Global Geologic Maps Are Tectonic Speedometers— Rates of Rock Cycling from Area-Age Frequencies

Global geologic maps are tectonic speedometers— Rates of rock cycling from area-age frequencies

Bruce H. Wilkinson1†, Brandon J. McElroy2, Stephen E. Kesler3, Shanan E. Peters4, and Edward D. Rothman3 1Department of Earth Sciences, Syracuse University, Syracuse, New York 13244, USA 2Department of Geological Sciences, Jackson School of Geosciences, University of Texas, Austin, Texas 78712, USA 3Department of Geological Sciences, University of Michigan, Ann Arbor, Michigan 48109, USA 4Department of Geology and Geophysics, University of Wisconsin, Madison, Wisconsin 53706, USA

ABSTRACT the Earth’s surface, age-frequency distribu- lion years suggested by map age-frequencies tions for plutonic and metamorphic rocks are the same as would be anticipated on the Relations among ages and present areas of exhibit lognormal relations, with modes at basis of hundreds of published rates of ero- exposure of volcanic, sedimentary, plutonic, ca. 154 and 697 Ma, respectively. A dearth sional uplift and exhumation determined by and metamorphic rock units (lithosomes) of younger exposures of plutonic and meta- more conventional geochronometers. This record a complex interplay between depths morphic rocks refl ects the fact that these agreement suggests that geologic maps serve and rates of formation, rates of subsequent rock types form at depth, and some duration as effective deep-time speedometers for the tectonic subsidence and burial, and/or rates of tectonism is therefore required for their geologic rock cycle. of uplift and erosion. Thus, they potentially exposure. Increasing modal ages, from Qua- serve as effi cient deep-time geologic speed- ternary for volcanic and sedimentary succes- INTRODUCTION ometers, providing quantitative insight into sions, to early Mesozoic for intrusive rocks, rates of material transfer among the principal to Neoproterozoic for metamorphic rocks, Since the fi rst complete geologic map of Eng- rock reservoirs—processes central to the rock demonstrate that greater amounts of geologic land, Wales, and Scotland was scribed and pub- cycle. Areal extents of lithosomes exposed on time are required for uplift to bring more lished by William Smith in 1815, geologic maps all continents from two map sources (Geolog- deeply formed rocks to the Earth’s surface. have increasingly become our most important ical Survey of Canada [GSC] and the Food The two different age-frequency dis- tools for visually representing variation in the and Agricultural Organization [FAO] of the tributions observed for these major rock Earth’s surfi cial geologic features. Geologic United Nations Educational, Scientifi c, and types—a general power-law age distribu- mapping serves as a linchpin of undergraduate Cultural Organization [UNESCO]) indicate tion for volcanic and sedimentary rocks education in the Earth sciences, and geologic that volcanic, sedimentary, plutonic, and and a lognormal distribution for plutonic maps now provide information on the distribu- metamorphic rocks occupy ~8%, 73%, 7%, and metamorphic rock ages—refl ect the tion of different types of rocks and structures and 12% of global exposures, respectively. interplay between depths of formation and for resource discovery, land use decisions, and Plots of area versus age of all mapped rock mean rates of vertical tectonic displacement. hazards assessments. In addition to more practi- types display a power-law relation where Age-frequency distributions for each of the cal applications, geologic maps are the basis for ~6.5% of continental area is resurfaced with major rock types are closely replicated by a study of the long and rich geologic history of younger (~10% volcanic; 90% sedimentary) model that presumes that individual crustal continents and the planet as a whole (e.g., Veizer units every million years, and where areas of elements behave as a large population of and Jansen, 1979, 1985). rock exposure decrease by ~0.86% for each random walks in geologic time and crustal The possibility that geologic maps might pro- 1% increase in outcrop age (r2 = 0.90). Area- depth, and where the processes of surfi cial vide quantitative insight into this history was age relations for volcanic and sedimentary erosion associated with tectonic uplift serve brought into focus by James Gilluly (1969), lithosomes are similar to the power-law dis- to impose an absorbing boundary on this who was the fi rst to fully examine relations tribution defi ned by all rock units (because random-walk space. Comparisons between between rock age and outcrop area at conti- ~81% of mapped area consists of these two model-predicted age-frequencies and those nental scales. Using nail scissors to cut out and lithologies) and refl ect progressive decrease apparent in global map data suggest that separate individual rock units represented on in amount of exposure with increasing age. mean rates of crustal subsidence and uplift geologic maps of North and South America, he Over the long term, continental surfaces are are approximately equal in magnitude, with determined areas from the proportional weights blanketed by new volcanic rocks and sedi- mean rates of vertical tectonic diffusion of of map fragments representing each major rock ments at rates of ~1.5 and 12.1 × 106 km2/Ma, lithosomes from crustal depths of formation age and type. Gilluly (1969) recognized that the respectively. of about half a kilometer per million years. log-area of rock exposure decreases with the log In contrast to power-law–distributed vol- Rates of uplift and subsidence are strongly of increasing age (Fig. 1). This realization led canic and sedimentary rocks that form at dependent on durations of tectonic disper- him to conclude that: “The completeness of the sion (lithosome ages); however, mean rates geologic record obviously diminished with the †E-mail: [email protected] on the order of hundreds of meters per mil- passage of time, not simply because younger

GSA Bulletin; May/June 2009; v. 121; no. 5/6; p. 760–779; doi: 10.1130/B26457.1; 18 ﬁ gures; 4 tables.

760 For permission to copy, contact [email protected] © 2009 Geological Society of America Geologic maps are tectonic speedometers rocks come to bury the older, but also because the younger have been largely derived by the cannibalization of the older.” Rather than being South America 10,000,000 5 -0.85 a manifestation of lower rates of rock cycling in Area = 8.2 x 10 Age r2 = 0.85 Qt the geologic past, Gilluly correctly interpreted Mean age = 800 Ma South America the pattern of decreasing rock area with increasing rock age as a manifestation of the unrelent- 1,000,000

/m.y.) Tpl ing importance of tectonic processes of uplift 2 and associated erosion balanced by generally North America equal amounts of subsidence and deposition that 100,000 Kt Tpa Sl serve to “drive” the geologic rock cycle. Ms Or Pa Examination of Gilluly’s (1969) data (Fig. 1) Tmi Tpl Teo raises several other questions related to those Tol 10,000 geologic processes that control outcrop age Jr and area. For example, one might wonder why Tr North America rock age and exposed area scale approximately Pm Area = 6.2 x 105 Age-0.64 2 linearly in log-log space. Such “power-law” (km exposed Area 1000 r = 0.74 relations characterize a wide range of scale- Cm Mean age = 750 Ma invariant geologic data (e.g., Turcotte, 1992; Newman, 2005). Why are area-age data on geologic maps log-log linear? 100 10 1 The log-area versus log-age relationship iden- tifi ed by Gilluly (1969; Fig. 1) is numerically Age (Ma) described by both an intercept and a slope, the Figure 1. Ages and areas of geologic map units exposed in North (open diamonds and black former being related to amount of new outcrop line) and South (gray circles and gray line) America for Phanerozoic periods and epochs formed over some unit of time, and the latter (after Gilluly, 1969). Note decreasing area of outcrop with increasing age, log-log relation of being related to rates of outcrop area reduction, outcrop age to area, and somewhat lower slope for North American (−0.64) relative to South either through uplift and erosion or through sub- American (−0.85) outcrops. sidence and burial by younger units. In the case of geologic maps, intercept and slope values must be interrelated because the net area of continental crust has remained relatively constant principally upon the progressive elevation of and Agricultural Organization (FAO) of the over at least the past one billion years or so (e.g., a region,” it follows that global geologic maps United Nations Education, Science, and Cul- Pearson et al., 2007); addition of new (young) may serve as excellent recorders of fi rst-order tural Organization (UNESCO). map units to a fi xed land area must therefore be rates of Earth surface-rock formation and The Geological Survey of Canada Open-File approximately balanced by equivalent loss of destruction. In order to further investigate the 2915d, Generalized Geological Map of the World older map areas. effi cacy of geologic maps as speedometers of and Linked Databases (Kirkham et al., 1995), Gilluly’s (1969) data from North America the geologic rock cycle, we therefore evaluate includes digital data in the form of geographi- (Fig. 1), for example, have a 1 Ma intercept of the relation between areas and ages of exposed cally referenced rock-unit polygons. Associated ~620,000 km2, which is ~2.9% of the total area rock units at the global scale using several newly attribute tables contain area, age, rock type, and of the continent, and a slope of about −0.64 indi- compiled geologic maps. name information for each of 7463 polygons cating that North American rock area is inferred (mean map unit area of ~18,000 km2). Ages of to decrease by ~0.64% for each 1% increase in SOURCES OF DATA rock units are assigned to early, middle, late, rock age. South American data (Fig. 1) defi ne an era- or eon-duration intervals, and are broadly intercept of ~820,000 km2, or ~4.9% of the total Data on areas and ages of rocks exposed at classifi ed as plutons, mixed intrusive and meta- area of the continent, and South American rock the Earth’s surface have been compiled for morphic terrains, sedimentary, mixed volca- area decreases by ~0.85% for each 1% increase various rock types, countries, and continents nic (volcaniclastic and sedimentary), and tec- in rock age (Fig. 1). Taken at face value, these (e.g., Higgs, 1949; Gilluly, 1969; Bluth and tonic assemblages (schist belts and mélanges). data suggest that rates of rock cycling in South Kump, 1991; Peucker-Ehrenbrink and Miller, Because time intervals are of unequal duration, America are perhaps ~1.7 (4.9/2.9) times faster 2002, 2003), but only the data of Blatt and areas used in our study were normalized for than in North America, and that mean rock age Jones (1975) encompass major rock types for interval duration using the recent time scale of in South America is somewhat younger (Fig. 1). all continental land masses. These, however, Gradstein et al. (2004). Based solely on Gilluly’s study, it is not possible are based on ages determined for only 802 ran- The Geologic World Atlas (Choubert and to unequivocally conclude that values from the domly selected points across global continents, Faure-Mauret, 1981), published by the United two American continents are in fact statistically a sampling density of about one determination Nations at a scale of 1:10,000,000, is a signifi - different. Nevertheless, they do serve to exem- for each 167,000 km2 (an area about the size of cantly more detailed source of data, but is not plify the potential utility of geologic maps in Wisconsin). To obtain data with higher spatial in geographic information system (GIS) format. quantifying long-term rates of rock cycling. In density, we tabulated data on areas and ages of We therefore digitally scanned each of the 18 conjunction with the presupposition of Dutton exposed rock bodies as mapped by the Geologi- continental map sheets and then determined (1882) that “Erosion depends for its effi ciency cal Survey of Canada (GSC) and by the Food rock areas using commercial image analysis

Geological Society of America Bulletin, May/June 2009 761 Wilkinson et al.

Sedimentary Plutonic and Metamorphic Volcanic software. Pixel counts for outcrop area on the scanned images were converted to continental surface area by scaling pixel area to real-world A North America area in several 1° × 1° areas over each map sheet. 80% These efforts resulted in the tabulation of ages, rock types, and areas for 47,705 mapped rock 60% units (mean exposed area ~2900 km2), each of which was assigned to one of 36 time bins, rang- 40% ing from epochs, through lower, middle, and upper eras or eons. Although some rock units 20% are assigned to one of up to 50 lithologic sub- divisions, many are only resolved as volcanic, sedimentary, plutonic, or metamorphic. As with FAO (1981) Gilluly (1969) Peucker-Ehrenbrink and Miller (2002, 2003) GSC data, FAO rock areas were normalized for GSC (1995) Higgs (1949) Suchet et al. (2003) interval duration using Gradstein et al. (2004). Here we explicitly assume that reported ages Earth among the four major rock groups as volcanic, B sedimentary, plutonic, and metamorphic litho- 80% Relative abundance Relative somes from either map source represent durations since extrusion, deposition, crystallization, 60% and peak metamorphism, respectively.

40% LITHOLOGIC AND AREA-FREQUENCY DISTRIBUTIONS OF EXPOSED ROCK 20% UNITS

Although determination of net areal extent of FAO (1981) Blatt and Jones (1975) Meybeck (1987) different rock types was not the primary objec- GSC (1995) Gibbs and Kump (1994) Suchet et al. (2003) tive of this study, our tabulations yielded these Figure 2. Relative abundances of major rock types exposed at the Earth’s surface as data for all the major continents (Fig. 2 and tabulated in this study compared to estimates made by others for (A) North America Table 1). Based on relative abundances of major and for (B) all continents. Based on the Food and Agricultural Organization (FAO) rock types from these two sources, volcanic, and Geological Survey of Canada (GSC) maps, North American volcanic, sedimen- sedimentary, plutonic, and metamorphic rocks tary, plutonic, and metamorphic rocks represent ~11%, 66%, 8%, and 14% of expo- represent 10%–12%, 68%–65%, 9%–7%, and sures, respectively. Globally, these values are ~9%, 73%, 7%, and 11%, respectively. 13%–15% of North American exposures, and

TABLE 1. PROPORTIONS OF DIFFERENT TYPES OF ROCKS EXPOSED OVER NORTH AMERICA AND ALL CONTINENTS TABULATED FROM THE FAO AND GSC MAPS AND FROM OTHER SOURCES Plutonic and Volcanic Sedimentary Plutonic Metamorphic Other metamorphic Source Area (%) (%) (%) (%) (%) (%) FAO North America 10 68 9 13 - 22 GSC North America 12 65 7 15 - 22 Gilluly (1969) North America 8 52 21 - 191 403 Higgs (1949) United States2 7 88 4 - 11 53

Peucker-Ehrenbrink 2 United States and Miller (2002, 8 67 8 16 - 25 and Canada 2003) Suchet et al. (2003) North America 10 58 - - - 33 Average 9 66 10 15 - 21

FAO Earth 7 77 8 8 - 16 GSC Earth 10 70 6 15 - 21

Blatt and Jones Earth 8 66 9 17 - 26 (1975)

Gibbs and Kump 4 Earth 7 73 - - 20 (1994) Meybeck (1987) Earth 8 66 - - - 26 Suchet et al. (2003) Earth 8 65 - - - 28 Average 8 70 7 13 - 23 1“Undetermined.” 2Exclusive of Hawaii. 3Plutonic and “undetermined.” 4Includes 27.5% reported as “fold belts.” Abbreviations: FAO—Food and Agricultural Organization; GSC—Geological Survey of Canada.

762 Geological Society of America Bulletin, May/June 2009 Geologic maps are tectonic speedometers

10%–7%, 70%–77%, 6%–8%, and 15%–8% of global exposures, respectively. Values for North America and for all continents are in Lithotopes = 7462 –0.0107 Rock area (km2) good agreement with values reported from more Frequency = 688 e 1000 general studies by Blatt and Jones (1975), Gibbs r 2 = 0.934 and Kump (1994), Gilluly (1969), Higgs (1949), Meybeck (1987), Peucker-Ehrenbrink and Miller (2002, 2003), and Suchet et al. (2003). 100 With respect to sizes of lithosome outcrop areas, even perfunctory examination of almost any regional geologic map leads to the gen- Frequency eral observation that there are relatively more 10 mapped lithosomes of small size than of large size, that small units tend to be spatially associated with other small ones while large units are near other large units, and that lateral lithosome extent is commonly related to both lithology and 100 200 300 400 degree of tectonic deformation. Laterally exten- 2 sive, fl at-lying sedimentary and volcanic succes- Rock area (km ) sions generally occupy one end of the spectrum, Figure 3. Size-frequency distributions of square roots (~diameters) of rock while smaller exposures of intensely deformed body outcrop areas (diamonds) derived from the Geological Survey of plutonic and metamorphic complexes are at the Canada (GSC) map. These represent area-frequencies of the 7460 rock other. It is also the case that areas of geologic exposures that collectively make up the Earth’s 135 × 106 km2 ice-free sur- map units are, by defi nition, dependent on the face. Bin sizes are 10 km2; heavy line is the best exponential fi t to the data. detail of subdivision desired by the geologist- cartographer making the map. Numbers and sizes of mapped units must sum to the total area of the region in question. As a result, numbers Hence, geologic map area-frequencies suggest Comparison of this theoretical size-frequency and sizes of small units must show a system- that lateral occurrences of exposed lithosome distribution to the areal extents of volcanic, sedi- atic relation to numbers and sizes of the large boundaries approximately result from geologic mentary, plutonic, and metamorphic exposures units; a greater abundance of smaller outcrops, processes that yield a continuous random prob- from the GSC map yields Pearson correlation for example, must co-occur with either fewer ability of crossing rock-type boundaries as one coeffi cients of 0.83, 0.92, 0.79, and 0.89, respec- numbers or smaller areas of the large. This tru- transects a mapped surface. That is, in a statis- tively (Fig. 4). This good agreement suggests ism requires that sizes (areas) and frequencies tical sense, the spatial occurrence of map unit that a theoretical model, in which geologic map (numbers) of geologic map units exhibit certain boundaries is largely indeterminate. For exam- area is randomly subdivided, closely approxi- relations to each other. ple, the 7462 areas of volcanic, sedimentary, plu- mates sizes of lithologic divisions of the Earth’s McElroy et al. (2005) described size-frequency tonic, and metamorphic exposure mapped by the surface. Values of k, which correspond to the distributions for several types of mosaics devel- GSC are closely approximated by a function that probability of crossing a mapped unit boundary oped across the Earth’s surface, such as large describes the sizes of mosaic elements on a ran- per linear kilometer transect on the GSC map, fl uvial drainage basins and geopolitical divisions domly partitioned surface. Frequency of occur- for volcanic, sedimentary, plutonic, and meta- (i.e., countries), and pointed out that these distri- rence (F) of any rock body of some given area morphic rocks are 0.0121, 0.0084, 0.0142, and butions are similar to those exhibited by exposed (A) is closely approximated (Fig. 4) by the rela- 0.0091 per kilometer, respectively. lithosome areas in global geologic maps. They tion in Equation 1, where N is the total number of Only two variables, the number of mapped contend that these similarities emerge because lithosome exposures designated over the Earth’s geologic units and the total area under consid- mosaic element diameters are exponentially dis- surface (volcanic, sedimentary, plutonic, and eration, determine the frequencies of lithosome tributed (Fig. 3). Such exponential size-frequency exposure area. Although the amount of conti- distributions are the same as those arising from FA()= e−πkA/ (1) nental land area is fi nite and, to a fi rst approxi- the classic “broken-stick model” (e.g., Baumiller mation, invariant during the Phanerozoic, the and Ausich, 1992) in which divisions (such as metamorphic exposures are 892, 4095, 1008, numbers of lithosome exposures may be largely map unit boundaries) along some linear transect and 949, respectively), and k is the incidence of a matter of defi nition. Mean exposure area on (such as across a geologic map) are randomly occurrence over the Earth’s surface, expressed the FAO maps, for example, is ~2900 km2 (an distributed. That is, area-frequency distributions as Equation 2, where area ~70% the size of Rhode Island), while the of individual rock types on geologic maps are mean area on the GSC map is ~18,000 km2 closely approximated by the distribution that (an area ~4.5 times the size of Rhode Island). Nπ would result from the partitioning of continental k = (2)As noted above, values of k for volcanic, sedi- 2T surfaces into n subregions, such that distances a mentary, plutonic, and metamorphic exposures between each boundary along a transect are on the GSC map are 12.1, 8.4, 14.2, and 9.1 exponentially distributed (e.g., Fig. 3). Exponen- Ta is the total area of mapped volcanic, sedi- per thousand linear kilometers, respectively. tial distributions are anticipated when boundar- mentary, plutonic, and metamorphic rock (10.1, In other words, the distribution of bodies of ies between different rock types occur randomly. 97.2, 8.0, and 19.8 × 106 km2, respectively). each rock type is such that, at this scale of GSC

Geological Society of America Bulletin, May/June 2009 763 Wilkinson et al.

Lithosomes = 892 Lithosomes = 4095 A 2 B Mean size = 10,381 km Mean size = 21,949 km2 2 1000 r = 0.83 r2 = 0.92 100

100

10 Volcanic Frequency Sedimentary Frequency 10

C Lithosomes = 1008 D Lithosomes = 949 2 Mean size = 7381 km Mean size = 19,299 km2 2 100 r = 0.79 r2 = 0.89 100

Plutonic 10 Frequency 10 Frequency Metamorphic

1000 10,000 1000 10,000 Rock area (km2) Rock area (km2) Figure 4. Areas of volcanic, sedimentary, plutonic, and metamorphic rock exposures extracted from the Geological Survey of Canada (GSC) map. The solid lines are not regressions; they are model lines derived presuming that outcrop areas are approximately equidimen- sional in all directions (are roughly circular) and that land area is randomly segmented into subregions of homogeneous lithology. They are the ideal distributions of Poisson magnitude frequencies that would result from populations of lithosome elements with randomly delimited boundaries. Areas of such elements are dependent only on number of mapped units and total mapped area for each rock type. For each rock type, lithosome size-frequency is closely approximated by this model distribution in which k deﬁ nes the probability of exiting that rock area (crossing some lithosome boundary) per kilometer of transect.

mapping, one would anticipate crossing about a nonrandom spatial structure in the distribution A = 8. 8× 106086Q− . (3) dozen lithologic boundaries for each thousand of exposure sizes. Rocks of similar type are kilometers of land surface traversed. While dif- obviously associated in space, and it therefore with area (A) expressed in km2/Ma and rock ferences between these numbers reﬂ ect the fact follows that larger map units will be clustered unit age (Q) expressed in Ma. Such a relation that exposures of mapped volcanic and plu- in space with larger and smaller with smaller. describes a steady-state system in which an tonic rocks are somewhat smaller than those of Thus, the probability of crossing a map bound- “original” (intercept at 1 Ma) outcrop area of metamorphic or sedimentary complexes, their ary (k) in a given surface transect also depends ~8,800,000 km2 decreases as it ages by ~0.86% absolute magnitudes more closely relate to the on where that transect happens to be located, a for each 1% increase in age. Given a total ice- continental scale of lithologic variation repre- fact that derives from the spatially structured free continental land area of ~135 × 106 km2, sented by these maps. Although more detailed distribution of crustal deformation and uplift this intercept value requires that ~6.5% of con- mapping of smaller areas would yield higher and subsidence apparent on any geologic map. tinents is resurfaced with younger volcanic and/ values of k (volcanic, sedimentary, plutonic, or sedimentary rocks every million years. The and metamorphic values from the FAO maps AGE-FREQUENCY DISTRIBUTIONS OF FAO and GSC data yield trends (Fig. 5) that are 27.4, 22.4, 33.2, and 18.2 per thousand EXPOSED ROCK UNITS differ only slightly. Because the FAO maps are linear transect kilometers, respectively), the approximately six times more detailed than that nature of the size frequency (Fig. 4) remains Age-frequency distributions of continental of the GSC, this similarity shows that mapping unchanged. rock exposures from FAO and GSC maps are detail is not a factor in determining relations While lithosome exposure area data sug- closely approximated by a power-law distribu- among frequencies of different exposure areas. gest that, in aggregate, continental surfaces tion in which the relation between logs of ages When these data are divided into volcanic, can be adequately described as being randomly and logs of areas deﬁ nes a straight line (Fig. 5, sedimentary, plutonic, and metamorphic rock partitioned, in actuality there is considerable Equation 3) as: lithosome exposures (Fig. 6), it becomes apparent

764 Geological Society of America Bulletin, May/June 2009 Geologic maps are tectonic speedometers that the general form of the age-frequency distribution for each group is closely related to those processes responsible for their formation. Rocks that originate (that acquire their “age”) at the Earth’s surface exhibit power-law distributions with modal ages near zero, a youth reﬂ ecting 10,000,000 All lithologies their initial abundance at or near exposed con- /m.y.) tinental surfaces. Their age-frequency distribu- 2 tions are nearly identical to that exhibited by km all rock units (Figs. 6 and 7) because more than 3 1,000,000 80% of global outcrop consists of volcanic and sedimentary sequences (Table 1). In contrast, plutonic and metamorphic age-frequency distri- 100,000 butions derived from both FAO and GSC maps are approximately lognormal in form (Fig. 7). In addition, the modal age of plutonic lithosomes GSC Area = 8.32 x 106 Age–0.852 10,000 is markedly younger than that of metamorphic 6 –0.862 Area exposed (10 Area exposed FAO Area = 9.28 x 10 Age suites (Table 2). FAO maps yield modal ages of 154 and 697 Ma for plutonic and metamorphic lithosomes compared to 174 and 3001 Ma for GSC maps. Globally, the most areally extensive 1000 100 10 sedimentary and volcanic suites are the young- Age (Ma) est, plutonic rocks have modal ages that are Figure 5. Log-log plot of age versus area relations from global geologic maps by the Food mid-Phanerozoic in age, and most metamorphic and Agricultural Organization (FAO) (solid black line and open circles) and the Geological suites are older (Fig. 7). These aspects of age- Survey of Canada (GSC) (solid gray line and gray diamonds). Both data sets describe nearly frequencies are evident in data from most of the indistinguishable power-law relations (dashed gray line) between exposure area and age in major continents and are also apparent in geo- which outcrop area decreases by ~0.86% for each 1% increase in rock age. logic map data tabulated by others (Table 2). That volcanic and sedimentary rock age- frequencies exhibit power-law distributions, and that plutonic and metamorphic rock age-frequencies are distributed lognormally, implies a linkage between the nature of the age-frequency distribution and the crustal depth at which dif- Volcanic ferent rock types tend to form. Qualitatively, because these map data represent rock “abun- 10,000,000 Sedimentary dance” at the Earth’s surface, and because Plutonic volcanic and sedimentary rocks originate on 1,000,000 /m.y.) this surface, modal ages of sediments and vol- 2 Metamorphic canics must be very young (Figs. 7A and 7B). In contrast, because intrusive rocks crystal- 100,000 lized at depth and had to travel to the surface before being designated on some geologic map, 10,000 exposed intrusive rocks must have a modal age that is older than that of sedimentary and 1000 volcanic rocks. Tectonic uplift and associated

denudation serve to expose intrusive rock bod- (km Area exposed 100 ies, and, depending on depths of their formation and mean rates of uplift, signifi cant amounts of geologic time must pass before this can occur. The decline in pluton area (from the Paleozoic 1000 100 10 into the Precambrian, Fig. 7C) of rocks older Age (Ma) than modal age refl ects the fact that tectonism eventually serves to destroy some of these mid- Figure 6. Log-log plot of relations between age and total outcrop area for major rock crustal lithosomes as they move upward through groups from the Food and Agricultural Organization (FAO) maps. Note log-linear the exposure window at the Earth’s surface or decrease in abundance of sedimentary and volcanic rocks with increasing age simi- downward where they undergo metamorphism. lar to that for all rock types (Fig. 5) and signifi cantly different patterns for plutonic Similarly, metamorphic rocks originate at even and metamorphic (basement) rock types. GSC—Geological Survey of Canada. greater crustal depths than most intrusive rocks, and their modal ages at the surface (Fig. 7D)

Geological Society of America Bulletin, May/June 2009 765 Wilkinson et al.

A B 20 600 Sedimentary

15 400 Volcanic 10 /m.y.) /m.y.) 2 2 200 5 km km 3 3

C D 8 15 Plutonic

6 Area exposed (10 Area exposed Area exposed (10 Area exposed 10 Metamorphic 4

5 2

1000 100 10 1000 100 10 Age (Ma) Age (Ma) Figure 7. Log-age versus area relations for volcanic, sedimentary, plutonic, and metamorphic rocks from the Food and Agricultural Organiza- tion (FAO) (solid black lines) and the Geological Survey of Canada (GSC) (solid gray lines) data. Note that volcanic and sedimentary sequences have Neogene modes, whereas the modes for intrusive complexes lie in the Paleozoic, and those for metamorphic suites lie in the Precambrian.

must, therefore, be older than intrusive rocks at Ag-Au, porphyry Cu, and orogenic Au deposits, and Wilkinson and Kesler (2007) formulated a the surface. Given these qualitative distinctions, which form at average depths of ~0.5, 1.9, and general time-depth model of ore deposit crustal it is likely that rock age-frequency distributions 10 km, exhibit age modes at ~2, 11, and 199 m.y., emplacement and tectonic dispersal that is in for populations of rock bodies that formed at dif- respectively, reﬂ ecting their increasing modal good agreement with observed age-frequencies. ferent depths might be used to determine mean age with depth of ore emplacement. Because Here, we generalize this time-depth model in rates of crustal uplift and subsidence. ages of exposed ore deposits presumably record order to further examine relations between geo- information about depths of ore formation and logic map age-frequency distributions and those A STEADY-STATE MODEL subsequent tectonic uplift, exhumation, and continent-scale tectonic processes that give rise exposure, Kesler and Wilkinson (2006, 2008) to greater or lesser exposure with age. Support for the general interpretation outlined above can be found in ages of three widespread and abundant types of hydrothermal ore deposits. TABLE 2. MODAL AGES OF PLUTONIC AND These have been discussed elsewhere at length METAMORPHIC ROCK LITHOSOMES TABULATED FROM DIFFERENT SOURCES* Plutonic Metamorphic (Kesler and Wilkinson, 2006, 2008; Wilkinson Source Area (Ma) (Ma) and Kesler, 2007) and will be reviewed only FAO North America 127 467 brieﬂ y here. The important point is that epith- FAO Eurasia 154 529 FAO Global 154 697 ermal silver-gold (n = 152), porphyry copper (n GSC North America 107 3051 = 455), and orogenic gold (n = 66) deposits, all GSC Eurasia 306 494 GSC Global 174 3001 of which form along continental margins during 1 Peucker-Ehrenbrink and Miller United States and 169 2651 tectonic convergence, exhibit age-frequencies (2002, 2003) Canada that are lognormal in form (as are plutonic and Gilluly (1969) North America 107 – Higgs (1949) United States1 156 – metamorphic age-frequencies), but differ sys- *Intrusive modal ages are younger than metamorphic ages in all instances. tematically with respect to their modal ages 1Exclusive of Hawaii. and emplacement depths (Fig. 8). Epithermal Abbreviations: FAO—Food and Agricultural Organization; GSC—Geological Survey of Canada.

766 Geological Society of America Bulletin, May/June 2009 Geologic maps are tectonic speedometers

Orogenic Au Porphyry Cu Epithermal n = 66, Emp Dpt = 10 km n = 455, Emp Dpt = 1.9 km n = 152, Emp Dpt = 0.5 km Mode = 199 Ma Mode = 11 Ma Mode = 3 Ma

10%

5% Proportion deposits of exposed

100 10 Age (Ma) Figure 8. Age-frequency plots for epithermal Ag-Au (white bars), porphyry Cu (light-gray bars), and Neoproterozoic and Phanero- zoic orogenic Au (dark-gray bars) deposits based on age compilations of Garwin et al. (2005), Kesler et al. (2004), and Simmons et al. (2005), Singer et al. (2005), and Goldfarb et al. (2005), respectively (modiﬁ ed from Wilkinson and Kesler, 2007). Solid lines are least-squares, best-ﬁ t lognormal distributions to these age frequencies. Note that modal age increases with emplacement depth (Emp Dpt), and that frequency distributions of all three types of deposits are well described by the lognormal distribution.

We begin with the simplifying assumption order question: If formation and destruction time (∆t); it can undergo uplift, it can remain at that the rock cycle works at a secularly invari- of the commonly classifi ed rock types were to its current crustal depth, or it can be buried to ant rate. This presumption is probably not true proceed at an invariant rate over typical depth some greater depth. The amount of per-model- all the way back into the early Precambrian ranges, what constraints on average speed of the step vertical displacement is defi ned here as the as, forward in time, the planet gradually loses rock cycle can be derived from areas and ages “tectonic step” of the random walk. heat needed to drive plate tectonics, and the of exposed rock bodies? Temporal evolution of Computationally, we emplace lithosomes over rock cycle should therefore slow. However, we crustal depths of rock formation and rates of some specifi ed average range of crustal depths believe this to be a valid fi rst-order approxima- rock formation or tectonism are not incorpo- (formation depth, Table 3), and iteratively input tion as here we are primarily interested in estab- rated into nor implied in any of our models. different model values of: (1) the areal extent lishing an association between the general form We formulate the model as a simple random of lithosomes that form at that mean depth per of rock age-frequencies and average rates of walk in geologic time-crustal depth space across unit time (formation rate, Table 3), and (2) the rock cycling. Any shorter-term deviations from a numerical grid, with the horizontal axis repre- proportion of lithosome area that experiences this starting assumption (manifest as differences senting elapsed time (age) and the vertical axis uplift, stasis, or subsidence during the model run between observed and model age-frequencies) representing depth beneath the continental sur- (“Up-St-Dn,” Table 3). For each iteration, we are acknowledged to record exceptions from this face (e.g., Figs. 9 and 10). Within this domain, calculate proportions of the initially emplaced assumption. The model assumes a steady-state a hypothetical amount of rock comprising some lithosome area that is presently at different system with respect to: (1) rates of lithosome lateral extent is deposited or emplaced on the crustal depths under different assumptions of formation among each of the four major rock surface or at some characteristic crustal depth. formation depth and subsequent tectonic disper- groups, (2) characteristic depths of rock forma- In subsequent time steps, this rock then moves sion (uplift, stasis, and/or subsidence). Because tion in or on the Earth’s continental crust, and vertically (up or down) as a random walk in here we are interested primarily in “age” fre- (3) rates of tectonic uplift and/or depression that crustal depth and geologic time space. Any pro- quencies of lithosome areas that have arrived at serve to change the vertical positions of each portion of total lithosome area can be displaced the upper absorbing boundary (i.e., the Earth’s lithosome relative to the surface of the Earth’s vertically a fi xed distance (∆X) relative to the erosional surface), the model is calibrated by continental crust. Here we merely ask the fi rst- Earth’s surface during each interval of model comparing, by conventional least-squares meth-

Geological Society of America Bulletin, May/June 2009 767 Wilkinson et al.

Crustal depth (km) –10–20 –30 –40 –50 –60

2 E Depth frequency — 500 Ma 1

D 2 Depth frequency — 1500 Ma 1

Frequency C 2 Depth frequency — 2500 Ma 1

B Age Frequency — 0 m

A –10

–20

–30

–40

Crustal depth (km) –50

–60

3000 2500 2000 1500 1000 500 Age (Ma) Figure 9. (A) Time (horizontal) versus depth (vertical) plot of random walk paths (gray lines) taken by 100 hypothetical plutonic lithosomes that were emplaced at a crustal depth of 10 km (arrow) and allowed to disperse vertically at a rate of 500 m/m.y. (B) Frequency distribution (gray curve) of “ages” (numbers of walk steps) of presently exposed lithosomes, which is the number of thin gray lines terminating at the crustal surface (heavy horizontal gray line in A). Like map data on plutonic and metamorphic rocks, these deﬁ ne a strongly skewed distribution, here with a modal age of 58 m.y. (C–E) Depth-frequency distributions of model lithosomes of different ages.

ods, the age-frequency of “exposed” model exposed lithosomes as derived from the model, types. The choice of appropriate depth is obvi- areas to the empirical age-frequency distribu- (3) the modal depth of each type of rock within ously most secure for rock suites forming at the tions (e.g., Fig. 11). In determining the best-ﬁ t, the model crust, and (4) the proportion of litho- Earth’s surface but becomes increasingly open age-frequency distribution of crustal rocks, we somes that have been buried and preserved ver- to discussion for those that originate at greater also arrive at predictions of the amount of each sus the proportion that have been uplifted and crustal depths. Virtually all volcanic and sedi- type of rock at depth in the Earth’s crust (e.g., removed by erosion over model time. mentary rocks now exposed at the Earth’s sub- Figs. 10 and 11). These include: (1) the total The largest uncertainty associated with this aerial surface have formed essentially on that areal extents and depths of each type of rock model is making the “correct” choice of crustal surface, and their abrupt decrease in area with within the model crust, (2) the modal age of depths of formation among the four major rock increasing age (Figs. 6 and 7) largely reﬂ ects

768 Geological Society of America Bulletin, May/June 2009 Geologic maps are tectonic speedometers

A — 0 km (modal age = 0 Ma)

B — 5 km (modal age = 15 Ma)

C — 10 km (modal age = 58 Ma)

D — 15 km (modal age = 125 Ma)

E — 20 km (modal age = 218 Ma)

E D –10 C B –20 A

–30

–40 Crustal depth (km)

–50

1000 100 10 Age (Ma) Figure 10. Time versus depth plot of random walk paths as in Figure 9, but here on the lower panel, formation is at 20 km (arrow), and the time (horizontal) axis is plotted as a log scale. The upper panels (A–E) show frequency distributions (gray dashed curves) of paths transected above the formation depth of 20 km. The frequency distribution in (A), for example, represents lithosome ages (walk paths intersected) along a transect at a depth of 20 km, while the frequency distribution in (E) represents lithosome ages along the surface, which is 20 km above the formation depth. Conversely, the frequency distribution in (A) would be that expected if rock formation took place at the Earth’s surface, as is the case for volcanic and sedimentary sequences.

subsequent area reduction by uplift and erosion ologies characteristically surround more deeply mapped as “plutonic” require a somewhat shal- and/or subsidence and burial. Semiquantita- emplaced igneous bodies. Average depths of lower average, and narrower range, of emplace- tively, depths of emplacement of granitic plutons metamorphism are even less well constrained. ment depths than those conventionally mapped are also reasonably well constrained, and many Although pressure-temperature (P-T) paths have as “metamorphic,” but it is difﬁ cult to readily studies interpret the tops of the shallowest of now been estimated for hundreds of metamor- arrive at more rigorous depth estimates. these to intrude sedimentary successions and to phic suites, we are unaware of any tabulation of However, this scarcity of data on means and form at depths of no less than several kilometers. mean depths and/or ranges of depths for region- ranges of depths of origination for plutonic and The literature on maximum depths of plutonism ally metamorphosed lithosomes. Age-frequency metamorphic suites is not fatal to the use of the is more meager, but typical metamorphic lith- distributions for lithosomes conventionally random tectonic walk model for understanding

Geological Society of America Bulletin, May/June 2009 769 Wilkinson et al. map-unit, age-frequency distributions. There TABLE 3. MAP DATA 1 AND MODEL2 PARAMETERS are two main reasons for this reprieve. First, any FOR AGE-FREQUENCIES OF GLOBAL ROCK TYPES (FIG. 11) Volcanic Sedimentary PlutonicMetamorphic uncertainty associated with estimating means Up-St-Dn2 33-34-33 29-41-30 34-32-34 36-28-35 % and ranges of actual crustal depths of rock for- Formation 2 0.2 ± 0.3 0.1 ± 0.1 10.0 ± 3.1 25.0 ± 5.1 km mation primarily affects the random walk model depth Formation rate2 2,053,932 39,545,996 4,186,012 6,353,460 km2/Ma by increasing or decreasing theoretical estimates Modal age2 0 0 142 953 Ma of the amount (distance) of vertical displacement Extant2 4.0% 3.8% 39.3% 61.7% % 2 needed to bring some map-derived, rock-unit Eroded 96.0% 96.3% 60.7% 38.3% % Exposed2 0.077% 0.088% 0.060% 0.045% % modal age to the Earth’s surface (e.g., Fig. 7; Modal m/Ma Table 2). In other words, the depths at which exhumation Surficial Surficial 70 26 (Formation depth 2 different lithosomes form and their modal ages rate divided by modal age) Tectonic 2 532 511 539 552 m/Ma (e.g., Fig. 7) are only related (in the model calcu- step lation) by the requisite amounts of vertical rates Model exposed2 5,995,331 132,474,490 9,528,877 10,748,329 km2 1 2 of tectonic movement needed to bring these two Actual exposed 9,738,735 104,277,071 10,168,638 11,471,408 km Note: Up-St-Dn refers to proportions of tectonic movement up, stationary, or down with each time step; parameters into agreement. Given some modal formation rate is lateral lithosome area per unit time; extant, eroded, and exposed are relative to total age, overestimation or underestimation of for- lithosome area; modal exhumation rate is formation depth divided by modal age. mation depth will merely translate into larger or smaller tectonic steps, respectively, that serve to disburse all, and ultimately expose some, of this population of lithosomes. with a modal age of 0 Ma (in agreement with sequent aggregate dispersion of crustal rocks, Second, and related to these dependencies map data), and suggest that, of all volcanic lith- at least at the global scale. between tectonic step size and emplacement osomes ever formed, ~4% are currently buried This conclusion is somewhat surprising in depth, here we are primarily concerned with a beneath the Earth’s surface, and ~96% have view of the fact that rocks are probably most determination of some mean rate of continental been destroyed by subsequent erosion (Table 3). rapidly “cycled” along convergent orogens, tectonism that serves to drive the global geo- The tectonic step needed to derive this best-fi t, and these are regions that might be thought to logic rock cycle. Thus, it follows that rates of volcanic rock model age-frequency is 532 m of be the focus of uplift and exposure, particularly rock uplift and erosion or subsidence and burial vertical displacement per million years, and the with respect to plutonic and metamorphic asso- that serve to control age-frequency distribu- model amount of exposed volcanic lithosome ciations. How can it be that rocks that are pri- tions for any one of the four major lithosome (0.08% of all volcanic rocks produced) is ~6 × marily uplifted and destroyed along convergent types should also operate at the same rate for 106 km2 (compared to a FAO-mapped area of margin settings exhibit map age- frequencies the other three. If so, we can then proceed by ~9.8 × 106 km2). Similar metrics are derived for suggesting that they also experience nearly determining the best fi t between model and sedimentary, plutonic, and metamorphic litho- equal amounts of subsidence? The most likely map age-frequency distributions simultaneously somes (Fig. 11; Table 3). explanation is that orogenic convergence also (e.g., Fig. 11) while assuming a similar tectonic acts to thicken the crust, causing signifi cant step for each, and then determine if means and Biases to Tectonic Diffusion amounts of burial both by subsidence and ranges of formation depths seem reasonable in thrusting, as well as uplift and erosion (e.g., light of independent geologic data (Table 3). Formulation of the general random-walk Haschke et al., 2002; Pedreira et al., 2003). model presumes that total areas of model litho- MODEL RESULTS somes experience equal magnitudes of uplift, Tectonic Diffusion, Map Areas, Geologic stasis, or subsidence with each time interval Time, and Crustal Depth Best agreement between model and observed (Figs. 9 and 10). However, when applying age-frequency curves (Fig. 11) is found when the model to data on age-frequency distribu- Several aspects of the geologic rock cycle are the tectonic step for the vertical dispersion of tions, we had no compelling reason a priori to clarifi ed by relations apparent from data on the lithosomes is about half a kilometer per mil- believe that this equality was appropriate. Dur- geologic maps discussed here: (1) volcanic and lion years when there is no signifi cant bias ing model runs, biases to random walks were sedimentary lithosome area-frequency distribu- to the tectonic random walk (uplift ≅ stasis ≅ therefore unconstrained, and crustal dispersion tions exhibit primarily power-law distributions, subsidence), and when volcanic, sedimentary, was allowed to range from 100% subsidence while those for plutonic and metamorphic litho- plutonic, and metamorphic associations are to 100% stasis to 100% uplift, and all possible somes are closely lognormal in form; (2) modal presumed to originate at crustal depths of 0.2 combinations thereof (but summing to 100%). ages for each of the four major rock groups ± 0.3, 0.1 ± 0.1, 10.0 ± 3.1, and 25.0 ± 5.1 km, Somewhat surprisingly, closest agreement to increase with depth of rock formation; (3) sedi- respectively (Table 3). The FAO area- frequency observed age-frequency distributions for each mentary and volcanic distributions experience distribution for volcanic rock (Fig. 11), for of the four major rock types considered here area loss (by erosion and burial) from the time example, is most closely matched with a model (Fig. 11) was achieved when proportions of of rock formation, whereas those of plutonic distribution derived when presuming: (1) that uplift, stasis, and subsidence were about the and metamorphic rocks refl ect a (younger than rates of uplift (33%), stasis (34%), and sub- same (Table 3). In other words, the model of modal age) time interval of uplift and exhuma- sidence (33%) are about equivalent; (2) that random tectonic diffusion is in closest agree- tion prior to subsequent area loss by erosion and volcanic rocks originate at the Earth’s surface ment with geologic map data and has no burial; and (4) age-frequencies for each of the (200 ± 300 m); and (3) that volcanic lithosomes important bias toward or away from the Earth’s major rock types are closely approximated by form at a rate of ~2 × 106 km2/m.y. (Table 3). surface; neither uplift nor subsidence has distributions anticipated for lithosomes forming These values result in a model age-frequency predominated during the formation and sub- at characteristic crustal depths that then undergo

770 Geological Society of America Bulletin, May/June 2009 Geologic maps are tectonic speedometers

A B 20 600 Sedimentary Volcanic 15 400 10 /m.y.) /m.y.) 2 2 200 5 km km 3 3

C D 8 15 Plutonic Metamorphic 6 10 4 Area exposed (10 Area exposed (10 Area exposed 5 2

1000 100 10 1000 100 10 Age (Ma) Age (Ma) Figure 11. Log-age versus area relations for volcanic, sedimentary, plutonic, and metamorphic rocks from the Food and Agricultural Organization (FAO) (1981; solid gray lines) data and best-ﬁ t, random-walk model approximations (e.g., Figs. 10A–10E). Model parameters derived from each curve are listed in Table 3. All four model curves are derived when presuming that global rates of uplift and subsidence are approximately equal (there is no bias to the random walk) and that global rates of vertical tectonism are approximately a few hundred meters per million years.

2 (x−µ) 1 − largely random uplift and subsidence at rates on f ()x = e 2V , (5) rock vertically relative to continental surfaces. the order of about half a kilometer per million 2πV This expression of tectonic diffusion, coupled years. Fuller understanding of these relations with Earth-surface erosion that acts as an necessitates additional consideration of varia- where µ is the mean of the distribution (crustal effi cient absorbing boundary, serves to effec- tions in three interrelated geologic parameters— depth of lithosome formation). tively describe the major features of map age- lithosome area, crustal depth, and geologic time. The net effect of such tectonic depth disper- frequencies (Fig. 11). Importantly, the rather Systems of random walks (e.g., Figs. 9 sion is that, with increasing age, the population signifi cant differences in the general structure and 10) exhibit many characteristics of age- of vertical distances (depths) of lithosomes from of volcanic, sedimentary, plutonic, and meta- frequencies derived from geologic maps. With their original depth of rock formation and the morphic rock age-frequencies (Figs. 6 and 7) increasing number of time steps (age), litho- present Earth’s subaerial surface behave in a pre- are each closely approximated (Fig. 11) when some paths become increasingly dispersed rel- dictable manner (Fig. 12). Moreover, presump- presuming that the “step” size of an unbiased ative to their original formation depth. At any tion of mean volcanic and sedimentary rock for- (uplift ≅ stasis ≅ subsidence) random tectonic specifi ed number of time steps (age), lithosome mation at the Earth’s surface, and mean plutonic walk (Figs. 9 and 10) is on the order of about depths comprise normally distributed popula- and metamorphic rock formation at depths of half a kilometer per million years (Table 3). tions relative to their starting depths, and depth ~10 and ~25 km, respectively (Table 3), yields Because compiling even approximate error variance increases linearly with time (e.g., good agreement between observed and modeled estimates for data and assumptions employed Figs. 9C–9E). Moreover, increase in variance age-frequencies (Fig. 11) when T is about half a in the derivation of this value is probably not (V) of the normally distributed depth popula- kilometer per million years. possible, the best that can be said is that geo- tion is only dependent on age (A) and lateral logic maps suggest mean rates of tectonism on (tectonic) step size per unit time (T) as: OTHER MEASURES OF ROCK-CYCLE the order of a few hundreds of meters per mil- “SPEED” lion years. 2 VTA= 2 . (4) Volcanic, sedimentary, plutonic, and meta- Continental Tectonism from Rates of Erosion 3 morphic rock age-frequencies from both FAO and GSC maps suggest that fi rst-order aspects As context for this inferred amount of ver- The normal distribution of rock lithosomes at of the geologic rock cycle primarily proceed in tical tectonism, estimates of volumetric fl uxes any crustal depth (x) is therefore approximated a conceptual system where tectonic processes of sediment to the Phanerozoic global sedi- by the probability density function: act to progressively disperse bodies of crustal mentary reservoir from data in Ronov (1980)

Geological Society of America Bulletin, May/June 2009 771 Wilkinson et al.

3% 80 35 70

30 ncy 60

2% ue 25 50

Lithosome area 20 40 1% h y ) t nc D 15 p ue e e q 30 Ma fre p D ( 0% t 10 e e h Ag 20 g ( A km 5 ) 10 0 0 Figure 12. Random walks in age-depth-frequency space (e.g., Fig. 9) showing the proportion of hypothetical lithosomes (Z axis) as a function of age (X axis) that are constantly emplaced at a crustal depth of 5 ± 0.5 km (Y axis). The X-axis parallel slice at a depth of 0 km (green line) is the (approximately lognormal, e.g., Fig. 11C) age- frequency distribution of currently exposed lithosomes that formed at a crustal depth of 5 km. Arrow is located at the modal age of 17 Ma. Lines normal to “Age” (e.g., blue line) are depth-frequency distributions of lithosomes of various ages (e.g., Figs. 9C–9E). Heavy yellow line at an emplacement depth of 5 km follows the approximately power-law age (X axis) -frequency (Z axis) trend of rock (such as volcanic and sedimentary, Fig. 11A) now exposed at the Earth’s surface (which is approximately their depth of formation).

and independent estimates of total areas of are determined from sedimentary rock volumes related to the rate (and changes therein) of subaerial continental crust undergoing erosion and modern river sediment loads only a fraction seafl oor spreading. Such lateral movement of from Scotese and Golonka (1992) allow for of those determined from age-frequencies of the Earth’s major tectonic plates embodies a calculation of mean rates of continental denu- the Earth’s exposed rock lithosomes? The rea- signifi cant expression of mantle convection, dation over the past ~542 m.y. of Earth history. son for this disparity is that erosion rates from and many authors contend that spreading rates These range from a middle Triassic low of rock volumes and river fl uxes are both deter- control a wide variety of geophysical, geobio- ~4 m/Ma to a Pliocene high of ~53 m/Ma and mined across the entirety of exposed continen- logical, and geochemical processes, including an average of ~16 m/Ma for all of Phanerozoic tal (land) surfaces, whereas those “rock cycle” mantle heat loss (e.g., Kominz, 1984), sea-level time (Wilkinson, 2007). Similarly, a literature processes of uplift, erosion, and volcanism that change (e.g., Gaffi n, 1987), transgression and on the general magnitude of riverine sediment serve to impart the greatest change to map area- regression (e.g., Pitman, 1978), carbon cycling fl uxes (e.g., Summerfi eld and Hulton, 1994; frequencies have largely operated along the (Berner et al., 1983), and seawater chemistry Syvitski et al., 2005), suggests that the current Earth’s major orogenic belts. The magnitude of (Sandberg, 1975; Hardie, 1996). Based on area annual riverine fl ux of weathering products to this difference (tens of meters per million years versus age relations for oceanic crust, it appears global oceans is equivalent to that required to across all continents versus hundreds of meters that rates of divergence have varied little, at least reduce all subaerial land surfaces by ~62 m/ per million across orogens) suggests that areas over the past several hundred million years. Ma. Assuming that the rock volume–derived of active rock cycling (orogens) on average Expressed as area, seafl oor has formed at a rate and river fl ux–derived values are approximately have comprised ~10% of continental areas over of ~3.4 km2/yr (Rowley, 2002). Expressed as correct (that continent-wide denudation occurs the entirety of Phanerozoic time. length, global half-spreading has occurred at a at rates on the order of a few tens of meters per rate of ~2.0–2.5 cm/yr (20–25 km/Ma) over this million years), it is important to note that these Oceanic Tectonism from Rates of Spreading time interval (Conrad and Lithgow-Bertelloni, rates are about an order of magnitude lower 2007). Because these rates are largely derived than the rates inferred from geologic map age- The most widely cited records of global tec- from maps of global seafl oor area versus age frequencies (hundreds of meters per million tonic rates that might be compared to our esti- (e.g., Müller et al., 1997), they are philosophi- years). Why are rates of continental erosion that mates from data on geologic maps are those cally analogous to our rates derived from ages

772 Geological Society of America Bulletin, May/June 2009 Geologic maps are tectonic speedometers

and areas of the major rock groups exposed on the Earth’s continents. Conversely, rates of oce- A All rates, n = 754 anic crust generation and destruction primarily 80 Mean = 877 m/Ma record the effects of lateral tectonism, whereas those derived from continents largely refl ect rates of vertical uplift and subsidence. In a context of 60 rates of tectonic deformation of the Earth’s lithosphere, these two processes are intimately interrelated. The mean rate of lateral oceanic crust 40 tectonism is ~40 times that occurring during the vertical deformation of continental crust. 20 Continental Tectonism from Rates of Uplift and Exhumation Durations <5012 yr, mean = 3636 m/Ma Other attempts to quantify amounts of tec- B Durations >5012 yr, mean = 210 m/Ma tonic movement have focused on determin- 50 ing rates of crustal uplift and exhumation by employing a wide range of geochronometers. 40 Although the terms “uplift” and “exhumation” Number of measurements have been used rather loosely in the geologic 30 literature, the sum of these processes generally equates with rates of rock displacement relative 20 to the geoid (e.g., England and Molnar, 1990). In an attempt to summarize vertical displace- 10 ment estimated from such studies, we have tabulated 754 durations and vertical amounts of change from over 200 recent papers containing the phrases “exhumation rate” and/or “uplift 1 100 10,000 1,000,000 rate” as a keyword or phrase in their title. Dura- Rate (m/Ma) tions and amounts of crustal movement exam- ined in these papers were inferred from a vari- Figure 13. Frequency distribution of (A) 754 “uplift” and “exhumation” rates and (B) fre- ety of geomorphic, geochemical, and isotopic quency distribution of rates determined over durations less than 5012 yr (median age of the techniques including 40Ar/39Ar, U-Pb, Rb-Sr, data—dark gray bars) and over durations greater than 5012 yr—open bars). Note that all Sm-Nd, apatite helium (AHe), zircon helium exhibit an approximate lognormal distribution. The mean rate of the short-duration popu- (ZHe), apatite fi ssion track (AFT), zircon fi s- lation is 3636 m/Ma, whereas the mean rate of the long-duration population is 210 m/Ma. sion track (ZFT), 10Be, 26Al, electron spin reso- nance (ESR), optically stimulated luminescence (OSL), and 14C methods. Changes range from a these time scales of consideration. The lower mean of only 210 m/Ma (Fig. 13B). This dif- few meters per million years over durations of bound of rate-frequencies, on the other hand, ference requires that rate of change is critically a few billion of years (e.g., Precambrian, Cana- is almost surely related to sampling bias. These dependent upon duration of observation. dian Shield; Flowers et al., 2006) to tens of studies encompass the use of geochronometers The nature of this effect is apparent when rates kilometers per million years over durations of that, by choice and application, are designed to of “uplift” and “exhumation” are plotted relative a few million years (e.g., Pliocene, Papua New record some inferred amount of change. Fewer to durations of change for the entire population Guinea; Baldwin et al., 2004). values refl ecting lower amounts and durations of values. Collectively, these defi ne a power-law Several aspects of these data merit note. of change almost surely refl ect a decreasing trend of decreasing rate of change with increas- First, rates determined from amounts and dura- likelihood of study in areas that are approxi- ing time interval of change as Equation 6. tions of inferred change exhibit an approximate mately stationary. lognormal distribution with mean and modal More importantly, separation of the 754 val- R = 170D−031. (6) values of 877 m/Ma and 1000 m/Ma, respec- ues on the basis of a median duration (5012 yr) tively (Fig. 13A). The shape of this distribution into two populations containing equal num- where R is the rate in m/Ma and D is the itself probably does not illustrate any impor- ber of measurements (377), and constructing duration in units of Ma. In other words, rate tant geological corollary. These data comprise rate-frequency distributions for each subset decreases by ~0.3% with each 1% increase in measures of various erosional processes that (Fig. 13B), demonstrates that each also exhib- process duration such that mean rates of vertical are ultimately related to ambient conditions of its an approximately lognormal distribution, change in the Earth’s surface due to processes climate and/or crustal tectonism, and decreas- but with signifi cantly different average rates. of rock “uplift” and “exhumation” decreases ing numbers of measured rates in excess of Those linear changes measured over durations by ~2 orders of magnitude (3000 to 20 km/ ~1 km/Ma along the upper bound of the dis- of less than 5012 yr (n = 377) have a mean of Ma) over the range of durations (months to bil- tribution (Fig. 13A) may therefore indeed 3636 m/Ma while those determined over time lions of years) encompassed here (Figure 14). refl ect some upper limit of such processes at spans in excess of 5012 yr (n = 377) have a Such dependence of inferred rate on dura-

Geological Society of America Bulletin, May/June 2009 773 Wilkinson et al.

Coseismic

m/Ma tectonic steps 10 kilometers Modal rates

100,000 UHP

1000

10 Rate (m/Ma)

100 meters

0.1 0.1 millime 1 centimeter Uplift rates 1 meter ter Exhumation rates

0.000001 0.0001 0.01 1 100 Duration (Ma) Figure 14. Log-log scatter plot of 754 uplift (open circles) and exhumation (gray diamonds) durations and rates determined from various geochronometers and geomorphic data. Dashed diagonals are amounts of equal uplift and exhumation (as length). Note that these deﬁ ne a trend (heavy black line) of decreasing rate with increasing duration of measurement (rate decreases ~0.3% for each 1% increase in duration). For reference, highest (darkly shaded circles and diamonds) at short and long durations represent rates of coseismic uplift and exhumation of ultra high-pressure (UHP) terrains, respectively. Solid black squares are per-million-year rates of tectonism that yield the best ﬁ ts between North American (Food and Agricultural Organization [FAO] and Geological Survey of Canada [GSC], Gilluly, 1969; and Peucker- Ehrenbrink and Miller, 2002, 2003) and global (FAO and GSC) geologic map areas. Shaded squares are modal rates (formation depth divided by modal age) for the same lithosomes.

tion of (ultimately tectonic) change has been volcanic, sedimentary, plutonic, and metamor- of exhumation that occurs over the “lifetimes” noted previously with respect to other natural phic age-frequencies? Before answering that of exposed lithosomes. systems. Many processes (such as uplift and question, it should be noted that agreement In the ﬁ rst case, because ages for rock bod- exhumation) that proceed with a high degree of between model and measured map area age- ies have uncertainties of least a million years, irregularity (such as that occurring along a ran- frequencies (Fig. 11) allow for the estimation of we computed time steps in the tectonic random dom walk) exhibit similar negative power-law two distinct but interrelated measures of crustal walk model at that (1 Ma) interval of time. For relations between net rate and the duration of uplift and denudation. These are: (1) the aver- walk steps of this duration, the amount of verti- time over which rate is established. This rela- age amount of tectonic uplift or subsidence (step cal movement necessary for arriving at agree- tion has been well documented for Earth sur- size in the random walk) experienced by each ment between model and observed volcanic, face progressions such as sediment deposition lithosome per unit time and (2) for plutonic or sedimentary, plutonic, and metamorphic fre- (Sadler, 1981), erosion (Gardner et al., 1987), metamorphic lithosomes that yield modal ages quencies is on the order of about half a kilo- and biological evolution (Gingerich, 1994). signiﬁ cantly different from times of rock forma- meter per million years (Table 4). This value is With these 754 values of uplift and exhumation, the amount of time necessary to bring the the average size of tectonic “steps” experienced tion serving as context, it is now possible to ask largest number of lithosomes of some particular by rock bodies during vertical crustal displace- the question: how do these magnitudes of uplift age (the modal age of the frequency distribution) ment over a period of 1 m.y. in duration. The and exhumation compare with vertical rates of to the Earth’s surface. This second value gives fact that step values for each rock type are about tectonic dispersion inferred from geologic map an indication of the magnitude of the mean rate the same is perhaps more than coincidental as,

774 Geological Society of America Bulletin, May/June 2009 Geologic maps are tectonic speedometers

broadly speaking, most rock bodies, regardless TABLE 4. MODAL EXHUMATION RATES AND TECTONIC STEPS of lithology, are primarily “cycled” along con- Exhumation rate vergent margin orogens. Source Area (m/Ma) Tectonic step (m/Ma) Plu Met Vol Sed Plu Met In the second, but related case, observed and FAO North America 137 61 323 188 809 928 model age-frequency distributions (Fig. 11) GSC North America 172 10 177 120 884 146 also provide an estimate of mean rates of Gilluly (1969) North America 76 19 467 449 428 448 Peucker- erosional denudation necessary to expose the Ehrenbrink United States2 149 12 513 379 762 196 greatest number of plutonic and metamorphic and Miller and Canada lithosomes at Earth’s surface. These rates of (2002, 2003)

“modal” exhumation, which are derived from FAO Eurasia 40 48 355 163 371 461 modal ages and emplacement depths (Table 4) GSC Eurasia 42 42 347 125 410 784 are about an order of magnitude lower than FAO Earth 70 26 532 511 539 552 rates estimated as the 1-m.y.–duration tectonic GSC Earth 89 16 212 147 637 452 steps for these same rock bodies, and again Note: Modal exhumation rates (ER) and per-one-million-year tectonic steps (TS) for volcanic (Vol), sedimentary (Sed), plutonic (Plu), and metamorphic (Met) outcrops on global, North American, and Eurasian make obvious the fact that net exhumation geologic maps. rates are critically dependent on durations of 1“Undetermined.” observation. 2Exclusive of Hawaii. Qualitatively, the reason for this dependence Abbreviations: FAO—Food and Agricultural Organization; GSC—Geological Survey of Canada. is perhaps most apparent from inspection of paths taken by random walks (e.g., Figs. 9 and 10). Consider those paths (in depth and time take on a characteristic lognormal distribution, logic random walk. Geologic map data are only space) that begin at some depth but eventually whereas volcanic and sedimentary rocks that resolved to epoch-duration intervals and, at this arrive at the absorbing barrier (the Earth’s ero- formed on continental surfaces exhibit a char- scale, some erosion undoubtedly occurs prior to sional surface). Routes of short duration (by acteristic power-law distribution (Fig. 11). subsidence and burial, while additional erosion necessity) also extend over short distances, and/or burial is currently reducing the areas of and resultant “rates” (∆distance/∆time) are Volcanic and Sedimentary Rock Age- exposed lithosomes. Although such processes therefore high. In contrast, those routes (from Frequencies serve to increase power-law slopes, they do greater depths) are of longer duration, refl ect- not obviate the conclusion that, like those log- ing the increasing numbers of steps both toward The linear nature of volcanic and sedimen- normal distributions characteristic of plutonic and away from the absorbing barrier; as a tary rock age-area distributions (Figs. 15A– and metamorphic rocks, these age-frequencies result, net unit change in depth per unit change 15D) merits additional comment. As pointed are also readily interpreted in the context of an in age is progressively lower. The dependence out by Newman (2005), a number of character- Earth’s crust behaving tectonically as a random of global uplift and exhumation rates on dura- istics of random walks are distributed accord- walk with an absorbing (erosional) boundary. tion of observation (Fig. 14) merely refl ects ing to power-laws. One of these is a randomly the high degree of temporal irregularity that is fl uctuating process that undergoes what is col- Area Reduction by Erosion and Burial characteristic of global tectonic and denuda- loquially referred to as a “gambler’s ruin”; such tional processes. runs have a power-law distribution of possible The logarithms of exposed areas of volcanic lifetimes. Imagine a random path defi ned by a and sedimentary rock decrease linearly with OTHER CONSEQUENCES OF walker who takes steps to the left or to the right. the logarithms of ages, and the logarithms of TECTONIC DIFFUSION If the walker starts at a position zero, the prob- exposed areas of plutonic and metamorphic ability that the walker returns to this position bodies show a similar decrease across time Agreement between model and observed after some number of steps is the “fi rst return spans that are older than their modal ages age-frequencies suggests that tectonic move- time” of the walk. We might consider the ages (e.g., Fig. 11). As noted by Gilluly (1969), this ment serves to vertically disperse continental of volcanic and/or sedimentary exposures in decrease refl ects the progressive uplift, erosion, rock bodies relative to their initial depth of a similar manner, in that these are units that and destruction of some exposed lithosomes formation by a process directly analogous to a originate at a depth of zero (relative to conti- and the progressive subsidence and burial of random walk in two dimensions. This is not to nental surfaces), but eventually (by defi nition) others by younger (volcanic and sedimentary) imply that any single rock body will randomly return to the same surface. Durations (fi rst rocks. Which process, uplift and erosion or move up and/or down during its entire geologic return times) of such histories exhibit a power- subsidence and burial, is the more important history. Rather, random dispersion refl ects the law distribution with a slope of ~2/3 (theo- in the progressive dwindling of exposed rock net movement experienced by all members retically, there is ~0.66% decrease in return area with age on geologic maps? Knowledge of of the aggregate lithosome population; some time-frequency for each 1% decrease in return total areas of volcanic and sedimentary litho- will certainly undergo more or less continual time duration). In reality, power-law slopes somes (extending throughout their subsurface uplift; others will experience prolonged inter- of volcanic and sedimentary age-frequencies extent) has been determined by Ronov (1978a, vals of stability; while still others will undergo (Figs. 15A–15D) are closer to unity. Actual 1978b, 1980) and coworkers. These papers prolonged long periods of subsidence, with or area of exposure at any rock age is somewhat include estimations of the entirety (surface and without later uplift. The net effect of all of these less than would be anticipated for a gambler’s subsurface) of areal extents and thicknesses of histories in time-depth space, however, is that ruin, probably because real-world sequences of Phanerozoic volcanic and sedimentary succes- collectively, age-frequencies of plutonic and volcanic and sedimentary rock do not experi- sions on each major continent (except Antarc- metamorphic rocks that formed at depth now ence abrupt vertical “steps” during their geo- tica) parsed by lithology. Because total areal

Geological Society of America Bulletin, May/June 2009 775 Wilkinson et al.

Volcanic outcrop Sedimentary outcrop A FAO maps B FAO maps 10,000,000 100,000 1,000,000

10,000 100,000 /Ma) /Ma) 10,000 2 2 1000 Area = 1.48 x 106 Age-1.05 Area = 1.21 x 107 Age-0.97 1000 r2 = 0.86 r2 = 0.87

Volcanic outcrop Sedimentary outcrop GSC map C D GSC map 10,000,000 100,000 1,000,000 Area exposed (km Area exposed 10,000 100,000 Exposed area (km

10,000 1000 5 -1.01 7 -1.17 Area = 8.68 x 10 Age Area = 2.23 x 10 Age 1000 r2 = 0.86 r2 = 0.88

Total volcanic lithosome area Total sedimentary lithosome area E Ronov (1980) F Ronov (1980) 100,000,000 /Ma) /Ma) 2 1,000,000 2

10,000,000

100,000 1,000,000 Area = 9.93 x 105 Age-0.30 Area = 3.15 x 107 Age-0.397 2 2 Total area (km Total r = 0.26 r = 0.17 Total area (km Total

1000 100 10 1000 100 10 Age (Ma) Age (Ma)

Figure 15. Log-log plots of age versus area relations for volcanic (A and C) and sedimentary rock (B and D) outcrops for the Food and Agricultural Organization (FAO) (A and B) and Geological Survey of Canada (GSC) (C and D) maps, and similar plots of total (exposed and subsurface) lithosome area (E and F) from data in Ronov (1978a, 1978b, 1980). Straight lines are best-ﬁ t power-law regressions through the data. Note that all four outcrop data sets deﬁ ne a slope of about −1.0 (~1% decrease in area for each 1% increase in age), whereas slopes from data on total lithosome areas are on the order of about −0.35 (~0.35% decrease in area for each 1% increase in age). This difference suggests that decreasing volcanic and sedimentary outcrop area with increasing age is primarily (70%) a result of burial by younger units, rather than by erosion.

776 Geological Society of America Bulletin, May/June 2009 Geologic maps are tectonic speedometers

extents of volcanic and sedimentary lithosomes account for only a few percent of bulk continen- decrease with increasing age, and because this tal crust, and only predominate lithologically in decrease is completely unrelated to burial by the uppermost few kilometers (Fig. 16). younger units, these data allow for an estima- While this realization is probably not sur- tion of that portion of map areas decrease that prising to geologists, it brings into focus the 5 is driven solely through processes of exposure fact that rocks that form near the Earth’s sur- Volcanic (2%) and erosion. From these data sources (Ronov, face inherently have a much higher probability 1978a, 1978b, 1980), we calculate the size of erosional destruction than those that form at 10 Sedimentary (4%) (volume) of the Phanerozoic volcanic (105 × greater crustal depths. Because random-walk 6 3 6 3 10 km ) and sedimentary (533 × 10 km ) con- models applied to geologic map data allow for 15 Plutonic (3%) tinental rock reservoir to be ~638 × 106 km3; estimates of amounts of surviving (buried) and ~16% and 84% of the total, respectively. These eroded (absorbed) lithosomes, it is possible to values are of the same proportional magni- compare relations between crustal depths of 20 Metamorphic (91%) tude as areas of currently exposed volcanic formation and proportions of all lithosomes Depth (km) and sedimentary rock as determined from the that now survive at various depths in continen- 25 FAO (8% and 92%) and GSC (12% and 88%) tal crust (e.g., Fig. 17). From the map data and maps. More importantly, when total areas model parameters discussed above (Table 3), of volcanic and sedimentary lithosomes are it appears that the amount of surviving rock 30 plotted relative to rock age, the resulting data increases by ~4% for each kilometer increase defi ne power-law trends with slopes of about in crustal depths of formation. At the end of −0.3 and −0.4, respectively (Figs. 15E and 2007, Georef listed some 3000 journal articles 20% 40% 60% 80% 15F). These slopes require that uplift and ero- with “crystalline basement” as a title (869) or Percent of lithologies sion alone serves to decrease total volcanic and keyword (2356) term; the omnipresence of Figure 16. Model-derived estimate of the pro- sedimentary sequence areas by ~0.3% to 0.4% older plutonic-metamorphic (“crystalline”) portional lithologic composition of continental for each 1% increase in rock age. Importantly, associations at greater (”basement”) crustal crust with depth from Food and Agricultural these slopes are about one-third those defi ned depths is a fundamental geologic axiom. Its Organization (FAO) global maps. Values in by analogous plots of exposures on geologic veracity, however, is derived only in part from parentheses are proportional totals integrated maps (about −1.0; Figs. 15A–15D), and serves the fact that plutonic and metamorphic litho- over the entire depth range; arrows at top to demonstrate that the ubiquitous decrease somes originate at crustal depth. Crystalline indicate actual proportions of outcrop at the in map area of exposed continental rock with rocks primarily predominate at greater depths Earth’s surface from the FAO maps (Table 1). increasing age is primarily (~2/3) due to burial because of their much greater potential for by younger volcanic sedimentary successions, preservation. and only secondarily (~1/3) due to exposure and erosion. Primeval Residuals surface. Moreover, calculation of the relative Bulk Lithologic Composition of the Upper A fi nal comment about geologic map fre- proportions of volcanic, sedimentary, plutonic, Continental Crust quency distributions derives from the obser- and metamorphic exposure with time (Fig. 18) vation fi rst made by Gilluly (1969) that log suggests that this 4 b.y. crust might consist of As discussed above, age-frequency distri- areas of surviving exposure decrease linearly generally subequal proportions (~36%, 24%, butions of the major rock groups are closely with the log of increasing age. Gilluly’s (1969) and 37%, respectively) of sedimentary, plu- mimicked when presuming that the enumerable slopes for North and South America (−0.67 and tonic, and metamorphic rocks. Loss of volca- structural elements that collectively make up −0.98, respectively; Fig. 1) are not notably dif- nic and sedimentary area through erosion and continental crust essentially behave as a popu- ferent from those derived here for the entire burial naturally serve to decrease area with age, lation of largely independent tectonic blocks Earth from the FAO and GSC global maps but, in the latter instance, sedimentary cover is experiencing random vertical displacement (−0.86 and −0.85, respectively; Fig. 5). Taking suffi ciently large at the start, that loss over the relative to the Earth’s surface. Because crustal either of these latter relations as characteristic past ~4 b.y. is approximately balanced by uplift diffusion models simulating such a system also of mapped global exposures, the simplest rela- and exposure of plutonic and metamorphic result in the determination of hypothetical paths tion that describes remaining global outcrop basement rocks (Fig. 18). In other words, areas taken by all rock lithosomes, it is possible to area (Ar) global as a function of age (t) is: of geologic units now exposed at the Earth’s sum the totality of each rock type over all model continental surfaces decrease in net area at a −086. depths in order to estimate the bulk lithologic Ar = At0 (7) ,rate of ~0.85% per 1% increase in their age. As composition of continental crust (Fig. 16). such, there is no compelling reason, at least on

This approximation suggests that while those where A0 is the FAO and GSC map intercepts the basis of these data, not to expect the pres- continental lithologies traditionally mapped as (Fig. 5). These values are the typical amount of ence of some Delaware-sized fragment or frag- being some form of “metamorphic” rock only new map area generated by volcanism and sediments of primal continental crust somewhere make up between 10% and 20% of continental ment deposition: ~9 × 106 km2/m.y. (Fig. 5). To at the modern Earth’s surface (e.g., Bowring exposures (Table 1), these lithologies comprise the degree that this relation can be realistically and Williams, 1999). Moreover, the probabili- fully ~90% of continental crustal volume. Sedi- extrapolated back in geologic time, some 6 × ties that this fragment is sedimentary, plutonic, mentary units, on the other hand, while making 103 km2 of 4 b.y. rock (an area about the size and/or metamorphic in lithologic constitution up 60%–70% of global exposures (Table 1), of Delaware) should be exposed on the Earth’s are nearly equal.

Geological Society of America Bulletin, May/June 2009 777 Wilkinson et al.

ACKNOWLEDGMENTS

We sincerely thank Sarah Smalheer, Erin Dimaggio, Marit Gamberg, Tammara Gipprich, Emily Johnson, 0.121 Depth 70% % Surviving = 0.040 e Jaye Kain, Tracy Kolb, Kelly Wells, and David Whipp r2 = 0.745 for assistance in compiling much of the map area–age- 60% frequency data that serves as the basis of this study. The focus of this study profi ted from discussions with John 50% Prucha and Pat Bickford; Bryce Hand, Andrew Hynes, Linda Ivany, Karl Karlstrom, James Metcalf, Scott 40% Miller, Jon Pelletier, and Jan Veizer read early drafts of the manuscript and offered many helpful comments 30% and suggestions. This work was supported by National Science Foundation grant EAR-99-02849. 20% REFERENCES CITED Proportion surviving 10% Baldwin, S.L., Monteleone, B.D., Webb, L.E., Fitzgerald, P.G., Grove, M., and Hill, E.J., 2004, Pliocene eclogite exhuma- 510152025 tion at plate tectonic rates in eastern Papua New Guinea: Nature, v. 431, p. 263–276, doi: 10.1038/nature02846. Mean depth of formation (km) Baumiller, T.K., and Ausich, W., 1992, The broken-stick model as a null hypothesis for crinoid stalk taphonomy Figure 17. Model-derived estimates of volcanic, sedimen- and as a guide to the distribution of connective tissue in tary, plutonic, and metamorphic lithosome preservation (Y fossils: Paleobiology, v. 18, p. 288–298. Berner, R.A., Lasaga, A.C., and Garrels, R.M., 1983, The car- axis) relative to inferred mean depths of rock formation (X bonate-silicate geochemical cycle and its effect on atmo- axis) from Food and Agricultural Organization (FAO) and spheric carbon dioxide over the past 100 million years: American Journal of Science, v. 283, p. 641–683. Geological Survey of Canada (GSC) maps. Volcanic and Blatt, H., and Jones, R.L., 1975, Proportions of exposed sedimentary rocks—open diamonds; plutonic lithosomes— igneous, metamorphic, and sedimentary rocks: Geo- lightly shaded diamonds; metamorphic suites—dark-gray logical Society of America Bulletin, v. 86, p. 1085– 1088, doi: 10.1130/0016-7606(1975)86<1085:POEIM diamonds. Note that preservation potential increases with A>2.0.CO;2. increasing inferred crustal depths of formation. These data Bluth, G.J.S., and Kump, L.R., 1991, Phanerozoic paleogeol- defi ne a trend suggesting that lithosome survival increases ogy: American Journal of Science, v. 291, p. 284–308. Bowring, S.A., and Williams, I.S., 1999, Priscoan (4.00– by ~4% for each kilometer increase in depth of formation. 4.03 Ga) orthogneisses from northwestern Canada: Contributions to Mineralogy and Petrology, v. 134, p. 3–16, doi: 10.1007/s004100050465. Choubert, G., and Faure-Mauret, A., 1981, editors, Atlas géologique du monde: Paris, Commission de la carte géologique du monde, Bureau de cartographie géologique internationale, United Nations Educational, Scientifi c and Cultural Organization 22 sheets. Conrad, C.P., and Lithgow-Bertelloni, C., 2007, Faster seafl oor spreading and lithosphere production during the mid-Cenozoic: Geology, v. 35, p. 29–32, doi: 80% 10.1130/G22759A.1. Dutton, C.E., 1882, Tertiary history of the Grand Canyon district, with atlas: U.S. Geological Survey Monograph 2, 264 p. 60% Volcanic England, P.C., and Molnar, P., 1990, Surface uplift, uplift Sedimentary of rocks, and exhumation of rocks: Geology, v. 18, p. 1173–1177, doi: 10.1130/0091-7613(1990)018<1173: Plutonic SUUORA>2.3.CO;2. Flowers, R.M., Bowring, S.A., and Reiners, P.W., 2006, Low 40% Metamorphic long-term erosion rates and extreme continental stability documented by ancient (U-Th)/He dates: Geology, v. 34, p. 925–928, doi: 10.1130/G22670A.1. Gaffi n, S., 1987, Ridge volume dependence on seafl oor gener- 20% ation rate and inversion using long term sea-level change:

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