reader is directed to reviews of AMS and gas mass meteoric contamination, whole rock samples and less spectrometry published elsewhere (Litherland, 1987; Tu- resistant minerals exposed to prolonged weathering niz and Klein, 1989; Tuniz et al., 1991; Finkel and Suter, should be avoided if possible * a catch22 situation if the 1993). objective is to determine the history of a weathered Before sampling, it is useful to calculate approximately surface. how much sample will be needed. Consult with the ana- lytical facility to determine the detection limits for geo- 4.3. How much sample is needed ? logical samples. It is also necessary to determine what level of reliability is required to address the question Rarely does the "eld sampling situation a!ord an being posed. If the goal is to distinguish between a lava endless supply of ideal samples characterized by suitable that was emplaced 1 Myr ago and 50 kyr ago, or if it is lithology and ideal geometry. Although extra sample is only necessary to determine the relative ages of two or useful for replicate analyses or sharing with other investi- more samples, then lower precision may be tolerated and gators, time, availability of suitable surfaces, and limita- a smaller sample mass may su$ce. However, if, for tions on transport of samples usually limit the collection example, the goal is to distinguish between moraines of of excess sample. The goal is to collect enough mass so 15 kyr and 12 kyr, larger samples are needed to attain the that su$cient nuclides can be extracted or released to required level of precision. In the case of Be, most of the J.C. Gosse, F.M. Phillips / Quaternary Science Reviews 20 (2001) 1475}1560 1539
Table 5 How muchsample is needed?
An example for cosmogenic Be from an estimated 20 kyr-old granitic surface on an Arctic shoreline
Estimated surface exposure age 20,000 yr Site production rate (adjust for shielding, uplift, erosion) 5.1 atoms Be per g qtz / yr ( Est. conc. of Be in quartz (ignore decay if sample age 0.03T12 ) 102000 atoms Be per g qtz Desired minimum AMS Be/Be 5;10\ atoms Be / atoms Be Desired mass BeO used (for 1hour analysis) 1 mg Number Be atoms in 1 mg BeO (assuming pure BeO): (0.001 g BeO ) 9/25 g Be/g BeO) / 9.0 g/mol ) 6;10 atom/mol" 2.4;10 atoms Be /in 1 mg BeO Number Be atoms needed for desired ratio: 5;10\ Be/Be 2.4;10 atoms Be /mg BeO " 1.2;10 atoms Be from the qtz Mass of pure quartz to dissolve: 1.2;10 atoms Be / 102000 atoms Be per g qtz " 11.8 g pure qtz 40% of the quartz is lost to remove meteoric Be 11.8 / 60% " 19.7 g qtz Rock only contained 10% quartz 19.7 / 10% " 197 g rock Only 40% of crushed rock has the proper grain size 197 / 40% " 500 g rock from site
These are minimum estimates. Additional sample will be needed for thin section and duplicate chemistry if necessary, and accidental wastage. best chemical blanks have Be/Be that are equal or gas TCN have the signi"cant advantage of requiring only (typically) greater than 2;10\ (sources of Be include a few grams of the target grains, although a few hundred the carrier, solutions, and airborne particles added dur- grams of rock are often needed to obtain those grains. ing chemistry). The detection limit for Be also varies withdi !erent accelerator mass spectrometer. Klein et al. 4.4. Strategies for concentration-depth proxles (1982) indicated that their machine required on the order of 4;10 atoms of Be to be loaded (in order to get 400 Muchof thepreceding discussion on sampling proced- counts for reasonable reliability, assuming detection of ure applies to both autochthonous and allochthonous 1/10000 Be at a sputter rate of 1 mg\ and the willing- surfaces. However, there are two signi"cant di!erences ness of the AMS facility to run for 1 h), but detection between sampling bedrock outcrops and sampling sedi- limits have improved since that time. Table 5 gives an ment: (1) the sediment is subject to vertical mixing near example of how to calculate the amount of rock sample the surface by a variety of turbation mechanisms required to make a 1 mg BeO sample witha comfortable (cyroturbation, bioturbation, pedoturbation); (2) because Be/Be of 5;10\. Alternatively, the forward ap- sediment is allochthonous, it is possible that the indi- proachcan be useful to determine howmuchBe-carrier is vidual clasts contain TCN inherited from previous expo- needed when the mass of the sample is limited. If the sure (muchas incompletely reset luminescence dates have required mass of rock sample is larger than permissible an inherited component). Sampling strategies for sedi- under stringent sampling strategies (i.e., you would have ment have evolved to reduce the e!ects of these sources of to sample on a steep slope), then a smaller AMS sample error from pre- and post-depositional processes. (e.g., 0.5 mg) can be produced by adding less carrier. Samples are selected where sedimentary structures in- However, a smaller sample means shorter run time before dicate there is no mixing (e.g., original #uvial bedding or the sample is completely sputtered (and therefore in- imbrication is preserved). Where unambiguous sedimen- creased Poisson error). A similar calculation can be made tary structures are absent, pedogenic features can be used for other isotopes. to determine if mixing has occurred. The presence of Nuclide-speci"c considerations can strongly a!ect the buried or complicated soils can indicate if there has been size of sample required. One of the most signi"cant accumulation or stripping, and these locations should be considerations is the abundance of particular mineral avoided if possible. The depth of the shallowest sample phases required for the analysis of speci"c nuclides. For beneatha forested surface will be controlled by theaver- example, 500 g of relatively pure quartzite may be pret- age tree rooting depthand may be greater than reated for a Be analysis, whereas 5 kg of rock may be z"100 cm. Areas of high relief knoll and cradle topogra- needed for the analysis of a "ne-grained quartz-poor phy from treethrow should be avoided because of the latite of the same age. Whole rock Cl analyses can di$culty in establishing the long-term sample depth. If routinely be performed on rock samples of 500 g or less unavoidable, the temporally varying relief and bulk den- because mineral separates are not required. The noble sity (organic material, compaction) may contribute 1540 J.C. Gosse, F.M. Phillips / Quaternary Science Reviews 20 (2001) 1475}1560 signi"cantly to the random error of a calculated age thonous landform. Notwithstanding the added insight (Section 6.1.1). into depositional history, the method remains prohibi- There are several sampling approaches to estimate the tively costly to determine the age of multiple surfaces of amount of inheritance in the sediment. (1) One approach similar or di!erent ages. In suchinstances, soil chrono- is to collect surface samples in proximal modern sedi- sequences tied to fan chronology may be the only means ments (modern shoreline, active #oodplain, active wash) to date multiple surfaces of a large region. Recently, that share the same catchment as the sediment being Gosse and McDonald (unpublished data) have shown in dated. If the concentrations are non-zero, the inherited the Amargosa Valley that it may be possible to use just concentration can be subtracted from the TCN concen- two aggregate samples (one surface sample on pavement tration in the studied deposit. Unfortunately, in non- and one subsurface sample below the mixing zone) to steady-state conditions the amount of inheritance will date alluvium older than about 50 kyr. (The inherited vary over time, depending on the frequency of the major component will compose a larger proportion of the total aggradation events. (2) A second approachinvolves col- measured concentration of younger and deeper sedi- lecting samples that are well below the penetration depth ment.) If the samples are in reasonable agreement, de- of fast neutrons, where the sediment has remained pending on the precision required, then these can be used shielded. This approach assumes that the shielded sedi- as a maximum age estimate (of, if the inherited compon- ment was deposited approximately concurrently withthe ent is known or negligible that will represent an average overlying sediment (i.e. it is the same depositional event). age estimate). This method does require shallow burrow The amount of inheritance in the deeper sediment may pits (generally (1.5 m) but avoids the need for deeper also be systematically greater than the inheritance in the pits and multiple analyses at one site, so that time and shallower sediments. This will occur if erosion proceeded money can be spent analyzing multiple surfaces corre- in layers, so the deeper sediment in the section originally lated on the basis of geomorphology and soils chrono- composed the top of the regolith and received a higher sequences. cosmic-ray dose. (3) Collecting multiple samples along a vertical transect in undisturbed sediment to measure the `concentration-deptha pro"le, constitutes a third ap- 5. Sample preparation and experimental data proach(Anderson et al., 1996). Samples containing in- interpretation herited components will have anomalously greater concentrations than the others for a given depth. A com- 5.1. TCN sample preparation bination of (ii) and (iii) is useful in the case that all samples have an inherited component. The goals of sample preparation are to purify the "eld Ideally, a natural or anthropogenic vertical section specimen of materials not suitable for analysis, to con- beneatha stable #at surface should have su$cient depth centrate the nuclide of interest su$ciently that it can be to enable access to shielded sediment (e.g. (1% produc- accurately analyzed, and to transform the sample mater- tion at the surface at 5 attenuation lengths, or approxim- ial into a form suitable for analysis. The sample prepara- ately 3.3 m in gravel with "2gcm\ assuming tion consists of two parts: (1) a pretreatment phase in " \ 130 g cm ). Subsurface sampling requires which target minerals are separated, concentrated, and measurement of the bulk density of the shielding material puri"ed; and (2) an isotope extraction phase in which the above the samples. If the sample density varies signi"- isotopes are isolated from the minerals and separated cantly (e.g. due to di!erences in soil parent material such from non-in situ cosmogenic isotopes. From start to as loess and gravel, di!erent grain sizes, or variable "nish, the highest priorities must be given to safety, waste pedogenic carbonate development), multiple measure- minimization, sample labeling and data recording, and ments of density will be needed to precisely compensate the minimization of contamination. for the variability. The number of sample agglomerates The nuclide concentrations are measured using either collected will depend on the level of precision desired and gas mass spectrometry (for the noble gases) or accelerator on the complexity of the sediment exposure history. mass spectrometry (AMS) (Litherland, 1987; Tuniz et al., Based on numerical simulations (Repka et al., 1997) 1991; Finkel and Suter, 1993; Synal, 1995). Ancillary a minimum of 20 similarly sized clasts should compose analyses are necessary to determine the concentration of eachagglomerate in order to signi "cantly improve pre- the rock matrix, the TCN element (e.g., Be or Al), the cision. Ayarbe et al. (1998) showed that samples com- target elements, or the concentration of radioactive ele- posed of '100 pea-sized clasts have averaged the ments in the rock which may produce non-cosmogenic inherited component at each depth, and Phillips et al. nuclides. These ancillary analyses are often done with (1996c) showed that sand-sized fragments may also be ICP.AES (Moore, 1989), ICP.MS (Montaser, 1998), reliable. atomic absorption (Welz, 1999) or similar analytical Depthpro "les of three or more samples are expensive methods. The detailed procedures required to prepare and laborious means to estimate the age of an alloch- samples for the gas MS or AMS and ancillary analyses J.C. Gosse, F.M. Phillips / Quaternary Science Reviews 20 (2001) 1475}1560 1541 are nuclide-speci"c and are too involved to include in this a single mineral phase; (2) the removal of non-cos- review article. However, this section provides a general mogenic nuclides from that phase. Mineral separation survey of approaches and practical issues in TCN sample can be completed withcombinations of magnetic or preparation. electrostatic separation (Franz Magnetic Separator, or Carpco separators), heavy liquid separation (e.g. reusable 5.1.1. Preparation time lithium metatungstate in a 1 L separatory funnel), hand The amount of time required in sample preparation picking to cull grains or remove unwanted phases with varies widely, depending on the nuclide, its concentra- tweezers under a dissecting binocular microscope, and tion, rock lithology, and the laboratory schedule. The selective chemical dissolution by di!erential leaching of noble gases He and Ne typically require careful isola- silicates. The latter involves a mixture of HF and HNO tion of speci"c mineral phases (e.g. olivine, pyroxene, or in hot ultrasonic baths (Kohl and Nishiizumi, 1992) or quartz) which can take weeks and may involve hand pyrophosphoric acid. These partial leaching methods picking. Once isolated and cleaned, the samples do not o!er the advantage of selectively dissolving the unwanted require chemical preparation before analysis. The other mineral phases while removing contaminating nuclides TCN ( Be, C, Al, and Cl) can require more than (suchas atmospheric Be adhered to fracture surfaces in four weeks for sample preparation because of the time the quartz grains). Examples of equipment used for selec- necessary to concentrate the target mineral phases tive dissolution include an acid digestion fumehood, 25- (quartz or other desired minerals) from the sample and gallon ultrasonic tank withheaterand water level safety the time to extract the radioisotopes from the minerals switch, and a means for acid neutralization. It has been and prepare them in a form suitable for AMS analysis. demonstrated by partial leaching experiments that at The mineral concentrations for these TCN are usually least 30% of the quartz must be dissolved to su$ciently never 100% pure because of the cost and time involved in remove the atmospheric Be (Brown et al., 1991; Kohl separation of large masses (often '20 g quartz is de- and Nishiizumi, 1992; Klein et al., 1997). The optimum sired). Also, it is di$cult to remove all of the feldspar grain sizes of the minerals used depend on the isotope content from myrmekite, poikilitic quartz, or ophitic extraction procedure. pyroxene. However, the mineral purity can be veri"ed to meet reasonable limits based on, for example, Al concen- 5.1.3. Isotopic extraction tration, staining for Ca or K, petrography, and other Following mineral separation and puri"cation, sam- qualitative tests. Samples for the analysis of some nucl- ples require chemical or thermal isotope extraction in ides can be prepared in a week if mineral separation can preparation for analysis. The goal in extraction is to: (1) be avoided (although presently only Cl is measured in collect as much of the TCN as possible; (2) separate the whole rock samples). Samples with low TCN concentra- TCN from non-cosmogenic nuclides (e.g. radiogenic or tions may require more mass which generally increases nucleogenic) or nuclides that were not produced in situ preparation time mostly due to the time it takes for (e.g. atmospheric); (3) separate the TCN from any dissolution. Low target mineral abundance (e.g. many possible isobars (isotopes of the same mass, e.g. Bisa basalts have (1% olivine phenocrysts) will also in- signi"cant isobar of Be which can make the mass crease preparation time because more of the original spectrometry of Be di$cult); and (4) transform the rock must be processed (Section 5.1.2). sample into a form that is suitable for analysis (e.g. Be and Al are precipitated as oxides, Cl as AgCl, Cas 5.1.2. Physical and chemical pretreatment graphite). Most of the samples have splits that are ana- Samples are washed or brushed to remove undesirable lysed for elemental concentrations (especially radioactive organics, carbonate, and dust. If the samples were not parents, native Al, Be, and Cl concentrations). Only sim- reduced in size in the "eld, they are broken into frag- pli"ed extraction procedures are outlined below and ref- ments suitable for crushing (collecting chips ((9cm) erences to published procedures are provided. rather than large pieces in the "eld is recommended to The chemistry-intense extractions of Al and Be are avoid this step in the laboratory). The samples are similar and so are generally conducted concurrently crushed, ground, and/or pulverized and sieved to a pre- (Nishiizumi et al., 1989; Brown et al., 1991; Nishiizumi determined grain size (sample- and nuclide-speci"c). Typ- et al., 1991a; Kohl and Nishiizumi, 1992; Ivy-Ochs, 1996; ical laboratory equipment for the physical preparation Ochs and Ivy-Ochs, 1997; Stone, 1998). A pre-determined includes a jaw crusher, cone crusher, disc pulverizer, mass (10}100 g, depending on the expected TCN concen- and/or shatter box, sieves and sieve shaker, and the tration) and grain size (e.g. 250}350 m fraction) of pret- cleaning equipment necessary to ensure safety and pre- reated quartz is used. To the quartz or quartz solution is vent cross contamination. added a known mass of the native element with negligible Mineral puri"cation is a necessary pretreatment for or known TCN concentration. In some samples there most analyses (except whole rock Cl). This aspect of is a su$cient amount of the native element naturally pretreatment involves two steps: (1) the isolation of present so no spike is added. Elemental analysis of the Al 1542 J.C. Gosse, F.M. Phillips / Quaternary Science Reviews 20 (2001) 1475}1560 and Be by ICP.AES or similar means is necessary to 1991), thermal isotope extraction method for Cin determine the amount of native element present in each quartz has only recently been developed (Lifton et al., sample (in addition to any carrier added). The presence of submitted). It does not involve the laborious chemistry of a known concentration of native element allows for the the other cosmogenic radioisotopes but does involve undesirable but usually unavoidable case when less than extensive care in keeping gas lines void of carbon con- 100% of the TCN is carried through the extraction tamination. Lifton et al. (submitted) used a step-heating chemistry, because only the ratio of the native element to method (analogous to the noble gas procedures) to re- TCN need to be determined by AMS. This isotope dilu- move the CasCO. A LiBO #ux is used to facilitate tion strategy is similar to the addition of eucalyptus or melting. The more loosely bound non-in situ cosmogenic other foreign pollen to subsamples collected for pollen CO is released at lower temperatures. The subsequent counts. Next, selective precipitations are conducted to cosmogenic CO is then graphitized and analysed by remove unwanted elements (e.g. Mg, Ca). Ion chromatog- AMS. A new method of extracting in situ cosmogenic raphy is conducted with anion and cation exchange C from carbonates uses cryogenic methods to separate \ resins, to separate solutions of Be and Al from Fe, Ti and cosmogenic CO from CO and CO (Handwerger other cations. Then Al(OH) and Be(OH) are precipi- et al., 1999). However, this method has the disadvantage tated (Be can be precipitated withanhydrousammonia that it requires an assumption of the CO/ CO gas to preclude the introduction of boron from glass production proportion, which they estimated from storage bottles). The hydroxides are oxidized and ana- measurements in ice. lysed by AMS. The chemical extraction of Cl is simpler and less time 5.2. Experimental data interpretation consuming then Be, but involves additional elemental analyses to determine the concentration of radioisotope Unlike dating facilities for radiocarbon and Ar}Ar and sources of non-cosmogenic Cl (Zreda, 1994; Bierman most other dating methods, the laboratories that provide et al., 1995a; Ivy-Ochs, 1996; Stone et al., 1996). The the TCN mass spectrometric measurements generally do procedure is slightly di!erent for whole rock or mineral not interpret the data. This is because in addition to the speci"c analysis. For the whole rock procedure, 50}100 g mass spectrometry data, the interpretation requires con- of sample can be used. In general, the chlorine is extrac- sideration of additional data, including sample site char- ted by dissolving the pretreated sand-sized aliquot and acteristics and sample geometry, ancillary elemental precipitating as AgCl. Chlorine carrier may be added, measurements, sample preparation procedures, adjust- and selective precipitation further separates undesirable ments for non-cosmogenic components, and the scaled hydroxides. The isobar S is similarly separated by production rate parameters described above for each precipitating BaSO.The"nal AgCl precipitate is used individual sample. The normal model for cosmogenic for AMS analysis. nuclide applications is formulated under the assumption The noble gas samples are prepared di!erently than that the sample acts as a closed system, i.e., that the only the other TCN (Craig and Poreda, 1986; Kurz, 1986a, b; source of the nuclide is from in situ cosmogenic produc- Poreda and Cerling, 1992; Staudacher and AlleH gre, 1991, tion and that no cosmogenic nuclide is lost except 1993; Laughlin et al., 1994; Niedermann et al., 1994; through radioactive decay. Any concentration from Bruno et al., 1997; Phillips et al., 1998). The pure mineral non-cosmogenic sources needs to be taken into account agglomerates bearing the cosmogenic He and Ne are and subtracted from the total measured concentration. split in two. One aliquot of the sample is prepared for This section provides a description of routine steps used analysis of the radioactive elements using standard pro- to interpret cosmogenic nuclide data. Some common cedures (e.g. for ICP analyses). The main aliquot of min- assumptions in interpreting TCN data are listed in eral grains is used for the gas mass spectrometry and Table 6. requires no further chemistry. The samples are crushed in The concentration (NK ) of the nuclide of interest vacuo to release the inherited isotopes of He and Ne. By (suchas Be) is calculated from the isotope ratio (R)of step-heating in a furnace attached to a gas mass spec- the stable and cosmogenic isotopes, as measured by trometer, the non-cosmogenic He or Ne in the crushed AMS: samples can be further separated from the in-situ cos- mogenic gases by the low temperature heating because N " the former are generally weakly bound. However, there is N Rm /mORX. (5.1) A generally some remaining component of the higher tem- perature volumes that is non-cosmogenic which must be Once a measured concentration is calculated, the com- subtracted from the total concentration measured by gas ponent of concentration that is produced in situ in the mass spectrometry. mineral phase during the geologic event (t) being dated Although experimental procedures for C extraction needs to be determined. This can be involved, depending from whole rock were attempted earlier (e.g. Jull et al., on the isotope-mineral system involved and the exposure J.C. Gosse, F.M. Phillips / Quaternary Science Reviews 20 (2001) 1475}1560 1543
Table 6 Assumptions made for many applications of TCN
Assumption Basis of Validation Consequences
1. Primary GCR #ux has been No known long term variations greater than TCN production rates will vary if the primary approximately constant over measured &10%; supernovae explosions are short lived GCR #ux varied exposure durations events 2. Secondary radiation #ux is directed Empirical measurements in the atmosphere and TCN production rates will vary withthe downward but azimuthally isotropic experimental observations and simulations of orientation of the surface if the #ux is products of nuclear transmutations in uniform azimuthally anisotropic. "elds show that particle trajectories are azimuthally isotropic. < " # ' 3. The concentration of the atmospheric For certain nuclides, P2!, P ,soC is C C2!, C .IfC 0, then the cosmogenic nuclide in prepared negligible. Atoms of certain TCN are chemically calculated ages will be higher than actual sample is zero mobile and do not readily adhere to mineral surfaces. unless correction for the C is made. Incremental measurements can be taken to determine if the TCN concentration decreases asymptotically with acid leaching as the C is removed. " # ' 4. The concentration of radiogenic Magmatic He*/ He can be estimated; no signi"cant C C2!, C*.IfC* 0, then the (magmatic) nuclides is known or radiogenic pathways exist for some nuclides, although calculated ages will be higher than actual is zero most have at least a minor radiogenic component; the unless correction for the C* is made. abundance of U, Th and other alpha emitters can be measured in the sample (Middleton and Klein, 1987). " # ' 5. The concentration of inherited TCN No inheritance of TCN is possible if dating the time C C2!, C .IfC 0, is known or is zero since formation of extrusive rocks (e.g. tu!s, rhyolite then the calculated ages will be higher than or basalt #ows). Radionuclides will not be inherited actual unless correction for the C is from exposures that occur prior to &10;half life; made. inheritance can be estimated then subtracted from total C 6. Adjustments for spatial and temporal Computer simulations, empirical and experiment If corrections for spatial and temporal variations in P2!, are known and measurements to calculate production rates, variations in TCN production rates are correct. comparison of TCN exposure ages withindependent incorrect, all exposure history calculations will dates of the same event; empirical and experimental be systematically incorrect. veri"cation of Lal (1991) and other scaling factors. Geomagnetic paleointensity variations are less signi"cant withlonger exposure durations because they are integrated over longer time. Temporal variations in paleointensity do not a!ect sites '583 geomagnetic latitude, corresponding to the cuto! rigidity of 0 GeV. 7. Measured estimates of all parameters Thermal neutron cross sections for Cl, decay The magnitude and direction of the e!ects of are correct within assumed uncertainty constants for radionuclides, attenuation lengths for error in these estimates will vary. muons, high energy nucleons, and thermal neutrons, and the density of the atomic targets and the density of the rock can or have been estimated experimentally or empirically. 8. Simple and ideal exposure history Under some circumstances there has never been Snow, sediment, water, ice, and rocks that assumes no erosion continuous, measurable erosion of the bedrock surface (e.g. very shield the surface and have subsequently been uninterrupted exposure of a 2 young lavas). E!ects of low erosion rates may be removed will cause the total long-term P to surface. insigni"cant if the exposure duration is short. It is be less than P, and therefore N will be lower. possible to eliminate the possibility for burial or If erosion is signi"cant N will be lower and rolling in some circumstances, suchas a highvertical N , depending on e, may be higher or lower face. than the N if the surface is considered uneroded, i.e. it was not eroded to a depth of ¹.
history of the sample. In general; lost due to radioactive decay. NK is the concentration inherited from all previous exposure events minus any " # # H# L # NK NK NK NK NK NK , (5.2) concentration lost to radioactive decay. Examples of inheritance include exposures of rock on hill slopes be- where NK is the concentration of the cosmogenic isotope fore incorporated into beachsediment, till, or alluvial that is produced in situ in the target mineral during the gravels; short-term storage near the surface during trans- geologic event being studied, minus any concentration portation of sediment before "nal deposition, and even 1544 J.C. Gosse, F.M. Phillips / Quaternary Science Reviews 20 (2001) 1475}1560 exposure of sand grains during the Cretaceous may be in the troposphere is a factor of about 1000 times greater signi"cant if the sediment is ultimately sampled in than for in situ BeK. This is partly why terrestrial Be a Quaternary landform for analysis of a noble gas. measurements in multimineralogic samples is very di$- Subaqueous exposure of sediments and bedrock before cult (Klein et al., 1997) and seldom attempted, but why isostatic or tectonic emergence is another example of Cl, witha muchlower atmosphericproduction rate inheritance which should be considered when dating and relatively higher mobility, can be successfully mea- raised shorelines. Anderson et al. (1996) consider sured in whole rock samples. inheritance to include changes in sample depth during Eq. (5.2) assumes no loss of the nuclide other than by subsurface exposure due to bioturbation, pedogensis, or radioactive decay. This is important for the noble gases cryoturbation. However, we consider these mixing because the di!usivity is a function of mineral structure, processes as factors that alter the production rate size, and temperature. (increase or decrease) during the exposure event. This way inheritance will always increase the NK. An inherited component can be interpreted in three 6. Uncertainty and sources of error ways. (i) If there was a period of burial (e.g. by a glacier) between the inherited event and the "nal exposure event, Wiser sampling procedures, better chemical prepara- the ratio of two isotopes in the same sample will plot tion and analytical methods, and a better understanding below the exposure-erosion island. Although this method of the physical processes responsible for TCN production does not quantify the NK , it does help to establish the have signi"cantly improved the reliability of TCN expo- presence of an inherited component. (ii) Using multiple sure methods since their conception. The technique is TCN dates from a single landform surface, it may be now being used to isolate short-lived sur"cial geology possible to identity older &statistical outliers' which may events (e.g. late Pleistocene glacial advances separated by carry an inherited component. (iii) Single clast samples a few thousand years, correlated to Heinrich events and collected along depthpro "les through sediment with no the Younger Dryas epoch (Gosse et al., 1995a; Phillips, evidence of bioturbation, cryoturbation, erosion, or 1996; Ivy-Ochs et al., 1999). A few publications have burial may show considerable scatter if there is a measur- explicitly dealt withaspects of uncertainty in TCN able inherited component in the clasts. (iv) Depth pro"les methods. For instance, Gillespie and Bierman (1995) consisting of numerous aggregated clasts may yield con- calculated the total precision of single or multiple nuclide sistent values at depth that are in excess of that consistent ages (and erosion rates) considering uncertainties in half- within situ production (Phillipset al., 1996c; Repka et al., life, measurement precision, and the estimate of erosion 1997; Hancock et al., 1999). The magnitude of this excess (or exposure duration). They showed that while uncer- quanti"es the inherited component. tainty in age increases withexposure duration, theuncer- H NK and NK are non-cosmogenic components, respec- tainty in erosion rate improves withduration. Finkel tively, from radiogenic reactions (the nuclide is a direct and Suter (1993) discuss uncertainty related to AMS daughter product of a radioactive decay) or nucleogenic and is a recommended reference. Other articles report interactions (nucleons produced from neighboring radio- uncertainty in production and erosion using Monte active sources may interact withtarget atoms), and they Carlo simulations of error (e.g. Phillips et al., 1996c; are typically summed together. The radiogenic and nuc- Stone et al., 1998b), describe treatment of blank subtrac- leogenic contribution may be important for the noble tion for high blank proportions (Davis et al., 1999), and gases if the rock age is older than the exposure age or for calculate total age uncertainty from multiple measure- long exposures. Many sampling strategies tend to favor ments on the same landform surface (Gosse et al., 1995a). pegmatitic lithologies which carry higher concentrations However, no complete detailed evaluation of the sources of the large radioactive incompatible elements such as of error and total uncertainty in the in situ TCN methods U and other important target elements such as Li and B. has been published. The following review outlines com- In addition to the in vacuo crushing method to determine mon error sources (Table 7) that in#uence the interpreta- the relatively loosely bound non-cosmogenic noble gas tion of TCN data and suggests how to treat uncertainty. content (Kurz, 1986a, b), measuring completely shielded rock under the exposed surface can also determine the 6.1. Sources of error geological background of the isotopes. NK includes all concentrations of the nuclide that Error sources are classi"ed as random or systematic have been derived from any contamination of the sample errors. Measurement uncertainties and errors a!ecting with nuclides that have not been produced in the rock, precision are mostly random. Systematic errors a!ect the including meteoric components. The potentially large accuracy of the calculated ages and erosion rates. The atmospheric component in rocks limits the use of Be to uncertainty in accuracy continues to outweightheuncer- mineral phases that are resistant to weathering, because tainty in precision, but when comparing ages determined \ \ \ the production rate (atoms (g cm ) yr ) for Be with the same method (e.g. Ne dating), many of the J.C. Gosse, F.M. Phillips / Quaternary Science Reviews 20 (2001) 1475}1560 1545
Table 7 Sources of error for TCN methods
1. Random Errors (8%) 2. Systematic Errors (10%)
1.1 Sample characteristics (5%) 2.1 Radionuclide half life (3%) 1.1.1 Surface geometry correction (1%) 1.1.2 Shielding correction (1%) 2.2 Production rate (9%) 1.1.3 Thickness (2%) 2.2.1 Basic calibration (5%) 1.1.4 Meteoric contamination (0%) 2.2.2 Whole rock theoretical estimates (na) 1.1.5 Erosion rate and style (4%) 2.2.3 Nuclear cross sections (na) 1.1.6 Burial (0%) 2.2.4 Attenuation lengths (rock and atmos.) (3%) 1.1.7 Prior irradiation (inheritance) (0%) 2.2.5 Altitude scaling, Standard Atmosphere (5%) 2.2.6 Latitude and longitude scaling (5%) 1.2 Sample preparation and analyses (3%) 1.2.1 Sample interchange (0%) 2.3 Temporal variations (3%) 1.2.2 Contamination from physical processing (0%) 2.3.1 Cosmic ray #ux (0%) 1.2.3 Weighing of sample (2%) 2.3.2 Solar modulation (0%) 1.2.4 Addition of carrier (2%) 2.3.3 Geomagnetic polar wander (0%) 1.2.5 Contamination withnon-target minerals (na) 2.3.4 Geomagnetic paleointensity (3%) 1.2.6 Analysis of stable isotope (1%) 2.3.5 Non-dipole uncertainties (0%) 1.2.7 Other major & trace elemental analyses (na) 2.3.6 Atmospheric thickness variations (0%)
1.3 Mass spectrometric measurement (4%) 2.4 Stable element measurements (2%) 1.3.1 Poisson (3%) 1.3.2 Background subtraction (0%) 2.5 Carrier and standards (2%) 1.3.3 Blank correction (0%) 1.3.4 Sample reproducibility and normalization (3%) 2.6 Fractionation, spectrometry (0%) 1.3.5 Precision of standard (1%) 1.3.6 Correction for non-cosmogenic gases (na) 2.7 Other assigned constants (0%)
2.8 Calculation errors (0%)
Error magnitudes (1) are based on estimates calculated by J. Klein (pers. comm., 2000) for "fteen Be exposure ages from quartz in boulders on a broad terminal moraine ridge approximately 22 kyr old, at 2250 m elevation, 433N latitude, using carrier manufactured from a shielded beryl, with blank less than 5% of the measured ratio for the unknowns. Boulders average 1.8 m high, were probably not covered by signi"cant snow or sediment, and rest on the crest of the moraines so are not shielded. Samples were less than 5 cm thick and were collected with chisel and hammer from the middle of #at-topped boulders. (na) indicates the error does not apply to Be TCN dating. systematic errors can be ignored (i.e. 2.1}2.3 of Table 7). calculated age due to sample attributes is low (e.g. error Although some error sources are common to all six in measurement of surface slope, shielding, and thickness TCNs (e.g. the uncertainty in spatial scaling for spal- of the sample will unlikely contribute more than 2% logenic production), there are uncertainties that are uncertainty (Section 3.7). In some instances, a parameter unique to individual nuclide systems and individual sam- assumed to be negligible may be non-zero (e.g. unrecog- ples (e.g. the thermal neutron cross section for Cl, or nized burial, which will decrease N, inheritance, and the geometrical correction on a self-shielding surface). meteoric contamination of a weathered rock). In these The magnitudes of errors (%) reported in Table 7 are cases, the error is guessed. Erosion rate and style (e.g. based on Be measurements in 1993 and 1994 at the dissolution, grain-scale, block-scale, gradual, episodic) University of Pennsylvania but can be calculated for can signi"cantly in#uence the reliability of calculated other nuclides, laboratories, and sites. Unless otherwise exposure ages if the amount eroded (Z) approaches the indicated, all uncertainties here are reported at the 1 e!ective attenuation length( ) (e.g. for spallogenic nucl- con"dence level. The total uncertainty in the age re- ides, about 140 g cm\, but muogenic nuclides are not as ported in Table 7 can be represented as sensitive) (Gillespie and Bierman, 1995; Lal, 1996). Esti- mates of inherited concentration of TCN from prior random#systematic "13%. (6.1) exposure have been attempted using deeply shielded samples, samples from modern wash(Brown et al., 1998a), and the depth pro"le method (Anderson et al., 6.1.1. Sample characteristics 1996; Phillips et al., 1996c; Repka et al., 1997; Hancock The random sources of error associated with sample et al., 1999). characteristics are calculated using equations provided The e!ect of meteoric contamination will be di!erent throughout this review article (Table 7). With the excep- for eachsample (Section 4.2). Signi "cant concentrations tion of erosion, the contribution to the uncertainty in the of cosmogenic nuclides are produced in the atmosphere 1546 J.C. Gosse, F.M. Phillips / Quaternary Science Reviews 20 (2001) 1475}1560
(e.g., C from N, 10Be from N and O, and Cl as a function of the number of counts (cf. Eq. (6.3)). In from Ar) at rates that in some cases are greater than AMS the number of counts for the cosmogenic isotope &10 times their terrestrial production (Brown et al., will vary considerably, depending on run time (8}60 min), 1989; Morris, 1991). If pure quartz is used, meteoric beam current (10}20 A of current is achieved for in situ contamination should be negligible. Less resistant min- Be) and most importantly, the concentration of cos- erals, especially clays, tend to be strong sinks of meteoric mogenic nuclide in the sample. Poisson errors estimate nuclides. Weathered olivines replaced with iddingsite the uncertainties in the ratio measurement itself, and yielded 36Cl exposure ages 30% older than unweathered therefore are good estimates of multiple runs on the same samples from the same surface at Lathrop Wells, NV, target (AMS) or mineral splits and step heating (gas MS). probably re#ecting the Cl contribution from the me- But they do not include uncertainty in the normalization teoric water withrelatively high Cl/Cl (Zreda et al., of the ratio, which comes into play when comparing 1993). Cosmogenic Be ages based on whole rock gran- measurements with other AMS laboratories or other ites and tu!s partially dissolved by 30% were as muchas dating methods. They also do not include other sources three times older than independent ages, whereas par- of error (discussed above) that may arise during chemical tially dissolved basalts withthickdesert varnishlayers preparation of completely separate samples. The esti- tended to yield equivalent ages (Klein et al., 1997). These mates in Table 7 are generous; reproducibilities are often examples attest to the variable nature of meteoric con- better than 0.5% and Poisson error can often be im- tamination. proved to better than 1% (10,000 counts) by longer run times. 6.1.2. Sample preparation and elemental analyses The other sources of random error usually only make Sources of random error associated with the physical minor contributions to the total uncertainty. Small back- and chemical processing of each sample has been dis- grounds after subtraction add linearly to the uncertainty, cussed previously (Section 5). Although potentially signif- i.e. a background of 10% will increase the uncertainty by icant, these random sources of error generally do not about 10%: contribute signi"cantly to the total uncertainty of the 1 method (average 3%, Table 7). The magnitudes of error " # . (1 2R) (6.2) assigned are based on experience and knowledge of the (N sample preparation procedure. Sample interchange oc- curs rarely but cross contamination will result if equip- withbackground subtraction, and ment (sieves, disc pulverizer, beakers) are not properly 1 " cleaned or during evaporation stages if samples are not . (6.3) (N adequately covered. Sample mass uncertainties are due to incomplete dissolution of the solid mineral, to loss of without background subtraction, where R is the ratio the minerals by static electricity (2% is probably gener- of the background to the number of counts (B/N). The ous), or to errors in weighing incompletely dried samples. di!erence is therefore: In most cases, error due to analytical balance calibration 1 is less than 0.2%. Analyses of the carrier element and ! " # ! . . [(1 2R) 1] other major and trace elements will each have errors (N associated withdrift, linearity, and contamination of the 1 machine used. With duplicate or triplicate measure- + " R R .. (6.4) ments, typical 1 total uncertainties in ICP or AA ana- (N lyses of elemental concentrations at the 0.1}100 ppm levels are generally greater than 2%. This may become Backgrounds are generally small for AMS and high pre- signi"cant for whole rock samples (e.g. for Cl) but is not cision gas MS. Uncertainties from blank subtraction are reported for Be because elemental analyses are unnec- also small for most samples but can add signi"cantly to essary if the Be/Be in the carrier is well known. the measurement uncertainty if the blank approaches the magnitude of the unknowns (Davis et al., 1999). In gen- 6.1.3. Mass spectrometry eral, the formula is The principles of random errors are similar for both R R AMS and gas mass spectrometry. Withtheexception of " + # , (6.5) R + R blank corrections, random errors associated withthe + isotopic measurements tend to be small for most nuclides but as R approaches 0, the 95% con"dence limit is used ratios (generally less than 5% for high precision measure- for the upper limit of the ratio ments involving long run times or samples withhigh R ratios to boost beam intensity). The uncertainty asso- {" # R 1.96 + , (6.6) ciated withPoisson counting statistics can be expressed R+ J.C. Gosse, F.M. Phillips / Quaternary Science Reviews 20 (2001) 1475}1560 1547
where R is the "nal isotopic ratio, R+ is the measured speci"c gravity and Be/ Be (Inn et al., 1987) and re- $ isotopic ratio, R is the isotopic ratio of the blank, ported a value for the Be half life of 1.34 0.07 Myr + is the measurement uncertainty (e.g. .) and (not included in the Holden (1990) evaluation). This was is the uncertainty of the isotopic ratio of the signi"cantly lower than (not within 2 limits of) the blank.In the case of Be/Be, blanks as low as 2;10\ half-life reported earlier that year, 1.51$0.06 Myr, by can be achieved by using a Be carrier manufactured from Hofmann et al. (1987). Middleton et al. (1993) compared shielded beryl (Middleton et al., 1984). Precision in the the NIST SRM 4325 standard and a separate standard measurements of standards between analyses of un- (A-N3.77) from ICN Biomedicals Inc. to their in-house known samples is generally better than 1%. AMS standard to estimate the Be half-life. They re- ported 1.53 Myr$5% and 1.48 Myr$5%, respectively, 6.1.4. Systematic errors as the half-lives from the relative comparison. Their Most of the systematic errors associated with sample measurements support the 1.52-Myr value (Holden, preparation and mass spectrometry (e.g. fractionation, 1990). mass discrimination, variable sputter or melting rates, The greatest sources of systematic error extend from memory of previous sample) are eliminated by proper estimates of time-integrated production rates. Unfortu- normalization. Uncorrected for systematic uncertainties nately many of these errors are not independent of each associated withelement and isotopic measurements vary, other. However, the dependent errors may be combined but are generally less than 2% after normalization. Un- before attempting error propagation. Production rate certainty in carriers and standards may increase due error sources that vary with site location should be to dilution or evaporation but can be veri"ed withrou- included in total uncertainties calculated for eachsite, or tine measurement. Uncertainties in assigned constants should be at least described in text accompanying the suchas atomic masses are less than0.01%. Calculation data. By basic calibration (2.2.1 of Table 7) we mean the and rounding errors and other human errors are hope- systematic uncertainty in the empirically derived produc- fully negligible. The weighted uncertainty (e.g. Holden, tion rates. Suchuncertainties may derive from invalid 1990) in radioactive half-lives (and thus decay constant assumptions regarding exposure history (e.g. no burial, and mean life) is 3% or lower (Table 8). The half-life of Table 6), from incorrect exposure durations determined Be has only recently reached an apparent consensus, by independent timescales, and uncertainties in measure- so it deserves additional comment here. In 1987, the ments of the cosmogenic nuclide. Table 7 indicates US National Institute of Standards and Technology that the basic calibration for Be (when scaled to sea (NIST) prepared a standard material withcerti "ed level and high latitudes as suggested by Stone, 1999) is
Table 8 Half-lives of radioactive TCN
TCN Decay schemes Half-life Unc Decay constant Mean life References (yr) (%) (yr\) (yr)
\P ; ; \ ; Be B 1.52 10 3.3 4.56 10 2.19 10 (Yiou and Raisbeck, 1972; Hofmann et al., [100%] 1987; Holden, 1990; Middleton et al., 1993)
\P ; \ C N 5730 0.52 1.213 10 8245 (Hughes and Mann, 1964; Holden, 1990) [100%]
> P ; ; \ ; Al , EC Mg 7.1 10 2.8 9.8 10 1.0 10 (Rightmire et al., 1958; Endt and Van der [82.1%,17.9%] Leun, 1973; Middleton et al., 1983; Holden, 1990; Norris et al., 1993)
\P ; ; \ ; Cl Ar, EC, 3.01 10 0.66 2.30 10 4.3 10 (Wu et al., 1949; Bartholomew et al., 1955; >P S Goldstein, 1966; Endt and Van der Leun, [98.1%,1.9%,0.2%] 1973; Bentley et al., 1986)
Lederer and Shirley (1978); , beta decay, EC, electron capture. Shirley (1998); and Holden (1990). The half life for C from Holden (1990) is 5715 yr. However, the C half life is more commonly reported as 5730$40 yr (Lederer and Shirley, 1978). Uncertainty, as reported for half lives in Lederer and Shirley (1978) and Holden (1990). ln2 " . L ¹ ¹ " . ln2 1548 J.C. Gosse, F.M. Phillips / Quaternary Science Reviews 20 (2001) 1475}1560 probably within 5%. Included in basic calibration is the tion rates globally (e.g. withmore robust rigidity-based uncertainty in the proportion of production components transport codes that are constrained by empirical data (spallation by fast neutron, thermal neutron capture, and Section 3.7), this error will decrease signi"cantly. muonic interactions). As discussed in Section 3.6.1, He is Temporal variations in production rates contribute also well calibrated, but other nuclides may have higher systematic errors when they are ignored. Most previous systematic uncertainties. Uncertainties in theoretical esti- studies have calculated ages according to a single time- mates of production rates for whole rock samples (e.g. for averaged production rate. This is generally appropriate Cl) depend on nuclear physics and the nuclear cross when comparing TCN ages to other TCN ages, but when section data. Also, signi"cant is the uncertainty in e!ec- other timescales are involved the error may be signi"- tive mean attenuation lengthof thedi !erent particles at cant. As described in Section 3.5.3, #uctuation of the di!erent sites (function of magnetic "eld e!ects) in both primary GCR is probably negligible over the last Myr, atmosphere and rock (Table 3). However, the largest and with the exception of late Holocene ages, the e!ect of errors still originate from uncertainty in scaling the calib- high frequency ((10 yr) solar modulation is probably rated production rates to di!erent positions (latitude, balanced by integrating over the entire exposure dura- longitude, and elevation). tion. Likewise, the e!ects of secular variation in the Systematic errors in the atmospheric scaling is caused position of the dipole axis and of non-dipole magnetic by uncertainty in attenuation lengths, uncertainty in the "eld e!ects will probably balance over long exposure model of atmospheric pressure over the range of possible periods. However, these latter e!ects are probably impor- altitudes, latitudes and longitude, and uncertainty in the tant for exposures less than 8 kyr when the time-averaged global interpolation of incomplete star production or "eld axis is not geocentric (Section 3.5.3). The possible neutron and proton data at di!erent altitudes. The Stan- e!ects of temporal variations in the &thickness of the dard Atmosphere hydrostatic model (CRC Handbook: atmosphere' (e.g. due to sea level change or isostatic Lide, 1999, 2000) commonly used (Stone, in press) is the rebound) have been calculated to be less than 1% over geopotential atmosphere with altitudinal pressure cha- long exposure periods. Variations in geomagnetic inten- nges derived from sity may produce systematic errors in ages for exposures as long as 50 kyr (Section 3.5.3). The e!ects can be P "P exp (!(M g/R ) (ln ¹ !ln(¹ !z ))), (6.7) X Q ? Q Q modeled using available paleointensity data and integ- \ ¹ where PQ is sea level pressure (1033.2 g cm ), Q is sea- rating the &apparent geomagnetic latitudes' or by using level temperature (288.15 K), is the dry air adiabatic more robust transport code simulations that vary cuto! ¹ \ lapse rate (d /dz, taken as 0.0065 K m ), M is the rigidity withthepaleointensity. However, more invest- mean molar mass of air (28.964 g mol\ at sea level), igation into the e!ects of paleointensity and better esti- R is the gas constant, g is the acceleration due to gravity mates of paleointensity are needed to evaluate the true at sea level, and z is altitude (Stone, in press). The Inter- error. Based on the agreements between independent national Civil Aviation Organization (ICAO) uses a empirical production rate calibrations for di!erent expo- similar approximation (see Dunai, 2000). The steady- sure intervals (Phillips et al., 1996b; Licciardi et al., 1999; state model represents mean annual atmospheric condi- Stone, 1999) it appears that the error due to #uctuating tions of the atmosphere from sea level to 1000 km at paleointensity for the past 20 kyr may be within the latitude 453N during a period of moderate solar activity. precision of the individual production rates. However, the "xed adiabatic lapse rate assumes dry air, and the model does not account for second-order pres- 6.2. Reporting the uncertainty sure variations outside the mid-latitude region (e.g. anomalies over Antarctica may have caused a 30% When characterizing the age uncertainty from underestimation in regional production rates (Stone, in a radiometric dating method (e.g. U-series, C, press). More empirical studies are needed to evaluate Ar/Ar), it is common to report a 1 or 2 uncertainty these uncertainties. that includes only an estimate of the precision of the The error in scaling the production rates for di!erent analysis for that run. This is considered reasonable be- latitudes (and longitudes) is still being evaluated, but cause dates from the same method will probably have the agreement between TCN ages and independent ages at same systematic uncertainties (e.g., uncertainty in the di!erent sites (e.g. (Phillips et al., 1996b; Licciardi et al., half-life of U) if laboratory-speci"c errors are balanced 1999), see discussion in Sections 3.1, 3.5.3 and 3.6.6) by normalization. However, if dates from di!erent suggests that at least for mid-latitude and arctic sites the methods are compared, it is necessary to report the total scaling by models suchas Lal (1991) is probably within uncertainty in the method (i.e. the uncertainty in the 10%. For samples collected at elevations and latitudes accuracy and the precision). Error analysis of ages deter- similar to those of the original calibration sites (mostly mined witha single methodmay also require more 30}453N, '1500 m asl), the scaling is less important than simple experimental uncertainty. Calculation of (Table 7). As we improve the method of scaling produc- production rates for any one of the TCN method involve J.C. Gosse, F.M. Phillips / Quaternary Science Reviews 20 (2001) 1475}1560 1549 adjustments for spatial and temporal variations in pro- which expands to duction rates, and therefore may have di!erent com- N pound uncertainties for individual samples. " In any case, the approach used to report the total R (1! N/P)P . uncertainty should be explicitly described in the publica- N ln(1!H,) tion. At a minimum, the following information should be # # . provided withany TCN data (Gosse et al., 1996d): mag- (1! N/P)P H nitude and precision of chemical and analytical blank N measurements; uncertainty in site and sample character- # +1 # '!. #1 ! . (6.10) istics (position, density, snow cover, erosion); isotope (1 N/P)P R C ratio measurement uncertainty (specify if it includes the uncertainty due to normalization, or indicate systematic This calculation clearly ignores many signi"cant un- uncertainty too); and method of determining time-integ- certainties listed in Table 7. However, including many of rated site production rate, including geometrical and the factors listed in Table 7 will not necessarily yield cover adjustments. Blank information should always be a more representative estimate of the measurement un- reported. When blank magnitudes are a signi"cant certainty because (i) it is pointless to under-estimate the portion of the magnitude of the unknown (e.g. ' 25%), true precision of the method by assigning maximum 1 it is crucial to report the magnitudes and analytical uncertainties to every variable; (ii) it is invalid to assume uncertainty in bothvalues (Davis et al., 1999) to avoid all uncertainties are independent; (iii) the uncertainties in underestimating the total uncertainty. some of the parameters are not well known (e.g., spatial Total uncertainty can be reported in four ways. scaling of the nucleon #ux through the atmosphere) and (1) A partial error propagation can be computed using our estimates might be too large; and (iv) many uncer- the three or four most signi"cant random error sources of tainties are systematic rather than random (e.g., half- known magnitude, and an error estimate that combines lives). When all possible errors are propagated through the error sources that are non independent. This provides the equations used to derive exposure durations or ero- an estimate of the precision of the method. Separate sion rates, the "nal uncertainties are usually muchlarger propagation of the most signi"cant systemic errors will than comparisons with other dating methods imply. One provide a means of evaluating the accuracy. (2) The reason for this discrepancy is that many of the uncertain- accuracy of the ages can be evaluated by comparison ties in Table 7 must be estimated, and these estimates are with other dating methods. (3) The sensitivity to speci"c either too large or represent errors that only rarely con- error sources can be reported. For instance, the max- tribute. It is necessary to consider how the date is going imum e!ect can be computed for a given source of error to be used to determine which factors should be included (e.g. the maximum thickness and density of snow pos- in the calculation of the measurement uncertainty. This is sible) or a Monte Carlo error simulation can be used to a second reason why error analyses including all error evaluate the sensitivity of multiple in#uences (e.g. Stone sources may be overestimates. In general, the uncertain et al., 1998b). (4) Variance in repeated measurements on e!ects of factors that a!ect all measurements in a com- multiple samples on the same surface provides another parison equally should not be included when the purpose means of estimating precision. is to combine or compare these measurements. For example, when comparing and combining dates from a single isotopic system, it is not appropriate to 6.2.1. Error propagation include uncertainties in half-life. When dates for a single As an example of error propagation, consider the vari- landform are being compared or combined, it is not ance () analysis (cf Bierman and Gillespie, 1994) for appropriate to include uncertainties due to factors that a spallogenic Al exposure age (t) from a #at surface they share (e.g. analytical uncertainties, such as carrier withsimple exposure historyusing Eq. (3.89) from Sec- concentration if all samples were prepared together, or tion 3.8 that includes the uncertainty in the AMS and snow cover, if all samples had similar burial histories). ICP.AES measurements, half-life, and site production Only after the samples are combined and when it is rate. The age of the sample is necessary to compare the results to other systems, should 1 N other systematic (and sometimes random errors) be in- t" ! ln1 . (6.8) cluded in the quoted uncertainty of the measurement. P (z) Assuming that each of the errors is independent, we 6.2.2. Evaluating accuracy by intercomparison can propagate errors using partial derivatives: A comparison of TCN ages withreliable ages deter- mined independently is one means of evaluating the *t *t *t " # # , (6.9) accuracy of the TCN ages. As an example of such an R *P . * H *N , intercomparison consider the results of Phillips (1997b), 1550 J.C. Gosse, F.M. Phillips / Quaternary Science Reviews 20 (2001) 1475}1560 who found that 8 out of 8 boulders on 100}150 kyr-old 6.2.4. Sensitivity analysis moraines in the Wind River Range yielded concordant It is di$cult to calculate the magnitude of some sys- Be and Cl ages. The agreement suggests: (i) the chem- tematic errors. For instance, it is impossible to determine ical procedures, calculations, and assumptions that are the duration, periodic thickness, and density of snow, ice, unique to eachmethodare equally good (or equally or loess cover over a surface for the past 100 kyr. A rea- poor) and (ii) di!erent TCN methods can yield the same sonable approach is to evaluate the sensitivity of the "nal ages for boulders of this lithology and age in this environ- age to a range of these factors. This may be done by using ment. The agreement also sets limits on burial and ero- a wide range of parameter magnitudes in appropriate sion rates since erosion and burial a!ect di!erent equations or statistically withMonte Carlo simulations nuclides di!erently, and even on the secular constancy of of uncertainty (Phillips et al., 1996b; 1998; Stone et al., the production rate since nuclides with di!erent half-lives 1998b). The sensitivity of several factors has been treated integrate changes in production rate di!erently. in detail in this review: variation of the cosmic ray #ux However, comparisons between two TCN ages do not withsurface inclination angle (Fig. 5) and shielding(Figs. test assumptions about systematic errors that are com- 14 and 15); signi"cance of post-glacial or tectonic emerg- mon to bothmethods(e.g. spatial scaling of nucleonic ence (Fig. 12); the most sensitive latitudes, longitudes, production rates for the boulder's latitude, longitude, and altitudes, and ages to geomagnetic changes (Figs. 8, 10 elevation). Comparisons withindependent (non-TCN) and 11); sensitivity of integrated production rates to short dating methods such as varve chronologies, U-Th, and high-amplitude paleointensity changes during excursions K-Ar provide more complete evaluations of accuracy or reversals (Fig. 9); signi"cance of ignoring snow cover (e.g. Gosse et al., 1999; Ivy-Ochs et al., 1999). For (Fig. 17) and erosion (Fig. 19) (see also Gillespie and example, the uncertainty-weighted mean of 21 Cl Bierman, 1995for a thorough discussion). An advantage age determinations from the Ashik Kol volcano in the of sensitivity analysis is its capacity to determine before Kun Lun Shan (northern Tibetan Plateau) was sampling if erosion rate or shielding by snow will be 66,000$1000 years. The result of a Ar/Ar age deter- signi"cant. For example, if bedrock or small boulders are mination on the same basaltic trachyandesite was being sampled, a simple calculation can reveal how much 62,000$1300 years (W. McIntosh, New Mexico Tech, sediment cover could be tolerated while still being able to person. comm., 1998). Unfortunately, there are very few answer the question posed. A surface that was de- locations with highly reliable independent estimates of glaciated 25 kyr ago but was covered under 5, 15, or exposure duration. Because of the continuous develop- 25 cm of sediment (2.0 g/cm) for the "rst 10 kyr, would ment of the TCN method, most sites with reliable inde- yield respective ages that were 2.5, 7, and 11% too low if pendent age control and known simple exposure history continuous exposure was assumed. are actually used to calibrate the TCN timescale.
7. Directions of future contributions 6.2.3. Multiple sample measurements Multiple independent measurements of age on a single If the past 15 years is any indication, we have surely landform surface improve the precision of the determina- not realized the full role of TCN exposure history charac- tion of the mean age of the surface. Multiple measure- terization in Quaternary science. Developments in TCN ments decrease the impact of an anomalous sample with methods are improving the reliability of landscape evolu- an exposure history that does not represent the history of tion, tectonic, and paleoclimate interpretations. We are the entire surface. In two separate tests on nine boulders expanding the ways in which the methods can be em- from late Pleistocene moraines from the Rocky Moun- ployed to assist in other "eld suchas archeologyand risk tains, the coe$cient of variation of individual measure- assessment. As more applications are discovered, Quater- ments about the means of Be exposure ages were 3.8% nary geologists are beginning to address questions that and 4.1% (Gosse et al., 1995a; 1995c). A similar result was had never before been asked. Here we list examples of attained for Al. These apparent precisions are signi"- future advances in TCN methods that are inevitable or cantly better than the total random error of 8% predicted critical to technique development. in Table 7. In another example, the coe$cient of 1. We need to improve estimates of terrestrial produc- variation of Cl ages from ten boulders sampled on a tion rates of individual nuclides and better establishthe similar-age moraine in the Sierra Nevada was 3.5%, production ratio of di!erent nuclide pairs or triplets. compared to an average analytical uncertainty of 4.0% A more rigid and complete numerical simulation model (F.M. Phillips, unpublished data). Unfortunately, is needed for TCN production in shallow rocks. The due to the costs and time involved in sample preparation transport code must account for aspects of the total and measurement, this approach is seldom possible (dipole and non-dipole "eld components) magnetic to the degree necessary to improve the reliability of "eld in#uences on GCR and secondary cosmic rays, the age. atmospheric a!ects, and terrestrial production. More J.C. Gosse, F.M. Phillips / Quaternary Science Reviews 20 (2001) 1475}1560 1551 empirical calibrations at well-characterized sites are durations where other nuclide ratios are not. We need to needed to establishtemporal variations in production support e!orts at the U. Arizona (T. Jull and N. Lifton) rates and place boundary conditions on the transport and other institutions who are perfecting the extraction model. As recommended at two recent TCN workshops procedures for isolating cosmogenic C from quartz. (Santa Fe, NM, in February 1996 (Gosse et al., 1996) and The number of TCN applications and their reliability West Lafayette, IN, in February 1999), calibration site will increase signi"cantly when this isotope system be- assessment should involve a group evaluation to prevent comes routinely measured. anomalous calibrations and to maximize the opportunity 5. Withimprovements in chemistryand a reduction in for measurement of multiple nuclides. required sample size, and a better understanding of pro- 2. We need to have better control on important nuclear duction rates in the Holocene, cosmogenic nuclides can physics parameters that a!ect the nuclear interactions in become more useful in paleoaltimetry, archeology, pale- rock. For instance, the muonic contribution of the nuc- ontology, and risk assessment. For instance, Phillips et leonic production of TCN at sea level must be more al. (1997a) have used Cl to constrain the maximum "rmly determined. This directly a!ects the reliability of exposure age of rock panels in Portugal that contain scaling production rates from one site to another and is prehistoric engravings. With re"nements in altitudinal an intricate and logical next step in future reducing scaling and the temporal variations in production, the uncertainties. Measurements in subsurface samples be- technique will become important as a means to deter- low four or "ve fast neutron attenuation lengths are mine surface uplift history (for a precocious example see needed to con"rm that the muonic contribution to Be Brook et al., 1995a). Paleoaltimetry di!ers from rock production is much less than assumed in the 1990s. uplift and denudation methods that are based on ther- Additionally, better resolution of the #attening of mochronology or erosion rates, and does not depend on the attenuation of fast neutrons just below the air rock assumptions of paleowater depths that fossil-based interface is needed. We also need to establishtheabsorp- paleoaltimetry methods require. tion mean free path lengths in shallow rock depths for all cosmic radiation that is responsible for TCN production. 3. We must address systematic issues (e.g., spatial scal- Acknowledgements ing, temporal variation, muonic contributions) so that the uncertainty in accuracy approaches our total random Many of the experimental results and numerical simu- error. This will open the possibility of solving many lations, as well as the time for the theoretical calculations, new societal and geological problems using TCN. that are the basis for FMP's contributions to this paper In additional to paleoclimate and neotectonic applica- were supported by the National Science Foundation tions, at this level of accuracy the methods would through grants ATM-9117566, EAR-941780, and EAR- be su$ciently reliable for many new risk assessments 9206037. JCG was supported by NSF (OPP-9618844), and environmental geology applications. For example, DOE Yucca Mountain program at Los Alamos National even at present accuracy levels, TCN have been Laboratory through C. Harrington, the Canada Geologi- instrumental in the characterization of the tectonic his- cal Survey, and the University of Kansas Research De- tory of Yucca Mountain, the potential U.S. high level velopment Award (1996) and General ResearchAwards nuclear waste repository (Zreda et al., 1993; Gosse et al., (1997 and 1998). JCG thanks Je! Klein for clarifying 1996b). many issues of the physics, mathematics, and uncertainty 4. We should continue to develop exposure techniques discussed in this review. Keran O'Brien gave useful sug- withdi !erent isotopes and mineral systems to further gestions for Sections 3.1}3.5. This manuscript bene"ted increase the universal applicability of the methods. For signi"cantly from a thorough review by Bob Reedy. John example, measurements of Be in magnetite (D. Lal, Stone, Nat Lifton, Tom Davis, and Susan Ivy-Ochs are pers. comm.), Be in olivine (Kong et al., 1999), and Ne thanked for sharing preprints of submitted articles. in garnet (W. Phillips, pers. comm.) are excellent pros- pects. In favorable instances other in situ cosmogenic nuclides, suchas Ca, may be useful if the TCN : stable References nuclide is su$ciently low for AMS analysis (Raisbeck and Yiou, 1979; Kubik et al., 1986; Klein et al., 1988; Ackert, R.P.J., Barclay, D.J., Borns, H.W.J., Calkin, P.E., Kurz, M.D., Middleton et al., 1989; Fink et al., 1990). As described in Fastook, J.L., Steig, E.J., 1999. Measurements of past ice sheet Sections 3.8 and 3.9, the short half-lives of C and Ca elevations in interior West Antarctica. Science 286 (5438), 276}280. makes it the radionuclide of choice for establishing ero- Ackert, R.P.J., Singer, B.S., Guillou, H., Kurz, M.D., 1998. Cosmogenic sion rates of rock and sediment surfaces because (i) it will He production rates over the last 125,000 years: calibration against Ar/Ar and unspiked K-Ar ages of lava #ows. GSA Annual reach equilibrium within 25 kyr or less, and (ii) when Meeting Abstracts withPrograms 30 (7), A }299. expressed as a ratio with another spallogenic nuclide, the Acton, G.D., Petronotis, K.E., Cape, C.D., Rotto Ilg, S., Gordon, R.G., steady state erosion island is useful for younger exposure Bryan, P.C., 1996. A test of the geocentric axial dipole hypothesis 1552 J.C. Gosse, F.M. Phillips / Quaternary Science Reviews 20 (2001) 1475}1560
from an analysis of the skewness of the central marine magnetic of Environmental Isotope Geochemistry. Elsevier, Amsterdam, anomaly. Earthand Planetary Science Letters 144, 337 }346. pp. 427}480. Albrecht, A., Herzog, G.F., Klein, J., Dezfouly-Arjomandy, B., Go!, F., Bierman, P., 1996. Cosmocalibrate. Science 271, 1906. 1993. Quaternary erosion and cosmic-ray-erosion history derived Bierman, P., Gillespie, A., 1994. Continuing Education Manual on from Be and Al produced in situ-An example from Pajarito Geomorphic applications of in situ produced cosmogenic isotopes, plateau, Valles caldera region. Geology 21, 551}554. Geological Society of America Annual Meeting, Seattle, Washing- Allkofer, O.C. and Grieder, P.K.F., 1984. Cosmic rays on earth. Physics ton, pp. 100}102. Data, 25-1. Fachinformationszentrum, Karlsruhe. Bierman, P., Gillespie, A., Ca!ee, M., Elmore, D., 1995a. Estimating Anderson, R.S., Repka, J.L., Dick, G.S., 1996. Explicit treatment of erosion rates and exposure ages with36Cl produced by neutron inheritance in dating depositional surfaces using in situ Be and activation. Geochimica et Cosmochimica Acta 59, 3779}3798. Al. Geology 24 (1), 47}51. Bierman, P., Larsen, P., Clapp, E., Clark, D., 1996. Re"ning estimates of Anderson, S.W., Krinsley, D.H., Fink, J.H., 1994. Criteria for recogni- Be and Al production rates. Radiocarbon 38 (1), 149. tion of constructional silic lava #ow surfaces. EarthSurface Pro- Bierman, P., Turner, J., 1995. Be and Al evidence for exceptionally cesses and Landforms 19, 531}541. low rates of Australian bedrock erosion and the likely existence of Anthony, E.Y., Poths, J., 1992. He surface exposure dating and its pre-Pleistocene landscapes. Quaternary Research44, 378 }382. implications for magma evolution in the Potrillo volcanic "eld, Rio Bierman, P.R., 1994. Using in situ produced cosmogenic isotopes to Grande Rift, New Mexico, USA. Geochimica et Cosmochimica estimate rates of landscape evolution: A review from the geomorphic Acta 56, 4105}4108. perspective. Journal of Geophysical Research 99 (B7), 13885}13896. Armstrong, T.W., Chandler, K.C., Barish, J., 1973. Calculations of Bierman, P.R., Gillespie, A.R., Ca!ee, M.W., 1995b. Cosmogenic ages neutron #ux spectra induced in the Earth's atmosphere by galactic for earthquake recurrence intervals and debris #ow fan deposition, cosmic rays. Journal of Geophysical Research 78 (16), 2715}2726. Owens Valley, California. Science 270, 447}450. Ayarbe, J.P., Phillips, F.M., Harrison, J.B.J., Elmore, D. and Sharma, Bierman, P.R., Marsella, K.A., Patterson, C., Davis, P.T., Ca!ee, M., 1999. P., 1998. Application of cosmogenic nuclides to fault-scarp chrono- Mid-Pleistocene cosmogenic minimum age limits for pre-Wisconsin logy: Preliminary results from the Socorro Canyon Fault. In: Har- glacial surfaces in southwestern Minnesota and southern rison, J.B.J. (Ed.), Soil, Water, and Earthquakes Around Socorro, Ba$n Island: a multiple nuclide approach. Geomorphology 27, New Mexico: Guidebook for the Rocky Mountain Cell of the 25}40. Friends of the Pleistocene 1998 Field Conference, 10}13 September Bierman, P.R., Steig, E.J., 1996. Estimating rates of denudation using 1998, New Mexico Tech, Socorro, 12 pp. cosmogenic isotope abundances in sediment. EarthSurface Pro- Ballantyne, C., Stone, J.O.H., Fi"eld, L.K., 1998. Cosmogenic Cl-36 cesses and Landforms 21, 125}139. dating of postglacial landsliding at The Storr, Isle of Skye, Scotland. Bland, C.J., Cioni, G., 1968. Geomagnetic cut-o! rigidities in non- The Holocene 8 (3), 347}351. vertical directions. Earthand Planetary Science Letters 4, 399 }405. Barbetti, M., Flude, K., 1979. Geomagnetic variation during the late Boella, G., Dilworth, C., Panetti, M., Scarsi, L., 1968. The atmospheric Pleistocene period and changes in the radiocarbon time scale. Na- and leakage #ux of neutrons produced in the atmosphere by cosmic ture 279, 202}205. ray interactions. Earthand Planetary Science Letters 4, 393 }398. Bard, E., Arnold, M., Fairbanks, R.G., Hamelin, B., 1993. Th-U Bourle` s, D.L., Brown, E.T., Raisbeck, G.M., Yiou, F., Grandin, G. et al. and C ages obtained by mass spectrometry on corals. Radiocar- 1992. Constraining the history of iron crust laterite systems using in bon 35, 191}195. situ produced cosmogenic Be and Al. EOS, Transactions of the Bard, E., Hamelin, B., Fairbanks, R.G., Zindler, A., 1990a. Calibration American Geophysical Union 73, 173. of the C timescale over the past 30,000 years using mass spectro- Brassart, J., Tric, E., Valet, J.-P., Herrero-Bervera, E., 1997. Absolute metric U-Thages from Barbados corals. Nature 345, 405 }410. paleointensity between 60 and 40 ka from the Kohala Mountain Bard, E., Hamelin, B., Fairbanks, R.G., Zindler, A., Mathieu, G., (Hawaii). Earthand Planetary Science Letters 148, 141 }156. Arnold, M., 1990b. U/Thand C ages of corals from Barbados and Briner, J.P., Swanson, T.W., 1998. Using inherited cosmogenic Cl to their use for calibrating the C time scale beyond 9000 years BP. constrain glacial erosion rates of the Cordilleran ice sheet. Geology Nuclear Instruments and Methods in Physics B 52, 461}468. 26 (1), 3}6. Barker, D., Jull, A.T.J., Donahue, D.J., 1985. Excess Carbon-14 abund- Brook, E.J., Brown, E.T., Kurz, M.D., Ackert, R.P., Raisbeck, G.M., ances in uranium ores: possible evidence for emission from ura- Yiou, F., 1995a. Constraints on erosion and uplift rates of Pliocene nium-series isotopes. Geophysical Research Letters 12 (10), glacial deposits in the Transantarctic Mountains using in situ- 737}740. produced 10Be and 26Al. Geology 23, 1063}1066. Bartholomew, R.M., Boyd, A.W., Brown, F., Hawkings, R.C., Loun- Brook, E.J., Kurz, M.D., 1993. Surface-exposure chronology using in sbury, M., Merritt, W.F., 1955. The half-life of Cl. Canadian situ He in Antarctic quartz sandstone boulders. Quaternary Re- Journal of Physics 33, 43}48. search39, 1 }10. Baski, A.K., Hsu, V., McWilliams, M.O., Farrar, E., 1992. Ar/Ar Brook, E.J., Kurz, M.D., Achert, R.P.J., Denton, G.H., Brown, E.T., dating of the Brunhes-Matuyama geomagnetic "eld reversal. Raisbeck, G.M., Yiou, F., 1993. Chronology of Taylor Glacier Science 256, 356}357. advances in Arena Valley, Antarctica, using in situ cosmogenic He Beer, J., Raisbeck, G.M., Yiou, F. (Ed.), 1991. Time variations of 10Be and Be. Quaternary Research39, 11 }23. and solar activity. The Sun in Time. The University of Arizona, Brook, E.J., Kurz, M.D., Ackert, R.P., Raisbeck, G., Yiou, F., 1995b. Tucson, pp. 343}359. Cosmogenic nuclide exposure ages and glacial history of late Quat- Beer, J., Siegenthaler, U., Bonani, G., Finkel, R.C., Oeschger, H., Suter, ernary Ross Sea drift in McMurdo Sound, Antarctica. Earthand M., WoK l#i, W., 1988. Information on past solar activity and Planetary Science Letters 131, 41}56. geomagnetism from Be in the Camp Century ice core. Nature 331, Brook, E.J., Nesje, A., Lehman, S., Raisbeck, G., Yiou, F., 1996a. 675}679. Cosmogenic nuclide exposure ages along a vertical transect in Bell, J.W., Brune, J.N., Liu, T., Zreda, M., Yount, J.C., 1998. Dating western Norway: implications for the height of the Fennoscandian precariously balanced rocks in seismically active parts of California Icesheet. Geology 24, 207}210. and Nevada. Geology 26 (6), 495}498. Brook, J.E., Brown, E.T., Kurz, M.D., Raisbeck, G., Yiou, F., 1996b. An Bentley, H.W., Phillips, F.M., Davis, S.N., 1986. Chlorine-36 in the Antarctic perspective on in-situ cosmogenic nuclide production. terrestrial environment. In: Fritz, P., Fontes, J.-C. (Eds.), Handbook Radiocarbon 38 (1), 150. J.C. Gosse, F.M. Phillips / Quaternary Science Reviews 20 (2001) 1475}1560 1553
Brown, E.T., Bourles, D.L., Burch"el, B.C., Oidong, D., Jun, L., Molnar, Chauvin, A., Duncan, R.A., Bonhommet, N., Levi, S., 1989. Paleo- P., Raisbeck, G.M., Yiou, F., 1998a. Estimation of slip rates in the intensity of the Earth's magnetic "eld and K-Ar dating of southern Tien Shan using cosmic ray exposure dates of abandoned the Louchadiere volcanic #ow (Central France): New evidence for alluvial fans. Geological Society of America Bulletin 110 (3), the Laschamp Excursion. Geophysical Research Letters 16 (10), 377}386. 1189}1192. Brown, E.T., Bourles, D.L., Colin, F., Raisbeck, G.M., Yiou, F., Desgar- Chauvin, A., Gillot, P.-Y., Bonhommet, N., 1991. Paleointensity of the ceaux, S., 1995a. Evidence for muon-induced in situ production of Earth's magnetic "eld recorded by two late Quaternary volcanic Be in near-surface rocks from the Congo. Geophysical Research sequences at the Island of La ReH union (Indian Ocean). Journal of Letters 22, 703}706. Geophysical Research 96 (B2), 1981}2006. Brown, E.T., Brook, E.J., Raisbeck, G.M., Yiou, F., Kurz, M.D., 1992a. Clark, D.H., Bierman, P., Gillespie, A.R., 1996. Be and Al produc- E!ective attenuation lengths of cosmic rays producing Be and tion rates and a revised glacial chronology for the Sierra Nevada. Al in quartz: Implications for surface exposure age dating. Geo- Radiocarbon 38 (1), 152. physical Research Letters 19, 369}372. Clark, D.H., Bierman, P.R., Larsen, P., 1995. Improving in situ Brown, E.T., Edmond, J.M., Raisbeck, G.M., Broules, D.L., Yiou, F., cosmogenic chronometers. Quaternary Research 44 (3), Measures, C.I., 1992b. Beryllium isotope geochemistry in tropical 366}376. river basins. Geochimica et Cosmochimica Acta 56, 1607}1624. Clark, D.H., Gillespie, A.R., 1997. Timing and signi"cance of late- Brown, E.T., Edmond, J.M., Raisbeck, G.M., Yiou, F., Kurz, M.D., glacial and holocene cirque glaciation in the Sierra Nevada, Califor- Brook, E.J., 1991. Examination of surface exposure ages of Antarc- nia. Quaternary International 38}39 (1), 21}38. tic moraines using in situ produced Be and Al. Geochimica et Clark, R.M., 1975. A calibration curve for radiocarbon dates. Antiquity Cosmochimica Acta 55, 2269}2283. 49, 251}266. Brown, E.T., Stallard, R.F., Larsen, M.C., Bourles, D.L., Raisbeck, Coe, R.S., 1978. Geomagnetic paleointensities from radiocarbon- G.M., Yiou, F., 1998b. Determination fo predevelopment denud- dated lava #ows on Hawaii and the question of the Paci"c ation rates of an agricultural watershed (Cayaguas River, Puerto Nondipole Low. Journal of Geophysical Research 83 (B4), Rico) using in-situ-produced Be in river-borne quartz. Earthand 1740}1756. Planetary Science Letters 160 (3-4), 723}728. Compton, A.H., 1933. A geographic study of cosmic rays. Physical Brown, E.T., Stallard, R.F., Larsen, M.C., Raisbeck, G.M., Yiou, Review 43 (6), 387}403. F., 1995b. Denudation rates determined from the accumulation of in Compton, R.R., 1962. Manual of Field Geology. Wiley, New York. situ-produced Be in the Luquillo Experimental Forest, Puerto Constable, C., Tauxe, L., 1996. Towards absolute calibration of sedi- Rico. Earthand Planetary Science Letters 129, 193 }202. mentary paleointensity records. Earthand Planetary Science Let- Brown, L., Klein, J., Middleton, R., Sacks, I.S., Tera, F., 1982. Be in ters 143, 269}274. island-arc volcanoes, and implications for subduction. Nature 299, Conversi, M., 1950. Experiments on cosmic-ray mesons and protons at 718}720. several altitudes and latitudes. Physical Reviews 79 (5), 749. Brown, L., Stensland, G.J., Klein, J., Middleton, R., 1989. Atmospheric Craig, H., Poreda, R.J., 1986. Cosmogenic He in terrestrial rocks : The deposition of Be and Be. Geochimica et Cosmochimica Acta 53, summit lavas of Maui. Proceedings of the National Academy of 135}142. Science U.S.A., vol, 83, pp. 1970}1974. Brown, W.W., 1954. Cosmic-ray nuclear interactions in gases. Physical Davis, P.T., Bierman, P.R., Marsella, K.A., Ca!ee, M.W., Southon, J.R., Reviews 93, 528}534. 1999. Cosmogenic analysis of glacial terrains in the eastern Cana- Bruno, L.-A., Baur, H., Graf, T., Schluechter, C., Signer, P., Wieler, R., dian arctic: a test for inherited nuclides and the e!ectiveness of 1997. Dating of Sirius Group tillites in the Antarctic dry valleys with glacial erosion. Annals of Glacialogy 28. cosmogenic He and Ne. Earthand Planetary Science Letters 1 }4 Davis, R.J., Schae!er, O.A., 1955. Chlorine-36 in nature. Annals New (1}4), 37}54. York Academy of Science 62, 105}122. Burbank, D.W., Leland, J., Fielding, E., Anderson, R.S., Brozovic, N., Dep, L., Elmore, D., Fabryka-Martin, J., Masarik, J., Reedy, R.C., Reid, M.R., Duncan, C., 1996. Bedrock incision, rock uplift and 1994a. Numerical simulation of cosmogenic nuclide production in threshold hillslopes in the northwestern Himalayas. Nature 379, rocks for various exposure geometries, Abstracts of the 8th Interna- 505}510. tional Conference on Geochronology, Cosmochronology, and Iso- Ca!ee, M.W., Goswami, J.N., Hohenberg, C.M., Marti, K., Reedy, R.C., tope Geology, U.S. Geol. Surv. Bulletin 1107, pp. 80. 1988. Irradiation records in meteorites. In: Kerridge, J.F. (Ed.), Dep, L., Elmore, D., Fabryka-Martin, J., Masarik, J., Reedy, R.C., Meteorites and the Early Solar System. University of Arizona Press, 1994b. Production rate systematics of cosmogenic nuclides in terres- Tuscon, pp. 205}245. trial rocks: Monte Carlo approachof investigation Cl(n,g)Cl. Cerling, T.E., 1990. Dating geomorphic surfaces using cosmogenic He. Nuclear Instruments and Methods B 92, 321}325. Quaternary Research33, 148 }156. Dep, L., Elmore, D., Lipschutz, M., Vogt, S., Phillips, F.M., Zreda, Cerling, T.E., Craig, H., 1994a. Cosmogenic He production rates from M.G., 1994c. Depthdependence of cosmogenic neutron-capture- 393Nto463N latitude, western USA and France. Geochimica et produced Cl in a terrestrial rock. Nuclear Instruments and cosmochimica Acta 58, 249}255. Methods in Physics Research B 92, 301}307. Cerling, T.E., Craig, H., 1994b. Geomorphology and in-situ cosmogenic Dep, W.H.L., 1995. Cosmogenic radionuclide production in terrestrial isotopes. Annual Reviews of Earthand Planetary Sciences 22, rocks: Accelerator mass spectrometry measurements and Monte 273}317. Carlo simulations. Ph.D. Thesis, Purdue University, West Cerling, T.E., Webb, R.H., Poreda, R.J., Rigby, A.D., Melis, T.S., 1999. Lafayette, Indiana, 155 pp. Cosmogenic He ages and frequency of late Holocene debris #ows Dixit, K.R., 1955. The statistics of 29000 stars observed in nuclear from Prospect Canyon, Grand Canyon, USA. Geomorphology 27 emulsions in Kenya. Zeitschrift fur Naturforschung 10a, (1-2), 93}111. 339}341. Channell, J.E.T., Hodell, D.A., Lehman, B., 1997. Relative geomagnetic Dockhorn, B., Neumaier, S., Hartmann, F.J., Petitjean, C., Faester- paleointensity and O at ODP site 983 (Gardar Drift, NorthAtlan- mann, H., Nolte, E., 1991. Determination of erosion rates with tic) since 350 ka. Earthand Planetary Science Letters 153, 103 }118. cosmic ray produced Cl. Zeitschrift Physik A 341, 117}119. Charalambus, S., 1971. Nuclear transmutation by negative stopped Donahue, D.J., Jull, A.J.T., Toolin, L.J., 1990. Radiocarbon measure- muons and the activity induced by the cosmic-ray muons. Nuclear ments at the University of Arizona AMS Facility. Nuclear Instru- Physics A 166, 145}161. ments and Methods B52, 224}228. 1554 J.C. Gosse, F.M. Phillips / Quaternary Science Reviews 20 (2001) 1475}1560
Dunai, T.J., 2000. Scaling factors for production rates of in situ produc- Gosse, J.C., 1994. Alpine glacial history reconstruction: 1. Application ed cosmogenic nuclides: a critical reevaluation. Earthand Planetary of the cosmogenic Be exposure age method to determine the Science Letters 176, 157}169. glacial chronology of the Wind River Mountains, Wyoming, USA; Dunne, J., Elmore, D., Muzikar, P., 1999. Scaling factors for the rates of 2. Relative dating of Quaternary deposits in the Rio Atuel Valley, production of cosmogenic nuclides for geometric shielding and Mendoza, Argentina. Dissertation Thesis, Lehigh University. attenuation at depthon sloped surfaces. Geomorphology27 (1-2), Gosse, J.C., Davis, P.T., Burr, G., Jull, A.T.J., Bozarth, S., Sorenson, C., 3}12. Klein, J., Lawn, B., Dahms, D., 1999. Late Pleistocene/Holocene Dyke, A.S., Morris, T.F., Green, D.E.C., 1991. Postglacial tectonic and glacial and paleoclimate history of Titcomb Basin, Wind River sea level history of the central Canadian Arctic. Geological Survey Range, Wyoming based on lake sediments and cosmogenic nuclide of Canada Bulletin 397, 56. dating. GSA Abstracts withPrograms 31 (7), A }56. Elmore, D., Phillips, F.M., 1987. Accelerator mass spectrometry for Gosse, J.C., Evenson, E.B., Klein, J., Lawn, B., Middleton, R., 1995a. measurement of long-lived radioisotopes. Science 236, 543}550. Precise cosmogenic Be measurements in western NorthAmerica: Elsasser, W., Ney, E.P., Winckler, J.R., 1956. Cosmic-ray intensity and Support for a global Younger Dryas cooling event. Geology 23 (10), geomagnetism. Nature 178 (4544), 1226}1227. 877}880. Endt, P.M., Van der Leun, C., 1973. Energy levels of A"21}44 A- Gosse, J.C., Gillespie, A.R., Harrington, C.D., Reedy, R.C., Poths, J., nuclei. V. Nuclear Physics A 214, 1}625. Klein, J., 1996a. Terrestrial cosmogenic nuclide dating: tested and Fabryka-Martin, J.T., 1988. Production of radionuclides in the earth ready for action. EOS, Transactions, American Geophysical Union and their hydrogeologic signi"cance, with emphasis on chlorine-36 77 (29), 275}276. and iodine-129. Ph.D. Thesis, University of Arizona, Tucson, Gosse, J.C., Grant, D.R., Klein, J., Klassen, R.A., Evenson, E.B., Lawn, 400 pp. B., Middleton, R., 1993. Signi"cance of altitudinal weathering zones Fairbanks, R.G., 1989. A 17,000-year glacio-eustatic sea level record: in Atlantic Canada, inferred from in situ produced cosmogenic in#uence of glacial melting rates on the Younger Dryas event and radionuclides, Geological Society of America Annual Meeting, Bos- deep-ocean circulation. Nature 342, 637}642. ton, pp. A}394. Fang, X.-M., Li, J.J., Van der Voo, R., Niocaill, C.M., Dai, X.-R., Kemp, Gosse, J.C., Grant, D.R., Klein, J., Lawn, B., 1995b. Cosmogenic Be R.A., Derbyshire, E., Cao, J.X., Wang, J.-M., Wang, G., 1997. A re- and Al constraints on weathering zone genesis, ice cap basal cord of the Blake Event during the last interglacial paleosol in the conditions, and Long Range Mountain (Newfoundland) glacial western Loess Plateau of China. Earth and Planetary Science Let- history. CANQUA-CGRG Conference Abstracts, Memorial Uni- ters 146, 73}82. versity of Newfoundland, St. Johns, CA19. Fink, D., Middleton, R., Klein, J., Sharma, P., 1990. Ca: Measurement Gosse, J.C., Harrington, C.D., Whitney, J.W., 1996b. Applications of in by accelerator mass spectrometry and applications. Nuclear Instru- situ cosmogenic nuclides in the geologic site characterization of ments and Methods B 47, 79}96. Yucca Mountain, Nevada, Materials ResearchSociety Symposium Finkel, R., Suter, M., 1993. AMS in the Earth Sciences: Technique and Proceedings, pp. 799}806. applications. Advances in Analytical Geochemistry 1, 1}114. Gosse, J.C., Harrington, C.D., Whitney, J.W., 1996c. Applications of in Fleming, A., Summer"eld, M.A., Stone, J.O., Fi"eld, L.K., Cressweld, situ cosmogenic nuclides in the geologic site characterization of R.G., 1999. Denudation rates for the southern Drakensberg Escarp- Yucca Mountain, Nevada. Materials ResearchSociety Symposium ment, SE Africa, derived from in-situ-produced cosmogenic Cl; Proceedings 412, 799}806. initial results. Journal of the Geological Society of London 156 (2), Gosse, J.C., Hecht, G., Mehring, N., Klein, J., Lawn, B., Dyke, A., 1998. 209}212. Comparison of radiocarbon- and in situ cosmogenic nuclide-de- Frank, M., Schwarz, B., Baumann, S., Kubik, P.W., Suter, M., Mangini, rived postglacial emergence curves for Prescott Island, Central A., 1997. A 200 kyr record of cosmogenic radionuclide production Canadian Arctic. Geological Society of America Abstracts with rate and geomagnetic "eld intensity from Be in globally stacked Program 30 (7), 298. deep-sea sediments. Earthand Planetary Science Letters 149, Gosse, J.C., Klein, J., Evenson, E.B., Lawn, B., Middleton, R., 1995c. 121}129. Beryllium-10 dating of the duration and retreat of the last Pinedale Friedlander, M.W., 1989. Cosmic Rays. Harvard University Press, glacial sequence. Science 268, 1329}1333. Cambridge, 160 pp. Gosse, J.C., Reedy, R., Harrington, C.D., Poths, J., 1996d. Overview Gaisser, T., 1990. Gamma rays and neutrinos as clues to the origin of of the Workshop on Secular Variations in the Production Rate of high energy cosmic rays. Science 247, 1049}1056. Cosmogenic Nuclides on Earth. Radiocarbon 38 (1), 135}147. Gaisser, T.K., Stanev, T., 1998. Cosmic rays Review of Particle Physics. Gosse, J.C., Stone, J.O., submitted. Terrestrial cosmogenic nuclide The European Physical Journal 3, 132}137. methods passing milestones toward palaeo-altimetry. EOS. Gall, R., 1960. The secular variation and the geomagnetic theory of cosmic Graf, T., Kim, J.S., Marti, K., Niedermann, S., 1995. Cosmic-ray- radiation. Journal of Geophysical Research 65 (11), 3545}3558. produced neon at the surface of the Earth in noble gas geochemistry Gillespie, A.R., Bierman, P.R., 1995. Precision of terrestrial exposure and cosmochemistry. Terra Scienti"c Publishing Company, Tokyo, ages and erosion rates estimated from analysis of cosmogenic iso- 115}123 pp. topes produced in situ. Journal of Geophysical Research 100 (B12), Graf, T., Kohl, C.P., Marti, K., Nishiizumi, K., 1991. Cosmic-ray 24,637}24,649. produced neon in Antarctic rocks. Geophysical Researc Letters 18, Glasstone, S., 1955. Principles of Nuclear Reactor Engineering. D. Van 203}206. Nostrand, Princeton, NJ. Graf, T., Marti, K., Wiens, R.C., 1996. The Ne production rate in a Si Goldstein, G., 1966. Partial half-life for b-decay of Cl. Journal of target at mountain altitudes. Radiocarbon 38 (1), 155. Inorganic Nuclear Chemistry 28, 937}939. Graham, I.J., 1996. Recent and planned research in cosmogenic iso- Gosse, J., Dort, W., Sorenson, C., Steeples, D., Grimes, J., Hecht, G., topes at GNS. Radiocarbon 38 (1), 157. 1997. Insights on the depositional age and rate of denudation of the Granger, D.E., Kirchner, J.W., Finkel, R., 1996. Spatially averaged long- pre-Illinioan till in Kansas from terrestrial cosmogenic nuclides. term erosion rates measured from in-situ produced cosmogenic Geological Society of America Abstracts withPrograms, North- nuclides in alluvial sediment. Journal of Geology 104, 249}257. Central Section 29 (4), A17. Granger, D.E., Kirchner, J.W., Finkel, R.C., 1997. Quaternary down- Gosse, J., Klein, J., 1996. Production rate of in situ cosmogenic Be in cutting rate of the New River, Virginia, measured from di!erential quartz at high altitude and mid-latitude. Radiocarbon 38 (1), decay of cosmogenic Al and Be in cave-deposited alluvium. 154}155. Geology 25 (2), 107}110. J.C. Gosse, F.M. Phillips / Quaternary Science Reviews 20 (2001) 1475}1560 1555
Gubbins, D., Kelly, P., 1993. Persistent patterns in the geomagnetic Zealand. Geogra"ska Annaler, Series A: Physical Geography 81 (2), "eld over the past 2.5 Myr. Nature 365, 829}832. 313}323. Guyodo, Y., Valet, J.-P., 1996. Relative variations in geomagnetic Ivy-Ochs, S., SchluK chter, C., Kubik, P.W., Dittrich-Hannen, B., Beer, J., intensity from sedimentary records: the past 200,000 years. Earth 1995. Minimum Be exposure ages of early Pliocene for the Table and Planetary Science Letters 143, 23}36. Mountain Plateau and the Sirius Group at Mount Fleming, Dry Guyodo, Y., Valet, J.-P., 1999. Global changes in intensity of the Valleys, Antarctica. Geology 23, 1007}1010. Earth's magnetic "eld during the past 800 kyr. Nature 399, Jackson, L.E.J., Phillips, F.M., Shimamura, K., Little, E.C., 1997. Cos- 249}252. mogenic Cl dating of the Foothills Erratics train, Alberta, Cana- Hampel, W., Schae!er, O.A., 1979. Al in iron meteorites and the da. Geology 25 (3), 195}198. constancy of cosmic ray intensity in the past. Earth and Planetary Johnson, C.L., Constable, C.G., 1995. Paleosecular variation recorded Science Letters 42, 348}358. by lavas over the last 5 Myr. Philosophical Transactions of the Hampel, W., Takagi, J., Sakamoto, K., Tanaka, S., 1975. Measurement Royal Society of London A 354, 89}141. of muon-induced Al in terrestrial silicate rock. Journal of Geo- Jokipii, J.R. (Ed.), 1991. Variations of the cosmic-ray #ux withtime. The physical Research 80 (26), 3757}3760. Sun In Time. The University of Arizona, Tucson pp. 205}220. Hancock, G.S., Anderson, R.S., Chadwick, O.A., Finkel, R.C., 1999. Jull, A.J.T., Donahue, D.J., Linick, T.W., Wilson, G.C., 1991. Spal- Dating #uvial terraces with Be and Al pro"les: application to logenic C in high-altitude rocks and in Antarctic meteorites. the Wind River, Wyoming. Geomorphology 27 (1-2), 41}60. Radiocarbon 31 (3), 719}724. Handwerger, D.A., Cerling, T.E., Bruhn, R.L., 1999. Cosmogenic Cin Jull, A.J.T., Lifton, N., Phillips, W.M., Quade, J., 1994a. Studies of the carbonate rocks. Geomorphology 27 (1-2), 13}24. production rate of cosmic-ray produced C in rock surfaces. Hayakawa, S., 1969. Cosmic Ray Physics: Nuclear and Astrophysical Nuclear Instruments and Methods in Physics Research B, 308-310. Aspects. Wiley, New York. Jull, A.T.J., Lal, D., Donahue, D.J., Mayewski, P., Lorius, C., Raynaud, Heidbreder, E., Pinkau, K., Reppin, C., SchoK nfelder, V., 1971. Measure- D., Petit, J.R., 1994b. Measurements of cosmic-ray-produced Cin ment of the distribution in energy and angle of high-energy neutrons "rn and ice from Antartica. Nuclear Instruments and Methods B 92, in the lower atmosphere. Journal of Geophysical Research 76, 326}330. 2905}2916. Jull, A.T.J., Wilson, A.E., Donahue, D.J., Toolin, L.J., Burr, G.S., 1992. Heimsath, A.M., Dietrich, W.E., Nishiizumi, K., Finkel, R.C., 1997. The Measurements of cosmogenic C produced by spallation in high- soil production function and landscape equilibrium. Nature 388 altitude rocks. Radiocarbon 34, 737}744. (6640), 358}361. Kim, J., Englert, P.A.J., Finkel, R., Krofcheck, D., 1999. Cosmic-ray- Heimsath, A.M., Dietrich, W.E., Nishiizumi, K., Finkel, R.C., 1999. induced Be and Al in subsurface samples from Macraes Flat, Cosmogenic nuclides, topography, and the spatial variation of soil East Otago, New Zealand. EOS, Transactions American Geophysi- depth. Geomorphology 271, 2151}2172. cal Union 80 (17), F1166}F1167. Heisinger, B., Niedermayer, M., Hartmann, J.F., Korschinek, G., Nolte, King, J.W., Banerjee, S.K., Marvin, J., 1983. A new rock-magnetic E., Morteani, G., Neumaier, S., Petitjean, C., Kubik, P., Synal, A., approachto selecting sediments for geomagnetic paleointensity Ivy-Ochs, S., 1997. In-situ production of radionuclides at great studies: application to paleointensity for the last 4000 years. Journal depths. Nuclear Instruments and Methods in Physics Research of Geophysical Research 88 (B7), 5911}5921. B 123, 341}346. Kitagawa, H., van der Plicht, J., 1998. Atmospheric radiocarbon calib- Henken}Mellies, W.U., Beer, J., Heller, F., HsuK , K.J., Shen, C., Bonani, ration to 45,000 yr B.P.: Late Glacial #uctuations and cosmogenic G., Hofmann, H.J., Suter, M., WoK l", W., 1990. Be and Be in isotope production. Science 279, 1187}1190. SouthAtlantic DSDP Site 519: Relation to geomagnetic reversals Klein, J., Evenson, E.B., Gosse, J.C., Lawn, B., Middleton, R., 1995. and to sediment composition. Earthand Planetary Science Letters A preliminary attempt to date terraces using Be EOS, Trans. 98, 267}276. American Geophysical Union Annual Fall meeting 76, F684. Hofmann, H.J., Beer, J., Bonani, G., von Gunten, H.R., Raman, S., Klein, J., Giegengack, R., Middleton, R., Sharma, P., Underwood, J.R., Suter, M., Walker, R.L., WoK l#i, W., Zimmermann, D., 1987. Be: Weeks, R.A., 1986a. Revealing histories of exposure using in situ Half-life and AMS-standards. Nuclear Instruments and Methods in produced Al and Be in Libyan Desert Glass. Radiocarbon 28 Physics Research B 29, 32}36. (2A), 547}555. Holden, N.E., 1990. Total half-lives for selected nuclides. Pure and Klein, J., Giegengack, R., Middleton, R., Sharma, P., Underwood Jr.,, Applied Chemistry 62 (5), 941}958. J.R., Weeks, W.A., 1986b. Revealing histories of exposure using Hudson, G.B., Ca!ee, M.W., Beiringer, J., Ruiz, B., Kohl, C.P., in-situ produced Al and Be in Libyan desert glass. Radiocarbon Nishiizumi, K., 1991. Production rate and retention properties of 28, 547}555. cosmogenic He and Ne in quartz. EOS 72 (44), 575. Klein, J., Gosse, J., 1996. Terrestrial factors that in#uence production Hughes, E.E., Mann, W.B., 1964. The half-life of carbon-14: comments rates. Radiocarbon 38 (1), 161}162. on the mass-spectrometic method. International Journal of Applied Klein, J., Lawn, B., Gosse, J., Harrington, C., 1997. Can terrestrial Radiation and Isotopes 15, 97}100. cosmogenic Be-10 be measured in whole rock samples to decipher Inn, K.G.W., Raman, S., Coursey, B.M., Fasset, J.D., Walker, R.I., 1987. surface exposure histories. Geological Society of America Abstracts Development of the NBS Be/Be isotopic standard reference withPrograms, 29(6). material. Nuclear Instruments and Methods in Physics B 29, 27. Klein, J., Middleton, R., Fink, D., Sharma, P., 1988. Ca in terrestrial Ivy-Ochs, S., 1996. The dating of rock surfaces using in situ produced samples: applications in dating and geomorphology EOS, Transac- Be, Al, and Cl, withexamples from Antarctica and theSwiss tions, American Geophysical Union, 1207. Alps. Ph. D. Thesis, Swiss Federal Institute of Technology Zurich, Klein, J., Middleton, R., Tang, H.-Q., 1982. Modi"cations of an FN Zurich, 196 pp. Tandem for Quantitative Measurements of Be. Nuclear Instru- Ivy-Ochs, S., Kubik, P.W., Masarik, J., Wieler, R., Bruno, L., Schluech- ments and Methods 193, 601}616. ter, C., 1998. Preliminary results on the use of pyroxene for Be Kocharov, G.E., Blinov, A.V., Konstantinov, A.N., Levchenko, V.A., surface exposure dating. Schweizerische Mineralogische und Pet- 1989. Temporal Be and C variations: a tool for paleomagnetic rographische Mitteilungen 78 (3), 375}382. research. Radiocarbon 31 (2), 163}168. Ivy-Ochs, S., SchluK chter, C., Kubik, P.W., Denton, G.H., 1999. Moraine Kohl, C.P., Nishiizumi, K., 1992. Chemical isolation of quartz for exposure dates imply synchronous Younger Dryas glacier measurement of in situ-produced cosmogenic nuclides. Geochimica advance in the European Alps and in the Southern Alps of New et Cosmochimica Acta 56, 3583}3587. 1556 J.C. Gosse, F.M. Phillips / Quaternary Science Reviews 20 (2001) 1475}1560
Kok, Y.S., Tauxe, L., 1996a. Saw-toothed pattern of relative paleoin- Lal, D., Craig, H., Wacker, F., Poreda, R., 1989. He in diamonds: The tensity records and cumulative viscous remanence. Earthand Plan- cosmogenic component. Geochimica et Cosmochimica Acta 53, etary Science Letters 137, 95}99. 569}574. Kok, Y.S., Tauxe, L., 1996b. Saw-toothed pattern of sedimentary Lal, D., Malhotra, P.K., Peters, B., 1958. On the production of radioiso- paleointensity records explained by cumulative viscous remanence. topes in the atmosphere by cosmic radiation and their application Earthand Planetary Science Letters 144, E9 }E14. to meteorology. Journal of Atmospheric and Terrestrial Physics 12, Kong, P., Nishiizumi, K., Finkel, R.C., Ca!ee, M.W., 1999. In situ 306. produced cosmogenic Be and Al in olivine. Eos, Trans- Lal, D., Peters, B., 1967. Cosmic ray produced radioactivity on the actions, American Geophyisical Union 1999 Fall Meeting 80 (46), earth. In: Sitte, K. (Ed.), Handbuch der Physik. Springer, Berlin, F1166. pp. 551}612. Kono, M., Hiroi, O., 1996. Paleosecular variation of "eld intensities and Lanci, L., Lowrie, W., 1997. Magnetostratigraphic evidence that &tiny dipole moments. Earthand Planetary Science Letters 139, 251 }262. wiggles' in the oceanic magnetic anomaly record represent geomag- Kovacheva, M., 1980. Summarized results of the archaeomagnetic netic paleointensity variations. Earthand Planetary Science Letters investigation of the geomagnetic "eld variation for the last 8000 yr 148, 581}592. in south-eastern Europe. Geophysical Journal of the Royal Astro- Larsen, P.L., Bierman, P.R., Ca!ee, M., 1995. Preliminary in situ nomical Society 61, 57}64. production rates of cosmogenic Be and Al over the past 21.5 ky Kovacheva, M., 1982. Archaeomagnetic investigations of geomagnetic from the terminal moraine of the Laurentide ice sheet, north-central secular variations. Philosophical Transactions of the Royal Society New Jersey. Geological Society of America Abstracts withPro- of London A 306, 79}86. grams 27, A59. Kubik, P.W., Elmore, D., Conard, D., Nishiizumi, K., Arnold, J.R., Laughlin, A.W., Poths, J., Healey, H.A., Reneau, S., WoldeGabriel, G., 1986. Determination of cosmogenic Ca in a meteorite withtan- 1994. Dating of Quaternary basalts using cosmogenic He and dem accelerator mass spectrometry. Nature 319, 568}570. C methods with implications for excess Ar. Geology 22, Kubik, P.W., Ivy-Ochs, S., Masarik, J., Frank, M., SchluK chter, C., 1998. 135}138. Be and Al production rates deduced from an instantaneous Lavielle, B., Marti, K., Jeannot, J.-P., Nishiizumi, K., Ca!ee, M., 1999. event within the dendro-calibration curve, the landslide of KoK fels The Cl}Ar}K} K records and cosmic ray production rates OG tz, Valley Austria. Earthand Planetary Science Letters 161 (1 }4), in iron meteorites. Earthand Planetary Science Letters 170, 93 }104. 231}241. Lederer, C.M., Shirely, V.S., 1978. Table of Isotopes. 7th edition. Wiley, Kubik, P.W., Korschinek, G., Nolte, E., 1984. Accelerator mass spectro- New York, 690 pp. metry of Cl in limestone and some palaeontological samples using Leland, J., Reid, M.R., Burbank, D.W., Finkel, R., Ca!ee, M., 1998. completely stripped ions. Nuclear Instruments and Methods B 5, Incision and di!erential bedrock uplift along the Indus River near 326}330. Nanga Parbat, Pakistan Himalaya, from Be and Al exposure Kurz, M.D., 1986a. Cosmogenic helium in a terrestrial igneous rock. age dating of bedrock straths. Earth and Planetary Science Letters Nature 320, 435}439. 154, 93}107. Kurz, M.D., 1986b. In situ production of terrestrial cosmogenic helium Lemaitre, G., Vallarta, M.S., 1933. On Compton's latitude e!ect of and some applications to geochronology. Geochimica et Cos- cosmic radiation. Physical Review 43 (2), 87}91. mochimica Acta 50, 2855}2862. Libby, F., Anderson, E.C., Arnold, J.R., 1949. Age determination by Kurz, M.D., Colodner, D., Trull, T.W., Moore, R.B., O'Brien, K., 1990. radiocarbon content: World-wide assay of natural radiocarbon. Cosmic ray exposure dating within situ produced cosmogenic He Science 109, 227}228. : Results from young Hawaiian lava #ows. Earthand Planetary Licciardi, J.M., Kurz, M.D., Clark, P.U., Brook, E.J., 1999. Calibration Science Letters 97, 177}189. of cosmogenic He production rates from Holocene lava #ows in Kurz, M.D., O'Brien, P., Garcia, M., Frey, F.A., 1985. Isotopic evolu- Oregon, USA, and e!ects of the Earth's magnetic "eld. Earthand tion of Haleakala volcano: Primordial, radiogenic and cosmogenic, Planetary Science Letters 172 (3-4), 261}271. helium. EOS 66, 1120. Lifton, N.A., Jull, A.J.T., Quade, J., submitted. A new extraction tech- Lal, D., 1958. Investigations of nuclear interactions produced by cosmic nique and production rate estimate for in situ cosmogenic Cin rays. Ph.D. Thesis, Tata Institute of Fundamental Research, Bombay. quartz. Geochemica et Cosmochimica Acta. Lal, D., 1987a. Cosmogenic nuclides produced in situ in terrestrial Light, E.S., Merker, M., Verschell, H.J., Mendell, R.B., Kor!, S.A., 1973. solids. Nuclear Instruments and Methods in Physics Research B 29, Time dependent worldwide distribution of atmospheric neutrons 238}245. and of their products 2. Calculation. Journal of Geophysical Re- Lal, D., 1987b. Production of He in terrestrial rocks. Chemical Geol- search78 (16), 2741 }2762. ogy (Isotope Geoscience Section) 66, 89}98. Lingenfelter, R.E., 1963. Production of C by cosmic ray neutrons. Lal, D., 1988. In situ-produced cosmogenic isotopes in terrestrial rocks. Reviews of Geophysics 1 (1), 35}55. Annual Review of Earthand Planetary Sciences 16, 355 }388. Lingenfelter, R.E., Flamm, E.J., 1964. Solar neutrons and the earth Lal, D., 1991. Cosmic ray labeling of erosion surfaces: in situ nuclide radiation belts. Science 144, 292}294. production rates and erosion rates. Earthand Planetary Science Litherland, A.E., 1987. Fundamentals of accelerator mass spectrometry. Letters 104, 424}439. Philosophical Transactions of the Royal Society of London A 323, Lal, D., 1996. On cosmic-ray exposure ages of terrestrial rocks: a sug- 5}21. gestion. Radiocarbon 37 (3), 889}898. Liu, B., Phillips, F.M., Fabryka-Martin, J.T., Fowler, M.M., Stone, Lal, D., Arnold, J.R., 1985. Tracing quartz through the environment. W.D., 1994. Cosmogenic Cl accumulation in unstable landforms, Proceedings of the Indian Academy of Science (Earth Planetary 1. E!ects of the thermal neutron distribution. Water Resources Science Section) 94, 1}5. Research30, 3115 }3125 (31, 1159). Lal, D., Arnold, J.R., Honda, M., 1960. Cosmic-ray production rates of Lockwood, J.A., Yingst, H.E., 1956. Correlation of meteorological Be in oxygen, and P,P,S in argon at mountain altitudes. parameters withcosmic-ray intensity. PhysicalReviews 104, Physics Reviews 118, 1626. 1718}1722. Lal, D., Arnold, J.R., Nishiizumi, K., 1985. Geophysical records of Looosli, H.H., 1983. A dating method with argon-39. Earth and Planet- at tree: new application for studying geomagnetic "eld and ary Science Letters 63, 51}62. solar activity changes during the past 104 years. Meteoritics 20, Macciaroli, P., Giegengack, R., Klein, J., Middleton, R., Lawn, B., 1994. 403}414. Late Quaternary glaciation of exposed rock surfaces along a ridge J.C. Gosse, F.M. Phillips / Quaternary Science Reviews 20 (2001) 1475}1560 1557
of the Appalachian Mountains, dated using Al and Be produced Middleton, R., Brown, L., Dezfouly-Arjomandy, B., Klein, J., 1993. On in situ. Geological Society of America. Abstracts withPrograms 26, Be standards and the half life of Be. Nuclear Instruments and A}125. Methods in Physics Research B 82, 399}403. Mankinen, E.A., Champion, D.E., 1993. Latest Pleistocene and Holo- Middleton, R., Fink, D., Klein, J., Sharma, P., 1989. Ca concentra- cene geomagnetic paleointensity on Hawaii, Science 412}416. tions in modern bone and their implications for dating. Radiocar- Marsella, K.A., Bierman, P.R., Davis, P.T., Ca!ee, M.W., in press. bon 31 (3), 305}309. Cosmogenic Be and Al ages for the last glacial maximum, Middleton, R., Klein, J., 1987. Al: measurement and applications. eastern Ba$n Island, arctic Canada. Geological Society of America Philosophical Transactions of the Royal Society of London A 323, Bulletin. 121}143. Marti, K., Craig, H., 1987. Cosmic-ray produced neon and helium in Middleton, R., Klein, J., Brown, L., Tera, F., 1984. Be in Commercial the summit lavas of Maui. Nature 325, 335}337. Beryllium. Nuclear Instruments and Methods B 5, 511}513. Martinson, D.G., Pisias, N.G., Hays, J.D., Imbrie, J., Moore, T.C.J., Middleton, R., Klein, J., Raisbeck, G.M., Yiou, F., 1983. Accelerator Shackleton, N.J., 1987. Age dating and the Orbital Theory of the Ice Mass Spectrometry with Al. Nuclear Instruments and Methods in Ages: Development of a high-resolution 0 to 300000 year chrono- Physics Research 218, 430}438. stratigraphy. Quaternary Research 27, 1}29. Millikan, R.A., Neher, H.V., 1936. A precision world survey of sea-level Masarik, J., Beer, J., 1999. Simulation of particle #ux and cosmogenic cosmic-ray intensities. Physical Review 50, 15}24. nuclide production in the Earth's atmosphere. Journal of Geophysi- Montaser, A., 1998. In: Inductively coupled plasma mass spectrometry. cal Research104 (D10), 12,099 }12,111. Wiley, New York, pp. 964. Masarik, J., Reedy, R.C., 1995. Terrestrial cosmogenic-nuclide produc- Moore, G.L., 1989. Introduction to Inductively Coupled Plasma tion systematics calculated from numerical simulations. Earthand Atomic Emission Spectrometry. Elsevier, Amsterdam, 340 pp. Planetary Science Letters 136, 381}395. Morris, J., Gosse, J.C., Brachfeld, S., submitted. Cosmogenic Be and Masarik, J., Reedy, R.C., 1996. Monte carlo simulation of in-situ pro- the Solid Earth: Studies in Geomagnetism, Subduction Zone Pro- duced cosmogenic nuclides. Radiocarbon 38 (1), 163}164. cesses, and Active Tectonics. Reviews of Mineralogy, Spec. Vol. Mazaud, A., Laj, C., Bard, E., Arnold, M., Tric, E., 1991. Geomagnetic Morris, J.D., 1991. Applications of Be to problems in the earth "eld control of C production over the last 80 ka: implications for sciences. Annual Review of Earthand Planetary Science 19, the radiocarbon time scale. Geophysical Research Letters 18, 313}350. 1885}1888. Morrison, P., Pine, J., 1955. Radiogenic origin of the Helium isotopes McCarroll, D., Nesje, A., 1993. The vertical extent of ice sheet in in rock. Annals of the New York Academy of Sciences 62, Nordfjord, western Norway: measuring degree of rock surface 71}92. weathering. Boreas, pp. 255}265. Moscariello, A., Pugin, A., Wildi, W., Beck, C., Chapron, E., de Batist, McClelland, E., Briden, J.C., 1996. An improved methodology for M., Girardclos, S., Ivy-Ochs, S., Rachoud-Schneider, A.-M., Signer, Thellier-type paleointensity determination in igneous rocks and its C., van Clauwenberghe, T., 1998. Deglaciation wuermienne dans usefulness for verifying primary thermoremanence. Journal of Geo- des conditions lacustres a la terminaison occidentale du bassin physical Research 101 (B10), 21,995}22,013. lemanique. Eclogae Geologicae Helvetiae 91 (2), 185}201. McElhinny, M.W., McFadden, P.L., 1997. Palaeosecular variation over Negrini, R.M., Verosub, K.L., Davis, J.O., 1987. Long-term non-geo- the past 5 Myr based on a new generalized database. Geophysical centric axial dipole directions and a geomagnetic excursion from the Journal International 131, 240}252. Middle Pleistocene sediments of the Humboldt River Canyon, McElhinny, M.W., McFadden, P.L., Merrill, R.T., 1996. The time- Pershing County, Nevada, U.S.A. Journal of Geophysical Research averaged paleomagnetic "eld 0-5 Ma. Journal of Geophysical Re- 92, 10,617}10,628. search101 (B11), 25,007 }25,027. Niedermann, S., Graf, T., Kim, J.S., Kohl, C.P., Marti, K., Nishiizumi, McElhinny, M.W., Senanayake, W.E., 1982. Variations in the geomag- K., 1994. Cosmic-ray produced Ne in terrestrial quartz: the neon netic dipole 1: the past 50,000 years. Journal of Geomagnetism and inventory of Sierra Nevada quartz separates. Earthand Planetary Geoelectricity 34, 39}51. Science Letters 125, 341}355. McHargue, L.R., Damon, P.E., 1991. The global beryllium 10 cycle. Niedermann, S., Graf, T., Marti, K., 1993. Mass spectrometric identi- Reviews of Geophysics 29 (2), 141}158. "cation of cosmic-ray-produced neon in terrestrial rocks withmul- McHargue, L.R., Damon, P.E., Donahue, D.J., 1995. Enhanced cos- tiple neon components. Earthand Planetary Science Letters 118, mic-ray production of Be coincident withtheMono Lake and 65}73. Laschamp geomagnetic excursions. Geophysical Research Letters Nishiizumi, K., Finkel, R.C., Ca!ee, M.W., Southon, J.R., Kohl, C.P., 22 (5), 659}662. Arnold, J.R., Olinger, C.T., Poths, J. and Klein, J., 1994. Cos- Merker, M., Light, E.S., Verschell, H.J., Mendell, R.B., Kor!, S.A., 1973. mogenic production of Be and Al on the surface of the earth and Time dependent worldwide distribution of atmospheric neutrons underground, Eighth International Conference on Geochronology, and of their products 1. Fast neutron observations. Journal of Cosmochronology and Isotope Geochemistry (U.S. Geol. Surv. Geophysical Research 78, 2727}2740. Circular 1107), Berkeley, California, 234 pp. Merrill, R.T., McElhinny, M.W., 1983. In: The Earth's magnetic "eld, its Nishiizumi, K., Finkel, R.C., Klein, J., Kohl, C.P., 1996. Cosmogenic history, origin, and planetary perspective International Geophysical production of Be and Be in water targets. Journal of Geophysical Series, 32. Academic Press, New York, pp. 401. Research101, 22,225 }22,232. Merrill, R.T., McElhinny, M.W., McFadden, P.L., 1996. The Magnetic Nishiizumi, K., Kohl, C.P., Arnold, J.R., Klein, J., Fink, D., Middleton, Field of the Earth: Paleomagnetism, the Core, and the Deep Mantle. R., 1991a. Cosmic ray produced Be and Al in Antarctic rocks: International Geophysics Series, 63. Academic Press, San Diego, exposure and erosion history. Earth and Planetary Science Letters 531 pp. 104 (2/4), 440}454. Meynadier, L., Valet, J.-P., 1996. Post-depositional realignment of Nishiizumi, K., Kohl, C.P., Shoemaker, E.M., Arnold, J.R., Klein, J., magnetic grains and asymmetrical saw-toothpatterns of magentiz- Fink, D., Middleton, R., 1991c. In situ Be - Al exposure ages at ation intensity. Earthand Planetary Science Letters 140, Meteor Crater, Arizona. Geochimica et Cosmochimica Acta 55, 123}132. 2699}2703. Meynadier, L., Valet, J.-P., Weeks, R., Shackleton, N.J., Hagee, V.L., Nishiizumi, K., Lal, D., Klein, J., Middleton, R., Arnold, J.R., 1986. 1992. Relative geomagnetic intensity of the "eld during the last Production of Be and Al by cosmic rays in terrestrial quartz in 140 ka. Earthand Planetary Science Letters 114, 39 }57. situ and implications for erosion rates. Nature 319, 134}135. 1558 J.C. Gosse, F.M. Phillips / Quaternary Science Reviews 20 (2001) 1475}1560
Nishiizumi, K., Elmore, D., Ma, X.Z., Arnold, J.R., 1984. Be and Cl Meteor Crater, Arizona, from cosmogenic Cl and C in rock depthpro "les in an Apollo 15 drill core. Earthand Planetary varnish. Geochimica et Cosmochimica Acta 55 (9), 2695}2698. Science Letters 70, 157}163. Phillips, F.M., Zreda, M.G., Smith, S.S., Elmore, D., Kubik, P.W., Nishiizumi, K., Winterer, E.L., Kohl, C.P., Lal, D., Arnold, J.R., Klein, Sharma, P., 1990. Cosmogenic chlorine-36 chronology for glacial J., Middleton, R., 1989. Cosmic ray production rates of Be and deposits at Bloody Canyon, Eastern Sierra Nevada. Science 248, Al in quartz from glacially polished rocks. Journal of Geophysical 1529}1532. Research94 (B12), 17,907 }17,915. Phillips, W.M., Lifton, N.A., Quade, J., Jull, A.T.J., 1994. In situ produc- Nishiizumi, N., Klein, J., Middleton, R., Craig, H., 1990. Cosmogenic ed C in late Quaternary lava #ows of the Zuni}Bandera volcanic Be, Al, and He in olivine from Maui lavas. Earthand Planetary "eld, New Mexico, New Mexico Geological Society Ann Spring Science Letters 98, 263}266. Mtg Proceeding VolNMIMT, Socorro, NM, 34 pp. Norris, T.L., Gancarz, A.J., Rokop, D.J., Thomas, K.W., 1993. Half-life Phillips, W.M., McDonald, E.V., Reneau, S.L., Poths, J., 1996c. Resolv- of Al. Journal of Geophysical Research, Proceedings of the Four- ing inherited cosmogenic nuclides in soils: a case study from the teenthLunar and Planetary Science Conference Part 1 (suppl. 88), Pajarito Plateau: New Mexico, USA. Geological Society of America pp. B331}333. Abstracts withPrograms 28 (7), A180. O'Brien, K., 1979. Secular variations in the production of cosmogenic Phillips, W.M., McDonald, E.V., Reneau, S.L., Poths, J., 1998. Dating isotopes in the earth's atmosphere. Journal of Geophysical Research soils and alluvium withcosmogenic Ne depthpro "les: case studies 84 (A2), 423}431. from the Pajarito Plateau, New Mexico, USA. Earth and Planetary O'Brien, K., 1996. Cosmic-ray neutrons at ground level: temporal and Science Letters 160, 209}223. geodetic variations. Radiocarbon 38 (1), 165. Plummer, M.A., Phillips, F.M., Fabryka-Martin, J., Turin, H.J., O'Brien, K., Burke, G.D., 1973. Calculated cosmic ray neutron monitor Wigand, P.E., Sharma, P., 1997. Chlorine-36 in fossil rat urine: An response to solar modulation of galactic cosmic rays. Journal of archive of cosmogenic nuclide deposition over the past 40,000 years. Geophysical Research 78 (16), 3013}3019. Science 277, 538}541. O'Brien, K., Sandmeier, H.A., Hansen, G.E., Campbell, J.E., 1978. Pomerantz, M.A., 1971. Cosmic Rays. Van Nostrand Reinhold, New Cosmic-ray-induced neutron background sources and #uxes for York, 168 pp. geometries of air over water, ground, iron, and aluminum. Journal Pomerantz, M.A., Potnis, V.R., Sandstrom, A.E., 1960. The cosmic-ray of Geophysical Research 83, 114}120. equator and the Earth's magnetic "eld. Journal of Geophysical Ochs, M., Ivy-Ochs, S., 1997. The chemical behavior of Be, Al, Fe, Ca, Research65 (11), 3539 }3543. and Mg during AMS target preparation from terrestrial silicates Poreda, R.J., Cerling, T.E., 1992. Cosmogenic neon in recent lavas from modeled withchemicalspeciation calculations. Nuclear Instru- the western United States. Geophysical Research Letters 19, ments and Methods in Physics Research B 123, 235}240. 1863}1866. Ohno, M., Hamano, Y., 1992,. Geomagnetic poles over the last 10,000 Poths, J., Anthony, E.Y., Williams, W.J., Heizler, M., McIntosh, W.C., years. Geophysical Research Letters 19 (16), 1715}1718. 1996. Comparison of dates fror young basalts from the Onuchin, A.A., Burenina, T.A., 1996. Climatic and geographic patterns Ar/Ar and cosmogenic Helium techniques. Radiocarbon 38 (1), in snow density dynamics, Northern Eurasia. Arctic and Alpine 167. Research28 (1), 99 }103. Quenby, J.J., 1966. The interaction of cosmic rays with the solar and Olinger, C.T., Poths, J., Nishiizumi, K., Kohl, C.P., Finkel, R.C., Ca!ee, terrestrial magnetic "elds 415}426. M.W., Southon, J., Proctor, I., 1992. Attenuation lengths of cos- Quenby, J.J., Webber, W.R., 1959. Cosmic ray cut-o! rigidities and the mogenic production of Al, Be, and Ne in Bandelier Tu!. EOS Earth's magnetic "eld. Philosphical Magazine 4, 90}113. 73 (14), 185. Quenby, J.J., Wenk, G.J., 1962. Cosmic ray threshold rigidities and the Peck, J.A., King, J.W., Colman, S.M., Kravchinsky, V.A., 1996. An Earth's magnetic "eld. Philosophical Transactions 7, 1457}1485. 84-kyr paleomagnetic record from the sediments of Lake Baikal, Quidelleur, X., Valet, J.-P., Courtillot, V., Hulot, G., 1994. Long-term Siberia. Journal of Geophysical Research 101, 11,365}11,385. geometry of the geomagnetic "eld for the last "ve million years: An Peng, T.-H., 1989. Changes in ocean ventilation rates over the last 7000 updated secular variation database. Geophysical Research Letters years based on C variations in the atmosphere and oceans. 21 (15), 1639}1642. Radiocarbon 31 (3), 481}492. Raisbeck, G.M., Yiou, F., 1979. Possible use of Ca for radioactive Phillips, F.M., 1996. Chronology for #uctuations in Late Pleistocene dating. Nature 277, 42}43. Sierra Nevada glaciers and lakes. Science 274, 749}751. Raisbeck, G.M., Yiou, F., Bourles, D., Kent, D.V., 1985. Evidence for an Phillips, F.M., Flinsch, M., Elmore, D., Sharma, P., 1997a. Maximum increase in cosmogenic Be during a geomagnetic reversal. Nature ages of the Co( a valley (Portugal) engravings measured withchlor- 315, 315}317. ine-36. Antiquity 71, 100}104. Raisbeck, G.M., Yiou, F., Bourles, D., Lorins, C., Jouzel, J., Barkov, Phillips, F.M., Leavy, B.D., Jannik, N.O., Elmore, D., Kubik, P.W., N.I., 1987. Evidence for two intervals of enhanced Be deposi- 1986. The accumulation of cosmogenic Chlorine- in rocks: a method tion in Antarctic ice during the last glacial period. Nature 326, for surface exposure dating. Science 231, 41}43. 273}277. Phillips, F.M., Stone, W.D., Fabryka-Martin, J., 2000. An Raisbeck, G.M., Yiou, F., Jouzel, J., Petit, J.R., Barkov, N.I., Bard, E., improved approachto calculating low-energy cosmic ray neutron 1992. Be deposition at Vostok, Antarctica during the last 50,000 #uxes near the land/atmosphere interface. Chemical Geology years and its relationship to possible cosmogenic production vari- submitted. ations during this period. In: Bard, E., Broecker, W.S. (Eds.), Nato Phillips, F.M., Zreda, M.G., Elmore, D., Sharma, P., 1996a. A reevalu- ASI Series: The Last Deglaciation: Absolute and Radiocarbon ation of cosmogenic Cl production rates in terrestrial rocks. Chronologies. Springer, Berlin, pp. 127}139. Geophysical Research Letters 23 (9), 949}952. Raisbeck, G.M., Yiou, F., Zhou, S.Z., 1994. Paleointensity puzzle. Phillips, F.M., Zreda, M.G., Gosse, J.C., Klein, J., Evenson, E.B., Hall, Nature 371, 207}208. R.D., Chadwick, O.A., Sharma, P., 1997b. Cosmogenic Cl and Reedy, R.C., Arnold, J.R., Lal, D., 1983. Cosmic-ray record in solar Be ages of Quaternary glacial and #uvial deposits of the Wind system matter. Science 219 (4581), 127}134. River Range, Wyoming. Geological Society of America Bulletin 109 Reedy, R.C., Nishiizumi, K., Lal, D., Arnold, J.R., Englert, P.A.J., Klein, (11), 1453}1463. J., Middleton, R., Jull, A.J.T., Donahue, D.J., 1994a. Simulations of Phillips, F.M., Zreda, M.G., Smith, S.S., Elmore, D., Kubik, P.W., terrestrial in-situ cosmogenic-nuclide production. Nuclear Instru- Dorn, R.I., Roddy, D.J., 1991. Age and geomorphic history of ments and Methods in Physics Research B 92, 297}300. J.C. Gosse, F.M. Phillips / Quaternary Science Reviews 20 (2001) 1475}1560 1559
Reedy, R.C., Tuniz, C., Fink, D., 1994b. Report on the Workshop on Simpson, J.A., Baldwin, H.W., Uretz, R.B., 1951. Nuclear bursts Production Rates of Terrestrial In-situ-produced cosmogenic nucl- produced in the low energy nucleonic component of the cosmic ides. Nuclear Instruments and Methods B 92, 335}339. radiations. Physical Review 84 (2), 332}339. Repka, J.L., Anderson, R.S., Finkel, R.C., 1997. Cosmogenic dating of Simpson, J.A., Fagot, W.C., 1953. Properties of the low energy nuc- #uvial terraces, Fremont River, Utah. Earth and Planetary Science leonic component at large atmospheric depth. Physical Review 90, Letters 152, 59}73. 1068}1072. Rightmire, V.R.A., Kohman, T.P., Hintenberger, H., 1958. Uber die Simpson, J.A., Fenton, K.B., Katzman, J., Rose, D.C., 1956. E!ective Halbwertszeit des langlebigen Al. Zeitschrift fur Naturforschung geomagnetic equator for cosmic radiation. Physical Review 102 (6), 13A, 847}853. 1648}1653. Roberts, A.P., Lehman, B., Weeks, R.J., Verosub, K.L., Laj, C., 1997. Simpson, J.A., Fonger, S.B., Treiman, S.B., 1953. Cosmic radiation Relative paleointensity of the geomagnetic "eld over the last 200,000 intensity-time variations and their origin, 1. Neutron intensity vari- years from ODP sites 883 and 884, NorthPaci "c Ocean. Earthand ation method and meteorological factors. Physical Reviews 90, Planetary Science Letters 152, 11}23. 934}950. Roberts, A.P., Verosub, K.L., Negrini, R.M., 1994. Middle/Late Pleis- Small, E., Anderson, R.S., 1998. Pleistocene relief production in Laram- tocene relative paleointensity of the geomagnetic "eld from lacus- ide mountain ranges, western United States. Geology 26 (2), trine sediments, Lake Chewaucan, western United States. 123}126. Geophysical Journal International 118, 101}110. Small, E.E., Anderson, R.S., Hancock, G.S., 1999. Estimates of the rate Robinson, C., Raisbeck, G.M., Yiou, F., Lehman, B., Laj, C., 1995. The of regolithproduction using Be and Al from an alpine hillslope. relationship between Be and geomagnetic "eld strengthrecords in Geomorphology 27 (1-2), 131}150. central NorthAtlantic sediments during thelast 80 ka. Earthand Small, E.E., Anderson, R.S., Repka, J.L., Finkel, R., 1997. Erosion rates Planetary Science Letters 136, 551}557. of alpine bedrock summit surfaces deduced from in situ Be and Roederer, J.G., 1952. Uber die absorption der nukleonenkomponente Al. Earthand Planetary Science Letters 150, 413 }425. der kosmischen strahlung in 21-o geomagnetischer breite. Zeit- Smart, D.F., Shea, M.A. (Ed.), 1985. Galactic cosmic radiation and solar schrift fur Naturforschung 7A, 765}771. energetic particles. Handbook of Geophysics and the Space Envi- Rossi, B.R., 1948. Interpretation of cosmic-ray phenomena. Reviews of ronment. Air Force Geophysics Laboratory, 6-1}6-29 pp. Modern Physics 20, 537}583. Soberman, R.K., 1956. High-altitude cosmic-ray neutron intensity vari- Rossi, B.R., 1964. Cosmic Rays. McGraw Hill Book Company, New ation. Physical Review 102 (5), 1399}1409. York, 268 pp. Srinivasan, B., 1976. Barites: anomalous xenon from spallation and Sandstrom, A.E., 1958. Cosmic ray soft component measurements neutron-induced reactions. Earthand Planetary Science Letters 31 during a #ight from Scandinavia across the North Pole and around (6), 129}141. Asia and Europe. Nuovo Cimento VIII (X, Suppl.), 263}276. Staudacher, T., AlleH gre, C.J., 1991. Cosmogenic Neon in ultrama"c Sarda, P., Staudacher, T., Allegre, C.J., Lecomte, A., 1993. Cosmogenic nodules from Asia and in quartzite from Antarctica. Earthand neon and helium at ReH union: measurement of erosion rate. Earth Planetary Science Letters 106, 87}102. and Planetary Science Letters 119, 405}417. Staudacher, T., AlleH gre, C.J., 1993. Ages of the second caldera of Piton Schaefer, J., Ivy-Ochs, S., Wieler, R., Leya, I., Baur, H., Denton, G., de la Fournaise volcano (ReH union) determined by cosmic ray pro- Schluechter, C., 1999. Cosmogenic noble gas studies in the oldest duced He and Ne. Earthand Planetary Science Letters 119, landscape on Earth; surface exposure ages of the Dry Valleys, 395}404. Antarctica. Earthand Planetary Science Letters 167 (3-4), 175 }182. Steig, E.J., Wolfe, A.P., Miller, G.H., 1998. Wisconsinan refugia and the Schneider, D.A., Mello, G.A., 1996. A high-resolution marine sedimen- glacial history of eastern Ba$n Island, Arctic Canada: Coupled tary record of geomagnetic intensity during the Brunhes Chron. evidence from cosmogenic isotopes and lake sediments. Geology 26, Earthand Planetary Science Letters 144, 297 }314. 835}838. Seidl, M.A., Finkel, R.C., Ca!ee, M.W., Hudson, G.B., Dietrich, W.E., Stephenson, R.M., 1954. Introduction to Nuclear Engineering. 1997. Cosmogenic isotope analyses applied to river longitudinal McGraw-Hill, New York. pro"le evolution: problems and interpretations. EarthSurface Pro- Sternberg, R., 1996. Workshop on `The Secular Variations in the Pro- cesses and Landforms 22, 195}209. duction Rates of Cosmogenic Nuclides on Eartha: paleomagnetic Sharma, P., Middleton, R., 1989. Radiogenic production of Be and averages of geomagnetic latitude. Radiocarbon 38 (1), 169}170. Al in uranium and thorium ores: implications for studying terres- Stone, J., Allan, G.L., Fi"eld, L.K., Evans, J.M., Chivas, A.R., 1994. trial samples containing low levels of Be and Al. Geochimica et Limestone erosion measurements withcosmogenic chlorine-36in Cosmochimica Acta 53, 709}716. calcite-preliminary results from Australia. Nuclear Instruments and Shea, M.A., Smart, D.F., 1983. A world grid of calculated cosmic ray Methods in Physics Research B 92, 311}316. vertical cuto! rigidities of 1980.0. 18thInternational Cosmic Ray Stone, J., Evans, J., Fi"eld, K., Cresswell, R., Allan, G., 1996. Cos- Conference Conference Papers 3, 415}418. mogenic chlorine-36 production rates from calcium and potassium. Shea, M.A., Smart, D.F., Gentile, L.C., 1987. Estimating cosmic ray Radiocarbon 38 (1), 170}171. vertical cut-o! rigidities as a function of the McIlwain L-parameter Stone, J.O., 1999. A consistent Be-10 production rate in quartz - muons for di!erent epochs of the geomagnetic "eld. Physics of the Earth and altitude scaling. AMS-8 Proceedings Abstract Volume, Vienna, and Planetary Interiors 48, 200}205. Austria. Shea, M.A., Smart, D.F., McCracken, K.G., 1965. A study of vertical Stone, J.O., in press. Air pressure and cosmogenic isotope production. cuto! rigidities using sixthdegree simulations of thegeomagnetic Journal of Geophysical Research. "eld. Journal of Geophysical Research 70, 4117}4130. Stone, J.O., Ballantyne, C.K., Fi"eld, L.K., 1998a. Exposure dating and Sheppard, M.K., Arvidson, R.E., Ca!ee, M., Finkel, R., Harris, L., 1995. validation of periglacial weathering limits, northwest Scotland. Ge- Cosmogenic exposure ages of basalt #ows: Lunar Crater volcanic ology 26, 587}590. "eld, Nevada. Geology 23, 21}24. Stone, J.O.H., 1998. A rapid fusion method for separation of beryllium- Shirley, V.S. (Ed.), 1998. Table of Isotopes, 1. Wiley, New York. 10 from soils and silicates. Geochimica et Cosmochimica Acta 62 Siame, L.L., BourleH s, D.L., SeH brier, M., Bellier, O., Castano, J.C., (3), 555}561. Araujo, M., Perez, M., Raisbeck, G.M., Yiou, F., 1997. Cosmogenic Stone, J.O.H., Evans, J.M., Fi"eld, L.K., Allan, G.L., Cresswell, R.G., dating ranging from 20 to 700 ka of a series of alluvial fan surfaces 1998b. Cosmogenic chlorine-36 production in calcite by muons. a!ected by the El Tigre fault, Argentina. Geology 25 (11), 975}978. Geochimica et Cosmochimica Acta 62 (3), 433}454. 1560 J.C. Gosse, F.M. Phillips / Quaternary Science Reviews 20 (2001) 1475}1560
Stoner, J.S., Channell, J.E.T., Hillaire-Marcel, C., 1995. Late Pleistocene 3rd Winter School on HADRONIC PHYSICS. Elsevier Science relative geomagnetic paleointensity from the deep Labrador Sea: Publishers, Folgaria (Trento), Italy, Feb 15}20, 1988, pp. 425}444. Regional and global correlations. Earthand Planetary Science Valet, J.-P., Brassart, J., Le Meur, I., Soler, V., Quidelleur, X., Tric, E., Letters 134, 237}252. Gillot, P.Y., 1996. Absolute paleointensity and magnetomineralogi- Stormer, C., 1934. On the trajectories of electric particles in the "eld cal changes. Journal of Geophysical Research 101 (B11), of a magnetic dipole with applications to the theory of cosmic 25,029}25,044. radiation: third communication. Astrophysica Norvegica 1 (1), Valet, J.-P., Meynadier, L., 1993. Geomagnetic "eld intensity and rever- 1}10. sals during the past four million years. Nature 366, 234}238. Stormer, C., 1935. On the trajectories of electric particles in the "eld of a Van der Woerd, J., Ryerson, F.J., Tapponnier, P., Gaudemer, Y., Finkel, magnetic dipole with applications to the theory of cosmic R., Meriaux, A.S., Ca!ee, M., Guaguang, Z., Qunlu, H., 1998. radiation: fourthcommunication. AstrophysicaNorvegica 1 (4), Holocene left-slip rate determined by cosmogenic surface dating on 115}184. the Xidatan segment of the Kunlun fault (Qinghai, China). Geology Strack, E., Heisinger, B., Dockhorn, B., Hartmann, F.J., Korschinek, G., 26 (8), 695}698. Nolte, E., Morteani, G., Petitjean, C., Neumaier, S., 1994. Deter- Verosub, K.L., 1996. Recent advances in determining absolute and mination of erosion rates withcosmogenic Al. Nuclear Instru- relative paleointensity variations of the geomagnetic "eld. ments and Methods B 92, 317}320. Radiocarbon 38 (1), 173. Stuiver, M., Grootes, P.M., Braziunas, T.F., 1995. The GISP O Vogt, S., Elmore, D., Sharma, P., Dunna, A., 1996. The Cl/Cl climate record of the past 16,500 years and the role of the sun, ocean, method for determining exposure time and erosion rates of surfaces. and volcanoes. Quaternary Research44, 341 }354. Radiocarbon 38, 122. Stuiver,M.,Reimer,P.J.,1993.ExtendedC data base and revised Vogt, S., Herzog, G.F., Reedy, R.C., 1990. Cosmogenic nuclides in CALIB 3.0 C age calibration program. Radiocarbon 35 (1), 215}230. extra-terrestrial materials. Reviews of Geophysics 28, 253}275. Summer"eld, M.A., Hulton, N.J., 1994. Natural controls of #uvial Wells, S.G., McFadden, L.D., Poths, J., Olinger, C.T., 1995. Cos- denudation rates in major world drainage basins. Journal of Geo- mogenic He surface exposure dating of stone pavements: Implica- physical Research B 99 (7), 13,871}13,883. tions for landscape evolution in deserts. Geology 23 (7), 613}616. Summer"eld, M.A., Stuart, F.M., Cockburn, H.A.P., Sugden, D.E., Welz, B., 1999. Atomic absorption spectrometry. Wiley, New York, Denton, G.H., Dunai, T., Marchant, D.R., 1999. Long-term rates of 941 pp. denudation in the Dry Valleys, Transantarctic Mountains, southern Wolfendale, A.W., 1963. Cosmic Rays. Philosophical Library Inc, New Victoria Land, Antarctica based on in-situ-produced cosmogenic York, 222 pp. Ne. Geomorphology 27 (1-2), 113}130. Wu, C.S., Townes, C.H., Feldman, L., 1949. Radioactivity of Cl. Swanson, T., 1996. Determination of Cl production rates from the Physical Review 76, 692}693. deglaciation history of Whidbey and Fidalgo Islands, Washington. Yamashita, M., Stephens, L.D., Patterson, H.W., 1966. Cosmic-ray- Radiocarbon 38 (1), 172. produced neutrons at ground level: neutron production rate and #ux Synal, H.-A., 1995. Accelerator mass spectrometry: new applications. distribution. Journal of Geophysical Research 71 (16), 3817}3834. Applied Radiative Isotopes 46 (6/7), 457}466. Yamazakia, T., Ioka, N., Eguchi, N., 1995. Relative paleointensity of the Tauxe, L., 1993. Sedimentary records of relative paleointensity of the geomagnetic "eld during the Brunhes Chron. Earth and Planetary geomagnetic "eld: theory and practice. Reviews of Geophysics 31 Science Letters 136, 525}540. (3), 319}354. Yiou, F., Raisbeck, G.M., 1972. Half-life of Be. Physical Review Templeton, D.H., 1953. Nuclear reactions induced by high energy Letters 29 (6), 372}375. particles. Annual review of nuclear science 2, 93}104. Yokoyama, Y., Reyss, J.-L., Guichard, F., 1977. Production of Teucher, M., 1952. Die absorption der nukleonenkomponente der ko- radionuclides by cosmic rays at mountain altitudes. Earthand smischen strahlung in luft zwischen seehohe und 4000 m. Zeitschrift Planetary Science Letters 36, 44}50. fur Naturforschung 7A, 61}63. Zentmire, K.N., Gosse, J.C., Baker, C., McDonald, E. and Wells, S., Tongiorgi, V.C., 1949. On the mechanism of production of the 1999. The problem of inheritance when dating alluvial fans and neutron component of the cosmic radiation. Physical Review 76, terraces with TCN: Insight from the Matanuska Glacier. GSA 517}526. Abstracts and Programs, 31. Treiman, S.B., 1952. Analysis of the nucleonic component based on Zreda, M., England, J., Phillips, F., Elmore, D., Sharma, P., 1999. neutron latitude variation. Physical Review 86 (6), 917}923. Unblocking of the Nares Strait by Greenland and Ellesmere ice- Tric, E., Valet, J.-P., Tucholka, P., Paterne, M., Labeyrie, L., Guichard, sheet retreat 10,000 years ago. Nature 398, 139}142. F., Tauxe, L., Fontugne, M., 1992. Paleointensity of the geomag- Zreda, M., Noller, J.S., 1998. Ages of prehistoric earthquakes revealed netic "eld during the last 80,000 years. Journal of Geophysical by cosmogenic chlorine-36 in a bedrock fault scarp at Hebgen Lake. Research97 (B6), 9337 }9351. Science 292 (5391), 1097}1099. Trull, T.W., Brown, E.T., Marty, B., Raisbeck, G.M., Yiou, F., 1995. Zreda, M., Phillips, F., Elmore, D., 1994. Cosmogenic Cl accumula- Cosmogenic Be and He accumulation in Pleistocene beachterra- tion in unstable landforms Simulations and measurements on erod- ces in DeathValley, California, U.S.A. Implications for cosmic-ray ing moraines. Water Resources Research30 (11), 3127 }3136. exposure dating of young surfaces in hot climates. Chemical Geol- Zreda, M.G., 1994. Development and calibration of the cosmogenic ogy 119, 191}207. Cl surface exposure dating method and its application to the Trull, T.W., Kurz, M.D., Jenkins, W.J., 1991. Di!usion of cosmogenic chronology of late Quaternary glaciations. Ph.D. Thesis, New He in olivine and quartz: implications for surface exposure dating. Mexico Institute of Mining and Technology, Socorro, 318 pp. Earthand Planetary Science Letters 103, 241 }256. Zreda, M.G., Phillips, F.M., Elmore, D., Kubik, P.W., Sharma, P., Tuniz, C., Bird, R., Klein, J., Herzog, G., 1991. Accelerator Mass Dorn, R.I., 1991. Cosmogenic Cl production in terrestrial rocks. Spectrometry. CRC, Littleton, MA in preparation. Earthand Planetary Science Letters 105, 94 }109. Tuniz, C., Klein, J., 1989. Ultra-high sensitivity mass spectrometry: Zreda, M.G., Phillips, F.M., Kubik, P.W., Sharma, P., Elmore, D., 1993. Applications to rare nuclear and cosmological processes archived in Cosmogenic Cl dating of a young basaltic eruption complex, geological samples. In: Cherubini, R., Dalpiaz, P., Minetti, B (Ed.), Lathrop Wells, Nevada. Geology 21, 57}60.