Comparison of Paleostress Magnitudes from Calcite Twins with Contemporary Stress Magnitudes and Frictional Sliding Criteria in T

Journal of Structural Geology 29 (2007) 86e99 www.elsevier.com/locate/jsg

Comparison of paleostress magnitudes from calcite twins with contemporary stress magnitudes and frictional sliding criteria in the continental crust: Mechanical implications

Olivier Lacombe

Universite´ P. et M. CuriedParis 6, Laboratoire de Tectonique, 75252 Paris, France Received 31 January 2006; received in revised form 23 July 2006; accepted 25 August 2006 Available online 20 October 2006

Abstract

The evolution with depth of paleo-differential stress magnitudes (mostly derived from calcite twinning paleopiezometry) in various tectonic settings is compared to the modern differential stress/depth gradients deduced from in situ measurements. Despite dispersion, both independent sets of stress data support to a first-order that the strength of the continental crust down to the brittle-ductile transition is generally controlled by frictional sliding on well-oriented pre-existing faults with frictional coefficients of 0.6e0.9 under hydrostatic fluid pressure. Some ductile mechanisms may, however, relieve stress and keep stress level beyond the frictional yield, as for instance in the detached cover of forelands. The main conclusion is that despite inherent differences, contemporary stress and paleostress data can be combined to bring useful information on the strength and mechanical behaviour of the upper continental crust over times scales of several tens of Ma. Ó 2006 Elsevier Ltd. All rights reserved.

Keywords: Calcite twins; Paleostress; Contemporary stress; Differential stress magnitudes; Friction; Strength; Continental crust

1. Introduction materials and deciphering various tectonic mechanisms, from those related to plate motions at a large scale to those causing The concept of stress is of primary importance when deal- jointing and faulting or even microstructures at a smaller scale. ing with the mechanics of materials. Although the validity of Many techniques of measurements of contemporary applying concepts of continuum mechanics to natural rock stresses were improved for applied geological purposes and masses that are neither continuous nor purely solid may be for a better understanding of current seismicity, active fault ki- questioned, in practice the idealisation of reality by the defini- nematics and crustal strength [e.g., Harper and Szymanski tion of an equivalent continuum has proved very powerful for (1991), Cornet (1993), Engelder (1993), Amadei and Ste- many mechanical purposes. The mechanical behaviour of phansson (1997) and more recently Ljunggren et al. (2003) rocks is in many instances very satisfactorily explained and and Zoback et al. (2003). See also Zoback and Zoback predicted by referring to stresses, which is in turn a good jus- (1989) and Zoback (1992) for a discussion of a quality ranking tification of the wide use of this concept in tectonics studies. and rationale for such ranking for a variety of contemporary The motivation to characterise the distribution of stresses in stress indicators]. These methods determine contemporary the crust arises from applied geological purposes such as geo- stress components by different techniques that rely upon dif- logical hazards, engineering activities and resource explora- ferent bases of measurement: fluid pressure for hydraulic fraction, but also from fundamental geological purposes, such as turing, i.e., a quantity directly related to stress; geometry of understanding the mechanical behaviour of geological finite deformation and/or reloading strains for borehole techniques; relief strains, evolution of relief strains, reloading strains, finite deformation state for techniques on cores; and E-mail address: [email protected] seismic radiation for earthquakes. Theoretically, methods

0191-8141/$ - see front matter Ó 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.jsg.2006.08.009 O. Lacombe / Journal of Structural Geology 29 (2007) 86e99 87 using hydraulic fractures, boreholes or rock cores all have the this volumedbut the ERV should, however, be sufficiently large potential for the complete determination of the stress tensor to avoid inhomogneities found at the grain scale. A rock mass is from a set of measurements at a point location but in practice assimilated to an equivalent continuum material and this equiv- this only applies when rock coring is undertaken. alence holds for volume larger than the ERV. Coevally, methods of paleostress reconstructions based on Because rocks are heterogeneous, the concept of stress refers mechanical interpretation of various structural or petrographic to mean forces per unit area for rock materials. The local stress elements in natural rocks have been set out in order to decipher tensor is defined (1) at any point in a rock mass by the compo- the past tectonic evolution. However, Earth scientists character- nents of the mean surface traction supported by the faces of ising contemporary stresses using in situ measurements or earth- the smallest cube which surrounds completely the ERV, and quake focal mechanisms and those improving and applying (2) at a given, instantaneous time. The complete determination methods of paleostress reconstructions seem not to speak the of the local stress tensor requires the appraisal of six indepen- same language and not to deal with similar mechanical concepts. dent variables which correspond to the eigenvalues and the ei- Despite few attempts at including results of paleostress recon- genvectors of the tensor (referred to as principal stress structions within young rock formations in the compilation of components s1, s2 and s3 and principal stress directions). the present-day global tectonic stress pattern (Zoback et al., The determination of stress always involves the direct mea- 1989), contemporary stress and paleostress studies are generally surement of some intermediate quantity and the implicit or ex- carried out separately and results have never been combined or plicit application of some constitutive relation that relates the even critically compared, especially in terms of stress magni- intermediate quantity to the stress. For example, the determi- tudes, an important topic in Earth Sciences. nation of stress commonly involves the measurement of a dis- The KTB deep drill hole program has led to characterisation placement in an elastic material and the determination of the of the orientations and magnitudes of contemporary stresses to stress from the equations of elasticity, either by calibration depth of 8 km (Brudy et al., 1997) and renewed considerations or by direct calculation. In nature, because the geological his- on the strength of the upper continental crust in intraplate set- tory of rock masses is usually complex hence never known tings have been proposed (Townend and Zoback, 2000; Zoback precisely, because the constitutive equations describing the and Townend, 2001), emphasising the importance of hydrostatic mechanical behaviour of rocks remain fairly approximate, fluid pressure in keeping the strength of the crust high. It is thus and because the detailed structure of a rock mass cannot be de- timely to try to compare these results with the increasing number termined exactly, it is impossible to evaluate by straight com- of results on paleostress magnitudes gained in various settings putation the natural stress field. For this reason, means have worldwide. It can be expected that the combination of both in- been developed to try to measure or to reconstruct it. The pur- dependent approaches could be fruitful for the understanding pose of most of these measurements/reconstructions is to de- of the rheology of the upper crust, provided that the concepts termine the local (contemporary or paleo-) stress tensor, or are similar or at least comparable and that the underlying me- some of its components, irrespectively of the various mecha- chanics is the same. nisms which may be its cause. This paper aims at comparing currently available paleo- Whereas in situ stress measurements deal with the true con- stress data with contemporary stress magnitudes in the conti- cept of local stress tensor, the basic concept in paleostress re- nental crust. For this purpose, the most commonly used constructions is that of a mean stress tensor. This means that paleopiezometry techniques based on development of me- the paleostress tensor considered is averaged over several chanical twins in calcite are first reviewed; then the pattern thousands or even several millions years (the duration of a tec- and the geological meaning of available estimates of paleo- tonic event) and over a given rock volume. Among the hypoth- differential stress magnitudes are discussed and compared to eses is that the stress field is homogeneous throughout the the stress-depth relationships derived from in situ stress mea- volume of interest from which measurements are taken (espe- surements. The ultimate purpose is to demonstrate that both cially, gradients such as gravitational stress are neglected). In independent sets of data can be reconciled and combined to practice, determining a mean stress tensor is equivalent to de- create a powerful tool for understanding crustal state of stress termining the mean stresses applied at the boundaries of the and rheology of the continental crust over time scales of sev- rock volume considered. For instance, the analysis of fault eral tens of Ma. slip data leads to a stress tensor which is averaged on time and space; the analysis of calcite twins (Section 2) yields 2. Concept of stress tensor vs. paleostress tensor also a mean stress tensor averaged over the time span of a tectonic event, but the small size of samples required for perform- Defining a stress tensor in a rock material requires theoreti- ing the study makes the determined tensor closer to the cally that an elementary representative volume (ERV) may be theoretical stress tensor, i.e., defined at a point. identified, which is the smallest volume for which there is equiv- Another difference between contemporary stress determi- alence between the continuum material and the real rock. The nations and paleostress reconstructions is that in situ stress ERV is the physical representation of the mathematical point. measurements provide ‘‘snapshots’’ of ambient crustal stresses The ERV is sufficiently small for its mechanical properties to while paleostress tensors reflect crustal stresses at the particu- be considered constantda direct consequence is that there is lar time of tectonic deformation (internal rock deformation/ no significant body force nor any resultant moment acting on fault zone reactivation). One has therefore to draw attention 88 O. Lacombe / Journal of Structural Geology 29 (2007) 86e99 on the actual meaning of a paleostress estimate (especially in provides 5 parameters among the 6 of the complete stress tensor. terms of magnitude) which is based on deformation that may It is to date the only technique which allows simultaneous calcu- have occurred over many millions of years. In the following lation of principal stress orientations and differential stress mag- for instance, in the absence of dynamical or fluid-enhanced re- nitudes from a set of twin data, and which therefore allows to crystallisation, paleopiezometry based on calcite twinning will relate unambiguously differential stress magnitudes to a given be considered to provide estimates of the peak differential stress orientation and stress regime. stress (s1 s3) attained during a particular event of the tec- The SIT assumes homogeneous state of stress at the grain tonic history of the rock mass. scale and constant critical resolved shear stress (CRSS) for twinning ta. The inversion process is very similar to that used for 3. Determination of the local paleostress tensor fault slip data (Etchecopar, 1984), since twin gliding along the components based on analysis of calcite twinning direction within the twin plane is geometrically com- twin data: principal stress orientations parable to slip along a slickenside lineation within a fault plane. and relative stress magnitudes But the inversion process additionally takes into account both the twin planes oriented so that the resolved shear stress ts Twinning of minerals depends on the magnitude of the (the component of the shear stress along the twinning direction) shear stress which has been applied to them. It has been pro- was greater than ta (i.e., effectively twinned planes), and the posed to make use of this property for evaluating the stresses twin planes oriented so that ts was lower than ta (i.e., untwinned which have been supported by a rock during its history (e.g., planes), a major difference with inversion of fault slip data Tullis, 1980). This may provide relevant information concern- (Lacombe and Laurent, 1996) recently re-highlighted by Fry ing the past stress field and the present stress field for recent (2001). The inverse problem thus consists of finding the stress deposits. Calcite is the most sensitive mineral for twinning tensor that best fits the distribution of measured twinned and un- and the most likely to provide useful tectonic information, es- twinned planes. This tensor must theoretically meet the major pecially in foreland settings where the outcropping formations requirement that all the twinned planes consistent with it should are mainly sedimentary rocks. sustain a resolved shear stress ts larger than that exerted on all Since the pioneering work of Turner (1953), several methods the untwinned planes. of stress analysis have been developed on the basis of calcite The inversion of slip (gliding) data along twin planes leads twin data (Jamison and Spang, 1976; Laurent et al., 1981; only to four parameters of the complete stress tensor T. These Laurent, 1984; Laurent et al., 1990; Etchecopar, 1984; Pfiffner four parameters, which define the reduced stress tensor T0, are and Burkhard, 1987; Nemcok et al., 1999). These methods are the orientations of the three principal stress axes and the stress 0 based on the widespread occurrence of e-twinning in calcite ellipsoid shape ratio F [F ¼ (s2 s3)/(s1 s3)]. T is such aggregates deformed at low pressure and temperature (Fig. 1). that the complete stress tensor T is a function of T0: 0 E-twinning occurs with a change of form of part of the host T ¼ kT þ lI, where k and l are scalars (k ¼ (s1 s3) > 0; crystal by an approximation to simple shear in a particular l ¼ s3) and I the unit matrix. The stress tensor solution is con- sense and direction along specific crystallographically defined sequently searched as a reduced stress tensor T0 and, in addi- e planes {01e12}, in such a way that the resulting twinned portion, the maximum differential stress (s1 s3) is scaled to 1 tion of the crystal bears a mirrored crystallographic orientation (Etchecopar, 1984). For this normalised tensor the resolved to the untwinned portion across the twin plane. shear stress ts acting along any twin plane therefore varies be- Methods of strain/stress analysis based on calcite twins tween 0.5 and 0.5. share the fundamental assumption that the measured twins The first step of the inversion consists of obtaining a solu- formed in a homogeneous stress field and were not passively tion by applying a number of random tensors. For each tensor rotated after formation. These methods are best applied to the stress components are calculated for all the twinned and very small strains (Fig. 1) that can be approximated by coaxial the untwinned planes. However, because the resolved shear conditions (Burkhard, 1993); in this case, the orientation of stress ts exerted on some untwinned planes may in practice small twinning strain can be reliably correlated with paleo- be greater than that exerted along some twinned planes com- stress orientation. In addition, the e-twinning in calcite is not patible with the tensor, the second step of the process consists thermally activated and is not sensitive to either strain rate of minimising the function, f, ideally equal to 0, defined as: or confining pressure; Spiers (1979) has further shown that deformation is distributed inhomogeneously between grains XN while the stress is much more homogeneous at the scale of f ¼ tsj ta0 the aggregate. Calcite twinning therefore fulfils most require- j¼1 ments for paleopiezometry. In contrast to Turner’s (1953) method which only yields s1 where ta0 is the smallest resolved shear stress applied on the and s3 orientations and to the technique of Jamison and Spang twinned planes compatible with the tensor, and tsj are the re- (1976) which only provides values of (s1 s3) without any in- solved shear stresses applied on the N untwinned planes j such formation on stress orientations and relative stress magnitudes that tsj > ta0 (for more details, see Etchecopar, 1984). The ta0 (see Section 4.1.1), the computerised inversion of calcite twin value is deduced from the inversion and corresponds to the data (stress inversion technique, SIT, summarised hereinafter) CRSS for the normalised tensor used for calculation. The O. Lacombe / Journal of Structural Geology 29 (2007) 86e99 89

Fig. 1. Example of calcite twin material commonly used for inversion and paleostress estimates. (A) Twinned grains within coarse-grained limestone from southern France. (B) Close-up of a calcite grain twinned on its 3 potential e-twin planes. (C, D) Twinned grains within coarse-grained limestones from Iran displaying low twin density (C) and high twin density (D) (courtesy of Khalid Amrouch). Internal strain is achieved under a thin-twin regime. Scale bar is about 200e300 mm. optimisation process leads to the reduced stress tensor solution envelopes to put additional constraints on the stress tensors de- that includes the largest number of twinned planes and simul- rived from inversion of fault slip data. Lespinasse and Cathe- taneously corresponds to the smallest value of f. The orienta- lineau (1995) then Andre´ et al. (2002) combined inversion of tions of the three principal stresses s1, s2, and s3 are fault slip data and fluid inclusions data to derive principal calculated, as well as the value of the F ratio that indicates stress magnitudes. the magnitude of s2 relative to s1 and s3. Numerous studies The alternative approach is based on the study of paleopiez- have demonstrated the potential of the twin inversion tech- ometers such as dislocation density in calcite (e.g., Pfiffner, nique to derive regionally significant stress patterns even in 1982), dynamic recrystallisation of calcite and quartz (e.g., polyphase tectonics settings (e.g., Lacombe et al., 1990, Twiss, 1977; Weathers et al., 1979; Kohlstedt and Weathers, 1994; Rocher et al., 1996, 2000, 2004; and references therein). 1980), and mechanical twinning in calcite and dolomite (e.g., Jamison and Spang, 1976; Rowe and Rutter, 1990; Lacombe and Laurent, 1992, 1996). Because a great part 4. How can absolute paleostress magnitudes be (more than the half) of reported paleostress estimates are determined using calcite twins? based on calcite twinning paleopiezometry (including the stress inversion technique) (Table 1), I summarise hereafter The study of absolute stress magnitudes in the crust is an how differential stress magnitudes can be determined using important topic in Earth sciences, but to date our knowledge calcite twinning, and further how combination with rock me- of the actual stress level sustained by the continental crust re- chanics data may help constrain the complete stress tensor. mains poor. Data on contemporary stress magnitudes in the crust are few (see Section 6), and inferring paleostress magnitudes from the development of natural geological structures is 4.1. Quantifying differential stress magnitudes inherently difficult. using calcite twins Paleopiezometry basically relies upon establishing a close relationship between the state of stress and the development 4.1.1. Summary of the principles of previous estimates of a conspicuous element in the rock itself and calibrating it of differential stress magnitudes based on experimentally. The first type of approach combines the inver- the techniques of Jamison and Spang (1976) sion of fault slip data with rock mechanics data and/or deter- and Rowe and Rutter (1990) mination of fluid pressures prevailing during brittle The basis of the widely used method of Jamison and Spang deformation. For instance, Bergerat et al. (1985), Reches (1976) is that in a sample without any preferred crystallo- et al. (1992) and Angelier (1989) used friction and/or failure graphic orientation, the relative percentages of grains twinned 90 O. Lacombe / Journal of Structural Geology 29 (2007) 86e99

Table 1 Characteristics of paleo-differential stress/depth data reported in Fig. 3A Differential stress Location Stress regime (Paleo-) piezometric Value of References magnitude/Depth technique used fluid pressure data A Causses, France Strike-slip Microfaults Unknown Rispoli and Vasseur, 1983 B1 Zagros, Iran (prefolding) Reverse/Strike-slip Calcite twins (SIT) Unknown Amrouch et al., 2005 B2 Zagros, Iran (postfolding) Reverse/Strike-slip Calcite twins (SIT) Unknown Amrouch et al., 2005 C SW Taiwan Foothills Strike-slip Calcite twins (SIT) Unknown Lacombe, 2001 D Appalachian Plateau, USA Strike-slip Dislocation density Unknown Engelder, 1982 in calcite E Germany Strike-slip/Reverse Microfaults/Frictional 0.4e1.4 MPa Bergerat et al., 1985 criterion F Appalachian Plateau, USA Strike-slip Residual stresses Unknown Engelder and Geiser, 1984 measured in situ G W Taiwan Foothills Reverse/Strike-slip Calcite twins (SIT) Unknown Lacombe, 2001 (prefolding) H Burgundy, France Strike-slip Calcite twins (SIT) Unknown Lacombe and Laurent, 1992 I Quercy, France Strike-slip/Reverse Calcite twins (SIT) Unknown Tourneret and Laurent, 1990 J Provence, France Strike-slip/Reverse Calcite twins (SIT) Unknown Lacombe et al., 1991 K W Taiwan Foothills Strike-slip/Reverse Calcite twins (SIT) Unknown Lacombe, 2001 postfolding L Morocco Strike-slip Microfaults/Frictional Unknown Petit, 1976 criterion M Paris Basin, France Strike-slip Calcite twins (SIT) Unknown Lacombe et al., 1994 N1 Subalpine Chain, France Reverse Calcite twins (JS) Unknown Ferrill, 1998 N2 Calcite twins (RR) O Cantabrian Zone, Spain Reverse Calcite twins (RR) Unknown Rowe and Rutter, 1990 P Moine Thrust, Scotland Reverse Quartz recrystallised Unknown Christie, 1963; Twiss, 1977 grain size Q Massif Central, France Strike-slip Microfaults/Frictional 50 10 Lespinasse and Cathelineau, criterion MPa whydrostatic 1995 R Pyrenees, Spain Reverse Calcite twins (JS) Unknown Holl and Anastasio, 1995 S McConnel Thrust Reverse Calcite twins (JS) Unknown Jamison and Spang, 1976 Rockies, Canada T Glarus Thrust, Alps, Reverse Dislocation density in calcite Unknown Pfiffner, 1982 Switzerland U Infrahelvetic complex, Reverse Dislocation density in calcite Unknown Pfiffner, 1982 Alps Switzerland V Shear Zone, Strike-slip? Quartz recrystallised Unknown Kohlstedt and Weathers, Colorado, USA grain sizeddislocation 1980 density in quartz W Pioneer Landing Fault Reverse Dolomite twins (JS/RR) Unknown Newman, 1994 Zone, USA X Shear Zone, Wyoming, USA Strike-slip? Dislocation density in quartz Unknown Weathers et al., 1979 Y1, Y2 Lorraine, France Strike-slip Calcite twins (SIT) Unknown Rocher et al., 2004

on 0, 1, 2 or 3 twin plane(s) depend on the applied (s1 s3) The first two criteria are found to be largely dependent on value. Since this relationship has been experimentally cali- grain size, since twinning is easier in large grains. The twin brated, knowing these relative percentages in a sample, and density (number of twins per mm) is poorly grain-size depen- under the hypothesis of a constant critical shear stress value dent. The use of this last criterion provides reasonable results for twinning, the order of magnitude of (s1 s3) can be esti- of (s1 s3) when applied at high temperature, but leads to mated. Among the limitations of this method is that it does not overestimates of differential stresses when applied at a low- take into account the grain size dependence of twinning, does temperature twinning deformation (see discussion in Ferrill, not check the mutual compatibility of measured twin systems 1998). As a result, the Rowe and Rutter paleopiezometer and does not allow to relate the differential stress estimates to best applies to twinning deformation at high temperatures (be- a given stress regime since principal stress orientations are not tween 200 and 800 C), and at large strains (7e30%), and is determined. not appropriate for evaluating differential stress magnitudes The method of Rowe and Rutter (1990) is based on the sen- from calcite twinning analysis in outer parts of orogens. In ad- sitivity of the twinning incidence, twin volume fraction and dition, this method shares the same limitation than the Jamison twin density to differential stress; in turn, estimates of these and Spang method in not checking the mutual consistency of parameters are used to infer differential stress magnitudes. twin sets from which differential stress values are derived and O. Lacombe / Journal of Structural Geology 29 (2007) 86e99 91 not allowing to relate differential stress estimates to a given and Rutter, 1990), the paleopiezometric technique used herein state of stress. yields the maximum differential stress ðs1 s3Þ related to a given paleostress orientation, because the differential 4.1.2. Quantifying differential stress magnitudes using stresses are computed by taking into account the maximum inversion of calcite twin data percentage of twinned planes consistent with the tensor and 0 The four parameters defining the reduced stress tensor T therefore the smallest ta0 value. In the absence of recrystallisa- (orientation of principal stress axes and F ratio) being derived tion, the meaning of such differential stress estimates is there- from inversion of calcite twin data (section 2), quantifying the fore that of the peak stresses sustained by rocks during a given deviatoric stress tensor TD defined as: episode of their tectonic history. In order to prevent bias due for instance to local record of TD ¼ T ½ðs1 þ s2 þ s3Þ=3I stress concentrations, which may lead to overestimated stresses which may be not representative of the far-field stress requires the determination of a fifth parameter of the complete of interest, several samples are usually collected for a given lo- stress tensor: the scalar k ( ¼ s1 s3). This determination re- cality and one usually retains the weighted mean of the differ- lies on the existence of a constant CRSS for twinning ta and ential stress values as the most reliable estimate. At all on the accurate estimate of ta0 that corresponds to the normal- localities, limestone samples are collected away from major ised value of the CRSS for the reduced stress tensor used for fault zones where the stress field is known to be very inhomo- calculation. geneous in both orientation and magnitude. The calcite twin- based paleostress estimates therefore meet the assumptions 4.1.2.1. Assumption of a constant Critical Resolved Shear of stress homogeneity and low-finite strain and are likely rep- Stress for twinning. Differential stress estimates using the resentative of stresses at larger scale. twin inversion technique are based on a constant CRSS ta for twinning. This assumption is also shared by the technique 4.2. Quantifying absolute stress magnitudes and of Jamison and Spang (1976). Using this technique, a constant estimating the depth at which peak differential stresses CRSS of 10 MPa is generally adopted (e.g., Craddock et al., recorded by calcite twinning prevailed 1993, 2002; Craddock and Van Der Pluijm, 1999; Gonzales- Casado and Garcia-Cuevas, 1999). Based on the analysis of Knowing the deviatoric stress tensor, a single parameter is experimentally deformed samples, Lacombe and Laurent missing in defining the complete stress tensor. This sixth pa- (1996) and Laurent et al. (2000) have demonstrated the reli- rameter corresponds to the isotropic component of the tensor ability of the twin inversion technique, but also emphasised that cannot be determined using calcite twinning only since that the CRSS is sensitive to strain hardening. Their results twinning does not depend on isotropic stress. In order to assess suggest that the CRSS for twinning can be considered constant the actual magnitudes of s1, s2 and s3, it is thus necessary to for samples displaying a nearly homogeneous grain size. For fix directly one of them, or at least to determine a third addi- w e samples displaying a mean grain size of 200 300 mm and tional relationship between them. e deformed between 0 and 100 Cat2 2.5% strain, it equals The method used herein to determine the complete stress e 10 MPa; for the same samples deformed at nearly 1 1.5% tensor relies upon combination of analyses of calcite twins strain, the CRSS rather equals 5 MPa (Lacombe, 2001). For and rock mechanics data (Lacombe and Laurent, 1992). For samples displaying different grain sizes, a crystal size-CRSS a given tectonic event and a given site, it consists of finding relationship such as that proposed by Rocher et al. (2004) the values of s1, s2, and s3 required for consistency between can be further adopted to improve differential stress estimates. newly formed faulting, frictional sliding along pre-existing planes, and calcite twinning. 4.1.2.2. Determination of differential stress magnitudes. Un- The differential stress value (s1 s3) determined from cal- der the assumption of a constant CRSS for twinning ta, the cite twins fixes the scale (i.e., the diameter) of the Mohr circle differential stress magnitudes can be determined as follows associated with the tensor. To completely describe the stress (Etchecopar, 1984; Lacombe and Laurent, 1996; Laurent regime (orientation and magnitude), the isotropic component et al., 2000): of the tensor is missing. The determination of this parameter, which corresponds to the position of the Mohr circle along the ðs s Þ¼t =t 0 1 3 a a normal stress axis in the Mohr diagram, can be done in the fol- and lowing way (Fig. 2).

ðs2 s3Þ¼Fðs1 s3Þ 4.2.1. Failure If subsets of newly formed faults and twins provide similar where ta0 is the smallest resolved shear stress applied on the reduced stress tensors in a given site (description of stress in- twinned planes accounted for by the stress tensor and therefore version applied to fault slip data is out of the scope of this pa- the normalised value of the CRSS when ðs1 s3Þ is scaled to per, see for instance Angelier, 1989), it can be reasonably 1. As for other techniques of paleostress estimation based on inferred that they formed during the same tectonic event, calcite twin analysis (e.g., Jamison and Spang, 1976; Rowe and therefore they may be thought to have developed 92 O. Lacombe / Journal of Structural Geology 29 (2007) 86e99

Shear Stress Failure enveloppe A

Normal stress σ3 σ2 σ1 (σ1-σ3) determined from inversion of calcite twin data

Shear Stress Friction curve B

Normal stress σ3 σ2 σ1 (σ1-σ3) determined from inversion of calcite twin data

Shear Stress C

Normal stress σ3 σ2 σ1 (σ1-σ3) determined from inversion of calcite twin data Effective vertical stress

Depth of burial from stratigraphic data

Shear Stress Failure enveloppe D

Normal stress σ3 σ2 σ1 (σ1-σ3) determined from inversion of calcite twin data Effective vertical stress

Depth of burial

Fig. 2. Principle of determination of principal stress magnitudes based on combination of inversion of calcite twin data with rock mechanics data. (A) Calcite twins, newly formed faults and fit with the fresh failure envelope. (B) Calcite twins, reactivated inherited faults and fit with friction curve. (C) Calcite twins Paleodepth estimate from stratigraphic data and determination of the magnitude of the vertical principal stress. (D) The use of above-mentioned failure or friction criterion fixes the magnitude of the vertical principal stress, which allows estimate of paleodepth of deformation. Hydrostatic fluid pressure is assumed.

‘‘contemporaneously’’ in terms of geologic time. As calcite development) curve yields values of principal stresses that twins record the ‘‘peak’’ stress reached during the entire his- prevailed just before rupture (Fig. 2A). tory of the rock mass, the maximum recorded differential stress should correspond to the stress which induced rock fail- 4.2.2. Friction ure, because fresh failure releases stress. Consequently, if new Because all points that represent reactivated pre-existing faults developed, fitting the (s3,s1) Mohr circle determined planes should lie above the friction curve (Byerlee, 1978)in from calcite twins with the intrinsic failure (or crack the Mohr diagram, fitting the (s3,s1) Mohr circle determined O. Lacombe / Journal of Structural Geology 29 (2007) 86e99 93 from calcite twins with the friction line, so that inherited faults directions and do not reflect local and/or temporal sources of are located above the friction line, allows determination of the stress perturbation as for instance the evolving-with-time to- principal stress values. This requirement imposes a constraint pography can be. As a result, it is generally correct to equal on the position of the Mohr circle along the normal stress axis the magnitude of the vertical principal stress to the overburden and yields principal stress magnitudes (Fig. 2B). Note that this load, (rgz Pf) where r is the average density of the overbur- may apparently contradict Byerlee’s law since each individual den. g is the acceleration of gravity, z is the depth, and Pf is the reactivated pre-existing plane should lie on (and not above) the fluid pressure. Paleodepth of overburden can be evaluated us- friction curve since a fault plane cannot sustain a shear stress/ ing stratigraphic data in favourable settings (Fig. 2C).The ac- normal stress ratio greater than that required for frictional slid- tual pore fluid pressure at the time of deformation (and the ing on it. It is simply a consequence of considering a mean porosity as well) being unfortunately often out of reach, hy- stress tensor, as previously discussed in Section 1. drostatic conditions are usually adopted as the most realistic conditions of fluid pressure. Results obtained in deep bore- 4.2.3. Evaluation of the vertical principal stress holes suggest that this assumption is reasonable and justified Most of paleostress reconstructions based on calcite twins in most cases (see Section 6). (and fault slips: e.g., Lacombe et al., 1990; Lisle et al., As the inversion of calcite twin data provides directly dif- 2006) yield a highly plunging principal stress axis, close to ferential stress magnitudes, the determination of the principal vertical (within the usual 10 range of uncertainties), provided stress magnitudes only requires one piece of information that passively rotated stress axes due to folding are interpreted among the above criteria. If the failure or the friction criterion after backtilting to their prefolding attitude. The verticality of is available, the magnitude of the vertical principal stress is one principal stress is also indicated by widespread joints in fixed. If the burial thickness is unknown, this estimate of the foreland environments which are very close to vertical, a con- value of the (effective) vertical stress can be used to estimate dition that is most likely if one of the principal stresses is ver- the weight of overburden, and therefore the depth at the time tical (Engelder and Geiser, 1980). Considering a vertical of deformation (Fig. 2D). This estimate can be compared with principal stress is also common in most in situ measurements stratigraphic information (if available) in order to check for of contemporary stresses. This assumption was assessed by consistency. Such a procedure has been applied in Taiwan to McGarr and Gay (1978), who concluded that it is basically derive Plio-Quaternary principal stress magnitudes in the valid although slight departures from this rule are common. Western Foothills (Lacombe, 2001). Most of the data reported by these authors were obtained in mines ‘‘often in regions of complex geology’’ and thus they 5. Evolution with depth of paleo-differential expected that orientations of stress in other areas might con- stress magnitudes form more closely to this assumption. In their compilations of different types of in situ stress indicators in of North Amer- 5.1. On the difficulty of establishing a paleostress/ ica, Zoback and Zoback (1980) made similar arguments which paleodepth relationship were later extended to the global compilation of in situ stress indicators (Zoback et al., 1989; Zoback, 1992). Further indica- Collecting data on contemporary stress and paleostress mag- tions for this assumption to be valid are given by the analysis nitudes with depth is fundamentally different. In drill holes, con- of focal plane solutions (e.g., Angelier, 2002) at various sites temporary stresses are determined directly at a given depth, or at which show that one of the principal stresses is often within least in a narrow depth interval. In contrast, paleopiezometers a few degrees of vertical. Brudy et al. (1997) also recently con- are generally sampled and analysed after they have reached cluded that the assumption was valid at the KTB site. Cornet the surface, i.e., after exhumation from an unknown depth, (1993), however, points out that the vertical direction is not and establishing a differential stress versus depth relationship a principal direction in the vicinity of the ground surface in for paleostresses requires independent determination of differ- mountainous area or, more generally, anywhere the ground ential stress and depth. In addition, in case of polyphase tecto- surface is not horizontal. The question then arises of determin- nism, deciphering the stress/depth evolution requires to ing the depth up to which this non-verticality of one of the unambiguously relate a differential stress value to both a depth principal stresses may be observed. When the vertical direc- of deformation and a tectonic event. As mentioned in Section 3, tion is not a principal direction, assuming that one principal inversion of calcite twin data provides an efficient tool to per- component of the local stress tensor is equal to the weight form such estimates in favourable cases. of overburden is of course wrong. Paleodepth estimates are usually derived from stratigraphic/ As mentioned before, paleostress reconstructions deal with sedimentological studies in forelands or even fold-thrust belts, stresses associated with tectonic deformation of rocks at depth, from paleothermometry coupled with considerations on paleo- hence generally of larger magnitudes and of longer duration thermal gradient, recrystallisation accompanying ductile de- (the duration of a ‘‘geological tectonic event’’) than ‘‘snap- formation or fabric development, or from metamorphism. shots’’ of ambient stresses provided by in situ measurements. Uncertainties on the stress versus depth relationship of interest These paleostresses are consequently ‘‘averaged’’ over several are partly due to uncertainties on depth estimates. millions years, so they are controlled to the first order by the Second, depending on the geological setting studied (fore- vertical (gravity) and the horizontal (tectonic forces) lands, fold-thrust belts or fault zones in metamorphic belts), 94 O. Lacombe / Journal of Structural Geology 29 (2007) 86e99 the paleopiezometric methods used are different (e.g., analysis strike-slip stress regimes (Table 1), sometimes to mixed re- of dislocation density in calcite, dynamic recrystallisation of verse/strike-slip stress regimes (subhorizontal s1 axis and calcite and quartz or mechanical twinning in calcite: Table low F values). The plot of these paleo-differential stress 1). The poor knowledge we have on the paleostress levels sus- data against depth suggests a trend of increasing differential tained by natural rocks is partially linked to the fact that the stresses with depth. In an attempt at interpreting this stress- paleopiezometric techniques do not share the same limitations, depth relationship in a more precise way, friction curves each of them having particular conditions of application; this were built and reported in Fig. 3A. Because the frictional leads to multiple sources of methodological uncertainties strength of a faulted rock mass depends on pore pressure which are superimposed to the variability of natural phenom- (Hubbert and Rubey, 1959), estimates of the frictional strength ena. This is illustrated by a method dependence of estimates of the brittle crust depend on the pore pressure at depth (Brace (e.g., Ferrill, 1998), which additionally group according to re- and Kohlstedt, 1980). Hence, for given stress and pore pres- gional versus fault zones studies (e.g., Newman, 1994). sure regimes, one can estimate the maximum differential stress expected on the basis of the frictional-failure equilibrium hy- 5.2. To what extent do paleostress magnitudes derived pothesis, and compare this with observations. For a favourably from paleopiezometry in the sedimentary cover oriented pre-existing cohesionless fault plane, the condition of reflect the (frictional) stress gradient in reactivation, which therefore applies to a critically stressed the deeper crystalline basement? crust, can be written as follows (Jaeger and Cook, 1969): 2 0:5 2 Many actively deforming forelands are earthquake defi- s1 Pf s3 Pf ¼½ m þ 1 þm cient. This is particularly true in the upper 2e4 km in the sedimentary cover where folds develop mainly by mechanisms This equation can be used to predict differential stress as including diffusion-mass transfer and other ductile mecha- a function of depth in a crust in frictional equilibrium. Because nisms such as calcite twinning. In this depth range (the up- most available paleostress magnitude data come from com- per-tier of the ductile flow regime in the sense of Engelder, pressional settings (i.e., with the largest principal stress s1 be- 1993), the so-called brittle crust creeps by ductile mecha- ing horizontal, so that states of stress are of strike-slip (s2 nisms. These mechanisms relieve stresses, so the differential vertical) or reverse-type (s3 vertical) regimes: Anderson, stress level is kept beyond the frictional yield that likely pre- 1951), the following equations for strike-slip and reverse- vails at greater depth in the basement (Section 6). This is par- type regimes have been considered: ticularly true in many settings where the cover is detached 2 0:5 2 s1 s3 ¼ 2r ðl 1Þð1 ½ m þ 1 þm Þ from basement. gz 0:5 The way differential stresses evolve with depth when cross- =ð1 þ½ m2 þ 1 þm2Þ ing a weak decollement within or at the base of the cover, and more generally when crossing a rheological contrast induced and by a local structural or lithological inhomogeneity also re- 2 0:5 2 quires attention. Cornet and Burlet (1992) reported for in- s1 s3 ¼ rgzðl 1Þð1 ½ m þ 1 þm Þ stance such a contemporary stress field discontinuity at the Echassieres site (France), related to a fault zone displaying with l ¼ Pf /rgz. l is close to 0.4 for hydrostatic conditions, breccia and a high kaolinite content. close to 0.9 for nearly lithostatic conditions and equals 0 for Since the stress/depth gradient above and below the de- dry conditions. The curves corresponding to strike-slip (SS) collement can possibly be different, the amount of coupling and reverse faulting (C) regimes for values of l of 0.38 (hydro- between cover and basement may at least partially control static) and 0 (dry) and for values of the friction coefficient m of the level of differential stresses sustained by cover rocks. If 0.6 and 0.9 have been drawn accordingly on Fig. 3A. coupling is low (e.g., efficient, weak decollement), paleostress Different stressedepth evolutionary trends can be distin- magnitudes derived from paleopiezometry in the cover may guished. A large set of paleostress data more or less fit the the- not reliably reflect deeper crustal stresses in that the stress gra- oretical curves of frictional-failure equilibrium corresponding dient can change when crossing the decollement. When base- to strike-slip (SS) and reverse faulting (C) regimes under ment/cover coupling is more efficient, as in stable forelands of nearly hydrostatic fluid pressure (l w 0.38) and friction coef- orogens and plate interiors despite the common widespread ficient m between 0.6 and 1 (I and II on Fig. 3A). These data occurrence of weak shale beds in basins, the stress gradient de- therefore support a critically stressed crust under hydrostatic rived from cover paleopiezometry can be extended with more conditions. Some data however reflect stress levels down to confidence to the crust. w7 km depth beyond the frictional limit (III on Fig. 3A), which suggests possible occurrence of some creep in the crust 5.3. Evolution with depth of paleo-differential which therefore relieves stresses and keeps the differential stress magnitudes stress level beyond the frictional yield (upper-tier of the ductile flow regime: Engelder, 1993). Below 10 km, some stress The paleo-differential stress magnitude data reported in data lie also under the frictional limit, and presumably reflect Fig. 3A correspond either to reverse stress regimes or to stresses at or just below the brittle-ductile transition (IV). O. Lacombe / Journal of Structural Geology 29 (2007) 86e99 95

A Differential stress (σ1 -σ3 ) (MPa) 1 10 100 1000 0.1

V. Overestimated stresses ? Stress concentrations ?

Y1 C A B2 H E Y2 J I. Frictional equilibrium K Compressional regime D ~hydrostatic conditions 1 I 0.6 < < 1.0 B1 II. Frictional equilibrium L M G Strike-slip regime ~hydrostatic conditions 0.6 < < 1.0 F

Depth (Km) Depth N1 N2 Q

III. Upper tier of the ductile flow regime T (Engelder, 1993) ? P λ S =0 Stress released by “ductile” mechanisms λ R O =0.38 λ λ 10 W =0 =0

λ U λ = V λ =0 0. = 38 λ 0.38 =0.38 20 X SS R μ =0.6 IV. Brittle-ductile transition ? μ =0.9

B Differential stress (σ1-σ3) (MPa) 50 100 150 200 250 0

Frictional equilibrium 1 Strike-slip regime 2 ~hydrostatic conditions 3 = 1.0 4 5 6 5

μ=1.0

Frictional equilibrium Strike-slip regime ~hydrostatic conditions μ=0.6 10 = 0.6

Approximate depth (Km) ?

Expected depth interval of brittle-ductile transition

Fig. 3. (A) Differential stress values derived from paleopiezometry versus depth relationship (log-log). Modified and completed after Davis and Engelder, 1985; Engelder, 1993; Ferrill, 1998; Lacombe, 2001. For details concerning stress/depth data, refer to Table 1. Calcite twin paleopiezometry: RR, Rowe and Rutter technique; JS, Jamison and Spang technique; SIT, Stress Inversion technique (Etchecopar, 1984. completed by Lacombe and Laurent, 1992 for the determination of the complete stress tensor). Dashed lines illustrate stressedepth relationships predicted using Coulomb frictional-failure theory for coefficients of friction m of 0.6 and 0.9, pore pressures of 0 (l ¼ 0) and hydrostatic (l ¼ 0.38) and various tectonic regimes (SS, strike-slip; R, reverse). (B) Differential stress versus depth relationship derived from in situ stress measurements (after Townend and Zoback, 2000; Zoback and Townend, 2001). 1, Fenton Hill; 2, Cornwall; 3, Dixie Valley; 4, Cajon Pass; 5, Siljan; 6, KTB. Site Dixie Valley reveals a normal stress regime; all other sites correspond to a strike-slip stress regime. Dashed lines illustrate stressedepth relationships predicted using Coulomb frictional-failure theory for coefficients of friction of 0.6 and 1.0. 96 O. Lacombe / Journal of Structural Geology 29 (2007) 86e99

Finally, some differential stress data lie above the frictional shows stresses well under the frictional limit. This suggests limit for the compressional regime (V) and cannot be easily that ductile mechanisms are possibly currently acting in interpreted. It can be suspected that these data reflect overes- some settings, that they relieve stress and keep the crustal state timated stresses: this is the case for the estimates by Bergerat of stress beyond the frictional limit. As a result, friction likely et al. (1985) (datum E on Fig. 3A). governs in numerous settings, but it is probably not a general rule for the entire upper crust, especially its uppermost part 6. Comparison with the evolution with depth of (the detached cover). contemporary differential stress magnitudes. A second arising point is that most data reported in Fig. 3B Implications for the strength and behaviour were collected in intraplate settings where a strike-slip type of the continental crust state of stress prevails. Therefore, collecting new stress data is crucial to confirm the general validity of both the applicabil- 6.1. What we know about the present-day differential ity of laboratory derived strength parameters to the crust Kohl- stress magnitudes at depth stedt et al., 1995 and the assumption that the crust is in a state of failure equilibrium in many different settings. Moreover, The most widely used model of crustal stress and strength because evidence comes only from in situ measurements is based on the assumption that the lithosphere is in failure which are essentially shallower than 8 km, outstanding ques- equilibrium with the state of stress in the upper crust con- tions about crustal stress magnitudes are whether the findings trolled by its frictional strength (Byerlee, 1978). Evidence sup- at this maximum depth reached by boreholes can be extended porting that intraplate continental crust is in (or at least close to midcrustal depths approaching or reaching the brittle-duc- to) a state of failure equilibrium are derived from studies of tile transition. seismicity and contemporary stresses. They have been discussed by Townend and Zoback (2000); they are: (1) the wide- 6.2. Comparison of the evolution with depth of spread occurrence of seismicity induced by either reservoir paleo- and contemporary differential stress impoundment (Simpson et al., 1988; Roeloffs, 1996)orfluid magnitudes, and discussion injection (e.g., Pine et al., 1983; Zoback and Harjes, 1997), (2) earthquakes triggered by other earthquakes (Stein, 1999), Compared to contemporary stress magnitudes reported on and (3) in situ stress measurements in deep wells and bore- Fig. 3B(Townend and Zoback, 2000), estimates of paleostress holes. Data on in situ stress magnitude measurements come magnitudes reported in Fig. 3A show a large dispersion, al- mainly from intraplate regions where the state of stress is gen- though an increase of differential stresses with depth is clearly erally of strike-slip or compressional type: United States, depicted. There are many reasons to explain this dispersion. It South Africa (McGarr and Gay, 1978); Scandinavia, central is mainly due to methodological uncertainties and to the vari- Europe (Rummel et al., 1986); Monticello, South Carolina ety of sampled natural settings. (Zoback and Hickman, 1982); Cornwall, England (Pine In contrast to most in situ measurements carried out at et al., 1983); Yucca Mountain, Nevada (Stock et al., 1985); depths shallower than 8 km in intraplate setting where Fenton Hill, New Mexico (Barton et al., 1988); Cajon Pass, a strike-slip type state of stress prevails, paleostress estimates California (Zoback and Healy, 1992; Vernik and Zoback, are of mixed origins, combining magnitudes from strike-slip 1992); KTB, Germany (Brudy et al., 1997; Zoback and Harjes, and compressional (reverse) regimes (Table 1); in addition, 1997). the usual collection of many paleostress magnitude data not Application of Coulomb faulting theory with laboratory-de- only away, but also close to, or within, orogens (and therefore rived coefficients of friction (e.g., Byerlee, 1978) allows pre- close to fault zones/past plate boundaries) may increase the diction of critical stress levels in reverse, strike-slip, and dispersion. Finally, the hypothesis of hydrostatic pore pressure normal faulting environments as a function of depth and usually adopted for paleodepth estimate may not be valid in pore pressure (e.g., Hubbert and Rubey, 1959; Sibson, 1974; some particular compression zones where it may be closer Jaeger and Cook, 1969; Brace and Kohlstedt, 1980). Fig. 3B to lithostatic than to hydrostatic. shows the data compiled by Townend and Zoback (2000) to- However, it is reasonable to consider that, at the present- gether with the theoretical curves for a critically stressed crust day state of our knowledge and with the available set of under hydrostatic conditions. Most of these in situ stress mea- data, most contemporary stress and paleostress data support surements are consistent with Coulomb frictional-failure the- a first-order frictional behaviour of the upper continental crust. ory incorporating laboratory-derived frictional coefficients, The mechanical strength of the brittle crust, away from (but m, of 0.6e1.0 and hydrostatic fluid pressure for a strike-slip also possibly close to) plate boundaries, is in numerous set- stress regime. The crust’s brittle strength is quite high (hun- tings governed by frictional sliding on pre-existing favourably dreds of mega-pascals) under conditions of hydrostatic pore oriented faults. The critically stressed upper continental crust pressure. Note, however, that the stress/depth gradient depends is therefore able to sustain differential stresses as large as explicitly on the stress configuration, i.e., normal, strike-slip or 150e200 MPa, so its strength makes it able to transmit a sig- reverse stress regime. nificant part of orogenic stresses from the plate boundary However, a complete stress profile taken from a three-well across the far foreland (Townend and Zoback, 2000; Lacombe, experiment on the Appalachian Plateau (Evans et al., 1989) 2001; Zoback and Townend, 2001). O. Lacombe / Journal of Structural Geology 29 (2007) 86e99 97

Theoretical strength profiles for the crust basically separate of the ‘‘intensity’’ of deformation, the style of deformation being the crust into an upper brittle and lower ductile regime. probably simply a function of the strain rate. Whereas the strength in the brittle part is controlled by the One has, however, to keep in mind that some data neverthe- frictional strength of pre-existing, favourably oriented faults, less indicate paleostress and contemporary stress conditions and varies with the tectonic regime (Sibson, 1974; see above), beyond the frictional limit, suggesting that stresses may be lo- the strength of the lower ductile part is described by flow laws cally relieved by ductile mechanisms (upper tier of the ductile for appropriate rock types, temperatures, and strain rates. The flow regime: Engelder, 1993), probably in the uppermost cover transition between these zones is usually depicted as the inter- part of the crust. These ductile mechanisms, such as diffusion- section of the two strength envelopes, but the transition pre- mass transfer, may prevent the stress level to reach the sumably occurs over an interval of several kilometres as the frictional limit, lowering the seismogenic potential of the rheology of the material gradually changes from brittle to duc- (detached) uppermost sedimentary cover. tile (e.g., Scholz, 1990). Commonly, the 350 C isotherm is Another argument that may support that crustal stresses are thought to be the onset of plasticity in rocks of gneissic and not always at the frictional yield comes from the works by granitic composition. For a temperature gradient of 27e30/km, Craddock et al. (1993) and Van der Pluijm et al. (1997). These this temperature corresponds to a depth of 11e13 km. There authors have documented a fall-off in differential stresses with is no present-day stress information of stress magnitudes in distance from the orogenic front in forelands of various oro- the 10e15 km depth interval, although this would provide gens. Because no information about the depth at which pa- a very useful complement to available stress data. Estimates leo-differential stresses were evaluated is available, there is of regional paleostress magnitudes corresponding to different no way to normalise each individual stress datum by the depth depths of deformation collected at various places worldwide, at which twin deformation occurred, so this fall-off may well especially including fault zone studies in metamorphic belts be an artefact of the different depths at which paleostresses where depth of deformation presumably has approached or were determined. However, this decay of differential stresses reached the brittleeductile transition, such as those reported is observed within the so-called undeformed foreland away on Fig. 3A, are therefore a way to extend our knowledge of from the deformation front; so one can infer that because no stress/depth relationship at depth. significant orogen-related deformation and therefore no large Models as well as simple extrapolation of the stress/depth lateral variations of erosion and exhumation have occurred gradient from shallower depths suggest that stresses at mid- in the foreland, rocks presently at the surface and from which crustal depth should be of the order of hundreds of MPa for measurements are taken were likely deformed at nearly similar near-hydrostatic pore pressure. Despite inhomogeneities of depths. The absence of orogen-related large deformation in the stress magnitudes which may expectedly arise in fault zones foreland indicate that far-field orogenic differential stresses due to the high finite strain of the rocks (grain-size reduction, presumably did not reach the stress conditions required for rotational deformation at the grain scale or dynamic or fluid- frictional faulting. If this decreasing trend in differential mag- enhanced recrystallisation may influence paleopiezometry) nitudes away from the deformation front does occur and has and the record of local effects such as stress concentrations, a geological meaning in terms of stress attenuation as stated the reported (unfortunately few) paleostress estimates at the by the authors, it indicates that lateral stress gradients may oc- brittle-ductile transition values appear to be lower than those cur in the upper crust; only ductile flow mechanisms character- expected by simply extrapolating frictional gradients istic of the upper-tier of the ductile flow regime are able to (Fig. 3A). Data are too few to unambiguously argue whether permit such stress gradients below the frictional stress limit. these lower stress values reflect a lower strength related to the onset of the crustal ductile behaviour at the place and at 7. Conclusion the depth where deformation within the fault zones occurred, or if an stress-depth gradient characteristic of the upper crust Quantitative estimates of crustal stresses and strength are can be extrapolated with confidence below 11 km. A fluctuat- central to many problems of lithospheric mechanics. This pa- ing brittle-ductile transition (350e450 C?) must be defined in per presents a first attempt at comparing and combining paleo- order to take into account the variable geotherm and therefore stress magnitude data with contemporary stress data. the settings where stress estimates in fault zones have been Concepts and techniques underlying determinations of con- performed. Taking into account such a fluctuating BDT, and temporary stresses and paleostresses are inherently different, although further studies are needed, one can safely consider and both types of stress data do not have strictly the same geo- that to a first order, available paleostress and stress magni- logical meaning: contemporary stresses measured in situ re- tudes, even at mid-crustal depths, are more or less in agree- flect local, instantaneous ambient crustal stresses, while ment with laboratory-derived friction laws. reconstructed paleostresses reflect ancient crustal stresses at As a result, at the present-day of our knowledge, independent the particular time of tectonic deformation, averaged over contemporary stress and paleostress data support that upper the duration of a tectonic event and over a given rock volume. crustal stresses are/were generally probably close to, and in all Although to this respect contemporary stresses and paleos- cases limited by, frictional faulting equilibrium. In settings tresses are not directly comparable, their analyses however where friction clearly governs stress, this implies uniform stress rely on the same mechanics, and they constitute complemen- differences at a given depth and a given stress regime, regardless tary stress data sets. 98 O. Lacombe / Journal of Structural Geology 29 (2007) 86e99

Combination of both types of stress data provides new con- Craddock, J.P., Jackson, M., Van Der Pluijm, B., Versical, R.T., 1993. Regional straints on the differential stress gradients with depth, which shortening fabrics in eastern north America: far-field stress transmission e are to date still poorly known. Combining contemporary and pa- from the Appalachian-Ouachita orogenic belt. Tectonics 12 (1), 257 264. Craddock, J.P., Kimberly, J.N., Malone, D.H., 2002. Calcite twinning strain leostress data allows us to extend our stress/depth database in constraints on the emplacement rate and kinematic pattern of the upper various settings, i.e., away horizontally from drill holes, and ver- plate of the Heart Mountain Detachment. J. Struct. Geol. 22, 983e991. tically by obtaining information on stress magnitudes at depth Davis, D.M., Engelder, T., 1985. Role of salt in fold-and-thrust belts. Tectono- more or less continuously down to the brittle-ductile transition. physics 119, 67e88. 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