GEOMECHANICAL ANALYSIS OF THE VOLCANIC TABLELAND EXTENSIONAL FAULT SYSTEM, BISHOP, CA, AND EVALUATION OF MECHANICS-BASED RESTORATION METHODS Peter Lovely1, Eric Flodin2, Chris Guzofski3, Frantz Maerten4, and David D. Pollard1 1Department of Geological and Environmental Sciences, Stanford University, Stanford, CA 94305 2Chevron ETC, San Ramon, CA, 94583 3Chevron ETC, Houston, TX, 77002 4IGEOSS, Montpellier, France e-mail: [email protected]

Abstract Keywords: Numerical models and field data are integrated to Fault growth, normal faults, Volcanic Tableland, perform a geomechanical analysis of the Volcanic Poly3D, restoration, finite element methods, subsidiary Tableland fault array, an outcrop analogue for faulting, paleostress subsurface normal fault systems. A geomechanical approach is used to infer 3D fault geometry from Introduction outcrop data, and a paleostress inversion technique is Faults play an important role in many hydrocarbon employed to establish appropriate physical boundary systems. Large faults often play a key role in conditions for forward models. Past studies suggest hydrocarbon migration and trap development by that larger Tableland faults developed through linkage juxtaposing stratigraphic units of different age and of smaller faults, implying that small faults may be the lithology (Allan, 1989), and accommodating the oldest in the study area. While this mechanism of fault development of reservoir-scale folds (Rich, 1934; growth is clear from mapped traces of some faults, Dahlstrom, 1969). Faults may act as barriers to cross- other large faults are relatively linear. We provide fault fluid flow, or as conduits for fault-parallel flow evidence in the form of throw distributions that even (Knipe et al., 1997; Aydin, 2000). A thorough long, linear fault traces likely grew by linkage of understanding of not only present-day fault geometry, smaller faults. Other studies suggest that but also the chronology of fault system development, is geomechanical models may be used to understand critical to a complete understanding of any faulted stress perturbations due to slip on large (seismic-scale) hydrocarbon system. faults, and thus to infer density and orientation of Large faults may be identified from 2D or 3D subseismic-scale faulting. Regions of densest seismic imaging. Typical industry data allows accurate subseismic faulting on the Tableland correlate with geometric interpretation of faults with greater than 10- tensile stress shadows, suggesting that it would be 20m throw (Yilmaz, 1987). Slip distributions often can inappropriate in the case of this field site to predict be interpreted by correlating stratigraphic reflector subseismic faulting from stress perturbations due to slip horizons across faults, and if growth horizons are on larger faults, and that the growth of larger faults has observed in conjunction with fault related folding, not led to initiation of new subseismic-scale faults, but temporal constraint may be placed on fault slip (Suppe, may inhibit the growth of existing faults. Further 1992). Such large faults are hereafter referred to as geomechanical models corroborate previous work that seismic-scale faults. Smaller (subseismic-scale) faults suggests Tableland faulting results from flexural and opening mode fractures are more difficult to stresses in the rollover anticline in the hanging wall of interpret. Power law size distributions (Childs et al., the Basin and Range-scale White Mountain fault, 1990; Walsh and Watterson, 1991; Slische et al., 1996) several kilometers to the east. We conclude by suggest that such small features are numerous, and comparing forward model kinematics with results of therefore likely play an important role in subsurface mechanics-based restoration models. A critical fluid flow, and should not be neglected in reservoir evaluation suggests that restoration models may not characterization. Cemented fractures, fault gouge, or accurately reflect the kinematics of forward clay smearing can impede fluid flow, while open deformation. fractures may act as conduits (Nelson, 1985). These features may have influenced hydrocarbon migration pathways, and have important consequences for reservoir engineering and optimal hydrocarbon extraction. Efforts have been made to interpret such

Stanford Rock Fracture Project Vol. 20, 2009 D-1 subseismic-scale faults from seismic anisotropy (e.g. of hydrocarbon migration, faults that are large and Bates et al., 1999); however success has been limited. continuous at present had not yet connected, barriers Discrete faults below seismic resolution can be and conduits for fluid flow, in the form of faults, may identified in the subsurface only in scattered 1D well have been relatively discontinuous. We combine logs. For reservoir engineering purposes, fault and geomechanical models representing slip on seismic- fracture models are typically populated using statistical scale faults and associated stress and strain methods (e.g. Harris et al., 2003); however, such perturbations with analysis of field data to better methods do not account for spatial heterogeneity of understand the sequence of fault development at the site subseismic fault density or orientation (Maerten et al., of this outcrop analogue case study. 2006), features which are governed in large part by Beside the forward modeling approach, on which geomechanical processes. the study of the Tableland fault system focuses, Bourne et al. (2000) and Bourne and Willemse mechanics-based restoration methods have been (2001) suggest that opening and shear fractures may be suggested recently as a method for deriving the predicted from stresses associated with slip on seismic- kinematic history of reservoir evolution (Fletcher and scale faults in an elastic continuum. Maerten et al. Pollard, 1999; Maerten and Maerten, 2006; Moretti et (2002, 2006) demonstrate that density and orientation al., 2006; Plesch et al., 2007; Moretti, 2008; Guzofski et of larger subseismic faults may be predicted from the al., 2009). Mechanics-based restoration is a relatively stress field generated by superposition of regional new approach to modeling in structural geology. The tectonic stresses and stress perturbations due to slip on method is based on principals of retrodeformation, and seismic-scale faults. Similar methods have been the primary boundary condition imposes vertical implemented subsequently in case studies by Wilkins displacements to restore a time-stratigraphic marker (2007) and Dee et al. (2007). This conceptual model horizon in its present day deformed state to an assumed for fault development is based on the premise that undeformed geometry (e.g. an unfaulted, continuous, subseismic-scale faults are subsidiary to larger faults, planar horizontal datum). Mechanics-based methods and that they grew due to stress perturbations generated employ finite element (FEM) numerical methods to by larger, older, but still active faults. This conceptual determine deformation throughout a linear elastic model is clearly applicable to some geologic settings, continuum, as opposed to traditional kinematic however, not everywhere. It is in apparent modeling approaches that prescribe a geometric contradiction with another conceptual model of fault mechanism of deformation. Faults are represented in growth, which suggests that larger faults form through the mechanical models as shear traction free contact linkage of smaller faults (Segall and Pollard, 1983; surfaces, between which separation and interpenetration Granier, 1985; Ellis and Dunlap, 1988; Martel et al., are prohibited. Details of two approaches to the 1988; Peacock and Sanderson, 1991; Peacock and modeling are discussed in Maerten and Maerten (2006) Sanderson, 1994; Anders and Slische, 1994; Trudgill and Guzofski et al. (2009). As with other restoration and Cartwright, 1994). Studies by Dawers and Anders techniques, the method is based on the premise that (1995), Willemse et al. (1996), Ferrill et al. (1999) and restoration displacement is equal in magnitude and Ferrill and Morris (2001) provide evidence for this opposite in orientation to the forward deformational conceptual model based on outcrop data from the system (Dahlstrom, 1969; Woodward et al., 1989). Volcanic Tableland, the field site of this study. Mechanics-based methods offer improvement over According to this model, small faults observed today traditional kinematic restoration methods by honoring likely formed early, perhaps as part of the original fault conservation of mass and momentum and employing a population, but have not grown and linked with other constitutive law to derive the kinematic variables, by faults to form larger faults. In this sense, large faults incorporating material heterogeneity in the form of consist of older segments, but in their present state, spatially variable elastic moduli, admitting non-uniform large faults are relatively younger structures. Assuming slip on faults, and accounting for mechanical interaction this sequence of fault system development, it may be of fault segments. Particularly for 3D applications in inappropriate to predict subseismic faulting from stress structurally complex regions, the method appears to perturbations resulting from slip on seismic-scale faults, offer better constrained solutions than kinematic particularly if seismic-scale faults originate as smaller methods. Because these models employ a constitutive faults that have coalesced and continued to grow, while law to define a stress-strain relation, theoretical stress other faults that may have initiated contemporaneously fields may be derived from restoration methods. If the have remained small. An understanding of the stress, strain, and displacement fields, each of which is mechanism of fault system development is important mathematically dependent upon the others (Chou and for this purpose because the sequence of fault Pagano, 1967), accurately represent reverse development could influence hydrocarbon migration deformation, it should be possible to identify regions of history and trap potential. For example, if, at the time intensified stress and strain, as well as principal stress

Stanford Rock Fracture Project Vol. 20, 2009 D-2 and strain orientations, from mechanics-based province (Figure 1, inset). The largest faults in the restoration models. Owens Valley, including the White Mountain fault to However, boundary conditions in these models are the east of the Tableland, accommodate kilometers of fundamentally different from those of the forward extension and right-lateral strike slip (Stockli et al., model, violating the traction free nature of the earth’s 2003; Kirby et al., 2006). Geologic and geophysical surface, and inappropriately treating other boundary evidence suggests, however, that Tableland extension is surfaces of the model as traction free. The mechanical primarily east-west, and the faults accommodate system represented by restoration methods, while primarily dip slip (Bateman, 1965; Dawers et al., 1993; geometrically similar, is fundamentally different from Ferrill et al., 1999). the forward models. While previous studies (Maerten The Volcanic Tableland is an ideal site for a field and Maerten, 2006; Moretti, 2008; Guzofski et al., based study of fault mechanics using linear elastic 2009) acknowledge that accurate stress fields may not theory because the relatively small strains accumulated be derived from such models, kinematic results have during a geologically brief period of deformation make not been questioned, but remain poorly understood. elastic deformation a realistic approximation, We present a qualitative assessment of the differences particularly for the brittle tuff. Fault scarp geometries between displacement and strain fields from forward suggest substantial mechanical interaction between and restoration models, in the context of the Tableland nearby faults (Willemse et al., 1996), behavior which field site. Our results offer valuable insights cannot be modeled by kinematic methods. The concerning the limitations of mechanics-based weathering resistant surface of the tuff represents a restoration methods. time-stratigraphic marker (Ferrill et al., 1999). Comparable contemporary tuff ashflow deposits such as Geologic Setting that deposited in the Valley of Ten Thousand Smokes during the 1912 eruption of Katmai Volcano, Alaska The Volcanic Tableland, north of Bishop, CA, in (Griggs, 1922) suggest that the Bishop tuff may be the Owens River Valley, boasts one of the world’s approximated as planar, and perhaps nearly horizontal, premier field outcrop exposures of an extensional fault at the time of deposition. Therefore, deviations from system. Gilbert (1938) and Bateman (1965) present a planarity can be attributed primarily to fault comprehensive overview of the Tableland and deformation, and throw across fault scarps represents surrounding geology, and Pinter (1995) mapped the total accumulated dip-slip since the tuff’s deposition. fault system in great detail. The site has been used for Substantial erosion in Fish Slough, at the base of the structural studies investigating normal fault slip Fish Slough fault scarp, prevents resolution of the time- distributions and growth (Dawers et al., 1993; Dawers stratigraphic marker in this region, a shortcoming that is and Anders, 1995; Willemse et al., 1996 Ferrill et al., overcome by projection of the marker horizon from 1999; Ferrill et al., 2001) and fault kinematics (Ferrill et west to east, across Fish Slough, into the footwall of the al., 2000), as well as micro-scale deformation Fish Slough fault. mechanisms (Evans and Bradbury, 2004) and fault While there would be advantages to a study area permeability (Dinwiddie et al., 2006). The Volcanic with quality subsurface data and 3D seismic coverage, Tableland is a plateau, formed by the weathering we selected the Tableland field site for the expansive resistant surface of the Bishop Tuff, a welded ash flow outcrop that enables detailed mapping of fault traces, erupted 757,000 +/-9000 years ago (Izett and including those of subseismic faults with greater than Obradovich, 1994), from the Long Valley Caldera, several decimeters throw. Additionally, resolution of roughly 40km to the northwest (Bailey, et al., 1976). the time-stratigraphic marker represented by the top of The tuff consists of a thin (7-8 m), densely welded unit the Bishop tuff in digital elevation models (DEMs) is that caps the sequence and defines the topography, more precise (approximately +/-3m) than could be underlain by units of variable thickness, characterized obtained from typical seismic data (+/-10m). by lesser degrees of welding (Evans and Bradbury, 2004). The total thickness of the tuff varies from 70 to 150m in the study area (Evans and Bradbury, 2004). Model Parameters The tuff is underlain by 1-2 km of relatively soft alluvial and lacustrine basin sediments, themselves Elastic moduli underlain by crystalline basement rock (Hollett et al., Laboratory tests by Lin et al. (1993) on tuff with a 1991). comparable composition to the Bishop tuff at Yucca The Tableland is located in the Owens River Mountain, Nevada, suggest Young’s moduli of 6 GPa Valley, immediately east of the Sierra Nevada, in the for unwelded tuff, and 33 GPa for densely welded tuff. Eastern California Shear Zone and Walker Lane Belt, Tests by Avar et al. (2003) on lithophysae rich tuff and at the western periphery of the Basin and Range from the same site suggest Young’s modulus ranging

Stanford Rock Fracture Project Vol. 20, 2009 D-3 from 2-8 GPa, depending upon porosity. Poisson’s distributed faulting, and other high resolution details ratio generally ranges from 0.2 to 0.25 (Lin et al., were omitted for the sake of discretization and 1993). While the uppermost unit of the Bishop Tuff is computational efficiency. Fault models were analyzed densely welded, and undoubtedly quite stiff, this unit is using Poly3D, a boundary element code that models thin (7-8 meters) and underlying units are non- to faults as triangular elements of displacement slightly-welded (Evans and Bradbury, 2004). For this discontinuity in a linear elastic isotropic and reason, we consider the softer Young’s modulus of 6 homogeneous half-space (Thomas, 1993; Maerten et GPa to be most appropriate for the bulk stratigraphy of al., in review). These faults were subjected to a range the Bishop Tuff. Bieniawski (1984) suggests that, due of remote uniaxial extensions, centered about 1.9% to fractures and other damage, effective stiffness of (Pinter, 1995) oriented N80ºW, orthogonal to the rock at outcrop and larger scales is between 0.2-0.6 of average strike of Tableland faults, a crude estimate of laboratory values, dependent upon rock quality, with a the regional strain tensor. Shear traction free and zero mean ratio of 0.4. Although weathering makes detailed normal displacement discontinuity boundary conditions mapping of joints and other fractures with less than a were specified on the faults. Vertical displacement of decimeter of displacement discontinuity difficult, the the model surface, analogous to the earth’s surface, was Bishop Tuff is highly fractured (Gilbert, 1938; calculated on a 30m grid. Displacements are compared Bateman, 1965). We use Young’s modulus of 2.5 GPa qualitatively and quantitatively with the 10m USGS and Poisson’s ratio of 0.25 throughout this study. DEM, modified to remove regional dip and adjusted Elastic heterogeneity of stratigraphic units is not such that mean elevation in the area of interest is considered because material heterogeneity is equivalent to the mean model vertical displacement. computationally costly in boundary element methods The fault geometry that minimizes the root mean square and because the primary, well-constrained difference between topography and vertical model heterogeneity is the relatively greater stiffness of the displacement is deemed the optimal model. thin unit at the top of the tuff, which is below the The selected fault model exhibits surface dips resolution of FEM meshes used for restoration models. exceeding 80º, substantial listricity, and faults extend uniformly to 600m depth, with the exception of the Fish Fault geometry Slough fault, which extends to 1500m. Qualitative observation suggests that surface displacements from Because subsurface data are not available in the this model reproduce features of the DEM quite well. Tableland, we use a geomechanical approach to infer Root mean square difference between model vertical 3D subsurface fault geometry from surface data, displacement and the DEM ranged from 6-10 meters for namely DEMs and detailed surface mapping of fault various fault models. This optimal fault geometry scarps. Focusing on a small (5-6 km2) area at the produces an RMS difference of 6.1m. These depths of southeastern corner of the Tableland with well- faulting correspond to geological boundaries cited in preserved topography produced by fault-related the hydrological literature (Hollett et al., 1991; deformation, we use differential GPS to map the Danskin, 1998), and based on geophysical data hanging wall and footwall cutoffs of 16 fault scarps including seismic refraction and gravity contours representing all major faults intersecting the surface in (Pakiser and Kane, 1962; Pakiser et al., 1964). The the area of interest. The resulting data were analyzed 600m depth of most faults corresponds to an increase in manually to interpret a detailed map of fault traces with seismic velocity, which could result from lithologic resolution of several meters, which documents variation or differential compaction, and the 1500m numerous splays, echelon fault segments, intact and depth suggested for the Fish Slough fault corresponds breached relay ramps, and areas where faulting is roughly to the depth of the sedimentary basin. This distributed over two or more subparallel fault segments independent evidence for geological boundaries at (Figure 2). These fault traces, and a map of the Fish similar depths corroborates our findings of fault Slough fault trace generated from interpretation of geometry from surface topography. aerial photography and topography, were projected Subsequent mechanical models (discussed later) down-dip to generate approximately fifty trial 3D fault focus on those faults that would likely be easily surface models. These models have surface dips discernable in a quality seismic reflection dataset ranging from 50º-85º, linear and listric down-dip (Yilmaz, 1987). These are the faults whose 3D projections, depth of faulting ranging from several geometry would be relatively well constrained in an hundred to several thousand meters, and uniform depth exploration or production setting. Models representing of faulting as well as faults with depths that scale with only seismic-scale faults enable us to investigate if and fault length at the surface. Model faults were how the stresses due to slip on these faults relate to discretized as triangulated surfaces, with elements subseismic-scale faulting observable in the field, and to roughly 75m on a side. Small splays, regions of discuss implications for fault system evolution and

Stanford Rock Fracture Project Vol. 20, 2009 D-4 whether subseismic features can be predicted from influence on mechanical interaction of fault segments, geomechanical models in the case of this outcrop but only on the magnitude of slip. Therefore, if friction analogue fault system. Also, in restricting the models were considered in this study, the magnitude of the to these largest faults, we maintain a computationally deviatoric paleostress tensor would be somewhat larger, manageable system of faults, and avoid questions of but fault slip distributions and associated stress ambiguous fault termination and cross cutting perturbations would likely not change substantially. relationships at subsurface fault intersections. Analysis is performed using the method of F. To avoid human bias in selecting seismic-scale Maerten and Kaven et al. (in preparation). Fault throw faults, we implement a simple algorithm in which a is measured along the traces of seismic-scale faults 10m DEM is interpolated onto a grid oriented N80ºW, from a 2m DEM assembled from an airborne LiDAR orthogonal to the average fault strike. We then scan the survey (Figure 1), flown in August 2008. Throw is grid, at each point examining elevation values in a equated to dip-slip, inducing a minimal error because window centered at the current location, with a width of faults are nearly vertical at the earth’s surface. Greater one pixel in the fault-parallel direction, but extending error is likely induced by erosion of the footwall, at the 20, 40, 60, 80, or 100m in the fault-perpendicular top of the scarps, and deposition on the hanging wall, at direction. If the maximum variation in elevation within the base of the scarps. As a result, throw measurements the window exceeds some threshold, the point at which and resulting paleostress calculations can be thought of the window is centered is considered part of a seismic- as minimum values. This source of error would not be scale fault trace, and plotting all such points results in a of concern in a study based on seismic imaging and map of seismic-scale fault traces (Figure 1). Based on subsurface data because, with the exception of non- typical seismic image resolution between 10 and 30m conforming surfaces, stratigraphic horizons in the for industry quality data (Yilmaz, 1987), we select a subsurface have been protected from the effects of 20m threshold and a window dimension of 40m, which erosion. Nonetheless, the effects of erosion on maps fault traces as continuous features, but without Tableland topography are likely less (probably less than blotches or noise. Using this fault trace map, we 3m) than the ambiguity in resolution of seismic generate a model of seismic-scale faults consisting of reflector horizons (~10m). The paleostress tensor is 10 small faults, plus the Fish Slough fault, which itself computed as a linear inverse problem, based on the consists of several distinct fault segments (Figure 1). forward problem solved by Poly3D (Thomas, 1993). The paleostress inverse problem determines the Boundary conditions and paleostress far-field deviatoric stress tensor that minimizes the analysis residual vector, calculated as the difference between slip measurements and slip predicted by the forward The selected fault geometry is used first for a model for both strike and dip components, on those paleostress analysis, which enables the establishment of elements where slip measurements are available. The physically based boundary conditions for subsequent method accounts for mechanical interaction of forward and reverse models. The paleostress tensor triangular elements of constant displacement represents the optimal deviatoric component of the far- discontinuity within a fault segment and mechanical field (regional) stress state that drives fault slip and interaction between fault segments. In the inversions, associated deformation, but does not uniquely strike-slip is considered as an unknown everywhere determine the isotropic component of the stress tensor, because only dip-slip can be inferred from throw, and which is influenced by lithostatic pressure and pore dip-slip is known only on those elements where throw pressure and is variable with depth. Knowledge of can be mapped from outcrop data. Fault-normal deviatoric stress enables complete resolution of shear displacement discontinuity (equivalent to fissure traction on fault surfaces, whereas isotropic opening or interpenetration of fault walls) is prohibited. contributions to the local stress state resolve only The numerical implementation of the paleostress normal traction on fault surfaces. Hence, considering inversion assumes the vertical component of the the forward problem in which slip may be uniquely paleostress tensor to be zero and to be a principal stress. determined by assuming complete shear stress drop on Vertical stress must be zero at the earth’s surface, and is the frictionless fault surfaces, only the deviatoric assumed to be a principal stress in the near surface; component of the far-field stress tensor is necessary to however, as discussed previously, the paleostress tensor prescribe complete boundary conditions for such represents deviatoric stress, not in situ stress, and does models. While real faults are not actually frictionless, not account for isotropic stresses, which would make precise values for fault friction are difficult to the vertical stress non-zero, but which not influence determine (e.g. Scholz and Hanks, 2004)), and previous deformation under the assumption of frictionless faults. studies (e.g. Aydin and Schultz, 1990) suggest that the The calculated paleostress tensor has a maximum effects of uniform friction do not have a strong tensile stress, σ1, of 160 MPa (we implement a tension

Stanford Rock Fracture Project Vol. 20, 2009 D-5 positive convention throughout this manuscript), lithostatic compression, which increases in magnitude oriented N1ºW, and σ2 of 72 MPa, oriented N79ºE with depth with a vertical gradient related to local rock (recall σ3 is vertical, magnitude 0). Without density (Jaeger et al., 2007). While such an isotropic considering extension due to faulting, these stress stress does not influence the kinematics of linear-elastic components correspond to principal elastic strains of frictionless systems, were we to consider frictional 5.7%, oriented N1ºW, and 1.3%, oriented N79ºE. Fault sliding on faults, an accurate representation of in situ geometry, principal components of the paleostress stress that accounts for lithostatic loading would be tensor, and contours of slip from a forward model using necessary (e.g. Kattenhorn et al., 2000). Additionally, the paleostress tensor to define the far field boundary viscoelastic or inelastic relaxation due to slip on condition are presented in map view in Figure 3a. subseismic faults is not represented in the model. However, this stress tensor is physically unrealistic Inelastic deformation or stress relaxation with time because the most tensile stress is oriented roughly could lead to an overestimation of stress magnitude. parallel to the fault traces, orthogonal to the east-west With a three dimensional fault model representing extension accommodated by faulting. This unphysical the seismic-scale faults and a well constrained result occurs because all elements for which slip is paleostress tensor that provides an appropriate far-field constrained are subparallel, striking north-south. The boundary condition, the necessary tools are available to result is an ill-conditioned inverse problem, which consider linear elastic models of fault-related resolves the east-west component of the stress tensor deformation. Forward mechanical models have a two- quite well, but resolves the north-south component fold purpose in this study. First, we discuss their poorly. This demonstrates the importance of carefully geological significance in the context of Tableland fault considering results and ensuring a well-constrained system development. Subsequently, results are inversion when performing paleostress analysis. compared with mechanics-based restoration models to We remedy the ill-conditioning by including one investigate qualitatively the capabilities and limitations additional fault in the paleostress model. This fault, of this method. Lithostatic loading is accounted for in located in the southeast corner of the Tableland, is forward model results analyzed for geologic insights somewhat of an aberration, striking roughly N45ºE, and (Figure 4) but not in subsequent models that consider dipping to the northwest. Although this fault was not restoration methods because the isotropic lithostatic detected as a seismic-scale feature by the algorithm stress tensor does not affect model kinematics. discussed previously, throw locally exceeds 20 meters, suggesting that the fault is only slightly below the Forward Models and Results threshold for detection. By including this fault, we Studies suggesting that large (seismic-scale) obtain a stress tensor with σ of magnitude 69 MPa, 1 Tableland faults developed through linkage of smaller oriented N87ºE, and σ of magnitude 23 MPa, oriented 2 faults (Dawers and Anders, 1995; Willemse et al., N3ºW, corresponding to principal strains of 2.5%, 1996; Ferrill et al., 1999; Ferrill and Morris, 2001), oriented N87ºE, and 0.2%, oriented N3ºW. Fault imply that the Tableland fault system initiated as a configuration, principal components of the paleostress distributed array of subseismic-scale faults, some of tensor, and contours of fault slip from a forward model which have subsequently grown and linked, as the using the paleostress tensor to prescribe far field system has evolved to its present state. It could be boundary conditions are presented in Figure 3b. The inferred from this conclusion that the smaller faults slip distribution predicted by this paleostress tensor is represent the oldest structures on the Tableland, and nearly identical to that described previously, in which larger faults have achieved their present state more the most tensile remote stress is oriented north-south, as recently. This hypothesis, however, does not preclude demonstrated by contours in Figure 3. This paleostress the possibility that additional small faults have formed tensor, calculated from a well constrained inversion, more recently, perhaps due to stress perturbations suggests greatest tension parallel to the east-west associated with slip on the larger Tableland faults, in extension, and is selected as an appropriate, physically accordance with the conceptual model of Maerten et al. based boundary condition for subsequent forward (2002, 2006) or due to accumulating tectonic load. models. A series of numerical models in which seismic- Rock, however, cannot support tensile stress of the scale faults on and around the Tableland are represented magnitude suggested by the paleostress tensor. Typical as non-planar surfaces in three dimensions, discretized tensile strength is approximately 10MPa (Bieniawski, as planar, triangular elements of uniform displacement 1984). It is important to recognize, as discussed discontinuity, are performed using Poly3D (Thomas, previously, that the paleostress tensor and associated 1993). These models provide insight to the nature of model stresses do not represent in situ subsurface stress the stress perturbations resulting from slip on seismic- magnitudes because they do not represent isotropic scale faults. Interpretation of these stress perturbations contributions to the local stress tensor, including

Stanford Rock Fracture Project Vol. 20, 2009 D-6 provides insights to the development of the Tableland address fault evolution, but starts with all faults given fault system, and whether or not infilling of subseismic- their present day geometry. Figure 4a presents contours scale normal faults likely occurred in recent times. We of maximum principal stress at the earth’s surface examine in map view and in vertical cross section the associated with the seismic-scale Tableland faults. The stress perturbations resulting from slip on seismic-scale orientation of this principal stress is generally east-west, faults due to the far-field paleostress boundary and faults and fractures would be expected to form condition, and compare stress perturbations with a parallel to the intermediate principal stress, generally detailed map of subseismic fault traces. oriented north-south. The greatest compression is The Coulomb stress and the Coulomb shear failure generally vertical, and increases with depth from zero at criteria (Coulomb, 1773; Jaeger et al., 2007) are the earth’s surface. The area of greatest tension is commonly applied in studies of fault development. indicated by the large red/brown region immediately Hubbert (1951), Hafner (1951), and Hubbert and Rubey west of the Fish Slough fault. This area has a relatively (1959) are among the earliest geologic applications of low density of mappable faults. The majority of Coulomb failure criteria. Subsequent studies have used subseismic faults mapped on the Tableland occur in a Coulomb failure theory to interpret the results of region of stress shadow, indicated by green/blue numerical models in the context of earthquake faulting shading, west of 374,000m easting. Figure 4b shows and seismicity (e.g. King et al., 1994) and the formation contours of maximum principal stress and principal of geologic fractures (e.g. Bourne and Willemse, stress orientations on the east-west cross-section A-A’, 2001). We, however, investigate Coulomb stress only located at 4,146,500m northing. Model results briefly, and focus on the most tensile stress, σ1. This consistently indicate that the greatest tension is in the focus is justified two ways. First, Coulomb stress is a near-surface, and that there is little correlation between linear function of σ1 and σ3 (Jaeger et al., 2007). the magnitude of maximum tensile stress and the Because Tableland faulting likely initiates at or near the location of subseismic faults. Finally, Figure 4c shows earth’s surface (discussed later), and because σ3 is contours of maximum Coulomb stress, calculated for a almost universally vertical and zero at the earth’s coefficient of internal friction µ = 0.6. Black vectors surface in this extensional setting (Anderson, 1951), indicate the 2D representation of shear failure planes, contours of Coulomb stress in the near surface differ along which subsidiary faults striking approximately from contours of σ1 only in magnitude. Contours of perpendicular to the cross section plane would be maximum tension and Coulomb stress have the expected to form. identical geometry. Model results indicate that That the greatest concentration of subseismic-scale contours of Coulomb stress and σ1 differ very little at faults occurs in a stress shadow of the forward model depth (Figure 4 b-c). Additionally, field evidence suggests that slip on seismic-scale faults distributed suggests that in regions of low confining stress, across the Tableland did not induce the formation of extensional faults develop through linkage and shearing additional subseismic-scale normal faults. To test this of opening mode joints (Segall and Pollard, 1983; conclusion, and to further our understanding of how the Martel et al., 1988; Willemse et al., 1997; Davatzes and Tableland fault system has evolved, additional models Aydin, 2003; Flodin and Aydin, 2004). This are considered. A model is analyzed that accounts only mechanism of fault formation is further supported by for slip and associated deformation on the Fish Slough the steep dip of faults in the near surface, as discussed fault, as well as two models that include the Basin and previously. If faults formed due to shear failure Range-scale White Mountain fault. The White according to the Coulomb criteria, the expected dip Mountain fault crops out 5-10km east of the Fish would be substantially shallower (~60 degrees), Slough fault. Its trace is beyond the study area but is depending upon the internal friction angle of the tuff shown in the inset of Figure 1, and is digitized for (Jaeger et al., 2007). Assuming this mechanism of fault model assembly from the map of Lee et al. (2001). We formation, faults would be expected to form in regions extend the fault to 15 km depth, roughly that of the of enhanced σ1, and therefore smaller faults are likely seismogenic portion of the crust (Nazareth and subsidiary structures if they occur in the vicinity of Hauksson, 2004), with a uniform 60º dip (Kirby et al., tensile stress perturbations from larger faults. On the 2006). contrary, if smaller faults are observed in the stress Models that do not include the White Mountain shadows of larger faults, or in regions of relatively little fault treat the Tableland as an isolated system. It is stress perturbation, no causative mechanism is important, however, to consider the effects of the White suggested. Mountain fault because that fault is undoubtedly older Because relative ages of individual Tableland than the Tableland fault system (Kirby et al., 2006), and faults are unavailable, we consider a model that therefore stress perturbations resulting from slip may accounts for stress perturbations due to all faults have influenced the evolution of the Tableland fault simultaneously. In other words, the model does not system.

Stanford Rock Fracture Project Vol. 20, 2009 D-7 Models that include the Fish Slough fault, but not 230m, that of the FEM mesh. The scarps of subseismic smaller seismic-scale Tableland faults, are considered faults that are not discretized in the model are because the Fish Slough fault is so much larger than represented in the topography of the model’s top; other Tableland faults. While data is not available to however, they are smoothed to the extent of mesh show that the Fish Slough fault is indeed older than resolution. Nonetheless, their influence is apparent in other Tableland faults, thereby proving that its stress restoration models in which topographic heterogeneity perturbation would influence the development of leads to regions of intensified strain. The surface smaller (younger) faults, its extraordinary size suggests representing the top of the tuff was projected west to that it may be among the oldest faults on the Tableland, east across Fish Slough, at a constant dip, into the and, if so, smaller faults could be induced by slip. footwall of the Fish Slough fault, in order to Figure 5 presents maximum principal stress compensate for erosion in this region. contours and principal stress orientations at the earth’s Although FEM models can accommodate material surface for the four different models. Surface stress is heterogeneity at the resolution of mesh discretization plotted because we suggest it is the best proxy for fault (unique elastic moduli may theoretically be specified initiation (see below). All models indicate the greatest for each tetrahedral element), we consider only tensile stress is found immediately west of the Fish homogeneous material models for several reasons. Slough fault, and models that do not include the White First, the only major elastic material heterogeneity on Mountain fault indicate a substantial stress shadow in which good spatial and material constraint is available the area of densest subseismic faulting. Models that is the contrast between the uppermost welded unit of include the White Mountain fault suggest substantially the Bishop tuff, and the underlying, softer, less welded greater tensile stresses across the Tableland than units. The thickness of this stiff, welded unit is more models that include only Tableland faults, particularly than an order of magnitude smaller than mesh in the vicinity of the densest subseismic faulting. resolution, and hence cannot be accurately represented Maximum principal stress is oriented roughly east-west in the model. Material elastic properties undoubtedly across the Tableland in all forward models considered. are heterogeneous across other lithological boundaries including the base of the tuff, the boundary inferred by Retrodeformational Models and geophysical and hydrological studies at approximately Results 600m depth, and the top of the crystalline basement; however, the location and material nature of these We use Dynel3D (Maerten and Maerten, 2006) to contrasts are poorly constrained. Additionally, the investigate mechanics-based restoration models in the study of an elastically homogeneous FEM volume context of the Tableland field site. The extent of the enables meaningful comparison of restoration model FEM model is represented by the dotted line in Figure results with the results of homogeneous forward models 1, and the tetrahedral mesh is presented in Figure 6. using the boundary element method. This comparison The mesh extends to roughly 2500m depth, and provides the basis for a qualitative but insightful seismic-scale faults are included as shear traction free evaluation of mechanics-based restoration methods. contact surfaces, across which nodes are split in order The restoration model is constrained by a vertical to permit shear displacement discontinuity, but between displacement boundary condition, which restores the which opening and interpenetration are prohibited. For model topography to a horizontal, planar datum. purposes of mesh generation and definition of fault Additionally, vertical boundary #3 (Figure 6) is compliance contact conditions, the representation of the constrained to zero displacement in the east-west Fish Slough fault is a simplified version of that used for direction, and vertical boundary #5 is constrained to paleostress analysis and forward models. The fault is zero displacement in the north-south direction, represented as two discrete fault segments, but the providing a fixed reference frame for the model. southern fault, which actually consists of several Vertical walls #1, #2, and #4 are treated as traction free intersecting echelon segments and breached relays surfaces, the default behavior of most mechanical FEM (Ferrill et al., 1999) (Figure 1), is represented as a packages in the absence of another prescribed boundary single, continuous surface. Otherwise, the FEM fault condition, and a typical procedure in mechanics-based geometry is identical to that used for paleostress restoration workflows (Maerten and Maerten, 2006; analysis and forward models. Topography from the Plesch et al., 2007; Moretti, 2008; Guzofski et al., USGS 10m DEM is used to generate the time 2009). Results of these models are presented as east- stratigraphic reference horizon represented by the top of west vertical cross sections in Figures 8b, 9b, and 10b. the Bishop Tuff. This surface is rotated to remove The signs of strain and displacement for restoration regional dip. While higher resolution data was models have been changed to correspond with the available from the LiDAR survey, computational forward model, results of which are presented in limitations required that we decimate the 10m DEM to Figures 8a, 9a, and 10a. Strain and displacement fields

Stanford Rock Fracture Project Vol. 20, 2009 D-8 have little in common between forward and restoration (Pollard and Segall, 1987), despite clear geologic models. evidence at the outcrop that the topography is generated That model kinematics are critically different from by fault slip. Most notable on the cross section forward models is a fundamental flaw of mechanics- presented are regions of enhanced extension in the based restoration methods, but this may be partially footwall of the westernmost fault and to the west of the rectified by incorporating a boundary condition that two adjacent faults near 373,000m easting, and local reverses the tectonic loading that drove the forward contraction in the hanging wall of the westernmost deformation, rather than treating vertical model fault. Also note that in these regions of enhanced boundaries as traction free surfaces. Strain distributions extension, maximum tensile stress is not parallel to the associated with such a model are presented in Figures model surface as it is in forward models. 8c and 9c. Again, the sign of stress and strain have Figure 9 illustrates contours of the vertical been changed to represent forward deformation. This component of the strain tensor. In forward models, model, hereafter referred to as the restoration and vertical strain is spatially homogeneous, with small reverse displacement model, is defined by the same perturbations in the immediate vicinity of fault surfaces. displacement boundary conditions used in the The restoration model and the model with restoration restoration model, supplemented by displacement and reverse boundary conditions are generally similar boundary conditions that translate vertical wall #1 to each other, and highly heterogeneous, unlike the 261m to the east and vertical wall #2 23m to the south. forward model. Regions of vertical extension in the These prescribed displacements are equal in magnitude footwall and compression in the hanging wall occur in and opposite in sign to the average displacement of conjunction with most seismic-scale faults represented vertical surfaces at the corresponding locations in the explicitly in the model, in addition to perturbations forward model. Hence they are derived, albeit associated with subseismic faults that are not indirectly, from the paleostress analysis. represented in the FEM mesh. The magnitudes of these Magnitude and distribution of strain perturbations vertical strains are comparable to extreme values of in the restoration model are very different from forward principal strains associated with tectonic forces and models, as are principal strain orientations (Figure 8). faulting in the forward model. Supplementing the Throughout most of the model space, the maximum restoration model with reverse boundary conditions principal strain suggested by the restoration model is reduces the size and magnitude of some perturbations much smaller (less extension) than for forward models, where seismic-scale faults are included in the model, and maximum principal strain orientation is but does not nearly eliminate them, and does little to heterogeneous, whereas in forward models it is address these artificial vertical strains imposed by the consistently oriented east-west, except near faults. restoration boundary condition where subseismic faults Note that in the restoration model, vector lengths are omitted from the model. representing principal strain orientations are Figure 10 presents in cross section the in-plane heterogeneous. This results from plotting principal displacements associated with forward and restoration strain vectors of constant magnitude in three models. Horizontal displacements in the restoration dimensions. Only in the restoration model is a model are much smaller than those in the forward substantial component of the maximum principal strain model. Displacements associated with the restoration in much of the cross section plane oriented north-south, and reverse displacement model are not presented, but orthogonal to the plane of view. Near the top of the are generally similar to displacements for the forward restoration models, the strain field is dominated by model. Although vertical strains imposed by the local ε1 perturbations that are absent from forward restoration boundary condition are large, the associated models, but that are of comparable magnitude to the displacements are very small relative to the horizontal greatest perturbations associated with faults in forward extension that drives faulting, making vertical models. displacements imposed by the restoration boundary In the model representing reverse and restoration condition difficult to discern. These displacements are boundary conditions, the maximum strain distribution nonetheless significant in the context of strain and the represents that of the forward model to first order. corresponding stress. Strain contours about fault tips are generally appropriate and in accordance with perturbations Discussion expected from fracture mechanics (Chinnery, 1961; Pollard and Segall, 1987), but, as in the restoration Evolution and geomechanics of the model, localized regions of positive and negative strain concentration, which are absent from forward models, Tableland fault system are observed in the near surface. These perturbations Dawers and Anders (1995), Willemse et al. (1996), do not resemble fault related strain distributions Ferrill et al. (1999) and Ferrill and Morris (2001)

Stanford Rock Fracture Project Vol. 20, 2009 D-9 suggest that the larger faults on the Tableland form most, if not all, such faults have developed by through the growth and subsequent linkage of echelon coalescence of multiple subseismic-scale faults, even if arrays of smaller faults. Evidence for this conceptual detailed trace maps are continuous and linear, without model of fault growth is based on surface trace maps strong evidence for coalescence. that suggest linkage of echelon fault arrays, and is Dawers et al. (1993) and Dawers and Anders bolstered by analysis of slip distributions on long faults (1995) suggest that Tableland faults initiated in the very whose trace geometry suggests growth by fault linkage, near surface from field evidence including consistent and by slip distributions on echelon fault arrays that and systematic slip-length ratios and consistent slip appear to be candidates for future coalescence into a gradients near fault tips. Greater variability of these single, larger fault. Several of the more complex fault characteristics would result from varying degrees of traces shown in Figure 2 clearly illustrate both intact fault maturity if faults initiated toward the base of the and breached relay ramps, strong evidence for growth Bishop Tuff, or deeper. Geomechanical evidence from of large faults by coalescence of smaller faults (Peacock this study supports this hypothesis. All of the forward and Sanderson, 1991 & 1994; Trudgill and Cartwright, models of the Tableland fault system investigated here 1994; Ferrill et al., 1999; Ferrill and Morris, 2001), as predict the greatest tensile stress magnitude near or at well as subparallel segments within a single fault zone, the earth’s surface, as illustrated in Figure 4b, and and sharp jogs. Not all seismic-scale tableland fault oriented roughly east-west, parallel to the tectonic traces, however, demonstrate such clear evidence for tension and perpendicular to the strike of subseismic growth by coalescence. and seismic-scale faults. This localized tensile stress in The west dipping fault trace, indicated by the bold the near surface would be further enhanced if the line in Figure 2, is a prime example. This relatively models accounted for material heterogeneity, as the linear fault trace, over two kilometers long, exhibits uppermost unit of the Bishop tuff is the stiffest subunit, none of the geometric complexities such as splays, and likely stiffer than the unconsolidated glacial, subparallel strands, or artifacts of breached relay zones alluvial, and lacustrine sediments directly beneath common to other faults of comparable size. A few very (Gilbert, 1938). For a given strain tensor, stresses are subtle jogs provide only weak evidence that this fault proportional to Young’s modulus, an elastic material trace may consist of coalesced smaller fault segments. property that increases with stiffness. The distribution of throw along this fault, however, The relatively short traces and small accumulated provides a strong case for segment linkage, despite the throw on Tableland faults, as well as the shallow simple, linear scarp (Figure 7). The throw profile suggested depth of faulting relative to nearby Basin and shows three distinct peaks, separated by local minima. Range faults, suggests that Tableland faults may be This suggests that the fault grew as at least three subsidiary structures that formed due to local stress distinct fault segments, each characterized by a slip perturbations associated with slip on larger faults. distribution tapering to zero at the segment tips, with a Small faults, like those observed in the Tableland, could maximum near the center. The local maxima on the potentially accommodate residual tension that is not present throw distribution are remnants of the maxima relaxed by slip on Basin and Range-scale faults such as on each of the original fault segments, and the local the White Mountain fault, but such small faults are minima represent the linkage points. The relatively unable to accommodate crustal-scale extension small throw at these points suggests that the segments associated with the Basin and Range because they do coalesced relatively recently. The northernmost not extend through the thickness of the brittle crust. segment, roughly 1000 m long, has a nearly elliptical Pinter (1995) suggests that Tableland faulting was throw distribution, as expected from a single fault that driven by flexural forces associated with a rollover is relatively little influenced by stress perturbations of anticline in the hanging wall of the White Mountain neighboring structures. The central segment is much fault. This hypothesis is equivalent, though more more asymmetric. This could stem from mechanical specific, to suggesting that Tableland faults are interaction with neighboring faults, or this portion of subsidiary faults to the White Mountain fault. The the fault may have originated as more than one distinct hypothesis is supported by the numerical model results fault segment whose individual maxima are difficult to presented in Figure 5 c & d. We do not present stress distinguish today. Throw along the southern segment results for a model that includes only the White of the fault has an apparent peak at the fault tip because Mountain fault. However, models that include the the fault terminates where the Tableland ends in an White Mountain fault among other faults indicate that eroded bluff, effectively a vertical free surface at which while local faults on the Tableland, including the Fish topography drops nearly 100 m to the alluvial plain Slough fault, release tension in the regions of most below. Although we have not thoroughly examined intense subseismic faulting, slip on the White Mountain trace geometry and throw distribution for every fault induces substantial east-west tension across the seismic-scale fault on the Tableland, we suggest that Tableland.

Stanford Rock Fracture Project Vol. 20, 2009 D-10 Regions characterized by the most tensile stress in We hypothesize that at this stage a broad array of small models representing slip on seismic-scale Tableland normal faults initiated on the Tableland. These faults faults do not correlate with regions of most intense may have initiated in the manner suggested by Segall subseismic faulting (Figure 5). In fact, the region of and Pollard (1983), Martel et al. (1988), Willemse et al. most intense subseismic faulting is found in a relative (1997), Davatzes and Aydin (2003) and Flodin and stress shadow of modeled seismic-scale faults. The Aydin (2004), through shearing and coalescence of region of greatest tension correlates with a region of cooling joints, which are abundant on the Tableland; relatively few mappable subseismic faults, although this however, this hypothesis cannot be substantiated observation may relate in part to erosion in Fish Slough, because outcrop data from cross section exposures are which could obfuscate some subseismic fault scarps. not available.. Some of these faults have grown and This unexpected region characterized by the greatest coalesced to form the seismic-scale faults observable tensile stress perturbation could also result from model today. According to this pattern of fault growth, limitations, such as inability to accommodate inelastic subseismic faults may be among the oldest structures on continuum deformation. Stress fields presented in the Tableland, remnants of the initial array of small Figures 4 & 5 suggest that subseismic Tableland faults faults, which have not coalesced with other faults, and are not subsidiary to seismic-scale faults on the whose growth has been inhibited by the stress shadows Tableland. Stress perturbations resulting from slip on of larger faults. In light of model results, it seems seismic-scale faults inhibit, rather than induce, the unlikely that new, subparallel north-south striking faults formation of new subseismic faults. Similarly, would develop if the existing faults remain active. deformation associated with the Fish Slough fault alone Geomechanical analysis in this study does not shed (Figure 5c) results in a stress shadow across much of much light on the evolution of the Fish Slough fault, the Tableland, suggesting that neither smaller seismic and why it has grown so much longer, and apparently nor subseismic faults are likely subsidiary faults deeper, than other Tableland faults. Although the resulting from induced tension in the hanging wall of inferred fault geometry suggests that it does not connect the Fish Slough fault. with deeply rooted basement faults, the rudimentary Previous studies suggesting correlation between inversion technique employed does not provide location and orientation of subseismic faulting with sufficient evidence for sound conclusions. stress perturbations due to seismic-scale faults (Maerten et al., 2002, 2006; Dee et al., 2007) consider more Retrodeformational modeling structurally complex regions than the Tableland, in Because mechanical restoration methods are based which subseismic faults are not aligned with seismic- on a complete mechanics, which honors conservation of scale faults. We suggest that the prediction of mass and momentum and implements a well- subseismic faulting using geomechanical methods may established constitutive law relating stress and strain, be most appropriate when there is clear evidence that one might supposed that these models should accurately subseismic faults are younger than larger faults (e.g. represent both the kinematics and mechanics of the Tableland faults are younger than the White Mountain deformational system being studied. Indeed, the Fault) or given evidence that subseismic faults are not method offers improvement over traditional kinematic subparallel to seismic-scale faults. Such nonparallel restoration methods for these reasons, and by orientations are particularly valuable if abutting accounting for mechanical interaction of fault relations may be established to confirm that subseismic segments, material heterogeneity, and non-uniform faults are younger than seismic-scale faults. While fault slip. While previous studies (Maerten and non-parallel orientation itself does not infer the Maerten, 2006; Moretti et al., 2008; Guzofski et al., subsidiary nature of subseismic faults, it is unlikely that 2009) acknowledge that stress cannot be derived from seismic-scale faults grew through coalescence of mechanics-based restoration models, a comparison of subseismic faults that were not subparallel to the trend restoration models with forward models of Tableland of the present day large fault. Therefore there is no deformation reveals that mechanics-based restoration implication that subseismic faults predate larger faults. does not reverse the kinematics of the forward process The tensile stress shadows resulting from slip on either. A carefully constrained mechanics-based seismic-scale Tableland faults, in conjunction with restoration may provide first order insights to the evidence that slip on the White Mountain fault induces geometric evolution of the fault system; however, tension across the Tableland, suggests that the stress stress, strain, and displacement fields are likely to differ state on the Tableland may have been most favorable substantially from the forward process. Attempts to for fault initiation early in the evolution of the fault infer details of fault related kinematics, including strain system, at which point tectonic stresses and stress history, from restoration models may result in perturbations due to slip accumulation on the White substantial error. Mountain fault likely dominated the local stress field.

Stanford Rock Fracture Project Vol. 20, 2009 D-11 By applying artificial displacement boundary magnitude of these perturbations is comparable to, or conditions on the model earth surface and neglecting to even greater than, the extreme magnitudes of principal account for the tectonic forces that drove forward strain perturbations suggested by the forward model, deformation, mechanical restoration methods simulate a but of a very different nature. These perturbations mechanical system that is fundamentally different from occur anywhere the model exhibits topographic relief, the forward deformational process. As a result, particularly if the structures that produced the relief are restoration models differ from forward mechanical not represented discretely in the model. Perturbations models, and stress, strain, and displacement fields in have roughly equivalent breadth and depth, and their restoration models do not represent those associated sign is dependent upon whether local topographic relief with the forward process. The structural geologist must is generally positive or negative. Although the consider very carefully the implications of restoration boundary conditions restore the top of the tuff to a boundary conditions before interpreting the mechanical supposed undeformed state in which it was flat and or kinematic results of restoration models as continuous across fault scarps, the large vertical strains representative of geomechanical processes. Forward within the continuum are clearly unphysical. Due to 3D models are a safer approach. While simplifications of mechanical processes, these large, artificial vertical real earth systems are inherent to any geological model, perturbations in the near surface are associated with forward elastic numerical models, such as those used in significant horizontal perturbations. this study, are driven by mechanically plausible Most Tableland topography may be attributed to boundary conditions and have provided valuable fault related deformation; however, the stress, strain insights for geologic applications (Thomas, 1993; and displacement fields resulting from restoring this Willemse et al., 1996; Crider and Pollard, 1998; topography do not resemble those that would be Kattenhorn et al., 2000; Bourne and Willemse, 2001; generated by a forward model, particularly where the Maerten et al., 2002; Maerten et al., 2006). It is for this faults generating topography are not explicitly included reason that only forward model results were used in the in the model. Fault tips generate well-defined and previous section of this study for analysis of distinct stress and strain perturbations in their vicinity geomechanical processes. (Pollard and Segall, 1987). In the case of an The most glaring difference between forward and extensional system such as the Tableland, enhanced restoration models, when considering principal strain tension/extension can be expected, and is observed in (Figure 8) or displacement (Figure 10), is the absence forward models, in the footwall near fault tips at depth, of regional extension in the restoration model. This and corresponding regions of enhanced compression are results from the omission of tectonic loading in the observed in the hanging wall. There is no reason to definition of restoration boundary conditions. Because expect such complex stress distributions to be observed vertical boundaries #1 & #2 (Figure 6) are treated as in restoration models in which structures are not traction free surfaces, restoration models do not explicitly included, but restoration of their topographic represent the east-west tectonic extension that produced representation has implications for stress and strain the Tableland fault system. This limitation may be distributions. The observed strain perturbations are addressed, as in Figures 8c and 9c, by prescribing unphysical, and provide no more information about the displacement boundary conditions on vertical deformational system than can be gleaned from a boundaries #1 & #2, with magnitudes appropriate to critical analysis of surface topography. In fact, because reverse the tectonic extension. Appropriate traction such drastic decimation of data resolution (230 m) is boundary conditions on these same model boundaries necessary for FEM modeling, topography data, even at would accomplish a similar purpose. Unfortunately, the resolution of seismic imaging, can provide much such boundary conditions, which we define through more detailed insight to structures omitted from the paleostress analysis, are difficult to define in many model than the restoration can provide. geological situations. Total extension and paleostress This manuscript touches only superficially and are often poorly constrained or unknown quantities. qualitatively on the implications of unphysical Even when these reverse boundary conditions are boundary conditions in mechanics-based restoration included in the restoration model, the mechanical models. A detailed analysis, which considers the system remains deficient, and the kinematic implications in the context of linear elastic theory, and implications are significant. All restoration models which analyzes in detail the consequences of restoration demonstrate large vertical strain perturbations in the boundary conditions in the context of synthetic near-surface (Figure 9), which are absent in forward examples, is currently in prepraration (Lovely and models, and which result from violating the traction Pollard, in prep.). free boundary condition of the model earth’s surface. The implications of these perturbations can be seen in plots of principal strain (Figure 8) as well. The

Stanford Rock Fracture Project Vol. 20, 2009 D-12 Conclusions Comparison of strain and displacement inferred from restoration models with results of forward models The results of this study emphasize the power of suggests that mechanics-based restoration methods do geomechanics, in conjunction with field or subsurface not accurately reflect the kinematics of forward data, for understanding reservoir-scale fault related deformation. Mechanics-based restoration models fail deformational systems. We investigate two potentially to capture the regional strain that drove the extension contradictory conceptual models of fault growth: 1) that accommodated by faulting, and the restoration large faults develop through growth and coalescence of boundary condition violates the earth’s traction free smaller faults and 2) that small faults are subsidiary surface, imposing large vertical strains and structures to larger faults, and their locations and displacements that are unphysical. The first of these orientations may be predicted from stress perturbations limitations may be addressed by imposing a traction or due to slip on seismic-scale faults. The first of these displacement boundary condition on the vertical walls models has been demonstrated in the context of the of the model that reverses the regional strain; however, Tableland field site (Dawers and Anders, 1995; this requires prior knowledge of fault system behavior, Willemse et al., 1996; Ferrill et al., 1999; Ferrill and which we acquire through the paleostress analysis. The Morris, 2001); however, efforts have focused on faults unphysical artifacts of the restoration boundary whose traces suggest breached relays and other condition are pervasive in all restoration models. evidence of fault linkage. We demonstrate through Although mechanics-based restoration offers analysis of slip profiles that this mechanism of fault improvements over kinematic methods, results suggest growth applies to all or most large Tableland faults, that, like kinematic methods, mechanics-based including those with relatively linear and continuous restoration offers only first order approximation of fault traces, which alone do not provide strong evidence for system kinematics. The application of any restoration fault growth by coalescence. method to infer subtle kinematic features, including the Numerical models of fault slip in an elastic evolution of strain associated with a fault system, may medium are used to investigate the second conceptual produce large errors. Forward numerical models model of fault growth. Mechanically optimal far-field incorporating a complete mechanics remain the best boundary conditions for these models are determined method of inferring fault related strain, and offer the from a paleostress inversion that considers available added benefit of providing insights to subsurface stress. data on fault geometry and distributions and accounts for mechanical interaction between fault segments. Forward models indicate that the densest concentration Acknowledgements of subseismic faults is in a tensile stress shadow of P. Lovely wishes to acknowledge Chevron’s seismic-scale faults, including the Fish Slough fault. Energy Technology Company for sponsoring the early This result suggests that subseismic faults are not stages of this project as a summer internship. The subsidiary faults to seismic-scale Tableland faults, and authors thank Chevron for acquiring and releasing the in the case of this field study, geomechanical models of airborne LiDAR data, and for granting permission to slip on local seismic-scale faults should not be used to publish in this volume. predict subseismic fault density or orientation. Models including the Basin and Range-scale White Mountain References fault suggest increased tensile stress across the Allan, U. S., 1989, Model for hydrocarbon migration and Tableland, a mechanics-based confirmation of the entrapment within faulted structures: AAPG Bulletin, v. hypothesis presented by Pinter (1995) that Tableland 73, p. 803-811. extension may be driven by flexural stresses associated Anders, M. H., and R. W. Schlische, 1994, Overlapping with the rollover anticline in the hanging wall of the faults, intrabasin highs, and the growth of normal faults: White Mountain fault. 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A., 1961, The deformation of the ground around and deformation in normal fault systems: Journal of surface faults: Bulletin of the Seismological Society of Structural Geology, v. 23, p. 619-638. America, v. 51, p. 355-372. Fletcher, R. C., and D. D. Pollard, 1999, Can we understand Chou, P. C., and N. J. Pagano, 1967, Elasticity; tensor, structural and tectonic processes and their products dyadic, and engineering approaches: Princeton, Van without appeal to a complete mechanics?: Journal of Nostrand, 290 p. Structural Geology, v. 21, p. 1071-1088. Coulomb, C. A., 1773, Sur une application des regles de Flodin, E. A., and A. Aydin, 2004, Evolution of a strike-slip Maximis et Minimis a quelques problems de statistique fault network, Valley of Fire State Park, southern relatives a l’Architecture: Memoires de Mathematiques Nevada: GSA Bulletin, v. 116, p. 42-59. et le Physique, Academie de Royal des Sciences par Gilbert, C. M., 1938, Welded tuff in eastern California: divers Savans, v. 7, p. 343-382. Geological Society of America Bulletin, v. 49, p. 1829- Crider, J. G., and D. D. Pollard, 1998, Fault Linkage: Three 1862. dimensional mechanical interaction between echelon Granier, T., 1985, Origin, damping, and pattern of normal faults: Journal of Geophysical Research, v. 103, development of faults in granite: Tectonics, v. 4, p. 721- p. 24373-24391. 737. Dahlstrom, C. D. A., 1969, Balanced cross section: Canadian Griggs, R. F., 1922, The Valley of Ten Thousand Smokes: Journal of Earth Sciences, v. 6, p. 743-757. Washington: The National Geogrpahic Society, 341 p. Danskin, W. R., 1998, Evaluation of the Hydrologic System Guzofski, C. A., J. P. Mueller, J. H. Shaw, P. Muron, D. A. and Selected Water-Management Alternatives in the Medwedeff, F. Bilotti, and C. Rivero, 2009, Insights into Owens Valley, California: U. S. Geological Survey the mechanisms of fault-related folding provided by Water-Supply Paper 2370-H: Washington, United States volumetric structural restorations using spatially varying Government Printing Office, 175 p. mechanical constraints: AAPG Bulletin, v. 92, 479-502. Dawers, N. H., M. H. Anders, and C. H. Scholz, 1993, Hafner, W., 1951, Stress distributions and faulting: Growth of normal-faults: Displacement-length scaling: Geological Society of America Bulletin, v. 62, p. 373- Geology, v. 21, p. 1107-1110. 398. Dawers, N. H., and M. H. Anders, 1995, Displacement-length Harris, S. D., E. McAllister, R. J. Knipe, and N. E. Odling, scaling and fault linkage: Journal of Structural Geology, 2003, Predicting the three-dimensional population v. 17, p. 607-614. characteristics of fault zones: a study using stochastic Davatzes, N. C., and A. Aydin, 2003, The formation of models: Journal of Structural Geology, v. 25, p. 1281- conjugate normal fault systems in folded sandstone by 1299. sequential jointing and shearing, Waterpocket Hollett, K. J., W. R. Danskin, W. F. McCaffrey, and C. L. monocline, Utah: Journal of Geophysical Research, v. Walti, 1991, Geology and Water Resources of Owens 108, doi:10.1029/2002JB002289. Valley, California: U. S. Geological Survey Water-

Stanford Rock Fracture Project Vol. 20, 2009 D-14 Supply Paper 2370-B: Washington, United States Moretti, I., F. Lepage, and M. Guiton, 2006, KINE3D: a New Government Printing Office, 77 p. 3D Restoration Method Based on a Mixed Approach Hubbert, M. K., 1951, Mechanical basis for certain familiar Linking Geometry and Geomechanics: Oil & Gas geologic structures: Geological Society of America Science and Technology, v. 61, p. 277-289. Bulletin, v. 62, p. 355-372. Moretti, I., 2008, Working in complex areas: New restoration Hubbert, M. K. and W. W. Rubey, 1959, Role of fluid workflow based on quality control, 2D and 3D pressure in mechanics of overthrust faulting: Bulletin of restorations: Marine and Petroleum Geology, v. 25, p. the Geological Society of America, v. 70, p. 115-166. 205-218. Izett, G. A. and J. D. Obradovich, 1994, 40Ar/39Ar age Nazareth, J. J., and E. Hauksson, 2004, The Seismogenic constraints for the Jaramillo Normal Subchron and the Thickness of the Southern California Crust: Bulletin of Matuyama-Bruhnes geomagnetic boundary: Journal of the Seismological Society of America, v. 94, p. 940-960. Geophysical Research, v. 99, p. 2925-2934. Nelson, R. A., 1985, Geologic Analysis of Naturally Jaeger, J. C., N. G. W. Cook, and R. W. Zimmerman, 2007, Fractured Reservoirs: Houston, Gulf Publishing Fundamentals of Rock Mechanics: Malden, Blackwell Company, 320p. Publishing, 475 p. Pakiser, L. C., and M. F. Kane, 1962, Geophysical study of Kattenhorn, S. A., A. Aydin, and D. D. Pollard, 2000, Joints Cenozoic geologic structures of northern Owens Valley, at high angle to normal fault strike: An explanation using California: Geophysics, v. 27, p. 334-342. 3D numerical models of fault perturbed stress fields: Pakiser, L. C., M. F. Kane, and W. H. Jackson, 1964, Journal of Structural Geology, v. 22, p. 1-23. Structural geology and volcanism of Owens Valley King, G. C. P., R. S. Stein, and J. Lin, 1994, Static Stress region, California – A geophysical study: U. S. Changes and the Triggering of Earthquakes: Bulletin of Geological Survey Professional Paper 438: Washington, the Seismological Society of America, v. 84, p. 935-953. United States Government Printing Office, 65 p. Kirby, E., D. W. Burbank, M. Reheis, and F. Phillips, 2006, Peacock, D. C. P., and D. J. Sanderson, 1991, Displacements, Temporal variations in slip rate of the White Mountain segment linkage and relay ramps in normal fault zones: Fault Zone, Eastern California: Earth and Planetary Journal of Structural Geology, v. 13, p. 721-733. Science Letters, v. 248, p. 168-185. Peacock, D. C. P., and D. J. Sanderson, 1994, Geometry and Knipe, R. J., Q. J. Fisher, G. Jones, M. R. Clennel, A. B. development of relay ramps in normal fault systems: Farmer, A. Harrison, B. Kidd, E. McAllister, J. R. Porter, AAPG Bulletin, v. 78, p. 147-165. and E. A. White, 1997, Fault seal analysis: successful Pinter, N., 1995, Faulting on the Volcanic Tableland, Owens methodologies, application and future directions: Valley, California: The Journal of Geology, v. 103, p. Norwegian Petroleum Society Special Publications, v. 7, 73-83. p. 15-38. Plesch, A., J. H. Shaw, and D. Kronman, 2007, Mechanics of Lee, J., J. Spencer, and L. Owen, 2001, Holocene slip rates low-relief detachment folding in the Bajiaochang field, along the Owens Valley fault, California: Implications Sichuan Basin, China: American Association of for the recent evolution of the Eastern California Shear Petroleum Geologists Bulletin, v. 91, p. 1559-1575. Zone: Geology, v. 29, p. 819-822. Pollard, D. D., and P. Segall, 1987, Theoretical displacements Lin, M., C. E. Brechtel, M. P. Hardy, and S. J. Bauer, 1993, and stresses near fractures in rock: with applications to Rock mass mechanical property estimation strategy for faults, joints, veins, dikes, and solution surfaces, in B. K. the Yucca Mountain site characterization project: High Atkinson, ed., Fracture Mechanics of Rock: London, Level Radioactive Waste Management, Proceedings of Academic Press, p. 277-349. the Fourth Annual International Conference, v. 1, p. 937- Rich, J. L., 1934, Mechanics of Low-Angle Overthrust 942. Faulting as Illustrated by Cumberland Thrust Block, Maerten, F., L . Maerten, and M. Cooke, in review, Solving Virginia, Kentucky, and Tennessee: AAPG Bulletin, v. 3D boundary element problems using constrained 18, p. 1584-1596 iterative approach: Computational Geosciences. Scholz, C. H., and T. C. Hanks, 2004, The strength of the San Maerten, L., P. Gillespie, and D. D. Pollard, 2002, Effects of Andreas Fault: A Discussion, in Karner, G. D., B. local stress perturbation on secondary fault development: Taylor, and N. W. Driscoll, eds., Rheology and Journal of Structural Geology, v. 24, p. 145-153. deformation of the lithosphere at continental margins: Maerten, L., P. Gillespie, and J. M. Daniel, 2006, Three- New York: Columbia University Press, p. 261-283. dimensional Geomechanical modeling for constraint of Segall, P. and D. D. Pollard, 1983, Nucleation and growth of subseismic fault simulation: AAPG Bulletin, v. 90, p. strike-slip faults in granite: Journal of Geophysical 1337-1358. Research, v. 88, p. 555-568. Maerten, L . and F. Maerten, 2006, Chronologic modeling of Stockli, D. F., T. A. Dumitru, M. O. McWilliams, K. A. faulted and fractured reservoirs using geomechanically Farley, 2003; Cenozoic tectonic evolution of the White based restoration: Technique and industry applications: Mountains, California and Nevada: Geological Society American Association of Petroleum Geologists Bulletin, of America Bulletin, v. 115, p. 788-816. v. 90, p. 1201-1226. Suppe, J., G. T. Chou, and S. C. Hook, 1992, Rates of folding Martel, S. J., D. D. Pollard, and P. Segall, 1988, Development and faulting determined from growth strata, in K. R. of simple strike-slip fault zones, Mount Abbot McClay, ed., Thrust Tectonics: London, Chapman Hall, Quadrangle, Sierra Nevada, California: Bulletin of the p. 105-121. Geological Society of America, v. 100, p. 1451-1465. Thomas, A., 1993, Poly3D: a three-dimensional polygonal element, displacement discontinuity boundary element

Stanford Rock Fracture Project Vol. 20, 2009 D-15 computer program with applications to fractures, faults, and cavities in the Earth’s crust, M.S. Thesis, Stanford University, Stanford, CA, 221 p. Trudgill, B., and J. Cartwright, 1994, Relay ramp forms and normal fault linkages, Canyonlands National Park, Utah: Bulletin of the Geological Society of America, v. 106, p. 1143-1157. Walsh, J. J., and J. Watterson, 1991, Geometric and kinematic coherence and scale effects in normal fault systems, in A. M. Roberts, G. Yielding, and B. Freeman, eds., The geometry of normal faults: Geological Society of London Special Publication 56, p. 193-203. Watterson, J., J. J. Walsh, P. A. Gillespie, and S. Easton, 1996, Scalinf systematic of fault sizes on a large scale- range fault map: Journal of Structural Geology, v. 18, p. 199-214. Wiklins, S. J., 2007, Fracture intensity from geomechanical models: Application to the Blue Forest 3D survey, Green River Basin, Wyoming: Geological Society of London Special Publications, v. 292, p. 137-157. Willemse, E. J. M., D. D. Pollard, and A. Aydin, 1996, Three- dimensional analyses of slip distributions on normal fault arrays with consequences for fault scaling: Journal of Structural Geology, v. 18, p. 295-309. Willemse, E. J. M., D. C. P. Peacock, and A. Aydin, 1997, Nucleation and growth of strike-slip faults in limestones from Somerset, U.K.: Journal of Structural Geology, v. 19, p. 1461-1477. Woodward, N. B., S. E. Boyer, and J. Suppe, 1989, Balanced Geological Cross-Sections: An Essential Technique in Geological Research and Exploration: Washington, D. C., American Geophysical Union, 132 p. Yilmaz, O., 1987, Seismic Data Processing: Tulsa, Society of Exploration Geophysicists, 526 p.

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Figure 1. Hillshade image of Tableland topography from 2m DEM. North-south trending features are fault scarps. Bold solid lines represent west-dipping seismic-scale faults and bold dashed lines represent east- dipping seismic-scale faults. The dotted line represents the extent of the FEM mesh used for Dynel3D models. Inset: regional map Tableland vicinity. Abbreviations: WMF – White Mountain Fault; IF – Inyo Fault; OVF – Owens Valley Fault.

Stanford Rock Fracture Project Vol. 20, 2009 D-17 Figure 2. Detailed map of fault traces interpreted from DGPS map of fault scarp boundaries in the southeastern corner of the Tableland. Complex patterns of intersecting fault segments, splays, and faulting distributed on subparallel segments are apparent. Dashed curves represent west-dipping faults and solid curves represent east-dipping faults. Throw on the bold fault is plotted in Figure 7.

Figure 3. Contour plot of fault slip magnitude calculated with Poly3D code using a) paleostress tensor constrained by only seismic-scale faults and b) paleostress tensor constrained by seismic-scale faults and the additional northeast striking fault in the southwest corner. Contour interval is 10m. Principal stress orientations and magnitudes from the paleostress inversion are shown in the upper left corner.

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Figure 4. Stress contours (MPa) calculated for forward models using seismic- scale faults and the paleostress far field boundary condition. An isotropic, depth- dependent lithostatic stress state has been added to all model results. a) Map view of the greatest tensile stress (σ1) at the earth’s surface. Bold black lines indicate seismic-scale faults included in the model and thin black lines represent smaller faults. Vectors plotted on an evenly spaced grid represent principal stress orientations: σ1=white; σ2=blue; σ3=red. b) Greatest tensile stress contours on cross-section A-A’. Principal stress vectors are plotted the same as in (a). Black lines represent seismic-scale faults and black stars at the surface represent where the cross- section intersects traces of smaller faults. c) Maximum Coulomb stress calculated for friction coefficient µ=0.6. Black vectors indicate the orientation of predicted shear failure surfaces. Faults are represented as in (b).

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Figure 5. Maximum tensile stress (σ1) contours at the earth’s surface. Bold black lines represent faults included in each model and thin black lines represent smaller faults. Vectors plotted at grid points represent principal stress orientations: σ1=white; σ2=blue; σ3=red. Models represent a) all seismic-scale Tableland faults, b) all seismic-scale Tableland faults and White Mountain Fault (not on map), c) Fish Slough Fault only, d) Fish Slough Fault and White Mountain Fault (not on map). The paleostress tensor is used to prescribe remote boundary conditions for all models.

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Figure 6. Tetrahedral FEM mesh used for Dynel3D models. Vertical walls are numbered 1-5 for reference in the description of boundary conditions.

Figure 7. a) Distribution of throw along strike of the seismic-scale fault in bold in Figure 3. b) The trace of the fault is plotted to scale with the horizontal axis of the throw distribution.

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Figure 8. Cross section plots show contours and orientation (black tics) of maximum principal strain (ε1) for forward deformation as calculated from a) forward model, b) restoration model, and c) restoration model with reverse displacement boundary conditions. Cross sections strike east west, and are located at 4,146,500m northing, the same location as cross section A-A’ in Figure 4. Bold black curves represent the seismic-scale faults included in the models.

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Figure 9. Cross section plots show contours of vertical strain for forward deformation as calculated from a) forward model, b) restoration model, and c) restoration model with reverse displacement boundary conditions. Cross sections strike east west, and are located at 4,146,500m northing, the same location as cross section A-A’ in Figure 4. Bold black curves represent the seismic-scale faults included in the models.

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Figure 10. East-west striking cross-section plots located at 4,146,500m northing show displacement vectors calculated for forward deformation. a) Deformation vectors calculated from the forward model. Vectors lengths are drawn to scale with the cross section. b) Deformation vectors calculated from the restoration model. Vectors are exaggerated by a factor of 4. To maintain a consistent reference frame and avoid distorting vector fields with rigid body translation, the eastern boundary of each model is fixed in the horizontal, and vertical displacements are normalized such that the mean vertical displacement is zero. Bold black curves represent the seismic-scale faults included in the models.

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