JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 97, NO. B8, PAGES 11,703-11,728, JULY 30, 1992

First- and Second-Order Patterns of Stress in the Lithosphere' The World Stress Map Project

MARY LOU ZOBACK

U.S. Geological Survey, Menlo Park, California

To date, more than 7300 in situ stress orientations have been compiled as part of the World Stress Map project. Of these, over 4400 are considered reliable tectonic stress indicators, recording horizontal stress orientations to within <_+25ø . Remarkably good correlation is observed between stress orientations deduced from in situ stress measurements and geologic observations made in the upper 1-2 km, well bore breakouts extending to 4-5 km depth and earthquake focal mechanisms to depths of-20 km. Regionally uniform stressorientations and relative magnitudespermit definition of broad-scale regional stress patterns often extending 20-200 times the approximately 20-25 km thickness of the upper brittle lithosphere. The "first-order" midplate stress fields are believed to be largely the result of compressional forces applied at plate boundaries, primarily ridge push and continental collision. The orientation of the intraplate stress field is thus largely controlled by the geometry of the plate boundaries. There is no evidence of large lateral stress gradients (as evidenced by lateral variations in stressregime) which would be expected across large plates if simple resistive or driving basal drag tractions (parallel or antiparallel to absolute motion) controlled the intraplate stress field. Intraplate areas of active extension are generally associated with regions of high topography: western U.S. Cordillera, high Andes, Tibetan plateau, western Indian Ocean plateau. Buoyancy stressesrelated to crustal thickening and/or lithosphericthinning in these regions dominate the intraplate compressionalstress field due to plate-driving forces. These buoyancy forces are just one of several categories of "second-order" stresses,or local perturbations, that can be identified once the first-order stress patterns are recognized. These second-order stress fields can often be associatedwith specificgeologic or tectonic features, for example, lithosphericflexure, lateral strength contrasts, as well as the lateral density contrasts which give rise to buoyancy forces. These second-order stresspatterns typically have wavelengths ranging from 5 to 10+ times the thickness of the brittle upper lithosphere. A two-dimensional analysis of the amount of rotation of regional horizontal stressorientations due to a superimposedlocal stressconstrains the ratio of the magnitude of the horizontal regional stressdifferences to the local uniaxial stress. For a detectable rotation of 15ø, the local horizontal uniaxial stressmust be at least twice the magnitude of the regional horizontal stress differences. Examples of local rotations of SHmax orientations include a 750-85ø rotation on the northeastern Canadian continental shelf possibly related to margin-normal extension derived from sediment-loadingflexural stresses, a 50ø-60ø rotation within the East African rift relative to western Africa due to extensional buoyancy forces caused by lithospheric thinning, and an approximately 90ø rotation along the northern margin of the Paleozoic Amazonas rift in central Brazil. In this final example, this rotation is hypothesized as being due to deviatoric compression oriented normal to the rift axis resulting from local lithospheric support of a dense mass in the lower crust beneath the rift ("rift pillow"). Estimates of the magnitudes of first-order (plate boundary force-derived) regional stress differences computed from modeling the source of observed local stress rotations magnitudes can be compared with regional stress differences based on the frictional strength of the crust (i.e., "Byedee' s law") assuminghydrostatic pore pressure. The examples given here are too few to provide a definitive evaluation of the direct applicability of Byerlee's law to the upper brittle part of the lithosphere, particularly in view of uncertainties such as pore pressure and relative magnitude of the intermediate principal stresses.Nonetheless, the observed rotations all indicate that the magnitude of the local horizontal uniaxial stresses must be 1-2.5+ times the magnitude of the regional first-order horizontal stress differences and suggest that careful evaluation of such local rotations may be a powerful technique for constrainingthe in situ magnitude stressdifferences in the upper, brittle part of the lithosphere.

INTRODUCTION digital data base. The focus of this effort has been to characterize the intraplate or midplate stress field (i.e., the The World Stress Map (WSM) project is a global cooper- state of stress within the plates) rather than the details and ative effort to compile and interpret data on the orientation complexities within and along the plate boundaries, where and relative magnitudes of the contemporary in situ tectonic the overall kinematics and deformation are generally well stress field in the Earth's lithosphere. The project was known. initiated in 1986 under the auspices of the International Preliminary results of the WSM global stress compilation Lithosphere Program and currently involves over 30 scien- were reported by Zoback et al. [1989] and corroborated tists from more than 18 different countries (Table 1) who findings of numerous regional compilations of in situ stress have been directly responsiblefor systematic compilation of and focal mechanism data and indicated that broad regions the available stressdata in the geographicregions indicated. within the interior of many plates are characterized by To date, over 7300 data points have been compiled in a uniformally oriented (___15 ø) horizontal stresses. These rela- This paper is not subject to U.S. copyright. Published in 1992 by tively uniform midplate stress orientations are documented the American Geophysical Union. in continental regions over distances up to 5000 km. Corre- Paper number 92JB00132. lations between regional intraplate stress orientations and

11,703

11,704 ZOBACK.'FIRST- AND SECOND-ORDER LITHOSPHERIC STRESSPATTERNS

TABLE 1. World Stress Map Project Participants

Region Covered Participant

North America John Adams, Geological Survey of Canada Sebastian Bell, Geological Survey of Canada Marian Magee, U.S. Geological Survey, Menlo Park, California Mary Lou Zoback, U.S. Geological Survey, Menlo Park, California Mark Zoback, Stanford University, California

Central America Max Suter, Universidad Nacional Aut6noma M6xico Geraldo Suarez, Universidad Nacional Aut6noma M6xico

South America Marcelo Assumpqo, Universidade de S5.oPaulo, Brazil Jacques Mercier, Universit6 Paris-Sud, France Michel Sebrier, Universit6 Paris-Sud, France

Australia David Denham, Bureau of Mineral Resources, Canberra, Australia

China Ding Jianmin, Institute of Crustal Dynamics, State Seismological Bureau, China Xu Zhonghuai, Institute of Geophysics, State Seismological Bureau, China

India T. N. Gowd, National Geophysical Research Institute, India Harsh Gupta, Cochin University, India Kusala Rajendran, University of South Carolina

Western Europe R. Brereton, British Geological Survey, Great Britain Robert Klein, BP Research, Great Britain Birgit Milllet, Universit/it Karlsruhe, Germany Larry Mastin, Universit/it Karlsruhe, Germany Fritz Rummel, Ruhr Universit/it, Germany Nazario Pavoni, Eidgen6ssischeTechnische Hochschule Zurich, Switerzerland A. Udias, Universidad Complutense, Spain Fennoscandia Soren Gregersen, Geodetic Institute, Denmark Ove Stephansson,Lulea University, Sweden

Central Europe P. Doeveny, E6tv6s University, Hungary G. Grunthal, Central Institute of Physics of the Earth, Potsdam, Germany Forenc Horvath, E6tv6s University, Hungary Peter Knoll, Central Institute of Physics of the Earth, Potsdam, Germany D. Stromeyer, Central Institute of Physics of the Earth, Potsdam, Germany

Eastern Europe and Central Alexei Gvishiani, Institute of Physics of the Earth, Moscow, and Western Asia Russia P. Kropotkin, Geological Institute, Russian Academy of Sciences, Moscow S. I. Sherman, Institute of the Earth's Crust, Siberia Russia Sergei Yunga, Institute of Physics of the Earth, Moscow, Russia Africa William Bosworth, Marathon Oil, Maadi, Egypt Nick Gay, COMRO, Rock Engineering Division, Johannesburg, South Africa

Oceanic Intraplate Eric Bergman, U.S. Geological Survey, Denver, Colorado

both absolute and relative plate motions were first noted by magnitude exist at a variety of scales. These variations may $bar and Sykes [1973], Yang and Aggarwal [1981], Gough be due to a variety of forces acting on the lithosphere: [1984], and Zoback and Zoback [1980, 1981, 1991] in North buoyancy and flexure forces on the broad wavelength end America. These correlations are discussed on a global scale (100-5000+ km, depending on the size of the load) to by Zoback et al. [1989] (see also Assumpcao [this issue], thermal, topographic, and other site specific effects on the Richardson [this issue], and Mt;i!!er et al. [this issue]) and very short wavelength end (<1 km). suggestthat the forces driving and resisting plate motion are The purposeof this paper is multifold. First, it servesas an the primary source of most of these very broad scale stress introduction to the other papers in this special section, fields. presentingthe current status of the global compilation effort Once "regional" stress fields are defined, it is possible to including a summary description of stress indicators and the identify local anomalies or perturbations to this regional philosophy behind the quality ranking scheme. By agree- field. Local variations in stress orientation and relative ment, the methodology and stress indicators used in the ZOB^CK: FIRST- ^ND SœCOND-ORDœRLITHOS•'HœRIC STRœSSP^TTœm•S 11,705

World Stress Map (WSM) project are discussedhere and not 1991), and the breakout catalog for Great Britain [Brereton given in detail in each of the individual papers. Second, this and Evans, 1987]. paper describes the general characteristics of the data set and provides an overview of both first- and second-order Stress Indicators and Quality Ranking broad-scale stress patterns identified in the data. These patterns are described in terms of the constraints that they Six types of geological and geophysical data in four place on the relative importance and magnitude of forces different categories are used to infer tectonic stress informa- acting on and within the lithosphere and also on their tion: earthquake focal mechanisms, well bore breakouts, in relationship to structure of the lithosphere. Finally, this situ stress measurements (hydraulic fracturing and overcor- paper develops a methodology to utilize rotations of the ing), and young geologic data including fault slip and volca- maximum horizontal stress due to local geologic and tectonic nic alignments. The assumptions, difficulties, and uncertain- structures to constrain regional horizontal stress magnitude ties of inferring in situ stressorientations from these different differences. This analysis serves as an example of how stress indicators have been discussedin detail previously [Zoback orientation data compiled in the WSM may be exploited in and Zoback, 1980; Zoback et al., 1989; Zoback and Zoback, the future to constrain in situ stress magnitudes at seis- 1991]. It should be stated at the outset that the age of mogenic depths. "young" geologic data is generally Quaternary. In some The accompanyingpapers in this special section focus on regions of active tectonism, recent changes in stress orien- three main subjects: interpretation of the stress data con- tation and style of faulting have been proposed in Pliocene- tained in the data base; the relationship of the stress field to Quaternary time on the basis of paleostress analysis prima- the tectonics and structure of individual regions; and utili- rily utilizing fault slip data (e.g., see Mercier et al. [this zation of the stress data to constrain geodynamic problems, issue] for recent stress changes in the Andes and Mercier et including the relative and absolute magnitudes of plate al. [1987a] for recent changes in the Aegean region). In tectonic forces and the forces responsible for intraplate these areas we have only compiled the youngest episode of deformation. deformation. However, in some tectonically stable midplate regions such as the eastern United States we have extended the time window back to include evidence of post-Miocene WORLD STRESS MAP DATA BASE faulting. The current version of the global stress data base is shown A quality ranking scheme was developed by Zoback and on a page size map in Figure 1 and on a large size color map Zoback [ 1989] to assesshow reliably an individual data point in Plate 1 (separatefolded map). On both maps the maximum records the tectonic stress field and also to permit compar- horizontal stress (SHEax) orientations derived from all the ison of orientations inferred from very different types of different stress measurement techniques described below are information. A detailed discussion of the rationale and plotted on a background of average topography. All of the criteria for assigning quality to data derived from different stress data are compiled in a digital data base which is types of indicators is given by Zoback and Zoback [1991]. available on floppy diskettes through World Data Center A The reader is referred to Zoback and Zoback [ 1991] for much at the National Geophysical Data Center in Boulder, Colo- of the basic theory and limitations associated with the rado. The data format is fairly complex because we have application of the various stress measurement techniques as tried to standardize and tabulate the maximum amount of this information is not repeated below. information from a wide variety of data types. We have tried Five qualities are used in ranking the data, A>B>C>D, to retain all information pertinent to stressorientation (num- and E. The quality ranking scheme is given in Table 2 and is ber of determinations, mean, standard deviation, and depth identical to that of Zoback and Zoback [1989] and Zoback range); however, by necessity, our data base is not complete and Zoback [1991] with the addition of the E quality cate- for all types of data. In particular, detailed stressmagnitude gory described below indicating analyzed data that contain information (e.g., individual stressdeterminations in a single no useful stress orientation information. As indicated in well) is not compiled; only the values at maximum depth or Table 2, the ranking criteria include accuracy of the mea- a gradient determination are given. However, in caseswhere surements, the number of determinations, the depth interval there is a clear change in stress orientation with depth, both and volume of rock sampled, and the general reliability of the shallow information and deep stress orientation informa- the particular method as a tectonic (as opposed to local) tion are included in the data base; in general, the deeper stress indicator (based primarily on the rock volume sam- information is given a higher-quality ranking. pled). For stress directions inferred from earthquake focal It is important to note that the WSM data base comple- mechanisms a magnitude cutoff is also used in the ranking, ments a number of regional data compilations which in many with the higher-quality ranking assigned to the larger earth- cases are more complete. The reader is referred to these quakes. regional data bases for additional information: Canadian The available evidence from the orientation of fault planes crustal stress data base (all data types) [Adams, 1987], observed in the field as well as inferred from earthquake Fennoscandian Rock Stress Database (overcoring and hy- focal mechanisms, attitude of dikes, and deep in situ stress drofracture measurements) [Stephansson et al., 1987], Har- measurements suggeststhat the principal stress field in the vard Centroid Moment Tensor catalogs (focal mechanisms) lithosphere lies in approximately horizontal and vertical [Dziewonski and Woodhouse, 1983] (now published with the planes [e.g., Anderson, 1951; McGarr and Gay, 1978; Zo- U.S. National Earthquake Information Center (NEIC) Pre- back and Zoback, 1980]. We assume then that the orienta- liminary Determination of Epicenters Catalog), European tion of the in situ stress tensor can thus be approximated Hydrofac Stress Database (maintained at Ruhr University of from the maximum horizontal stress(SHmax) azimuth. The A Bochum, Germany (F. Rummel, written communication, quality data described in Table 2 are believed to record the 11,706 ZOBACK-'FIRST- AND SECOND-ORDERLITHOSPHERIC STRESSPATTERNS

.. ,• ...% • .•...-'- ...:.": ZOBACK: FIRST- AND SECOND-ORDER LITHOSPHERIC STRESSPATTERNS 11,707

TABLE 2. Quality Ranking System for Stress Orientations

A B C D E

Focal Mechanism (FM) Average P axis or Well-constrained single- Single-event solution Single composite Large historic event with formal inversion of event solution (M -> (constrained by first solution no reliable focal four or more single- 4.5) or average of two motions only, often Poorly constrained mechanism event solutions in well-constrained based on author's single-event solution Event with P, T, B axes close geographic single-event solutions quality assignment) Single-event solution for all plunging 250-40ø proximity (at least one (M -> 3.5)determined (M -> 2.5) M < 2.5 event Event with P and T axes event M -> 4.0, other from first motions and Average of several both plunging 40o-50ø events M -> 3.0) other methods (e.g., well-constrained moment tensor composites (M waveform modeling or >2.0) inversion)

Well Bore Breakout (IS-BO) Ten or more distinct At least six distinct At least four distinct Less than four Wells in which no breakout zones in a breakout zones in a breakouts with s.d. consistently oriented reliable breakouts single well with s.d. single well with s.d. <25 ø and/or breakouts or <30 m detected <-12 ø and/or combined <-20 ø and/or combined combined length combined length in a Extreme scatter of length >300 m length > 100 m >30 m single well orientations, no Average of breakouts in Breakouts in a single significant mean two or more wells in well with s.d. ->25 ø determined (s.d. >40 ø) close geographic proximity with combined length >300 m and s.d. <- 12 ø

Hydraulic Fracture (IS-HF) Four or more hydrofrac Three or more hydrofrac Hydrofrac orientations Single hydrofrac Wells in which only orientations in single orientations in a single in a single well with measurement at <100 stress magnitudes well with s.d. <-12ø, well with s.d. <20 ø 20ø < s.d. <25ø; m depth measured, no depth >300 m Hydrofrac orientations distinct hydrofrac information on Average of hydrofrac in a single well with orientaiton change orientations orientations for two or 12ø < s.d. <-25ø with depth, deepest more wells in close measurements geographic proximity, assumed valid s.d. -< 12 ø One or two hydrofrac orientations in a single well Petal Centerline Fracture (IS-PO) Mean orientation of fractures in a single well with s.d. <20 ø

Overcore (IS-OC) Average of consistent Multiple consistent (s.d. Average of multiple All near-surface Multiple measurements (s.d. -< 12ø) <20 ø) measurements measurements made measurements with at a single site or measurements in two in one or more near surface (depth s.d. >15 ø, depth <5 m locality with no or more boreholes boreholes extending >5-10 m) at two or All single measurements significant mean (s.d. extending more than more than two more localities in at depth >40 ø) two excavation radii excavation radii from dose proximity with Multiple measurements from the excavation excavation well, depth s.d. -<25ø at depth with s.d. wall and far from any > 100 m Multiple measurements >25 ø known local at depth > 100 m disturbances, depth with 20 ø < s.d. <25 ø >300 m

Fault Slip (G-FS) Inversion of fault-slip Slip direction on fault Attitude of fault and Offset core holes Not complied data for best fitting plane, based on mean primary senseof slip Quarry popups mean deviatoric stress fault attitude and known, no actual Postglacial surface fault tensor using multiple observations slip vector offsets Quaternary age faults of the slip vector; inferred maximum stress at 30 ø to fault

Volcanic Vent Alignment* (G-Va) Five or more Quaternary Three or more Single well-exposed Volcanic alignment Not compiled vent alignments or Quaternary vent Quaternary dike inferred from less than "parallel" dikes with alignments or Single alignment with five vents s.d. <12 ø "parallel" dikes with at least five vents s.d. <20 ø

s.d., standard deviation. *Volcanic alignmentsmust be based, in general, on five or more vents or cinder cones. Dikes must not be intruding a regionaljoint set. 11,708 ZOBACIC: FIRST- AND SECOND-ORDER LITHOSPHERIC STRESSPATTERNS orientation of the horizontal tectonic stress field to within relative magnitudesof the principal stresses.However, most _+10ø-15 ø, the B quality data to within _+15ø-20 ø, and the C focal mechanism data are B or C quality data (see Table 2) quality data to within _+25 ø. D quality data describedin Table since P and T axes for an individual earthquake may differ 2 are considered to yield questionable tectonic stressorien- significantly from the actual stress orientations producing tations for several reasons: widely scattered or sometimes the slip [e.g., McKenzie, 1969]. For that reason, no single- bimodal orientations observed at a single site (breakout, event focal mechanism is given an A quality, regardless of hydraulic fracture, or overcoring measurementswith a stan- how well-constrained that mechanism might be or the mag- dard deviation (s. d.) >25ø); the small volume of rock nitude of the event. Mean best fitting deviatoric stress sampled(e.g., small (m < 2.5) earthquakesor less than four tensors or geometrically determined mean directions of P breakouts); or very shallow near-surface measurements po- and T axes for focal mechanisms from a single source region tentially perturbed by topographic or even thermal stresses are assigned an A quality since these mean directions or (overcoring) or near-surfacefracturing (hydrofractures). For inversion results approximate quite well the regional stress this reason, only orientations from the "reliable" A-C data field as represented by independent data [e.g., Michael, are plotted on Plate 1 and on most of the maps included in 1987; Zoback, 1989]. this special section. In some cases, orientations from the D Qualities are based in part on how well the mechanism is quality data agree well with the surrounding information; constrained (generally determined by investigator construct- however, in many other cases they contribute a great deal of ing the focal mechanism) and also based on earthquake scatter to the regional picture. Therefore we have adopted magnitude as an indication of the volume of rock sampled rather conservative criteria for our compilation, preferring to and the amount of strain released. Very small magnitude possibly downgrade some "good" data rather than trying to events (m < 2.5) are assigned a D quality. Even if the focal plot every piece of information collected in a region. mechanisms for these events are reliable, these earthquakes In a few cases, data are upgraded in quality by the may represent deformation due to the complex interaction of investigator who collected them for specific circumstances active faults rather than deformation in response to the not adequately accounted for in the general quality ranking regional stress field. This is often the case for aftershocks; table. For example, the mean stress direction inferred from hence only main shock mechanisms are compiled. breakouts in two or more wells in close proximity may be Well-constrained mechanisms (B quality data) are gener- given a higher quality than would be strictly indicated by the ally available for large magnitude earthquakes, particularly total breakout length; the rationale being that multiple, for those events with M > 4.5-5.0 which are recorded consistent orientations in different depth intervals in adja- cent wells are a significant observation. In nearly all cases teleseismically and some waveform modeling or inversion the reason for the quality upgrade is noted in the comments technique has been used in addition to first motions to accompanying the data in the data base. constrain the nodal planes. However, in areas of a dense Data in the fifth quality category, "E", have been ana- seismic network and detailed crustal structure and velocity lyzed and found to yield no reliable information regarding information (e.g., California), well-constrained focal mech- principal stress orientations. Examples of this type of infor- anisms may be available for smaller-magnitude events. mation are given in Table 2. There are at least two good Mechanisms for moderate earthquakes (4.0-6.0) based only reasons for including these data in the data base. Sometimes on local first motions from a sparse regional network are extreme scatter and the lack of consistent stress orientations given a C quality. in a given well or at a given locality may be a very valuable The centroid moment tensor (CMT) inversions done by piece of information regarding the local state of stress; for the Harvard group [Dziewonski and Woodhouse, 1983] (and example, the stress field may be locally horizontally isotro- now published in the NEIC Preliminary Determination of pic and the effects due to small-scale perturbations of the Epicenters catalog, as mentioned previously) are generally stress field due to presence of fracturing or interacting faults also assigneda C quality if there is no additional study of the may dominate. Furthermore, the E category is useful for event. This lower quality, despite the fact that magnitudes record-keeping purposes; for example, if data from a partic- are typically ->5.0, is due to the relatively poor resolution of ular hole, region, or earthquake have been examined once, it the CMT inversion for the vertical dip-slip components of is helpful to know that that examination yielded no useable faulting in shallow focus events [Sipkin, 1986; Anderson, information. Generally, statements in comments accompa- 1988]. Assumpcao [this issue] conducted an analysis of CMT nying each entry in the data base indicate the problem, for solutions in South America in which he checked the solution example, "well-log quality was too poor to be read or for consistency with P wave polarities at World-Wide Stan- interpreted." In general, there are many gaps in E entries; dard Seismograph Network (WWSSN) stations and some since they yield no useful stress orientation information, high-gain Brazilian stations and found that 18 of 20 CMT they have not been systematically compiled. solutions he investigated were compatible with the regional As mentioned above, the limitations associated with the polarity data and two solutions were not. various types of stress indicators and the evaluation criteria As indicated in Table 2, composite focal mechanisms are for assigningquality were developed previously [Zoback and generally given a D quality. Often these mechanisms are Zoback, 1991] and are only summarized below. The distri- done for local very diffuse seismicity or for aftershocks bution of the data by type of indicator is shown in Figure 2a. (which as mentioned above are generally not included). Note that here and throughout the paper statistics are done However, if a rock volume is deforming in response to a on only the "reliable" (A-C) quality data. uniform regional stresstensor, careful objective (grid search) Earthquake focal mechanisms. As shown in Figure 2a, composites of a large number of events may yield reliable the focal mechanism data are by far the most abundant in the stress information. Xu et al. [this issue] demonstrated this data set (54%) and provide valuable information on the with a series of tests creating composites of randomly ZOBACK.'FIRST- AND SECOND-ORDER LITHOSPHERIC STRESS PATTERN•S 11,709

VOLCANIC ALIGNMENTS = 4.1% structural geologists [Carey, 1979; Carey and Brunier, 1974; FAULT SLIP = 5.5ø/ø Angelier, 1979, 1984]. The slip vector and mean attitude of

=3.4% the fault plane for historic or prehistoric events are treated as paleofocalmechanisms with the P axis inferred at 30ø to the = 4.5% known fault plane [after Raleigh et al., 1972] rather than the standard45 ø and are given a B quality since these surface FOOAL MI ruptures generally correspond to earthquakes with rn > 6.0-6.5 [e.g., Bonilla and Buchanan, 1970]. The C quality data represent a less accurate estimate of stress orientation, usingonly the strike of young faults and the primary senseof offset. For example, the trends of very young grabens are believed to indicate the orientation of the horizontal stresses to within +__25ø. Stress directions inferred from the trends of joint sets are presently not considered in the WSM data base. Recent analyses of joint systems have shown that criteria can be Fig. 2a. Distribution of reliable (A-C quality) data in WSM data defined for "neotectonic" joints based on field observations base by type of stress indicator. that may make them useful stress indicators. Such criteria include evidence for consistentextensional origin and verti- selected polarities for a series of randomly selected fault cal distribution. These neotectonic joint systems have been planes with slip vectors computed from a known stress identified in several regions and are found to parallel direc- tensor. The composite mechanismsthat he created with this tions of contemporary SHmaxdirections inferred from other randomly generated data set closely replicated the initial stress indicators [Hancock and Engelder, 1989; Hancock, stress tensor, provided there was enough diversity in his 1991]. selected fault planes. Rivera and Cisternas [1990] provide a Borehole breakouts. Although breakout analysis was theoreticaljustification for such an approach and suggestan only established as a reliable stress determination technique inversion of polarity observations(rather than nodal planes) in the late 1970s and early 1980s, it is significant that these to obtain deviatoric stress tensors, which are often close to data now comprise 28% of the data base (Figure 2a) and the P and T axes of best fitting "composite" mechanisms. probably represent the greatest potential for producing new This inversion method holds much promise for obtaining data in relatively aseismic areas. This stress determination additional regional stress data since it bypassesthe need to technique utilizes the natural stress concentration around invert individual fault planes from what may be relatively the borehole, which has been modeled as a hole in an elastic poorly constrained individual focal mechanisms. plate. Borehole breakouts represent shear failure of the The focal mechanism data provide valuable information boreholewall centeredon the S hmindirection, the azimuth of on stress regime or relative magnitudes of the principal maximum circumferential compressive stress [see Gough stresses. As described below, stress regime (or style of and Bell, 1982; Zoback et al., 1985]. faulting) is defined on a set of criteria using the plunge of P, The analysis technique was first described by Cox [1970], B, and T axes. and his initial analyseswere extended to a greater number of Fault slip data. Young geologicfault slip data have been wells by Babcock [1978]. Bell and Gough [1979] were the treated in a similar manner as the focal mechanism data. The first to interpret these features as a stress-related phenome- highest-quality ranking is reserved for inversions of fault non. Techniques for identification and interpretation of well striations on fault planes with a variety of trends, the bore breakouts have been described in numerous publica- so-called "neotectonic analyses" pioneered by French tions (see Bell [1990] and Zoback and Zoback [1991] for

Number

200 400 600 800 I • I 0.00- 0.05 iiiiIIIIIII I[IIIIIIl[,',','i!;i;i;i';i:i;t ' 0.05- 0.30

0.30- 1.00 I FOCAL MECHANISMS 1.00- 2.00 171 BREAKOUTS

2.00- 3.00 I HYDROFRACS :,D OVERCORING 3.00- 4.OO El! FAULT SLIP I'q VOLCANIC ALIGNMENTS 4.O0- 5.OO

5.00-10.00

10.00 - 20.00

>20.00

Fig. 2b. Depth distribution of reliable WSM data. 11,710 ZOaACI•: FIRST- AND SECOND-ORDER LITHOSPHERIC STRESSPATTERNS useful summaries of references) and rely on analysis of the Volcanic vent alignments. The strike of dikes and the cross-sectional shape of a well bore through the use of a alignment of volcanic vents are considered to represent an magnetically oriented four arm caliper tool (most common analog of a natural massive hydrofrac experiment where the method) or an acoustic borehole televiewer [e.g., Plumb and pressurizing fluid is magma, not water. The trend of the Hickman, 1985]. alignment should be perpendicular to S hmin[Nakamura, Breakout data are especially important in this compilation 1977; Nakamura et al., 1978]. Alignments may be inferred becausethey generally sample a depth interval intermediate from linear zones of cinder cones or other vents or from the between earthquake focal mechanisms and in situ stress trends of feeder dikes. Often in the regions of youngest measurements and geologic data (see Figure 2b). They also volcanism, not enough erosion has occurred to expose the provide multiple observations of stress orientations over underlying feeder dike system. All the data included in the considerabledepth range. The large number of observations data base have been dated as Quaternary in age either allows a statistical determination of stress orientation and its radiometrically or based on field relationships. scatter about the mean especially when detailed analyses of Two basic approaches have been utilized in analysis of breakouts are performed with borehole televiewers [e.g., volcanic alignment data: (1) Nakamura's method for defining Barton et al., 1988; $hamir et al., 1988]. In assessingquality the elliptical orientation of zones of eruptive vents on flanks we have tried to assure that multiple distinct breakout zones and adjacent to active volcanoes and (2) simply identifying are sampled over a significant depth range. Note that A specific individual alignments in a field not dominated by a quality results may result from averaging of stress orienta- single large volcano. For Nakamura et al.'s [1978] data tions obtained from two or more wells in close proximity. (primarily from the Aleutian arc in Alaska and a few points Similarly, averages of wells in close proximity can be in Japan)we have used the same A-D quality ranking system assigned a B or C quality if the combined number or length they applied to their own data. In all other casesthe volcanic of breakouts and the standard deviation fit the range of alignment data in the data base come from analysis of values indicated. individual vent alignments in a volcanic region, and qualities Hydraulic fracturing stress measurements. This stress are assigned according to the criteria in Table 2 which are measurement technique also takes advantage of the stress based both on the number and consistency of alignments concentration around the well bore and, ideally, provides within a given field. determinations of both horizontal stress magnitudes and A potential drawback with this technique is that near- orientations [e.g., Haimson and Fairhurst, 1970; Zoback surface intrusions can sometimes utilize preexisting joint and Haimson, 1983]. Hydraulic fracturing is used in both sets [Delaney et al., 1986]. However, as Delaney et al. engineering and scientific investigations and involves pres- indicate, thesejoint sets must strike nearly perpendicular to surizing a portion of the well bore until a tensile fracture the current Shrnindirection to accommodatethe intrusion, so develops striking in the direction of SHmax,the azimuth of that errors in using dike orientation are likely to be small. An the minimum compressive circumferential stress. Interpre- exception to this would be the case when the two horizontal tation of pressurization and pumping curves permits an stressesare approximately in magnitude, a condition with accurateestimate of the magnitudeof Shminand limits on the the general regional consistencyof stressorientations in the magnitudeof SHrnax.Vertical stressis typically assumedas WSM data base argues against as being common. equal to the weight of the overburden, and thus an approx- "Overcoring" stress measurements. Included in this imate stress tensor can be determined. One disadvantage of category are a variety of stress or strain relief measurement this technique is that in order to make measurements of techniques (see summary of these techniques by McGarr stress orientation, intact portions of the borehole must be and Gay [1978] and a detailed summary by Engelder [1992]). tested, and it is sometimes difficult to detect the induced These techniquesinvolve three-dimensional measurement of fracture. the strain relief in a body of rock when isolated from the However, a measurement technique called the Hydraulic surrounding rock volume; the three-dimensional stress ten- Tests on Preexisting Fractures (HTPF) method utilizes pres- sor can subsequently be calculated with knowledge of the surized reopening of preexisting fractures of a variety of complete compliance tensor for the rock. There are two trends to determine the stress field in a least squares sense primary drawbacks with this technique which restrict its [Cornet and Valette, 1984]. Cornet and Burlet [this issue] usefulness as a tectonic stress indicator: measurements must have used this technique in their investigation of the regional be made near a free surface, and strain relief is determined stress field in France. over very small areas (a few square millimeters to square Detailed hydraulic fracturing testing in a number of bore- centimeters). Furthermore, near-surface measurements (by holes beginningvery close to the surface (10-20 m depth) has far the most common) have been shown to be subject to revealed marked changes in stress orientation and relative effects of local topography, rock anisotropy, and natural magnitudes with depth in the upper few hundred meters fracturing [Engelder and Sbar, 1984]. In addition, many of possibly related to effects of nearby topography or a high these measurementshave been made for specificengineering degree of near-surface fracturing [e.g., Haimson, 1978]. As applications (e.g., dam site evaluation, mining work), places many hydraulic fracturing (hydrofrac) tests are done for where topography, fracturing, or nearby excavations could engineering evaluation of stress conditions near dam sites or strongly perturb the regional stress field. other structures, the reliability of these tests to record For all of the above reasons we have adopted a conserva- tectonic stress fields must be evaluated in terms of local site tive quality ranking criterion to evaluate overcoring data. In conditions. If this information is not available, we have cases where information is not available on the local site taken a conservative approach and have generally given conditions we have assigned these data D quality (a large stress orientations obtained by hydraulic fracturing tests for number of overcoring data in China and Korea fall into this a purely engineering study a D quality. category). In Fennoscandia, overcoring data believed to be ZOBACK:FIRST- AND SECOND-ORDERLITHOSPHERIC STRESS PATTERNS 11,711

TABLE 3. StressRegime Characterization (and Method of DeterminingSHmax Azimuth) Based on Plunge(pl) of P, B, and T Axes or $1, $2, and $3 Axes

Plunge of Axes P/S1 B/S2 T/S3 Regime SHmaxAzimutha pl -> 52ø pl -< 35ø NF azimuthof B axis 40ø -< pl < 52ø pl -< 20ø NS azimuthof T axis + 90ø pl < 40ø pl -> 45ø pl -<20ø SS azimuthof T axis + 90ø pl -< 20ø pl -> 45ø pl < 40ø SS azimuthof P axis pl -< 20ø 40ø -< pl < 52ø TS azimuthof P axis pl -< 35ø pl -> 52ø TF azimuthof P axis aFor someovercoring and hydraulic testing of preexistingfractures measurements, the magnitudes of the full stresstensor are determinedand the SHmaxazimuth can be calculateddirectly from the eigenvectorsof thetensor. However, the stress regime characterization in these cases is stillbased on the plungesof the principal axes. influencedby overlying or adjacent excavationsin mines Sv > Shmin), corresponding to faulting with dominantly were simply not included in the WSM data base since a horizontal slip; and a thrust faulting stressregime (S Hmax> completecompilation of these data are availablein Fennos- Shmin> Sv), correspondingto reversedip-slip faulting. In candianrock stressdata base [Stephanssonet al., 1987]. The some areas, the stress field appears to be transitional be- Fennoscandianovercoring data included in the WSM data tween regimes;that is, two of the stressesare approximately base were those assessedto be uncontaminated by local site equalin magnitude.A stressfield of the form Sv • SHmax>> effects by O. Stephansson(Lulea University, Sweden). Shmincan producea combinationof bothnormal and strike- Similarily, "reliable" overcoringdata from minesin the Ural slip faulting, whereas a stress field of the form SHmax>> Mountains of Russia were compiled by P. Kropotkin (Geo- Shmin• Sv producesa combinationof strike-slipand thrust logical Institute, Russian Academy of Sciences, written faulting. Other possibleend-members for stressmagnitudes communication,1990) and from mines in South Africa by N. (SHmax-- Shmin ) produce radial compressionor radial Gay (COMRO, Rock EngineeringDivision, written commu- extension dependingon whether the horizontal stressesare nication, 1990), although detailed information of local con- greaterthan or lessthan the vertical stress,respectively. As ditions was not available. mentioned above, while such a horizontally isotropic stress There have been a number of shallow overcoring measure- state may exist in some places [Haimson, 1984; Zoback, ments carried out specificallyto investigate the regional 1989;Adams, 1989], the regional uniformity of SHmaxorien- stressfield. In these cases, care was taken to avoid siteswith tationsargues that suchstress states are not commonin the nearby topographyand/or extensivejoint or fracture sys- Earth' s crust. tems, and depthswere believed sufficientto avoid thermal For the WSM data basewe have used plungesof measured effects. A summaryof such measurementsmade in western S1, S2, S3 axesor P, T, andB axesto dividethe data into Europe is presented by Becker and Paladini [1991]. As five main stressregime categories.In addition, an unknown indicated in Table 2, these well-controlled near-surface categoryis usedwhen the data provideno informationabout measurements(depths generally between 5 and 10 m) were relative stress magnitudes(e.g., well bore breakout data). assigned a C quality. The stressregime categoriesinclude normal faulting (NF), predominatelynormal with strike-slip component (NS), Relative Stress Magnitudes and Determination strike-slipfaulting (includesminor normal or thrust compo- of Stress Regimes nent) (SS), thrust faulting (TF), predominatelythrust with While meaningfulabsolute stressmagnitude information strike-slipcomponent (TS), and unknown (U). The cutoff (madeat depths> 100m) was availablefor only about4% of valuesfor plungesof P, T, and B axes (or S•, S2, and S3) the data in the data base (1.1% from shallow overcoring for these various categories are given in Table 3 together measurementsand 3.1% from hydrofracs), information on with the choice of axes used in the data base to infer the relative stressmagnitudes or stressregime could be inferred maximum horizontal stress (SHmax)orientation. For exam- from the more numerous focal mechanism and fault slip ple, the S//maxorientation is taken as the azimuthof the B data. In addition, an extensionalstress regime was assigned axisin caseof a pure normalfaulting regime (NF) and as (90ø to volcanicalignment data in the westernUnited Statesand + T axis azimuth) in the NS case when the B axis generally in Mexico on the basis of Quaternary normal faulting asso- plungesmore steeply than the T axis. ciated with these young basaltic volcanic fields. While the exact cutoff values defining the stress regime Throughout this paper, stress magnitudesare defined categoriesare subjective,we have attemptedthe broadest usingthe standardgeologic/geophysical notation with com- possiblecategorization consistent with actual P, T, and B pressivestresses positive, so that S• > S2 > S3 indicates axes values. The NS and TS categories represent mixed- that S• is the maximumprincipal compressive stress and S 3 mode faulting. In these two categories,either the minimum is the minimum principal compressivestresses. Following stressor T axis (normal faulting) or the maximum stressor P Anderson [1951], three stress regime categories can be axis (thrust faulting) is approximatelyhorizontal, and the defined on the basis of relative stress magnitudes: exten- vertical and other horizontal axes rotate in a perpendicular sionalstress regime (Sv > SHmax> Shmin),corresponding to plane.NS is distinguishedfrom SS by virtue of the fact that normal dip-slip faulting; strike-slipstress regime (SHmax> the maximum stressor P axis is the steeper plunging of the 11,712 ZOBAC•C:FIRST- AND SECOND-ORDERLITHOSPHERIC STRESS PATTERNS

6O Eastern North America [] FAULTSLIP 5O mean = N 63øE _. 28 ø N = 364

4O El aRF.•OUTS

3O

2O

10

155 165 175 5 15 25 35 45 55 65 75 85 95 105 115 125 135 145

8O Western Europe FAULTSLIP mean = N 144øE _+ 26 ø

6O N = 332

aRF_•OUTS FOCALIV•CHN•ISMS

2O

0 65 75 85 95 105 115 125 135 145 155 165 175 5 15 25 35 45 55

Azimuth with respect to North (degrees) Fig. 3. Histogramof reliableSHmax orientations broken down by type of indicator.(a) EasternNorth America (regionbetween 31.5 ø and 5 IøN latitude,55 ø and 100øWlongitude). (b) WesternEurope (region between 46.2 ø and 55øN latitude, 10øWand 17øElongitude).

P andB axes, and similarly,TS is distinguishedfrom SS by the datain the data baseby stressmeasurement technique is the fact that the minimumstress or T axis is the steeper shownin Figure2a. Figure2b givesthe depthdistribution of plungingof the B and T axes (see Table 3). the A-C quality data: the geologic and in situ stress mea- Plunges of axes of some of the data fall outside of the surementdata are generallyrestricted to the surfaceor very rangesdefined in Table 3. When the differenceswere only a near surface (less than 1-2 km depth), earthquake focal few degrees, these data were inspectedindividually and mechanismsprovide coveragefor depths between about 5 assigned to the most appropriate category. However, a and 20 km, and well bore breakout data (which come number of mechanisms,notably for smaller and often less primarilyfrom petroleumexploration wells) commonly sam- well constrained focal mechanisms, had P, B, and T axes ple 1-4 km deep and in some cases as deep as 5-6 km, which did not fit at all into the defined categories.The providing a valuable link between the near-surface and the anomalousmechanisms fell in two main groups:(1) all three focal mechanismdata. It is also important to note that the axes have moderateplunges (between 25 ø and 45ø ) or (2) both breakoutand in situ stressmeasurement data provide valu- P and T axes have nearly identicalplunges, in the rangeof able informationon the stressfield in nonactive(nonseismic 400-50 ø. In both cases it is difficult to infer the true maximum regions). and minimumhorizontal stress azimuths. These data points As can be seen on Figure 1 and Plate 1, there are a number may represent deformation due to principal stress fields of regionsof very uniformSHmax orientations: eastern North tilted out of horizontaland vertical planes.The data which America,western Canadian Basin (region directly east of the fell into this category compose less than 2% of all focal Canadian Rockies), central California, the Andes, western mechanismsand were assigned an U (unknown) stress Europe, the Aegean, and northeastern China. Detailed anal- regime and given an E quality, indicatingthat the maximum horizontal stress azimuth was not well defined. ysis of the stressdirections within theseregions of uniform coverage indicates that stress orientation inferred from dif- ferent types of indicatorsyield consistentorientations. Fig- General Characteristics of the Data Base ure 3 plots stress orientationsbroken down by different As of December 1991,7328 stressdata were compiledas indicator type for two very large regions: eastern North part of the World StressMap project, 1141of these were E America (betweenlatitude 31.5ø and 51øNand longitude55 ø quality with no reliable information on stressinformation. Of and 100øW)(Figure 3a); and western Europe (between the remaining6214 entries, 4413 are consideredto yield latitude46.2 ø and 55øN and longitude 10øW and 17øE)(Figure reliable information on tectonic stress orientations(A-C 3b). Assumpcao[this issue]has madea similarcomparison quality) and are plotted on Figure 1 and on the large, folded for the Andes. In both areas shown in Figure 3 there is a color map (Plate 1). As mentionedabove, the distributionof well-definedmean $Hmax direction indicated, although there ZOBACK: FIRST- AND SECOND-ORDERLITHOSPHERIC STRESS PATTERNS 11,713 is considerable scatter about this mean and this scatter The most recent references for detailed descriptions of the appears in all data types over these broad regions. Many regional stress fields are also given in Table 4. small regions in Figure 1 and Plate 1 show an excellent Some regional stress patterns listed in Table 4 are newly correlation between the different stress measurement tech- defined (i.e., not discussedby Zoback et al. [ 1989]) and merit niques, indicating that the criteria defined in Table 2 are brief discussion. In particular, the existence of a region in resulting in consistent determinations of the tectonic stress western and north central Africa of compressional tectonism field despite the different volumes of rock and different depth with an approximately E-W S Hmax orientation has been intervals sampled. identified on the basis of new data. These data include focal mechanisms determined from waveform modeling of large- magnitude earthquakes occurring in west Africa between FIRST-ORDER GLOBAL STRESS PATTERNS 1939 and 1983 [Suleiman et al., 1989; D. I. Doser, written In addition to stress orientations, relative stress magni- communication, 1990] as well as some recent CMT solutions tudes (stress regimes) are indicated on Plate 1 using the which all show a consistent pattern of strike-slip deformation following definitions:extensional stress regime (Sv > SHmax with a roughly E-W P axes orientation. An approximately > S h) (normal dip slip), includes categories NF and NS E-W S Hmaxorientation is also observed in breakout data (rakes generally >50ø); strike-slipstress regime (SHmax> S v from 11 wells covering a region over 1000 km wide in the > $h) (dominant horizontal slip), SS category (rakes gener- Sudan [Bosworth et al., this issue]. In addition, a zone of ally >40ø); and thrust stress regime (SHmax> S h > Sv) NNW compressionis identified along the northern boundary (reverse dip slip), includes categories TF and TS (rakes of the African plate consistent with the convergence of generally >50ø). Africa and Eurasia. The data shown in Figure 1 and Plate 1 reinforce the As noted by Zoback et al. [ 1989], the plate tectonic setting broad-scale patterns and general conclusions regarding the of Africa (surrounded by mid-ocean ridges and a continental global data base summarized by Zoback et al. [1989]: collision to the north) suggests a midplate compressional 1. In most places a uniform stressfield exists throughout stress field. Buoyancy forces related to asthenospheric up- the upper brittle crust as indicated by consistent orientations welling and lithospheric thinning in the east Africa rift from the different techniques which sample very different system clearly dominate the stress field in that area. How- rock volumes and depth ranges. ever, the new data suggeststhat a regional intraplate stress 2. The interior portions (variously called intraplate and field related to plate-driving forces may exist outside of the midplate regions) are dominated by compression(thrust and area of high topography and asthenospheric upwelling. As strike-slip stress regimes) in which the maximum principal discussed below in the section on second-order stresses, the stress is horizontal. amount of rotation of the horizontal stress directions be- 3. Active extensional tectonism (normal faulting stress tween west African and the east African rift places a strong regime) in which the maximum principal stress is vertical constraint on the ratio of the magnitudes of the regional generally occurs in topographically high areas in both the stresses relative to the local buoyancy forces, suggesting continents and the oceans. that the horizontal extensional buoyancy stress must be 4. Regional consistency of both stress orientations and about 1.2 times the magnitude of the regional horizontal relative magnitudes permits the definition of broad-scale stress differences. regional stress provinces, many of which coincide with One place where stress patterns have been recently clar- physiographic provinces, particularly in tectonically active ified somewhat is in Australia. Stress orientations there still regions. show a great deal of scatter; however, additional breakout This final point, regionally uniform stressorientations and data on the NW continental shelf [Hiller, 1991], the occur- relative magnitudes, is emphasized in a generalized global rence of the three Ms = 6.3-6.7 earthquakes in the 1988 stress map shown in Figure 4, which shows mean stress Tennant Creek region [Choy and Bowman, 1990], and a directions and dominant stress regime for clusters of data reassessmentof the quality of several moderate-magnitude, plotted on Figures 1 and Plate 1. The arrow sizes on Figure relatively poorly constrained thrust faulting focal mecha- 4 represent a subjective assessmentof "quality" related to nisms, recorded only locally, has clarified the stress patterns the degree of uniformity of stressorientation and also to the somewhat. In particular, much of central and northeastern number and density of data. Stress regime was inferred Australia indicates a compressionalstress field dominated by primarily from earthquake focal mechanisms and style of NNE compression,whereas available data from both south- Quaternary faulting. Thick inward pointing arrows indicate eastern and southwestern Australia indicate E-W compres- S/•maxorientations in areas of compressional(strike-slip and sion. thrust) stress regimes. Thick outward pointing arrows give By contrast, as can be seen on Figure 1 and Plate 1, the Shminorientations in areas of normal faulting regimes. Re- extents of some regions of relatively uniform SHmaxorien- gions dominated by strike-slip tectonics are distinguished tation are enormous. The region of uniform ENE S Hmax with the thick inward pointing arrows and orthogonal, thin orientation in midplate North American covers nearly the outward pointing arrows. entire continental portion of the plate lying at an average The broad regions of the Earth's crust subjected to uni- elevation of less than 1000 m (excluding the west coast) and form stress orientation or a uniform pattern of stress orien- may also extend across much of the western Atlantic basin tation (such as the radial pattern of stress orientations in [Zoback et al., 1986]. Thus here the stress field is uniform China) are referred to in this paper as "first-order" stress over roughly 5000 km in both an E-W direction and a N-S provinces. These regions and the stress orientation patterns direction. In western Europe the region of relatively uniform are briefly summarized plate by plate in Table 4, which also NW S Hmaxorientation extends over 1500 km in an E-W serves as a guide to the generalized map shown in Figure 4. direction and about 2200 km in a N-S direction. 11,714 ZOBACK:FIRST- AND SECOND-ORDERLITHOSPHERIC STRESS PATTERNS ZOBACK.'FIRST- AND SECOND-ORDER LITHOSPHERIC STRESSPATTERNS 11,715

TABLE 4. First-Order Global Stress Patterns

SHmaxor References Shmin Stress Primary Source of Stress Region Orientation a Regimet' andComments State of Stress Stress Modeling

North American Plate Midplate region ENE T/SS primarily ridge push, lateral Adams and Bell [1991] and Richardson and Reding stress variations predicted Zoback and Zoback [1991] for basal drag not [1989, 1991] observed, regionally extensive(--•2 x 107km 2) Western Cordillera, complex stress patterns many references, see Central America, beyond scope of summaries by Zoback and Alaska discussion, largely related and Zoback [1989, to superpositionof 1991], $uter [1991], buoyancy forces and $uter et al. [this issue], distributed shear related to and Estabrook and Pacific-North American Jacob [1991] relative motion

South American Plate Continental E T/SS primarily ridge push, torque Assumpcao [this issue] Stefanick and Jurdy [this analysis suggestsdriving issue] and MeUer and drag possibly major force Wortel [this issue] [Meijer and Wortel, this issue] High Andes N NF trench suction or buoyancy Froidevaux and Isacks Whittaker et al. [this due to thick crust and/or [1984] and Mercier et al. issue] and Stefanick thinned lithosphere [this issue] and Jurdy [this issue]

Eurasian Plate Western Europe NW SS combined effects of ridge Klein and Barr [1987], Brudy [1990] and push and continental Gregersen [this issue], Gtiinthal and collision with Africa Griinthal and Stromeyer Stromeyer [this issue] dominate, absolute [this issue], and MM!er velocity • 0; thus et al. [this issue], and resistive or driving basal Rebai et al. [1992] drag probably not important; lateral variations in lithospheric structure may locally influence stress field China/eastern Asia N to E SS continental collision force Molnar and Tapponnier England and Houseman domimates, indentor [1975], Molnar and [1989], Tapponnier geometry extremely Deng [1984], and Xu et and Molnar [1976], important al. [this issue] and Vilotte et al. [ 1984, 1986] Tibetan Plateau WNW NF Buoyancy (due to thick crust Molnar and Tapponnier England and Houseman and/or thinned upper [1978], Mercier et al. [1989] and Vilotte et mantle) overcomes [1987b], and Burchfiel al. [ 1986] compression due to and Royden [1985] continental collision force

African Plate East African rift NW NF Buoyancy force overcomes Bosworth et al. [this issue] ridge push compression Midplate (western and E SS ridge push dominates this paper, using data of southern Africa) absolute velocity • 0; Bosworth et al. [this thus drag probably not issue], Suleiman et al. important [1989], and D. I. Doser (written communication, 1990) North Africa N to NW T/SS continental collision with Rebai et al. [1991] and Europe dominates Kamoun and Hfaiedh [1985]

Indian Australian Plate India N to NE T/SS continental coilsion Gowd et al. [this issue] Cloetingh and Wortel [ 1985, 1986] Central Indian Ocean N to NW T/SS complex interaction collision Bergman [1986], C. Stein C!oetingh and Wortel and trench forces, long- et al. [1989], and Petroy [1985, 1986] and Gover wavelength basement and Wiens [1989] et al. [this issue] undulations due to stress- induced flexure? 11,716 ZOBACK:FIRST- AND SECOND-ORDERLITHOSPHERIC STRESS PATTERNS

TABLE 4. (continued)

SHmaxor References Shmin Stress Primary Source of Stress Region Orientationa Regimet' andComments State of Stress Stress Modeling

Indian Australian Plate (continued) West Indian Ocean N to NW NF high level of intraplate Bergman et al. [1984], Cloetingh and Wortel seismicitywith Shmin Wiens and Stein [1984], [1985,1986], Bratt et al. parallel to nearby mid- and Stein et al. [1987] [1985], and Gover et al. ocean ridges, due to [this issue] thermoelastic stresses or comple geometry of plate-driving forces.9 Central Australia and N to NE TF much scatter in stress this paper Cloetingh and Wortel northwest shelf orientations; however, [1985, 1986] best data suggest consistent north to NNE SHmaxdirections Southern coastal E TF source of E-W stress Australia unknown

Pacific Plate Young (<70) crust NE SS ridge push, slab pull, drag Okal et al. [1980] and Richardson et al. [1979], all give same orientation Wiens and Stein [1984] Bai et al. [this issue], Wortel et al. [1991], and Gover et al., [this issue] Older crust (>70) NW? T/SS driving drag would predict Wiens and Stein [1985] Richardson et al. [1979], extension, not observed and Zoback et al. [1989] Bai et al. [this issue], compression; extension Wortel et al. [1991], and predicted due to mantle Gover et al. [this issue] upwelling central Pacific also not observed

Nazca Plate Midplate only one earthquake focal Wortel and Cloetingh mechanism available [1985] and Richardson and Cox [1984]

Antarctic Plate Midplate expected stress state is Johnston [1987] radial compression (surrounded by ridges), one focal mechanism available, seismicity suppressed by ice sheet? West Antarctic rift E to NE NF Cenozoic rift system with Behrendt et al. [1991] and basalts as young as Behrendt and Cooper Holocene; buoyancy [1991] forces dominate midplate compression

asHmax orientationgiven for thrustor strike-slipfaulting stress regimes; Shmin given for normalfaulting stress regimes. t'NF,normal faulting stress regime' SS, strike-slip faulting stress regime' TF, thrust fauting stress regime' T/SS, combined thrust and strike-slipregimes (see text for definitionsof stressregimes).

The likely sources of broad-scale stress fields are related guishedfrom the other possibleforces actingon the plate. to plate tectonic driving forces. Following Forsyth and (See, for example, Stefanickand Jurdy [this issue],Richard- Uyeda [1975]and Chappieand Tullis[1977], a seriesof body son [this issue], and Richardson and Reding [1991] for forcesand tractionsare definedas actingalong plate bound- summariesof the sourcesand relative magnitudesof the aries. The primary forces that either drive or resist plate plate-driving forces.) motion include slab pull, ridge push (actually a distributed For purposes of evaluating the broad-scale patterns of force acting over the entire portion of cooling oceanic intraplatestresses it is importantto keep in mind that the net lithosphere thickening with age), collisional resistance, slab pull, collisionalresistance, and trench suctionforces all trench suction,and basal drag. Analysisof relative magni- act normalto plate boundariesand that ridge pushforces act tudesof the plate-drivingforces based on balancingthe net in a direction perpendicular to the isochrons in oceanic torque acting on each plate [Forsyth and Uyeda, 1985; lithosphere.Ridge push and collisionalresistance generate Chappie and Tullis, 1977] indicatesthat the two largest intraplatecompression; trench suctionresults in intraplate forcesacting on the platesare the negativebuoyancy of the extension. The sign of the net slab force has been estimated subducting slab and the resistance to subduction(both as a function of age [Cloetingh and Wortel, 1986] and is viscousand friction). They concludethat the net slabforce, generally extensional and perpendicular to the trench. The the sum of these two forces, is small and cannot be distin- effects of drag forces are more difficult to estimate because ZOBACK'. FIRST- AND SECOND-ORDER LITHOSPHERIC STRESS PATTERNS 11,717 there are several possible configurations: resistive drag at ridge push and continental collision) and the geometry of the the base of the plate opposingplate motions, driving drag in plate boundaries that these forces act on. The effects of the direction of plate motion, drag due to "counterflow" forces are felt thousands of kilometers from the actual plate (mass flow from trenches back to ridges), and drag due to boundary probably due in part to the lateral variations in deep mantle flow. Drag resisting or driving plate motions density/lithospheric structure associated with these bound- should generate stresses aligned with the absolute plate aries, particularly the ridge push force which results from motion directions. A clear disagreement between observed thickening of oceanic lithosphere with age. ENE compression in eastern North America and NW-SE 2. Horizontal extensional stressesinduced by buoyancy directed counterflow predicted beneath that region [Chase, in regions of high elevation locally dominate the midplate 1979; Hager and O'Connell, 1979] implies either that the compression generated by plate boundary forces. counterflow must occur at a level too deep to influence stress 3. It is difficult to evaluate the role of drag using stress state in the lithosphere [Zoback et al., 1986] or that the shear orientation data alone since for most plates, absolute veloc- coupling between this counterflow and the lithosphere is ity and ridge push torque poles are nearly identical [Rich- quite weak. Bai et al. [this issue] provide some estimates of ardson, this issue]. However, numerous observations sug- the stress effect in the lithosphere due to deep mantle flow. gest that simple resisting or driving drag (parallel or Zoback et al. [1989] demonstrated a correlation between antiparallel to plate motions) is not very important in con- SHmax orientation and the azimuth of both absolute and trolling the stress field in the uppermost, brittle part of the relative plate velocities (using histogramsof point by point lithosphere. Lateral stressgradients associatedwith an order comparisons)for several intraplate regions (see Figure 4 for of magnitude variation in stress values across large plates, regions of correlation). However, as demonstrated by Rich- such as predicted for models in which drag dominates ardson [this issue], the ridge push torque pole is very similar [Richardson, this issue; Richardson and Reding, 1991], are to the absolute velocity pole for most plates; thus a compar- not observed in relative stress magnitude data [Zoback, ison with absolute velocity trajectories can do little to 1991]. The complex pattern of stresses in Australia and the distinguishbetween ridge push and basal drag as a source of lack of correlation with absolute plate motion suggest that stress. In fact, comparison between stress directions and resistive drag, possibly enhanced beneath an old, cold, fast local azimuths computed from velocity poles is an overly moving continent, is not a major source of the upper simplistic approach to evaluating the influence of plate- lithospheric stress field. Furthermore, Wiens and Stein driving force on the intraplate stress field. At best, these [1985] concluded that a general state of compression in old correlations demonstrate the important role of the plate oceanic lithosphere (as inferred from available earthquake boundary forces and can be used to conclude that the net focal mechanisms) indicates that the integrated ridge push balance of forces driving the plates also stresses them force dominates drag for all ages. Predictions of stresses [Zoback et al., 1989]. The actual orientation of the intraplate related to whole mantle flow inferred from mantle tomogra- stressfield of course depends on the balance of forces acting phy [Bai et al., this issue], while generally producing mid- on the plate and the plate geometry on which they act and plate compression, do not match well the broadest scale can only accurately be predicted by detailed modeling (such patterns observed in the stress data [Zoback, 1991]. as finite element modeling). Much of our knowledge of the relative magnitudes of the INFERRING CRUSTAL STRESS MAGNITUDES various plate-driving forces comes from modeling of the FROM STRESS ROTATIONS kinematics of plate motions. However, as $tefanick and Jurdy [this issue]point out, there is an inherent problem with The WSM data base offers the possibility to infer stress this kinematic approach; because the motion of a rigid plate magnitudes using local stress rotations (relative to "region- is the result of the integrated effect of all torques acting on it, al" first-order stress orientations) resulting from stresses different combinations of forces (with the same net torque) caused by specific geologic and tectonic features. The can produce the same plate motion. Numerous finite element amount of rotation constrains the magnitude of local stresses modeling attempts (beginning with the global models of relative to regional stress differences as has been discussed Richardson et al. [1979]) have demonstrated that knowledge previously by Sonder [1990]. As described above, first-order of the first-order intraplate stress orientations and relative patterns of stress in the lithosphere are generally correlat- stressmagnitudes (stress regimes) is a powerful constraint in able with plate-driving forces and have extremely large constraining force models. Table 4 also includes a summary lateral extents, of the order of 50+ times the thickness of the of the results of this finite element modeling of the intraplate upper, brittle part of the lithosphere (approximately 20 km). stress field by various investigators (many included in this Second-order sources considered here are also tectonic in special section) and provides an assessmentof the relative origin and have length scales up to many times the brittle role of the various plate tectonic forces in determining the lithosphere thickness but are not necessarily "plate tecton- intraplate stress field, based on the correlations with ob- ic" in origin. Three main categories of local sources of served orientations and relative magnitudes as well as the stresses within the lithosphere are considered here: litho- modeling results. spheric flexure, localized lateral density contrasts, and lat- The first-order stress patterns shown in Figure 4 and eral strength contrasts. These three sources of stress are described in Table 4 provide constraints on the relative described below with estimates of the stress magnitudes importance of various broad-scale sourcesof stressacting on associated with these features and an evaluation of their the lithosphere: influence on the regional stress field with examples. 1. The orientation of midplate compressive stress field The interference of a regional stress field and a superim- can be explained largely as a function of the applied com- posed uniaxial local stress field can be evaluated quantita- pressive plate boundary forces (primarily resulting from tively and depends on the angle between the regional stress 11,718 ZOBACK' FIRST- AND SECOND-ORDER LITHOSPHERIC STRESSPATTERNS

SHmax o'x = 1/2(o'•,,+ O'y,)+ 1/2(o'•,,- O'y,)cos 20 X I = 1/2o't,(1 - cos 20) (2) I REGIONAL Shmin I y o'y= 1/2(o'•,,+ o'•,) - 1/2(o'x, - o'•,) cos20

= 1/2o't,(1 + cos 20) (3)

where 0 is the angle between the normal to the uniaxial stress direction (strike of structure) and the regional S•/maxdirec- X L tion (angle between x' and x); see Figure $. The regional and local stresses are then superimposed in the reference re- LOCAL gional coordinate system to determine a new resultant stress field:

. •'xy= 1/2•r/• sin 20 (4)

o'x -- SHmaxq- 1/2•r/•(1 - cos 20) (5)

RESULTANT $t•min" I y ,, O'y= Shminq- 1/2•r/•(1+ cos20) (6) As the regional reference coordinate system was a principal one,the only contribution to •'xyis fromthe local stress. The orientation of the resultant principal stresstensor is given by x", y", z. Its orientation relative to the reference, regional anglesmeasured in directionshown, clockwise angles are positive stressfield •s determined from the following expression from Fig. $. Geometry for evaluating stress rotations due to local Jaeger and Cook [1979, p. 13]: sourcesof stress(modified from Sonder [1990]). SHmax,S'bmax and S hmin, S'•tmin correspond to maximum and minimum horizontal 2 Txy stresses,respectively. tan 2 7 = (7) O'x -- O'y Substituting equations (4)-(6) into (7), we can compute the system and the local structure as well as on the the relative amount of rotation of the regional stressfield in the horizon- magnitudes of the regional and local stress. Following tal plane: Sonder [1990] and as shown in Figure 5, we define a reference coordinate system x, y, z which coincides with the sin 2 0 regional principal stress directions. Assuming that the re- 7 = 1/2 tan-I (8) (SHmax-- Shmin)/O'L-- COS2 0 gional stress field lies in horizontal and vertical planes, the S Hmaxdirection correspondsto the x axis, Shmincoincides where 3/is the angle between the regional S Hmaxand the with the y axis, and the z axis is vertical downward. The resultant local S Hmax(angle between x and x") (the new local stress field due to a long structure of arbitrary orienta- Shminorientation is just 3/+ •r/2). This expressionis equiv- tion is defined in a x', y', z coordinate system, where x' is alent to that of Sonder [1990], taking into account the the strike of structure and y' is the orientation of normal, difference in nomenclature and sign convention of the local uniaxial stress. The magnitude of the local horizontal devi- stress. atoricstress is crL:cr x, = 0, •ry, - •rL (thelocal structure is Equation (8) is plotted in Figure 6, the amount of horizon- assumedto be long enough that variations in stressin the x' tal stressrotation (7) is given as a function of the orientation direction can be ignored). In the case of local buoyancy of the structure (0) for various ratios of the regional horizon- forces, a vertical deviatoric stress of equivalent magnitude to tal stressdifference to the local stress,(SHmax -- S hmin)/O'L. the horizontal stress but opposite in sign will also be pro- The sense of rotation depends on the orientation of the duced: •rz = -•rt.. This vertical stress does not cause structure and whether the local stress is compressive horizontal stress rotations but can change the relative stress ((SHmax -- Shmin)/O'L ) 0) or extensional ((SHmax -- magnitudes (stress regime), as discussed below. Note that S hmin/O'L• 0). compression is assumed positive in this paper; thus •r/• is As can be seen in Figure 6, for a negligibly small local negative for a deviatoric extensional stressand positive for a stressfield, (SHmax-- Shmin)/O'L • •, there is no rotation deviatoric compressivestress (opposite of the conventionof (3' = 0); alternately, if the local stress field dominates the Sonder [ 1990]). regional stress field, (SHmax -- S hmin)/O'L • 0, then the The potential horizontal stress rotations due to a local stressfield rotates into alignment with the local stress field. horizontal deviatoric compressionor extension can be eval- For a stressratio (SHmax-- Shmin)/O'L= ñ2.0 the maximum uated using simple tensor transformation in the horizontal possiblerotation is only 15ø , roughly the detection threshold plane. The shear and normal stressesdue to the local stress using stressorientations in the WSM data base. Thus resolv- source in the reference coordinate system are given by [e.g., able local rotations imply that the local uniaxial stress must Jaeger and Cook, 1979, p. 14] be greater than about half the regional horizontal stress •'xy= -1/2(crx'- cry,)sin 20 difference. Note also from equation (8), and as shown on Figure 6, that there is a discontinuity in the rotation curves = 1/2crt, sin 20 (1) at 0 = +-90ø and (SHmax-- Shmin)/O'L= +-1. For I(SHmax-- ZOBACK: FIRST- AND SECOND-ORDERLITHOSPHERIC STRESS PATTERNS 11,719

I 90 ! I ! I extension superimposed compression

60

ß

-1.05 1.05 '

m 0 E

o • 1.05 -1 .o5 ._ o -30

-60

superimposed compression ' superimposed extension -9O

-90 -60 -30 0 30 60 90 0, anglebetween strike of structureand SHmax(degrees)

Fig. 6. Stress rotation of regional horizontal stresses(3') as a function of 0, the angle between the strike of the local feature producing the horizontal uniaxial compressionor extension and the regional $Hmaxdirection, computed from equation (8). Numbers on curves refer to values of the ratio of regional horizontal stress differences to magnitude of local uniaxial stress,(SHmax -- S hmin)/CrL;positive values indicate superimposeduniaxial compressionand negative values indicate superimposeduniaxial extension.

Shmin)/rrLI > 1.0 thereis no rotation,only a changein the considered deviatoric stresses (normalized with respect to regional principal stress values, whereas for all stress ratios the vertical stress)and computed the resultant stressregime I(SHmax-- Shmin)/CrLI< 1.0 thereis complete90 ø rotation. for a superimposedlocal buoyancy force with both a hori- For 0 = _+90 ø the rotation is not defined because both zontal (trr) and vertical (-trr) component. The resultant horizontal stressesare equal when (SHmax-- Shmin)/rrL = stress regime is a function of both the ratio of the magnitude _+1. of the regional to local stress and the strike of the local Equation (8) and Figure 6 are valid for all regional stress structure relative to the regional stress field. Her calcula- states. Because the amount of rotation is inversely propor- tions for a strike-slip reference stress state are replotted in tional to the difference of the two horizontal stress magni- Figure 7 as a function of the stressratio used here, (S Hmax-- tudes, the larger the horizontal stress difference, the smaller Shmin)/rrL . It is clear that a strike-slipreference state will be the rotation (all other factors being equal). In a strike-slip faulting stress regime where S] = SHmaxand S3 = Shmin, one can expect the largest horizontal stress differences REGIONAL STRIKE-SLIP REGIME (SHmax-- Shmin)= (Sl -- 53). By contrast, for a regional ß I I i i i . I . i i i i i 4 4.0 thrust or normal faulting regime the horizontal stress differ- ences (SHmax-- S hmin)are smaller (equivalent to (S] - S2) • thrust .E 2.0 . I•- strike- . or (S2 - S 3), respectively); therefore the expected rotation E in a thrust or normal faulting stress regime due to local • 0.0 . superimposed stress would be larger than that in the strike- slip regime. For the case in which S2 lies exactly halfway normal -• between S ] and S 3 in magnitude(qb = 0.5, where qb= (S 2 -- S3)/(S• - S3), the so-called "stress deviator" [Angelier, ,,•a•a••strike.slip• I I I I I i I I I I I 1979]), the corresponding rotation in a thrust or normal -9O -60 -30 0 30 60 90 regime due to an equivalent local stress would be twice that 0, relative strike of structure(degrees) in a strike-slip faulting regime. As noted above, in addition to rotating the principal stress Fig. 7. Expected "local" stress regime for a buoyancy stress field, the superpositionof the local stressalso influencesthe (horizontal stress component crL, vertical stress component -crL) relative magnitudesof the stressesand can result in a change superimposedon a regional strike-slip regime. Stress regime is a function of the angle between the local structure 0 and the strike of in the magnitude of one or both of the horizontal stress SHmaxregionally and the stressratio ($Hmax -- Shmin)/CrLß (Super- magnitudesrelative to the vertical stress (hence a change in imposed extension corresponds to negative values of (SHmax -- relative stress magnitudes or stress regime). Sonder [1990] S hmin ) / O'L. ) 11,720 ZOBACiC:FIRST- AND SECOND-ORDER LITHOSPHERIC STRESSPATTERNS converted locally to a normal or thrust faulting stress regime data density is probably only great enough to evaluate this when I(SHmax- Shmin)/rrLI< 2.0--4.0 (dependingon the possibility on the northwestern Australian and eastern North strike of the local structure). Thus recognizable local stress American shelves. On the northwestern Australian shelf, rotations may often be accompanied by local changes in stress orientations inferred from breakouts trend both par- stressregime, as has apparently occurred in east Africa (see allel and perpendicular to the local trend of the continental below). slope, so extensional stressesnormal to the slope (indicated by S Hmax parallel to the slope) clearly do not dominate everywhere; also the S Hmaxdirection in the continental of SECOND-ORDER STRESS PATTERNS Australia is poorly constrained. However, on the passive AND POSSIBLE SOURCES margin off the eastern United States where the ENE regional

Flexural Stresses S Hmax orientation within the midcontinent is well con- strained, the S Hmaxorientations on the shelf generally do Loads on or within an elastic lithosphere cause deflection parallel the shelf-slope break (Figure 1). This stress state and induce flexural stresseswhich can be quite large (several cannot be simply attributed to local topographic effects of hundred megapascals) and can perturb the regional stress the slope because the wells are deep and many breakouts field with wavelengths as much as 1000 km (dependingon the come from sections of the wells which are much deeper than lateral extent of the load) [e.g., McNutt and Menard, 1982]. the topography [Dart and Zoback, 1987]. Some potential sources of flexural stress influencing the These rotations of the regional stress field can be used to regional stress field include sediment loading, particularly constrain the relative magnitude of the local margin-related along continental margins; glacial rebound; seamount load- stressesrelative to the regional stress field due to far-field ing; and the upwarping of oceanic lithosphere oceanward of plate-driving forces. Probably the most dramatic examples the trench, the "outer arc bulge" [Hanks, 1971; Chapple and of rotation of the regional stress field can be observed Forsyth, 1979]. The final two examples occur in oceanic offshore of eastern Canada, where the stress data on the lithosphere and have been analyzed extensively theoretically continental shelf suggest an S Hmax orientation of about and using bathymetry data. These examples of superim- N 15ø--25øEin contrast to an approximately N55ø--65øEorien- posed flexural stressescan not presently be used, however, tation onshore. The trend of the continental slope in this to evaluate stress magnitudes quantitatively, as we have region is roughly N15ø-25øW; thus 0 = +(75 to 85)ø and the only very limited information on regional stress orientations observed rotation of the stressfield is y = -(35 to 45)ø. As in the adjacent oceanic crust. shown in Figure 6, this indicatesa (SHmax-- Shmin)/CrL = Sediment loading on continental margins. A major -1.0. source of stress at passive continental margins is the sedi- Regional stressdifferences can be predicted assumingthat ment load, often more than 10 km thick [Walcott, 1972; maximum stress differences are limited by the frictional Turcotte et al., 1977; Cloetingh et al., 1982]. S. Stein et al. strength of the crust, often called Byerlee's law using the [1989] evaluated the sources of stress acting on passive frictional coefficients from Byedee [1978]: continental margins and concluded that the flexural stress due to sediment loading should be the dominant effect. Their (S1 - P)/(S3 - P) = [(1 + /-I.2) 1/2 + /-I,]2 (9) calculations of sediment-loading stresses for a variety of where S l and S3 are the maximum and minimum principal viscoelastic lithosphere models indicate margin-normal ex- stresses, respectively; P is pore pressure; and /x is the tensional stresses on the loaded continental shelf and mar- frictional coefficient of the most well-oriented faults [e.g., gin-normal compression in the adjacent oceanic lithosphere Sibson, 1974; Brace and Kohlstedt, 1980; Zoback and with corresponding stress magnitudes of the order of 100 Healy, 1984]. For a regional thrust faulting stress regime MPa. These stress magnitudes are roughly an order of (probably most appropriate for this region based on earth- magnitude greater than the magnitudes of other stressesthat quake focal mechanisms), Byerlee's law (equation (9)) yields they consideredwhich act along the margins: stressesdue to S• - S3 values of about 200 MPa for 4.5 km depth (the plate-driving forces (ridge push or basal drag), spreading average breakout depth) for a/x = 0.65 and hydrostatic pore stress due to the lateral density contrast between oceanic pressure.Assuming that S3 is equal to the lithostat and S2 is and continental crust (see following section), and effects of midway between S• and S3 (•b = 0.5) implies regional glacial rebound (see below). S. Stein et al. [1989] point out, horizontal stress differences (SHmax-- Shmin) • 100 MPa. however, that there is considerable uncertainty as to how Using the (SHmax- S hmin)/CrL = -- 1.0 from the observed much of the total sediment load to consider. Specifically, rotation, the predicted margin-normal extensional stress are how much of that load has been relaxed with time? They also estimated at about 100 MPa, consistent with S. Stein et al.'s note that there is no clear case that passive margin earth- [ 1989] estimate of order 100 MPa for these stresses. quakes are preferentially associated with the most heavily Glacial rebound stresses. Another obvious source of sedimented margins. flexure stressis the rebound of the lithosphere in responseto Breakout data are now available from the continental the removal of 10,000-20,000 years ago of thick (1-5 km) ice shelves of a number of passive margins: eastern North sheets which covered the Fennoscandia and and east central America; McKenzie delta, NW Canada; eastern China; Canada (Laurentide) regions. There is a relatively high level Australia; and India. If the models of S. Stein et al. [1989] of intraplate seismicity in both the Laurentide and Fennos- are correct, the state of stress on the continental shelves candia rebounding regions which has been noted by many should be dominated by the sediment-loadingeffect, and the workers. In Fennoscandiathe intraplate seismicity indicates SHmax orientations shown on Figure 1 and Plate 1 should a complex mixture of dominantly thrust but also strike-slip tend to parallel the continental slope (indicating an S hmin and normal deformation with no clear and consistent rela- direction perpendicular to the margin). Continental shelf tionship to the rebounding region [Gregersen, this issue; ZOBACK: FIRST- AND SECOND-ORDER LITHOSPHERIC STRESSPATTERNS 11,721

Mt;iller et al., this issue]. Analysis of focal mechanism data plates reflects the overall net force balance. Several specific in the Laurentide region has indicated a local perturbation examples of the effects of buoyancy forces related to lateral in relative stress magnitudes unaccompanied by any hori- variations in lithosphere thickness are given below as well as zontal rotation of stress axes [Zoback, this issue]. Earth- examples of other possible stress effects related to lateral quakes in southeastern Canada appear to be occurring in density variations within the crust. response to a thrust faulting stress regime, whereas those in Example of rotations due to lithospheric thinning: The the central and eastern United States occur in response to a East African rift. One of the broadest scale stress patterns strike-slip faulting stressregime. While this lateral variation which can be attributed to effects of lithospheric thinning is in stress regime or relative stress magnitude is spatially the NW directed contemporary extension (SHmaxoriented correlated with the southern edge of the Laurentide ice N40ø-50øE) in the east African region [Bosworth et al, this sheet, estimates of rebound-related flexural stresses [S. issue]. As described above, new stress data in central and Stein et al., 1989; Clark, 1982] are at least an order of western Africa suggesta midplate compressive (strike-slip) magnitude too low to explain the observed difference in stress regime with an S Hmaxorientation of approximately stressregime computed according to Byerlee' s law assuming E-W (N100øE). Gravity data suggest that lithospheric thin- Ix - 0.65 and hydrostatic pore pressure [Zoback, this issue]. ning in the East African rift occurs along approximately a N-S axis [Brown and Girdler, 1980] which should produce a local deviatoric extensional stress oriented approximately Lateral Density Contrasts/Buoyancy Forces E-W. The contemporary N40ø-50øE SHmaxdirection of the Numerous workers have demonstrated that topography modern stress field within the East African rift can then be and its compensation at depth can generate sizable stresses use to constrain the ratio of the regional to local stress. capable of influencing the tectonic style [Frank, 1972; Arty- According to equation (8) and Figure 6, for 0 = + 80ø and •, - ushkov, 1973; Fleitout and Froidevaux, 1982; Sonder, 1990]. -(50 to 60)ø, the stress ratio (SHmax-- Shmin)/CrL = --0.8; Density anomalies within or just beneath the lithosphere that is, the local extensional stresses related to buoyancy constitute major sourcesof stress. The integral of anomalous must be about slightly greater than (1.2 times) the regional density times depth (density moment of Fleitout and Froi- horizontal stressdifferences. Referring to Figure 7, it is clear devaux [ 1982]) characterizes the ability of density anomalies that the local resultant stressregime for (SHmax-- Shmin)/trL to influence the stress field and to induce deformation. In = -0.8 and 0- +80 ø should be extensional. general, crustal thickening or lithosphere thinning (negative Stress differences at 8 km depth (approximately the middle density anomalies) produces extensional stresses, while of the uppermost brittle layer) in the regional strike-slip crustal thinning or lithospheric thickening (positive density regime can be determining using Byerlee's law (equation anomalies) produces compressional stresses. In more com- (9)). For hydrostatic pore pressure and a IX = 0.65 the plex casesthe resultant state of stressin a region depends on predicted stress difference for a strike-slip faulting stress the density moment integrated over the entire lithosphere. In regime is (SHmax-- S hmin)= 144 MPa, for tb = 0.5. The a collisional orogeny, for example, where both the crust and (SHmax-- S hmin)/CrL = --0.8 determined from the observed mantle lid are thickened, the presence of the cold litho- rotation thus implies a mean value for the local deviatoric spheric root can overcome the extensional forces related to extension in the upper brittle crust of trL = -180 MPa, crustal thickening and maintain compression [Fleitout and assuming that Byerlee's law is valid for predicting the Froidevaux, 1982]. regional stress magnitudes. Regional stress fields globally show numerous examples of Sonder [1990] estimated the near-surface buoyancy stress stresspatterns related to lateral density anomalies, many of magnitudes for long-wavelength (mantle) density anomalies which are tied to compensation of topography. This influ- to be crL = AprIL/3, where Ap is the density contrast and L ence is probably most striking in the regions of active is the thickness of the anomalous density layer. Gravity and extensional tectonism within the largely compressional mid- teleseismic data from the East African rift suggest a mean plate regions, which are usually areas of high topography: /Xp= -30 kg/m3 for anomalousupper mantle over a thick- East African rift, Baikal rift, western U.S. Cordillera, high ness of L = 170 km [Achauer, 1992], yielding a crL of the Andes, and the Tibetan plateau. The presenceof thin crust in order of 17 MPa. This implies a regional (SHmax-- S hmin) the East African rift, the Baikal rift, and the western U.S. value of only 13.6 MPa based on the rotation. The order of Cordillera indicates that the source of the high elevation is magnitude difference in stress magnitudes inferred from a related to a thinned mantle lithosphere and upwelling hot rotation due to a modeled local stress and that calculated by asthenosphere (see references of Zoback and Magee [ 1991]). Byerlee's law (with 4• - 0.5 and hydrostatic pore pressure) In both the Andes [Isacks, 1988] and the Himalayas [Fleitout demonstrates how little is known about in situ stress magni- and Froidevaux, 1982; England and Houseman, 1989] the tudes in the brittle crust at seismogenicdepths and points to elevation and extensional tectonism have been attributed the potential usefulnessof analysis of local stressrotations in both to a thickened crust as well as to a thinned mantle constraining these stress magnitudes. lithosphere. Froidevaux and Isacks [1984] used the geoid Examples of rotation due to lithospheric thickening: Col- anomaly associated with the 4000-m-high Altiplano-Puna orado Plateau and the Western Alps. Because mantle plateau of the Andes to compute a buoyancy-related force lithosphere is denser (colder) than the surrounding astheno- (perunit length of boundary)of between4 and5 x 1012N/m. sphere, there is a tendency for a thick cold mantle root to This is comparable to the total ridge push force per unit sink and generate compression along its margins. Such a lengthof 2-3 x 1012N/m [Frank,1972; Lister, 1975; Parsons mechanism has been invoked to explain the 90ø rotation of and Richter, 1980]. Thus buoyancy-related forces clearly are S hmin directions between the Colorado Plateau and the as important in the overall force balance of the plates and the adjacent Basin and Range province in the western United plate-driving forces, and the stress distribution within the States. Both areas show an extensional state of stress [Wong 11,722 ZoB^cK: FIRST- AND SECOND-ORDER LITHOSPHERIC STRESSP^TTERNS and Humphrey, 1989; Zoback and Zoback, 1989]. Gravity, and because they both indicate N-S compression [Assump- geoelectric, and seismic evidence, however, suggests the cao and Suarez, 1988], which is in sharp contrast to the presence of a thicker, colder mantle lid beneath the plateau regional E-W compression direction for much of the South relative to the Basin and Range [e.g., Thompson and Zo- American plate (see Figure 1, Plate 1, and Assumpcao [this back, 1979]. Thompson and Zoback [1979] suggestedthat issue]. "ridge push" type forces acting on this keel of mantle lid It is hypothesizedthat the apparent 90ø rotation of S/-/max material were responsiblefor the 90ø rotation of horizontal orientation in the vicinity of the rift results from the effects of stressesand for producing compressionaltectonism within a dense lower crustal "rift pillow" probably initially formed the Colorado Plateau interior. However, since this initial as a result of mafic magmatic intrusion during rifting and is suggestion, additional stress data have become available for now frozen into the lower crust. The excess mass is sup- the Colorado Plateau. While the 90ø rotation of Shmindirec- ported by the strength of the now cool lithosphere, inducing tions is still valid, the stress state in the plateau interior is deviatoric compressionperpendicular to the rift axis. now known to be extensional [Wong and Humphrey, 1989] Richardson and Zoback [ 1990]presented two-dimensional rather than compressionalas originally suggestedby Thomp- finite element models of the Amazonas rift constrained by son and Zoback [ 1979] and Zoback and Zoback [1980]; thus surface geometry, geology, and gravity data. The plane the buoyancy-related compression appears large enough to strain models include both lithospheric material which can rotate the horizontal stresses but not to change the stress support elastic stressesand asthenospheric material which regime. cannot support elastic stressesfor long times. The modeling Another example of the stresseffect due to a thick mantle results indicate that the rift pillow (density contrast Ap = keel may be the approximately 50ø counterclockwise rota- + 150kg/m 3) is capableof generating60-200 MPa of rift- tion of SHmaxorientations in the Western Alps, a region normal (approximately N-S) deviatoric compression within characterized by approximately E-W compression, in the crust [Richardson and Zoback, 1990]. Model stressesare marked contrast to the general pattern of NW compression greatest at midcrustal depths, consistent with the observed observed throughout western Europe [Gr•nthal and Strom- depth of the nearby thrust earthquakes. eyer, this issue; Miiller et al., this issue]. Fleitout and Note that in Figure 6 because the rift structure is parallel Froidevaux [1982] and Griinthal and Stromeyer [this issue] to the regional SHmaxdirection (0 = 0ø) and the observed suggestthat the presence of a nearly 200-km-thick, approx- rotation is about 90ø (•, = 90ø), the only real constraint on imately N-S trending lithospheric root beneath this region (SHmax-- Shmin)/rrL is that the ratio must be >1.0 (corre- may be responsible for the observed rotation. In this exam- spondingto the discontinuity in the curves discussedprevi- ple, 0 = -35 ø and •, = -50 ø, indicatinga stressratio (SHmax ously). This implies that the regional horizontal stressdiffer- -- Shmin)/rrL ----+0.4, implying that the local compressional ences should be >60-200 MPa based on the results of the stress must be more than 2.5 times the regional stress finite element modeling of the density structure described differences. above. This value can be compared with predicted regional Crustal contrast at ocean/continent boundary. Bott and stre•s magnitudescomputed using Byedee's law for an Dean [1972] suggested that the lateral variation in crustal inferred regional thrust faulting stress regime with hydro- thickness and density along continental margins should static pore pressure and Ix = 0.65. To explain the observed induce margin-normal extension within the continental crust 90ø local stressrotation, the regional Shminmagnitude must and margin-normal compression in the adjacent oceanic be increasedabove the regional SHmaxvalue. The maximum crust. S. Stein et al. [1989] estimate the magnitude of these stressdifference (Sl - S3) predicted by Byerlee's law at 20 "crustal spreading" stresses to be ---10 MPa. Since the km depth (approximately the depth of one of the two induced stresseson continental margins have the same sign earthquakes)in a thrust regimeis quite large (SHmax-- S v) • as flexural stressesrelated to sediment loading, it is difficult 800 MPa; the corresponding horizontal stress differences to separate these two effects. The crustal spreading stresses (SHmax-- Shmin)however, are poorly constrainedbecause of may be more concentrated in regions where the continental uncertainty as to the relative magnitude of the intermediate shelf is narrow and slope is quite steep, such as in northern stress.For an assumedqb - 0.5, (SHmax-- Shmin)---- 400 MPa. South America (see Assumpcao [this issue] for a discussion However, the computed rrr > 60-200 MPa may be consis- of seismicity along the easternmost coast of Brazil). tent with the stressmagnitude prediction based on Byerlee's Lateral density contrast in crust "rift pillow." Perhaps law due to the lack of constraint on the regional qbvalue. The one of the most convincing examples of a local stress vertical stressis also somewhat reduced in the upper crust rotation due to lateral density contrasts within the crust due to the presenceof the densebody in the lower crust. The occurs within the South American craton in north central computed reduction in vertical stress above the rift pillow, Brazil along the northern boundary of the E-W trending however, is less than 10% of the induced horizontal com- Amazonas rift. This Paleozoic rift zone is marked by a rift pression (R. Richardson, written communication, 1990) basin filled with up to 7 km of gently dipping, shallow water amounting to about 10-20 MPa and probably not really sediments of Ordovician to Permian age and an associated significantat 20 km depth. ---100 mGal Bouguer gravity high [Nunn and Aires, 1988]. Seismic refraction data indicate the presence of a lower Nunn and Aires [1988] demonstrate that the observed grav- crustal rift pillow (P wave velocity between 7.2 and 7.5 ity anomalies can be explained by a steep-sidedzone of high km/s, intermediate between normal lower crust and upper density in the lower crust varying from 100 to 200 km in mantle velocities) beneath many continental rifts, both mod- width. Two moderate-sizedmidplate thrust earthquakes(m b ern and ancient [Mooney et al., 1983]. In young, active rifts = 5.1 and 5.5) have occurred along the northern boundary of this dense load is compensated by lithospheric thinning; the rift in the last 30 years. These events are anomalous in however, after active rifting has ended (possibly in response that they are deep (21 and 45 km) for intraplate seismicity to changesin far-field stress state), this dense load remains ZOBACK: FIRST- AND SECOND-ORDER LITHOSPHERIC STRESSPATTERNS 11,723 and must be supported by the strength of the lithosphere. scatter of data in Australia may be an example of such an The induced rift-normal compression may help explain the effect. Many shield regions are rather poorly sampled in often observed correlation between intraplate seismicity and terms of stress orientations; however, the southeast margin old rift zones [e.g., Johnston, 1989; Johnston and Kantor, of the Canadian shield is well sampled, and the stress 1990; Mitchell et al., 1991]. This rift pillow induced com- directions are rather consistent. pression may also provide a mechanism to enhance basin Major Precambrian boundaries and sutures, where sam- inversion (in addition to simple cooling and thickening of the pled, seem to have little effect on the regional stress orien- lithosphere). tations. Gregersen [this issue] detected no effects or devia- tions of stress orientations in the Fennoscandia region associated with known geologic boundaries, such as edge of Lateral Strength Contrasts the Precambrian Baltic shield. Similarly, stress orientations The largest-scale example of the possible influence of a in the eastern United States do not seem perturbed by the lateral variation in crustal strength is the approximately boundary of the Grenville front, a major NE trending suture fault-normal compression observed adjacent to the San trending approximately from Missouri to New York. Andreas right-lateral strike-slip fault. In this case the Stress data also demonstrate that at least some major strengthcontrast is presumed to be due to the effect of a fault Proterozoic orogenic belts do not significantly perturb the of low frictional shear strength embedded in a frictionally regional stress field. Perhaps the best example is the NE strongcrust. SHmaxdirections in a 100- to 125-km-widezone trending Paleozoic Appalachian belt in the eastern United on either side of the San Andreas fault are typically oriented States. This major compressionalmountain belt formed as a 700-85ø to the local trend of the fault [Mount and Suppe, result of NW compression; however, contemporary SHmax 1987; Zoback et al., 1987; Zoback, 1991; Mount and Suppe, orientations trend ENE along and across the chain, consis- this issue] rather than the expected 300-45ø . These stress tent with the midplate North American stress orientation. data are consistent with geologic evidence of young (<4 Clearly "residual stress" related to this orogenic belt has no m.y.) folding and reverse faulting with axes and reverse fault influence on the modern stress field. In fact, this consistency trends oriented subparallel to the fault. Thus, because of the of modern ENE SHmaxorientation is maintainedin detail in presumed low shear strength of the San Andreas (inferred eastern New York and Pennsylvania through a region where independently from heat flow data [e.g., Lachenbruch and the Appalachian orogenic belt makes a 40ø bend in strike Sass, 1980]) the regional stress field appears to have rotated [Evans, 1989]. Similarily, Miiller et al. [this issue] note only approximately 50ø so that the fault becomes nearly a princi- local perturbations to the western Europe stress directions pal stressplane, thereby minimizing the shear stress on that related to the Tertiary Alpine belt. In the westernmost and plane. Assuming a frictional strengthbased on Byedee's law southwesternmostportions of the Alps, SHmaxdirections are in the crust surroundingthe fault, Zoback et al. [1987] used normal to the Alpine front and form an approximately radial the observed 500-60ø stress rotation in the zone adjacent to pattern consistent with the trends of Pliocene folds. This the fault to limit the shear strength of the San Andreas to radial pattern has been interpreted as the result of crustal 5-20 MPa, a value consistent with the maximum shear stress indentation related to the continued convergence of Europe allowable by heat flow constraints. and Africa [Pavoni, 1961], or alternately, as mentioned This phenomenon does not appear limited to the San above, the E-W compression in the Western Alps may be Andreas fault in central California. Zoback [1991] argues related to the stress effects of a deep cold mantle lithosphere that the extension observed in the Gulf of California and root extending to 200 km depth beneath the region [Fleitout Salton Sea/Imperial Valley region is also due to the low and Froidevaux, 1982; Granthal and Stromeyer, this issue]. strengthof the plate boundary. Mount and Suppe [this issue] Thus the stress field with its regional uniformity within an document fault-normal compression adjacent to the Great enormously complex, inhomogeneous,and anisotropic litho- Sumatran right-lateral strike-slip fault. Both Mount and sphere appears to be a fundamental observation. This obser- Suppe [this issue] and Ben Avraham and Zoback [1992] vation is very strong evidence for a lithospheric stress state describe evidence of contemporary fault-normal extension strongly dependent on the contemporary forces applied and compressionalong a number of transform plate bound- along the boundaries of the plates. Residual stressesfrom aries. past orogenic events to not appear to contribute in any substantial way to the modern stress field.

CRUSTAL INHOMOGENEITIES AND THE STRESS FIELD CONCLUSIONS The average value of stress induced in the lithosphere by the plate-driving forces probably depends primarily on the Over 4400 reliable data on tectonic stress orientations in thickness of the lithosphere carrying the load [e.g., Kusznir the upper brittle part of the lithosphere have been compiled and Bott, 1977]. This results in lower mean stresses in thick, globally. Consistency between shallow, near-surface stress cold "cratonic" lithosphere. The significanceof this stress orientations and those inferred at depth from earthquake amplification (or deamplification) effect may be viewed, focal mechanisms indicates a relatively uniform stress field most simply, in terms of the influence of an inhomogeneous, throughoutthe brittle part of the crust. The data also indicate nonuniform (e.g., spatially varying elastic properties) litho- broad regions (up to 5000 km long on a side) of uniform sphere (exactly the model which most geologists and geo- stress orientation and relative magnitude within the interior physicistsaccept) on the state of stressin the lithosphere. If portions of many plates. The orientation and general com- the mean magnitude of stressin the lithosphere derived from pressional nature of many of these "first-order" stress plate-driving forces is lower, for example, in shield areas, patterns indicate that these midplate stressfields are largely then local effects could be expected to dominate. The large the result of compressional plate-driving forces, primarily 11,724 ZOBACK.'FIRST- AND SECOND-ORDERLITHOSPHERIC STRESS PATTERNS those of ridge push and continental collision, acting on plate regime. (Assuming a •b = 0.5 in which S2 lies halfway geometry. The far-reaching effects of these forces, particu- between S l and S3, the horizontal component of the re- larly ridge push, are probably related to the broad-scale gional shear stressfor thrust or normal regimes would be 1/2 lateral density anomalies associated the plate boundaries. that in a strike-slip faulting regime.) Thus, in regional normal The role of slab pull forces related to subduction zones is and thrust regimes, larger rotations (relative to a regional more difficult to evaluate because there are few stress data in strike-slip regime) are possible for similar values of the local the oceans. However, compressional deformation observed stresses. for all focal mechanismsin old oceans suggeststhat midplate Apparent examples of local rotations of S Hmaxorienta- compression dominates any extensional slab pull forces tions include a 75o--85 ø rotation on the northeastern Canadian [Wiens and Stein, 1985]. continental shelf possibly related to margin-normal exten- The influence of drag on the midplate stressfield cannot be sion derived from sediment-loading flexural stresses, a 50ø-- evaluated using orientations alone since the ridge push 60 ø rotation with the East African rift relative to western torque poles are very similar to the absolute motion poles for Africa due to extensional buoyancy forces associated with most plates [Richardson, this issue]. However, large lateral lithospheric thinning, a 50ø rotation in the Western Alps stress gradients across plates predicted for models domi- possibly related to the presence of a dense lithospheric root, nated by drag forces [e.g., Richardson et al., 1979; Richard- and an approximately 90ø rotation along the northern margin son and Reding, 1991] are not observed [Zoback, 1991]. In of the Paleozoic Amazonas rift in central Brazil. In this final addition, the large scatter of stress orientations in Australia example, the rotation is hypothesized to result from devia- and the poor correlationbetween SHmaxand absolutemotion toric compressionoriented normal to the rift axis due to local directions particularly in the southeastern and southwestern lithospheric support of a dense mass in the lower crust, a parts of this old, cold, and fast moving continent suggestthat so-called "rift pillow." This rift-normal compression due to simple driving or resisting drag is not a dominant force support of the rift pillow may be a common feature of the old affecting the intraplate stress field. More complex models of rift zones in intraplate regions and may provide a physical drag related to convection patterns inferred from mantle explanation for the often noted correlation between intra- mass anomalies are just now becoming possible [see Bai et plate seismicity and old rift zones [e.g., Johnston, 1989; al., this issue]. However, becauseplate tectonics represents Johnston and Kantor, 1990]. the uppermost part of the Earth's convection system, the Estimates of regional stress differences determined from intraplate stress field ultimately has its origin in convection modeling the source of local stress rotations can be com- system in the Earth's mantle. pared with regional stress magnitudes computed using By- Recognition of the broad-scale "first-order" stress pat- erlee's law to test the applicability of this law to the upper terns derived primarily from plate driving forces allows brittle lithosphere. The examples of superimposed local identification of local stress perturbations related to known stresses analyzed here (extensional flexural stresses on the geologic or tectonic features. Buoyancy forces related to NE Canadian margin, buoyancy-related stresses in the East crustal thickening and/or lithospheric thinning are probably African and Amazonas rifts) are too few to provide a responsible for some of the largest of these perturbations. definitive evaluation of the direct applicability of Byerlee's Intraplate areas of active extension are generally associated law, particularly in view of uncertainties in pore pressure with regions of high topography: western U.S. Cordillera, and relative magnitudes of the intermediate principal high Andes, Tibetan plateau, and also the western Indian stresses. Nonetheless, the observed rotations all indicate Ocean plateau (however, extension here has also been that the magnitude of the local deviatoric stresses must be explained in terms of slab pull-induced extension [Stein et 1.0 to at least 2.5 times the first-order regional horizontal al., 1987] and thermoelastic stresses [Bergman, 1986; Berg- stress differences in the crust which are believed to be man et al., 1984]. In these regions, buoyancy-derived exten- derived primarily from plate-driving forces. These few ex- sional stressesdominate the intraplate compressional stress amples do demonstrate that careful evaluation of such local field and indicate that buoyancy forces derived from lateral rotations is potentially a very useful technique for constrain- variations in crust and upper mantle structure supporting ing the magnitude of deviatoric stressesin the upper brittle topography can be on the same order of magnitude as part of the lithosphere, particularly at depths below which plate-driving forces, a conclusion reached independently by direct measurements of stress magnitude may be possible. direct calculation of these forces [e.g., England and Molnar, 1991]. Other sources of local perturbations or second-order Acknowledgments. This project would not have been possible stress fields include flexural stresses, smaller-scale lateral without the hard work and willing cooperation of a large number of individuals; all of the scientists listed in Table 1 devoted a lot of time density contrasts, and lateral variations in crustal strength. to the relatively thankless task of compiling their own data and that Often these local features result in a rotation of the horizon- of others in a common format and of checking and rechecking that tal stresses. A two-dimensional analysis of the amount of data. Two individuals merit special mention: Birgit Mtiller (Karl- rotation of regional horizontal stress orientations due to a sruhe University) for her indefatigable efforts to unite Europe, at superimposedlocal horizontal uniaxial stress constrainsthe least within a stress data base framework and Marian Magee (U.S. Geological Survey and Stanford University) both for her constant ratio of the horizontal regional stress differences to the local vigilance over the data base and her careful interpretation of the uniaxial stress. For a detectable rotation of 15ø, the local many varied and creative formats in which data were submitted as horizontal uniaxial stress (rrL) must be at least half the well as for software development for producing the stress maps. magnitudeof the regional horizontal stressdifferences (rr L = Special thanks to Mara Schiltz, Harold Gurrola, and Linda Shijo, who have assistedin data compilation, map software development, 0.5(SHmax -- S hmin)).In thrust or normal faulting stress and data base management over the years. Many of the ideas regimes, the horizontal component of the regional stress presented here, as well as the conceptual approach to evaluation of differences would be less than that in the strike-slip faulting tectonic stress indicators, have evolved over years of collaboration ZOBACK: FIRST- AND SECOND-ORDER LITHOSPHERIC STRESSPATTERNS 11,725 with Mark Zoback. Discussions with Art McGarr and Randy Rich- Ben-Avraham, Z., and M.D. Zoback, Transform normal extension ardson have also increased my understandingof stressin the Earth; along weak plate boundaries: an alternative to the pull-apart any shortcomingsin this understandingare my own, however. Their model, Geology, in press, 1992. reviews of this paper led to a number of substantiative improve- Bergman, E. A., Intraplate earthquakes and the state of stress in ments. I thank Bob Simpsonfor providing critical reins on wild ideas oceanic lithosphere, Tectonophysics, 132, 1-35, 1986. and also for providing the initial software and continued assistance Bergman, E. A., J. L. Nabelek, and S.C. Solomon, An extensive for the map plotting. And finally, I am indebted to Karl Fuchs, who, region of off ridge normal-faulting earthquakes in the southern as president of the International Lithosphere Program from 1985 to Indian Ocean, J. Geophys. Res., 89, 2425-2443, 1984. 1990, conceived this project, promoted it globally, and continues to Bonilla, M. G., and J. M. Buchanan, Interim report on world-wide provide ideas as well as impetus and opportunities for third world historic surfacefaulting, U.S. Geol. Surv. Open File Rep., 32 pp., countries to participate. The U.S. Nuclear Regulatory Commission 1970. provided financial support for much of the breakout analysis and Bosworth, W., M. R. Strecker, and P.M. Blisniuk, Integration of interpretation in the United States. Funds for travel and workshops East African paleostressand present-day stressdata: Implications were provided by the International Lithosphere Program and the for continental stressfield dynamics, J. Geophys. Res., this issue. special research program at Karlsruhe University SFB 108, "Stress Bott, M. H. P., and D. S. Dean, Stress systems at young continental and Stress Release in the Lithosphere" (of the Deutsche Forschun- margins, Nature Phys. 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