JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 113, B12415, doi: /2008jb005809, 2008

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1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 113,, doi: /2008jb005809, 2008 Forces acting on the Sierra Nevada block and implications for the strength of the San Andreas fault system and the dynamics of continental deformation in the western United States N. P. Fay 1,2 and E. D. Humphreys 1 Received 18 May 2008; revised 18 August 2008; accepted 19 September 2008; published 30 December [1] We present an analysis of the forces acting on the Sierra Nevada block in the western United States. Vertically integrated loads acting on the block are quantified through numerical modeling of the state of stress in the interior of the block constrained by stress observations. The Sierra Nevada block is located adjacent to the Pacific North American plate boundary allowing determination of (1) the vertical distribution of shear stress at the plate boundary and the strength of the San Andreas fault system, (2) the horizontal distribution of shear stress coupling the Pacific and North American plates, and (3) the magnitude of stresses transmitted between rigid crustal blocks. We find that the San Andreas fault system supports a relatively large vertically integrated shear stress of 2.4 ± 0.4 TN/m to the northwest of San Francisco and only 0.3 TN/m to the southeast. The majority of this load is likely supported in the frictional portion of the crust, and therefore, the San Andreas fault system is both frictionally strong and weak. Shear stress coupling the Pacific and North American plates diminishes away from the plate boundary from 1.5 TN/m on the western margin of the Sierra Nevada block to 1.1 TN/m on the eastern side. A south directed load of 2.4 TN/m on the northern end of the block balances this reduction in shear stress across the Sierra Nevada block and indicates that the Sierra Nevada block is compressing the rigid Cascade fore arc from the south, contributing to the forces causing N S compression of the Pacific Northwest. Citation: Fay, N. P., and E. D. Humphreys (2008), Forces acting on the Sierra Nevada block and implications for the strength of the San Andreas fault system and the dynamics of continental deformation in the western United States, J. Geophys. Res., 113,, doi: /2008jb Introduction [2] Deformation of the lithosphere is a response to the forces applied to it. These forces arise from tectonic plate interaction, coupling to the convecting interior, and buoyancy variations internal to the lithosphere itself. The magnitudes of these forces remain difficult to determine, largely because of difficulty in directly observing stress magnitude and insufficient knowledge of the three-dimensional distribution of lithospheric strength. In this paper we focus on improving our understanding of the state of stress in the western U.S. continental lithosphere and thereby the forces driving its active deformation. We do so by identifying and quantifying the forces acting on the Sierra Nevada block (Figure 1). Three processes dominate western U.S. tectonics and dynamics: (1) shear owing to relative Pacific plate motion, (2) extension and compression related to 1 Department of Geological Sciences, University of Oregon, Eugene, Oregon, USA. 2 Now at Department of Geosciences, University of Arizona, Tucson, Arizona, USA. Copyright 2008 by the American Geophysical Union /08/2008JB005809$09.00 subduction of the Juan de Fuca plate, and (3) gravitational collapse of the elevated continental interior [e.g., Atwater, 1970; Flesch et al., 2000; Humphreys and Coblentz, 2007]. The Sierra Nevada block is a rigid crustal block [e.g., Dixon et al., 2000; McCaffrey, 2005] that is fortuitously located adjacent to the Pacific North American plate boundary fault system, the San Andreas fault system, the Cascadia subduction zone, and the high gravitational potential energy (GPE) Basin and Range province, and is thus well situated to study the influence of these processes in the western United States. [3] In our study we address three outstanding questions regarding the magnitude and distribution of stresses driving continental lithospheric deformation. First, a recurring question is the magnitude of coupling between the Pacific and North American plates and the long-term strength of the San Andreas fault (e.g., see Scholz [2006] for a review). We find that the San Andreas fault system has both frictionally weak and strong sections and that shear stress coupling Pacific and North American motion decreases away from the plate boundary and penetrates a limited distance into the Basin and Range province. Second, the vertical distribution of lithospheric strength is not clear [Jackson, 2002a, 2002b; Burov and 1of18

2 Figure 1. Map of study area showing elevation (gray scale), the Sierra Nevada block (double black line), faults (thin black lines), and motion of the Pacific plate (PAC) [DeMets and Dixon, 1999], Juan de Fuca plate (JdF) [Wilson, 1993; Miller et al., 2001], and Sierra Nevada block (SN) [Argus and Gordon, 1991; Dixon et al. 2000; McCaffrey, 2005] relative to North America (NA). The Oregon Coast block (OC, stippled) is that of Wells et al. [1998] and Wells and Simpson [2001]. The open boxes in the inset map indicate the areal coverage of this and subsequent figures. SEB, San Emigdio Bend; MTJ, Mendocino Triple Junction; GAR, Garlock fault; WLB, Walker Lane Belt; KM, Klamath Mountains region; SAF, San Andreas fault. Watts, 2006; Flesch et al., 2007; Thatcher and Pollitz, 2008]. We constrain the distribution of the present-day vertically integrated stress, and with knowledge of the thermomechanical evolution of the plate boundary, infer that the majority of the lithospheric strength is likely supported in the seismogenic portion of the crust. Third, the degree to which motion and deformation of the crust is driven by interactions of neighboring crustal blocks [e.g., Thatcher, 2007] or by coupling to a broadly deforming viscous upper mantle [e.g., Bourne et al., 1998; Whitehouse et al., 2005] is not resolved. Our modeling indicates the state of stress in the westernmost United States is strongly influenced by the interaction of the Sierra Nevada block and the Oregon Coast block [Wells et al., 1998] implying the dynamics of lithospheric deformation in the Pacific Northwest and California are related by stresses transmitted within the crust. 2. Observational Constraints [4] To constrain our modeling, we use observations of lithospheric stress orientation (maximum horizontal compressive stress, s Hmax ) and stress regime (e.g., extensional, strike-slip, compressional) shown in Figures 2 and 3. Stress observations used in this study are taken from the World Stress Map (WSM) [Zoback, 1992; Heidbach et al., 2007; J. Reinecker et al., The 2005 release of the World Stress Map, available at pub/stress_data/stress_data_frame.html], a global data set of s Hmax orientation determined largely from earthquake 2of18

3 Figure 2. Lithospheric stress observations in the westernmost United States from the World Stress Map (thin bars) [Heidbach et al., 2007; J. Reinecker et al., The 2005 release of the World Stress Map, available at and focal mechanism inversions (wide bars) [Provost and Houston, 2003]. Orientation of the bar indicates the direction of maximum horizontal compressive stress, and color gives stress regime parameter A Y [Simpson, 1997], with stress regime indicated with pairs of arrows above the scale. focal mechanisms, but also from in situ borehole stress measurements and young geologic stress indicators such as fault slip vectors and volcanic vent alignments. In the vicinity of the Sierra Nevada block (Figure 3), 75% of the WSM stress orientations are derived from earthquake focal mechanisms and the majority of the remainder from wellbore breakouts. The average quality of these data is B (J. Reinecker et al., The 2005 release of the World Stress Map, available at pub/stress_data/stress_data_frame.html), i.e., the orientation of s Hmax is known to within 20. [5] We supplement the WSM data set with a subset of the stress inversions in central and northern California obtained by Provost and Houston [2003]. The subset excludes relatively poorly known s Hmax orientations (uncertainty >35 ), and s Hmax determined from earthquake focal mechanisms that occur on major faults (see next paragraph). Figure 2 presents the entire data set in the westernmost United States, and Figure 3 presents the data in the vicinity of the Sierra Nevada block. Coverage is relatively complete along the western and eastern edges of block, although somewhat sparse along the center and northern end. 3of18

4 Figure 3. Stress observations in the vicinity of the Sierra Nevada block. Seven stress observations that were obviously different from their neighbors (bars with thick outlines) were removed from the data set to decrease very short wavelength variations in stress orientation or regime in the interpolation of Figure 4. This removal does not significantly affect our results or interpretations. The two black and white bars in the southeast corner of the block were added to prevent a sharp bend in the interpolated stress field of Figure 4. [6] Most stress indicators are in fact strain indicators from which stress is inferred [e.g., Zoback and Zoback, 1980] and we assume that stress and strain tensors are isotropic. There are potential problems with this assumption when anisotropic material properties are present and may cause stress and strain tensors to be misaligned [e.g., McKenzie, 1969; Bird, 2002]. For example, the focal mechanism inversions of Provost and Houston [2003] are grouped into on-fault and off-fault bins, i.e., events that are located on (or very near) and away from active faults (San Andreas, Maacama, Bartlett Springs, etc.). The on-fault s Hmax orientation observations, based on focal mechanism inversions, are likely biased by the fact that these are dominantly vertical strike-slip faults and can only accommodate horizontal motion in their strike direction. The focal mechanisms for events on these faults will place the compressional axis (s Hmax for a strike-slip event) near 45 to the fault, no matter the actual orientation of true maximum horizontal compressive stress. Provost and Houston [2003] note a systematic difference between onfault and off-fault s Hmax orientations, consistent with this behavior. We therefore use only the off-fault data where, presumably, stress-strain anisotropy is less severe and focal mechanism estimates of s Hmax are more reliable. In a regional sense, azimuthal consistency of s Hmax observations from different depths and deformation styles [Zoback and Zoback, 1980] suggests this problem should not significantly bias our estimate of the regional stress field. [7] In addition to s Hmax orientation, we use information on stress regime, which is an indication of the relative magnitudes of principal stresses and which one is vertical. The WSM provides this information in categories (compressional, strike- slip, extensional, transitional, or unknown), whereas Provost and Houston [2003] provide a quantitative measure of the relative magnitude of the principal stresses (called a form ratio). We recast all of these regime estimates into the term A y [Simpson, 1997], which ranges from 0 to 180 and is a continuous function of relative principal stress magnitudes. (Strictly speaking, A Y is an angular measure from 0 to 180 though we consider it a unitless variable to avoid confusion with s Hmax orientation.) A y < 90 indicates tensional to transtensional stress regime, and A y > 90 indicates transpressional to compressional stress regime. In Figures 2 and 3, A y lies between 30 (pure normal faulting) and 150 (pure thrust faulting), with the majority of the data in the range 60 < A y < 120. Data from the WSM with unknown regime were given values according to a distance-weighted nearest-neighbor interpolation. 4of18

5 Figure 4. The s Hmax orientation and stress regime smoothed and interpolated to the centers of the quadrilateral finite element mesh (thin gray lines). These stresses are used to constrain our modeling. [8] Several general features of the data in Figures 2 and 3 deserve discussion. First, s Hmax is orientated NE SW along the San Andreas fault and progressively rotates more N S as one moves to the NE. This stress rotation is strongest at the northern end of the Sierra Nevada block and is consistent with the N S s Hmax direction and N S compressive stress in western Oregon and Washington (Figure 2) [Wang, 2000; Lewis et al., 2003]. Second, the majority of the stress indicators in and near the Sierra Nevada block indicate strike-slip stress regime (A y near 90). This may be expected considering the region is dominated by shear strain accommodating Pacific plate relative motion. [9] Third, the stress data along the western margin of the Sierra Nevada block indicate a mixture of strike slip and compression, consistent with the active strike-slip faulting on the San Andreas and subordinate faults and compression perpendicular to the San Andreas associated with shortening and uplift of the California Coast Ranges [Namson and Davis, 1988;Wentworth and Zoback, 1989; Unruh and Moores, 1992; Page et al., 1998]. This mix of compressional and strike-slip deformation style indicates the s 1 (principal stresses s are boldfaced and s 1 > s 2 > s 3 ) is horizontal and s 2 and s 3 are similar in magnitude. Fourth, the data along the eastern margin of the Sierra Nevada block indicate a mixture of strike slip and tension, consistent with local tectonics of shear strain accommodating the relative motion of the Sierra Nevada block [Unruh et al., 2003; Faulds et al., 2005] and extension at this westernmost extent of the Basin and Range province [e.g., Wernicke, 1992; Wernicke and Snow, 1998]. This mix of strike-slip and normal faulting indicates s 1 and s 2 are similar in magnitude and s 3 is horizontal. [10] Fifth, s Hmax data at the northern end of the block in the Klamath Mountains region are sparse. There is little historic seismicity in this region and geologic strain indicators are rare. This is not surprising given that the Euler pole for the relative motion of the adjacent Oregon Coast and Sierra Nevada crustal blocks lies between them [Wells et al., 1998; Wells and Simpson, 2001]. Nonetheless, NW SE shortening at the northern end of the Sierra Nevada block [Unruh et al., 2003], contemporary NW SE shortening near the Oregon-California border [Hemphill-Haley, 1999; Hammond and Thatcher, 2005; Kreemer and Hammond, 2007], and the fact that surrounding s Hmax orientations are consistently NW SE to N S, suggest the Klamath Mountains region is under tectonic compression oriented NW SE. [11] The stress field that we wish to model is that created by regional loads acting on the Sierra Nevada Great Valley lithosphere, and this field is relatively smooth compared to the scale of the loads and the thickness of the lithosphere. We therefore smooth and interpolate the observed stress data using the algorithm of Hansen and Mount [1990]. This both interpolates information into areas where data are sparse and removes short wavelength features that originate from noise and small-scale processes that we are not interested in (and cannot model). The stress regime and s Hmax orientation data 5of18

6 Figure 5. The angle (b) between s Hmax and the western margin of the Sierra Nevada block (i.e., the San Andreas fault system) as a function of distance from the northwest end of the block (star). The dots in inset map show location of data points within 100 km of the western edge of the block. The mean values of b in the gray northern and southern regions are significantly different to greater than 99% statistical confidence. Angle b determined from the smoothed and interpolated stress field (Figure 4) for the elements adjacent to the western side of the block is given with the double black line. The jagged nature of the interpolated values is because the boundary of the block is defined by a discrete number of points connected by straight line segments; adjacent segments can differ in orientation by as much as MTJ, Mendocino Triple Junction; SEB, San Emigdio Bend. are mapped onto the mesh shown in Figure 4. This long wavelength stress field is seen to represent the observed data well, and is consistent with regional tectonics and geologic data. Thus, Figure 4 provides a reasonable estimate of the relatively long wavelength tectonic stress field that we use to constrain our modeling. [12] The angle b between the maximum horizontal compressive stress and local fault strike is indicative of the relative magnitudes of shear and normal stress resolved on the fault plane; a relatively large normal or small shear stress results in an increase in b. The large angle between the San Andreas fault and s Hmax (approaching 90 ) in central California implies the San Andreas fault supports relatively little long-term shear stress [e.g., Mount and Suppe, 1987; Zoback et al., 1987; Townend and Zoback, 2001]. Figure 5 shows a progressive increase in b as a function of distance from the Mendocino Triple Junction (i.e., from the incipient northern San Andreas fault system to the mature fault at San Emigdio Bend). This trend in b was noted by Provost and Houston [2003] as evidence for a reduction in fault strength along strike, although b also depends on the magnitude of stress normal to the fault, which may also vary along strike. We explicitly test this hypothesis in our modeling, discussed in the next section. 3. Geodynamic Modeling: Quantifying the Loads Acting on the Sierra Nevada Block [13] Our primary modeling objective is to quantify the loads acting on the Sierra Nevada block and the stress they create in its interior. To do so, we calculate the stress field from individual loads and invert for the linear sum of these fields that best fits the smoothed data shown in Figure 4. Below we discuss (1) the forward modeling to obtain the stress field resulting from each modeled load, (2) the various modeled loads acting on the Sierra Nevada block, and (3) the inversion procedure and results. We use stress to refer to deviatoric stress (i.e., the total stress tensor minus pressure, (s 1 + s 2 + s 3 )/3), and load refers to the vertically integrated stresses acting on the sides of the Sierra Nevada block, expressed in TN/m (10 12 N/m), and subduction related basal tractions acting on the base, expressed in Pa Governing Physics and Forward Modeling [14] Dynamic equilibrium requires that the vector sum of torque acting on the plates on the Earth s surface be zero [e.g., Solomon and Sleep, 1974; Chapple and Tullis, 1977], i.e., X Z * * r F da ¼ 0; ð1þ N where r * is the vector from the Earth s center to the point at which the force F * from load N is applied. Integrated over the area da of plate P, these torques sum to zero. This applies to any arbitrary area, and we choose the Sierra Nevada block (or microplate [e.g., Argus and Gordon, 1991]), because it is a long-lived and rigid piece of lithosphere in the plate boundary deformation zone. The Sierra Nevada block is also largely bounded by faults allowing us to estimate the stresses supported by those faults. [15] To calculate the stress field within the Sierra Nevada block arising from each load, we adopt the basis function approach following Reynolds et al. [2002]. This is accomplished in three steps. First, the total torque (T t ) from each 6of18

7 Figure 6. Gravitational potential energy per unit area (GPE) in the western United States from Humphreys and Coblentz [2007]. The gradient in GPE (black arrows) is largest within the Sierra Nevada block (double black line) and generally is directed to the southwest. Death Valley (see text) is indicated with the white dot. unit load is calculated with the left-hand side of equation (1). Second, an accompanying basal traction field, distributed over the entire base of the plate, is determined analytically [Solomon and Sleep, 1974] that exactly cancels T t such that the total torque is zero. Third, the resulting stress field within the block from the load and its basal traction field is found by solving the equilibrium equations with the finite element method using the commercial code ABAQUS. Because the data do not provide full three-dimensional constraint on the state of stress on scale of this study, the Sierra Nevada block is treated as a thin (two-dimensional) elastic cap in spherical coordinates and we model vertically integrated stresses. The finite element mesh consists of 288 nodes and 249 linear elements (e.g., see Figure 4). The density of elements was chosen so as to adequately capture the relatively long wavelength variations in stress observations (Figure 4) while minimizing the number of elements. With this method, each load (with its basal traction field) is torque free, and the stress fields (basis functions) can be summed linearly and compared to observations. In the inversion (section 3.3) we seek the scalar multiples of the stress field basis functions such that the sum best matches the data Loads Acting on the Sierra Nevada Block Gravitational Potential Energy [16] Horizontal variations in the vertical distribution of lithospheric density create gravitationally driven stresses that must be balanced by applied forces or frictional and viscous resistance to deformation [Artyushkov, 1973; Fleitout and Froidevaux, 1982; Molnar and Lyon-Caen, 1988]. Gravitational potential energy per unit area (GPE), the vertically integrated lithospheric density moment [e.g., Fleitout and Froidevaux, 1982; Jones et al., 1996], provides a quantitative measure of the lateral variations in lithospheric buoyancy. High GPE in the western United States, owing in part to relatively buoyant upper mantle [e.g., Thompson and Zoback, 1979], is thought to be responsible for driving extension in the Basin and Range province [Jones et al., 1996; Flesch et al., 2000, 2007; Humphreys and Coblentz, 2007], westward motion of the Sierra Nevada block, extension in eastern California, and shortening in the California Coast Ranges [Eaton, 1932; Jones et al., 2004]. [17] Figure 6 shows GPE in the westernmost United States [Humphreys and Coblentz, 2007], calculated using the CRUST2.0 crustal thickness model (Laske et al., The Reference Earth Model Web site, rem.html) and the geoid. Assuming local isostasy, the horizontal stress generated by lateral variations in GPE is simply the difference of GPE in adjacent columns. The largest gradients in GPE in the western United States occur across the Sierra Nevada block (Figure 6), where GPE variation of 1.8 TN/m occurs over less than 100 km. The dominant effect of GPE variations on the Sierra Nevada 7of18

8 Figure 7. Stress applied to the Sierra Nevada block owing to variations in GPE. Black vectors show the difference in GPE of adjacent elements applied perpendicular to their shared element face. The dominant effect of the relatively high GPE on the eastern side and low GPE on the western side of the block is a net southwest push with an average magnitude of 1.5 TN/m (integrated perpendicular to the long axis of the block). block is a SW directed push [Flesch et al., 2000; Hammond and Thatcher, 2004; Jones et al., 2004]. The GPE load is included in the finite element model by applying the difference in GPE of adjacent elements as a stress on their shared element edge (Figure 7), following Richardson and Reding [1991]. This GPE load is based on GPE gradients estimated in absolute value and therefore is taken as known and not varied during the inversion San Andreas Fault [18] The Sierra Nevada block is bounded on the west by the faults composing the San Andreas fault system in central and northern California that accommodate the 35 mm/a of relative Pacific Sierra Nevada motion [Sieh and Jahns, 1984; Freymueller et al., 1999]. The amount of longterm shear stress supported by large-offset faults such as the San Andreas is not well known [e.g., Zoback et al., 1987; Scholz, 2000; Townend and Zoback, 2004; Scholz, 2006]. Humphreys and Coblentz [2007] estimate an along-strike average of the vertically integrated shear stress supported by the San Andreas fault system of 1.5 ± 0.5 TN/m. We incorporate this constraint from the plate-scale stress modeling in North America. We require that the integrated force for the shear load acting on the western margin of the Sierra Nevada block be the same as for a uniform shear load of 1.5 TN/m, but allow the shear stress to vary along strike in several ways shown in Figure 8. Two basis functions are constructed that connect to form a smooth step function. We have also tried uniform and linear-taper basis functions. The step function shear load results in models that match the data significantly better, especially near the San Andreas fault. Our San Andreas perpendicular basis function is the sum of two loads, one that is constant along the length of the block and one with a constant slope. This allows for the possibility of along-strike change in normal stress that may contribute to the change in b (Figure 5) Garlock Fault [19] The left-lateral Garlock fault [e.g., Davis and Burchfiel, 1973] bounds the southern end of the Sierra Nevada block and accommodates NE relative motion of the Mojave block. It is dominantly a transform structure, but active shortening approximately perpendicular to the fault [Keller et al., 1998, 2000; Stein and Thatcher, 1981] suggests the Sierra Nevada block is being compressed across the fault. We use two basis functions, one parallel to the strike of the Garlock to represent shear stress and one perpendicular to represent normal stress Walker Lane Belt [20] The Sierra Nevada block is bounded on the east by the Walker Lane Belt, a transtensional fault system accommodating 12 mm/a of approximately NNW motion of the Sierra Nevada block relative to the continental interior [Argus and Gordon, 1991; Hearn and Humphreys, 1998; Dixon et al., 2000; Oldow, 2003; Unruh et al., 2003; McCaffrey, 2005]. The Walker Lane Belt has accumulated less net offset and is structurally immature compared to the San Andreas fault [Wesnousky, 2005a], and becomes progressively younger and less organized to the north [Faulds et al., 2005; Wesnousky, 2005b]. If shear stress supported by a fault system depends on its structural organization, the Walker Lane Belt may weaken to the south. However, because of the relatively sparse data along the eastern margin of the Sierra Nevada block we use a uniform shear 8of18

9 Figure 8. Various shear stress basis functions used for the San Andreas fault system. Curves show load (vertically integrated shear stress) applied to the western side of the Sierra Nevada block as a function of distance from the NW end of the block. The total force (area under the curve) for the linear taper (dashed line) and smooth step function (solid line) is the same as for the uniform 1.5 TN/m load (dash-dot-dashed line). The best fitting model utilizes the smooth step function that decreases from 2.4 TN/m to 0.3 TN/m (values determined by the inversion, see sections 3.3 and 3.4). The location and wavelength of the step was chosen to correspond to the change in angle between s Hmax and fault strike shown in Figure 5. stress basis function for simplicity. A Walker Lane Belt perpendicular basis function is applied on the southeast end of the block, south of 38 N, to determine whether the data require any tensional stress associated with Basin and Range extension there. Experiment has shown that a tensional load along the entire length of the Sierra Nevada block is rejected by the data, and so such a basis function is not included Klamath Mountains [21] The northern boundary of the Sierra Nevada block lies in the Klamath Mountains region of northern California. Sparse seismicity [Miller et al., 2001; Wells and Simpson, 2001] and diffuse geodetic shortening [Hammond and Thatcher, 2005; Williams et al., 2006] do not suggest there is a distinct boundary between the two provinces. Therefore we have drawn the northern end of our Sierra Nevada block simply, so as to connect the San Andreas faults on the west to the Walker Lane Belt on the east. To minimize possible model dependence on the imperfectly known shape of the northern end of the block, we apply two orthogonal basis functions, one parallel and one perpendicular to the long axis of the block, and seek their vector sum Subduction Basal Tractions [22] The northern end of the Sierra Nevada block is adjacent to the Mendocino Triple Junction (Figure 1) and therefore overlies the subducting Juan de Fuca/Gorda plate (Figure 1). Stress can be exerted on the overriding plate in a subduction system either via direction contact [e.g., Bird, 1988] or by coupling to trenchward mantle flow induced by the subducting slab [e.g., Wdowinski and O Connell, 1991]. The southern Juan de Fuca (Gorda) plate dips steeply beneath the Sierra Nevada block and is 100 km below the majority of the block [McCrory et al., 2006]. Therefore stresses exerted by direct contact with the subducting slab are unlikely to be important and we consider only the coupling to the flow in the mantle wedge. [23] The Juan de Fuca plate is subducting obliquely relative to North America. We combine Euler poles of Sierra Nevada North America ( W, N, /Ma [McCaffrey, 2005]) and Juan de Fuca North America relative motion ( E, N, /Ma, [Miller et al., 2001]) to derive a Juan de Fuca Sierra Nevada pole of rotation ( E, 7.52 N, /Ma). The expected mantle flow direction, driven by relative motion of the Juan de Fuca with respect to the Sierra Nevada block, has both trench-perpendicular and trench-parallel components and is shown in Figure 9. This is not meant to represent the entire mantle flow field, rather only that caused by subduction. This predicted mantle flow direction ignores the toroidal component of mantle flow caused by a finitelength subducting Juan de Fuca slab [Piromallo et al., 2006; Zandt and Humphreys, 2008], although the effect on the basal traction field is relatively small at this particular location [Zandt and Humphreys, 2008]. [24] The magnitude of mantle flow basal tractions must in some way decrease as a function of distance from the trench and subducting plate. We assume that these tractions taper linearly over a distance of 300 km from the northwest end of the block (see Figure 9). This is the only basis function in our model evaluated in units of stress (Pa), compared to the vertically integrated stress units (N/m) of the other loads Inversion Procedure [25] The inversion seeks the scalar multiples of the stress field basis function that produce a net stress field that best matches the data. The modeled stress tensor in each element provides two values, s Hmax orientation and stress regime A Y. We use a simulated annealing algorithm to minimize the misfit function 1 X n M ¼ 1 þ D i m q i d q i qs 2! þ D m A Yi d A 2 Yi 2 AY s g i g m! ; ð2þ 9of18

10 Figure 9. Motion of the Juan de Fuca/Gorda plate and modeled tractions on the base of the Sierra Nevada block caused by subduction-induced mantle flow. Open vectors show the motion of the Juan de Fuca relative to North America and gray vectors show relative to the Sierra Nevada block (see text for Euler poles and references). The predicted tractions induced by this oblique subduction on the base of the Sierra Nevada block (black vectors) have a component toward the trench (corner flow in the mantle wedge) and a component of northward shear. We expect these tractions will diminish with distance from the subducting plate and therefore taper the magnitude linearly over 300 km from the northernmost end of the block. where M is model misfit, d and m represent data and model respectively, q is azimuth of s Hmax, qs is one standard deviation of d q, g i is the surface area of element i, g m is the mean element surface area, AY s is one standard deviation of d A Y, and D is a used to weight the data types. We find that the results are not strongly dependent on D, indicating s Hmax and A Y provide similar constraint, and therefore set D = 1 (equal weighting). Misfit is scaled by relative element surface area (g i /g m ) so that misfit is not influenced by the distribution of elements. This misfit function resembles a least squares c 2 misfit metric though we do not refer to it as such because the number of model-data comparisons (n) is not fixed in that it depends on the coarseness of our finite element mesh. We have found that our results, however, do not depend strongly on mesh density. We have also found that a similar L 1 norm produces similar results. [26] The observation uncertainties ( q s and AY s) are assigned as follows. J. Reinecker et al. (The 2005 release of the World Stress Map, available at uni-karlsruhe.de/pub/stress_data/stress_data_frame.html) classify the WSM according to data quality. Quality A data have s Hmax known to within 15,qualityBtowithin20 and quality C to within 25. We use A, B, and C quality data that have an average uncertainty of 20. We take this value as 95% confidence and assign q s =10. Uncertainty in stress regime, AYs, is assigned the same value. [27] Parameter uncertainties are estimated in two different ways. First, we simply estimate the model parameters with two assumed San Andreas shear loads (1.0 and 2.0 TN/m, as deemed permissible by Humphreys and Coblentz [2007]) and difference the these estimates for each parameter. More formally, we numerically calculate the parameter covariance matrix for the best fit model. The results from these independent methods agree to within 0.1 TN/m and the one standard error uncertainties using the first method are presented in this paper Results [28] The results of the best fitting model are shown in Figures Figure 10 shows the loads acting on the edges (black vectors) and base (gray vectors) of the Sierra Nevada block. All of the loads are resolvable and statistically different from zero, i.e., their magnitudes are greater than twice their uncertainties (95% statistical confidence) indicating each makes an important contribution to the total stress field. [29] The San Andreas fault dextral shear load diminishes from 2.4 ± 0.4 TN/m (1 standard error uncertainties) in the northwest to 0.3 ± 0.1 TN/m in the southeast via the smooth step function in Figure 8. The San Andreas fault normal load increases from 1.6 ± 0.4 TN/m near the Mendocino Triple Junction to 2.1 ± 0.4 TN/m at the southeast end of the block. This compression is consistent with active San Andreas fault perpendicular shortening [Wentworth and Zoback, 1989; Argus and Gordon, 2001], and possibly the result of compression of the Sierra Nevada block into the Pacific Plate by local GPE gradients [Jones et al., 2004]. Although the data prefer a larger compression to the south, this is not particularly well resolved because the magnitude of the linear taper component of the load (0 0.5 TN/m) is not significant (uncertainty of 0.4 TN/m). This is because the difference in predicted stress field values, s Hmax orientation and A Y, for the loads in Figure 11 and for a model with a uniform San Andreas perpendicular load (1.6 TN/m), are small (e.g., <5 for s Hmax azimuth). [30] The 1.1 ± 0.2 TN/m of shear supported by the Walker Lane Belt is smaller than the 1.5 TN/m of average shear on the San Andreas fault by 25%, indicating a 10 of 18

11 Figure 10. Best fitting set of loads acting on the Sierra Nevada block. Load magnitudes are expressed in TN/m for all loads acting on the sides (black vectors) and MPa for the subduction-related basal tractions (gray vectors). Shear load vectors are shown offset from the edge of the block for clarity. Values in parentheses give one standard error uncertainties. GAR_shear and GAR_norm give the loads representing shear and normal stress on the Garlock fault. WLB_shear gives the shear load acting in the Walker Lane Belt on the eastern side of the block. DV_norm represents the normal load on the southeast corner of the block south of 38 N. Klamath_SW and Klamath_SE (not shown) are the two orthogonal loads at the northern end of the block that sum to Klamath_tot oriented S9 E. SAF_shear gives the San Andreas shear stress that changes along strike from 2.4 TN/m to 0.3 TN/m according to the smooth step function in Figure 8. SAF_norm gives the load normal to the San Andreas that increases linearly from northwest to southeast. modest reduction of shear stress with distance from the plate boundary. A small tensional normal load (0.8 ± 0.2 TN/m) is resolved along the southeast end of the block. The blockperpendicular and block-parallel loads at the northern end of the block (Klamath_SW and Klamath_SE, not shown in Figure 10) sum to 2.4 ± 0.4 TN/m (Klamath_tot in Figure 10) oriented approximately south (S9E). [31] The stress field resulting from this set of loads is shown in Figures 11 and 12. Figure 11 portrays the stress tensor in each element as the orientation of s Hmax and stress regime parameter. Figure 12 shows the orientation and magnitude of the horizontal principal stresses (vertically integrated); s 1 and s 3 are horizontal nearly everywhere, indicating the stress field is dominated by strike-slip state of stress with localized areas of compression in the NW and SW regions and localized tension along the SE margin. The long wavelength southwest to northeast counterclockwise rotation in s Hmax is recovered by the model, and the predicted stress regime (Figure 11) is similar to that observed. The north to south clockwise rotation of s Hmax along the western margin of the block, largely related to the decrease in shear load along the San Andreas fault system, is also successfully produced by the model. [32] Vertically integrated horizontal principal stress magnitudes average 1.7 TN/m in compression and 1.3 TN/m in tension. Averaged over a 100 km thick lithosphere, these values correspond to 17 MPa and 13 MPa, respectively, consistent with the vertically averaged deviatoric stress magnitudes of 10 MPa estimated in western North America [Flesch et al., 2007; Humphreys and Coblentz, 2007]. The largest principal stress (3.1 TN/m of compression, 31 MPa averaged over 100 km) occurs in the far NW part of the block. This is where the relatively large San Andreas fault, Klamath, and subduction basal traction loads converge (Figure 12), causing strong compression. [33] Misfit between model and data is shown in Figure 13. In general, the model fits the data well and the misfits in s Hmax and stress regime are relatively small; the rootmean-square misfit in s Hmax azimuth is 7.5 and 13.8 in stress regime, indicating we are fitting the data to within their uncertainties more often than not. The misfits are approximately normally distributed with near-zero means (Figure 13, inset) indicating the inversion is not likely to be significantly biased by outliers. The total misfit (equation (2)) is and 0.25 normalized by the number of observations (twice the number of elements). The model overpredicts compression at 11 of 18

12 Figure 11. Best fitting stress field resulting from the loads in Figure 10. Bars give orientation of s Hmax, and color illustrates stress regime (as in Figures 2 4). Most of the Sierra Nevada block experiences a strike-slip state of stress (green), with localized areas of transpression (light blue) and transtension (yellow/ orange). The model successfully captures the variation in orientation of s Hmax along the western side of the block from 45 to the edge of the block in the northwest to nearly perpendicular in the southeast. the northern end of the block but successfully predicts s Hmax orientation there. The model underpredicts compression in the SW corner of the block although an additional San Andreas fault normal load related to compression of the Sierra Nevada block and western Transverse Ranges [e.g., Bohannon and Howell, 1982] is rejected by the data because it degrades the fit to s Hmax orientation more than it improves the fit to A Y. [34] An alternative model with the San Andreas shear load constrained to linearly decrease from 3.0 TN/m in the northwest to 0 TN/m in southeast (see Figure 8), results in the same best fit set of parameters (to within their estimated two standard error uncertainties) and a 4% increase total misfit (126.9). However, the step function model is most consistent with the stress observations near the San Andreas fault, where data are most abundant (Figures 2 and 3) and the interpolated values constraining our modeling are most robust. For example, holding the other parameters in Figure 10 fixed, the linear taper shear load produces a stress field that increases the average misfit in s Hmax by 7.5 for all data, and 12.9 for data adjacent to the San Andreas fault system. In either case, it is clear the data are most consistent with a strong decrease in shear load along strike and we take the step function as the preferred model. 4. Discussion 4.1. Strength of the San Andreas Fault System and Evolution of the Pacific North American Plate Boundary [35] We find that the vertically integrated strength of the San Andreas fault system changes by approximately a factor of 8 along its length, from 2.4 ± 0.3 TN/m between the Mendocino Triple Junction and San Francisco Bay to 0.3 ± 0.1 TN/m to the southeast in central California. We also find that the load normal to the San Andreas fault increases to the southeast, but this is insufficient to reorient b as much as is observed (Figure 5), corroborating the suggestion of Provost and Houston [2003] the shear strength of the San Andreas decreases to the southeast. The relatively large San Andreas shear load on the northern end of the block is required to produce NE SW s Hmax orientation in northern California and to drive the Sierra Nevada block into Oregon to create the N S s Hmax observed there. At the southern end of the block, the high angle of s Hmax to the San Andreas fault requires a low applied shear load. 12 of 18

13 Figure 12. Best fitting stress field shown as principal stress orientation and magnitude. Black indicates compressional, and white indicates tensional (deviatoric) stress. Everywhere except in the extreme NW and SW corners of the block (where s 3 is vertical) s 1 and s 3 are horizontal, indicating a dominantly strike-slip stress regime. The average horizontal principal stress magnitude is 1.5 TN/m (15 MPa averaged over a 100 km thick plate). [36] Active deformation away from the San Andreas fault is also consistent with this distribution of plate boundary shear load. For example, if we constrain the San Andreas fault system shear load to be more uniform and taper from 2.0 to 0.8 TN/m, and invert for the remaining parameters, the load normal to the Garlock fault is found to be 0 TN/m. Such a low normal load is inconsistent with the approximately Garlock-normal shortening and left-lateral faulting occurring in the southern San Joaquin Valley [e.g., Stein and Thatcher, 1981; Bawden, 2001]. [37] Low vertically integrated shear stress requires little long-term lithospheric strength at all depths, and attributing significant plate margin strength to viscous deformation processes occurring at subseismogenic depths is difficult along the San Andreas fault system. This would require subseismogenic lithospheric strength to somehow vary laterally in just the manner that the seismogenic fault strength varies. However, at the northern end of the San Andreas fault system, progressive removal of the Gorda slab associated with northward propagation of the Mendocino Triple Junction is accompanied by asthenospheric upwelling and lithospheric heating [Lachenbruch and Sass, 1980; Zandt and Furlong, 1982; Furlong et al., 1989], and thus we expect the lower crust and lithospheric mantle beneath the northern San Andreas fault system to be weaker than to the south. Therefore the majority of the shear load is likely held in the seismogenic portion of the crust, consistent with the arguments of Jackson [2002a, 2002b] and Flesch et al. [2007]. [38] If the shear load is supported entirely in the seismogenic crust (upper 15 km [Nazareth and Hauksson, 2004]), 2.4 and 0.3 TN/m produce 160 and 20 MPa, respectively, of depth-averaged shear stress supported by the San Andreas fault system. These stresses are consistent with the strong and weak predictions of Byerlee-type friction [Byerlee, 1978] with friction coefficients of >0.6 and <0.2, respectively. Thus, the high strength [Scholz, 2000] and anomalous weakness [e.g., Zoback et al., 1987] attributed to the San Andreas fault system are not ubiquitous and it appears to exhibit both frictionally strong and weak behavior. [39] The marked transition in San Andreas fault system shear strength coincides spatially with the transition from multiple subparallel faults in the NW to a structurally simple, single strand south of San Juan Bautista, where the San Andreas fault creeps. This suggests that the degree of structural organization and simplification, which tend to increase as fault systems accumulate offset [Wesnousky, 1988, 2005a], is strongly related to the amount of stress they can support. Structurally complex fault systems maintain high strength because the individual faults may be strong, but also because they are separated by high strength, intact regions that may decrease the frequency of seismogenic stress drops by inhibiting throughgoing earthquake ruptures that nucleate elsewhere. If the individual fault segments in northern California support stresses on the order of 100 MPa, the absence of a frictionally generated heat flow anomaly [Lachenbruch and Sass, 1980] suggests the importance of advective heat transport [Scholz, 2006] or dynamic weakening [e.g., Sibson, 1973; Di Toro et al., 2004] to allow earthquake slip at stresses much smaller than the static value. [40] Fault weakening mechanisms such as anomalous pore pressure [Rice, 1992] or frictional [Moore and Rymer, 13 of 18

14 Figure 13. Misfit between the smoothed observed (Figure 4) and model-predicted (Figure 12) stress fields. The orientation of the bars gives the angular misfit of s Hmax azimuth; bars oriented at 0 azimuth indicate perfect fit, and bars oriented at 90 azimuth indicate complete misfit. The mean and standard deviation of s Hmax misfit are 0.5 and 7.5, respectively. Color gives misfit of the stress regime parameter A Y where blue/red indicates the model is overpredicting/underpredicting compression. The mean and standard deviation for A Y misfit are 3.5 and 13.3, respectively. The histograms show A Y (shaded) and s Hmax (open) normalized misfit, i.e., misfit divided by the maximum possible misfit (90 for s Hmax and 180 for A Y ). 2007] properties at the creeping section of the San Andreas fault may severely limit the amount of tectonic shear stress it can support. However, our model also prefers low levels of shear stress to the SE of Parkfield, where the San Andreas fault is seismogenic, leading us to conclude that the mechanism(s) allowing it to creep cannot alone explain the absence of large shear stresses Distribution of Pacific North America Shear Stress in the Western United States [41] Shear stress and strain clearly dominate near the Pacific North American plate boundary. The Sierra Nevada block is bounded on the west by the predominantly strike-slip San Andreas fault system and on the east by the transtensional Walker Lane Belt. Shear deformation is not active east of central Nevada [Thatcher et al., 1999; Bennett et al., 2003; Hammond and Thatcher, 2004] where extension dominates in the Basin and Range. The finite width of shear strain penetration across the continental margin is consistent with the San Andreas transform system being of finite length [England et al., 1985; Sonder et al., 1986; Sonder and Jones, 1999]. [42] We find 1.1 TN/m of vertically integrated shear stress in the Walker Lane Belt, which is 25% less than the alongstrike average of 1.5 TN/m along the San Andreas fault system. Further inland, Pacific North American shear stress appears to diminish to negligible values in central Nevada [Humphreys and Coblentz, 2007], similar to the distribution of active deformation. This suggests that present-day deformation in the western Basin and Range is driven largely by plate interaction stresses, consistent with the observations that western Basin and Range strain is generally anticorrelated with that predicted by lithospheric buoyancy variations [Hammond and Thatcher, 2004]. [43] Postorogenic extension prior to the inception of the San Andreas fault shear system [Sonder and Jones, 1999; Liu, 2001] suggests GPE gradients may have been sufficient to drive significant extension in the past, although the results just discussed suggests that contemporary deformation in the western Basin and Range is dominated by plate interaction shear stress that modulates an equal or lesser buoyancy related tensional stress field [Flesch et al., 2000; Flesch et al., 2007]. Progressive rotation of principle extension directions in the Basin and Range that closely track the NW migration of the Mendocino Triple Junction [Zoback et al., 1981; Bird, 2002], and strong temporal correlation between changes in motion of the Pacific plate and Sierra Nevada 14 of 18

15 block [Atwater and Stock, 1998; Wernicke and Snow, 1998], suggest this plate interaction influence on Basin and Range deformation has existed since the inception of the San Andreas fault system and should increase in spatial extent as the San Andreas fault system lengthens Sierra Nevada Block and the Dynamics of the Pacific Northwest [44] Force balance on the Sierra Nevada block and western Basin and Range lithosphere requires that the decrease in Pacific North American shear stress with distance from the plate boundary be balanced by a S SE directed load. One possibility is a S SE directed shear traction on the base of the lithosphere, although long wavelength [e.g., Becker and O Connell, 2001] or more local [Zandt and Humphreys, 2008] estimates of mantle flow do not produce tractions on the base of the western United States lithosphere with the correct orientation. The alternative source of the S SE load is a compressional/ tensional load acting on vertical planes on the northwestern/ southeastern ends of the Sierra Nevada block. We find a relatively large compressional load, oriented SSE, on the northern end of the Sierra Nevada block (2.4 ± 0.4 TN/m, Klamath_tot of Figure 10). This load balances the excess (0.4 TN/m) NW-directed load on the block owing to the lesser along-strike average Walker Lane Belt shear compared to the San Andreas fault system, the NW directed subduction-related basal tractions, and the 1.0 TN/m NW-directed compressive stress across the Garlock fault. [45] The compressional load on the northern end of the Sierra Nevada block, similar in orientation to the N S mean orientation of s Hmax in western Oregon and Washington (Figure 2), reveals dynamic crustal interaction of the Sierra Nevada block and the rigid Cascade fore arc (hereafter referred to as the Oregon Coast block [e.g., Wells et al., 1998]). Clockwise rotation and northward migration of the Oregon Coast block is well documented in geologic and geophysical data [Magill and Cox, 1981;Magill et al., 1982; Sheriff, 1984; Pezzopane and Weldon, 1993; Walcott, 1993; Wells et al., 1998; McCaffrey et al., 2000; Wells and Simpson, 2001; Lewis et al., 2003; McCaffrey et al., 2007]. The northward motion of this rigid block into the nondeforming Canadian lithosphere results in N S compressive stress (Figure 1) and shortening in the Puget Sound region [e.g., Wells et al., 1998; Wang,2000]. [46] Oblique subduction of the Juan de Fuca plate beneath western North America (Figure 1) [Wilson, 1993] may drag the Oregon Coast block northward and contribute to N S compression in the Pacific Northwest. However, the south directed load on the northern end of the Sierra Nevada block cannot be explained by subduction alone and implies that the Sierra Nevada block pushes northward on the Oregon Coast block with an appreciable total force. This is consistent with E W folding and thrust faulting at the northern end of the Sierra Nevada block [Unruh et al., 2003], and active NW SE shortening [Hammond and Thatcher, 2005] and areal contraction [Kreemer and Hammond, 2007] near the Oregon-California border. Crustal deformation in the Pacific Northwest is therefore caused in large part by northward compression of the Oregon Coast block by the Sierra Nevada block, itself driven largely by Pacific North America transform interaction. This process illustrates the ability of rigid crustal blocks to effectively transfer stresses over relatively large distances, on the order of 1000 km in this case, and the potential importance of the interactions between rigid blocks in driving lithospheric deformation in the western United States. [47] The Sierra Nevada Oregon Coast block interaction may also provide an explanation for the anomalous sense of rotation of the Sierra Nevada block. Clockwise rotation of the Pacific plate relative to North America should cause clockwise rotation of blocks (relative to either plate) in the plate boundary deformation zone [McCaffrey, 2005]. However, numerous studies have suggested that the Sierra Nevada block is rotating counterclockwise relative to North America [Argus and Gordon, 1991; Argus and Gordon, 2001; Hearn and Humphreys, 1998; Dixon et al., 2000; Bennett et al., 2003] and therefore also counterclockwise relative to the Pacific. McCaffrey [2005] argues that the Sierra Nevada block is in fact rotating clockwise relative to North America at 0.4 /Ma. However, this rate is 0.2 /Ma slower than the 0.6 /Ma of the Pacific plate, and therefore the Sierra Nevada block rotates 0.2 /Ma counterclockwise relative to the Pacific. [48] The obliquity of the Sierra Nevada and Oregon Coast block compressional stress (N S) relative to the orientation and transport direction of the Sierra Nevada block (N40 W, see Figure 11) imparts a counterclockwise torque on the Sierra Nevada block that would cause a counterclockwise rotation. The basal tractions on the northern end of the block associated with subduction-driven mantle flow have a similar effect in imparting a counterclockwise torque and rotation. Thus the counterclockwise rotation of the Sierra Nevada block (relative to either North America or the Pacific) is a result of a reduction in the clockwise rotation induced by the dextral shear of the relative motion of the Pacific and North American plates by other processes such as the strong compression with the Oregon Coast block to the north Tensional Stress in the Western Basin and Range [49] A small but resolvable tensional load (0.8 ± 0.2 TN/m) is found on the southeast end of the Sierra Nevada block (Figure 10), effectively along the western margin of the Basin and Range province. Active deformation here is largely horizontal, i.e., strike slip [e.g., Beanland and Clark, 1994; Dixon et al., 2003], consistent with s Hmax oriented approximately 45 to the strike of major faults (see Figures 3 and 4). Nonetheless, tensional stress normal to the SE end of the block is expected for blocks such as the Sierra Nevada embedded in the dextral shear couple of the Pacific North American plate boundary. This is because the clockwise torque imparted on the block by the right-lateral shear tractions applied to its western and eastern sides (i.e., the San Andreas and Walker Lane shear loads) would tend to rotate the block clockwise, which would produce tension on the SE end of the block. Tension also would be expected at the NW end of the block, but as discussed above, other processes are thought to overwhelm this effect. Interaction of the Sierra Nevada block and Oregon Coast block and tractions caused by subduction of the Juan de Fuca plate modulate the rotation of the Sierra Nevada block in an 15 of 18