Small-Scale Upper Mantle Convection and Crustal Dynamics in Southern California

Home , Laguna Salada Fault, Walker Lane

Article Geochemistry 3 Volume 9, Number 8 Geophysics 12 August 2008 Geosystems Q08006, doi:10.1029/2008GC001988 G ISSN: 1525-2027 AN ELECTRONIC JOURNAL OF THE EARTH SCIENCES Published by AGU and the Geochemical Society

Click Here for Full Article Small-scale upper mantle convection and crustal dynamics in southern California

N. P. Fay, R. A. Bennett, and J. C. Spinler Department of Geosciences, University of Arizona, Tucson, Arizona 85721, USA ([email protected]) E. D. Humphreys Department of Geological Sciences, University of Oregon, Eugene, Oregon 97403, USA

[1] We present numerical modeling of the forces acting on the base of the crust caused by small-scale convection of the upper mantle in southern California. Three-dimensional upper mantle shear wave velocity structure is mapped to three-dimensional density structure that is used to load a finite element model of instantaneous upper mantle flow with respect to a rigid crust, providing an estimate of the tractions acting on the base of the crust. Upwelling beneath the southern Walker Lane Belt and Salton Trough region and downwelling beneath the southern Great Valley and eastern and western Transverse Ranges dominate the upper mantle flow and resulting crustal tractions. Divergent horizontal and upward directed vertical tractions create a tensional to transtensional crustal stress state in the Walker Lane Belt and Salton Trough, consistent with transtensional tectonics in these areas. Convergent horizontal and downward directed vertical tractions in the Transverse Ranges cause approximately N–S crustal compression, consistent with active shortening and transpressional deformation near the ‘‘Big Bend’’ of the San Andreas fault. Model predictions of crustal dilatation and the forces acting on the Mojave block compare favorably with observations suggesting that small-scale upper mantle convection provides an important contribution to the sum of forces driving transpressional crustal deformation in southern California. Accordingly, the obliquity of the San Andreas fault with respect to plate motions may be considered a consequence, rather than a cause, of contractional deformation in the Transverse Ranges, itself driven by downwelling in the upper mantle superimposed on shear deformation caused by relative Pacific–North American plate motion.

Components: 12,968 words, 12 figures. Keywords: stress; dynamics; crustal deformation; small-scale convection; crust-mantle interaction. Index Terms: 8164 Tectonophysics: Stresses: crust and lithosphere; 8120 Tectonophysics: Dynamics of lithosphere and mantle: general (1213); 8111 Tectonophysics: Continental tectonics: strike-slip and transform. Received 12 February 2008; Revised 2 June 2008; Accepted 20 June 2008; Published 12 August 2008.

Fay, N. P., R. A. Bennett, J. C. Spinler, and E. D. Humphreys (2008), Small-scale upper mantle convection and crustal dynamics in southern California, Geochem. Geophys. Geosyst., 9, Q08006, doi:10.1029/2008GC001988.

1. Introduction Bend; see Figure 1), i.e., a large left-step in the right- lateral San Andreas fault system. The San Andreas [2] The forces driving active deformation of the fault is offset 120 km through the Big Bend lithosphere at a tectonic plate boundary are the sum (Figure 1), which is 8 times the average seismo- of those driving global plate motion transmitted genic depth [Nazareth and Hauksson, 2004], through the rigid plates from the far-field to the 4 times the average crustal thickness of 30 km plate boundary [e.g., Atwater, 1970], and those [Zhu and Kanamori, 2000; Yan and Clayton, 2007] created locally by variations in local density struc- and greater than the average lithospheric thickness ture [Artyushkov, 1973; Fleitout and Froidevaux, in southern California of 90 km [Yang and 1982; Molnar and Lyon-Caen, 1988]. On a global Forsyth, 2006a; Humphreys and Hager, 1990]. scale, the stresses exerted on plates from flow [4] Dynamically, however, it is not clear why the induced by the mantle’s internal density structure lithosphere maintains this apparently energetically (e.g., sinking slabs) seem to be an important unfavorable geometry [Kosloff, 1977]. Mountain contribution to the sum of forces acting on plates building in the Transverse Ranges, i.e., thrust [Becker and O’Connell, 2001; Steinberger et al., faulting and crustal shortening and thickening, 2001; Conrad et al., 2004; Ghosh et al., 2006]. On requires work against gravity and frictional and the scale of a few 100 km it may be more difficult viscous resistive forces. There are other active to determine the importance of small-scale convec- structures such as the Elsinore-Laguna Salada fault tion on crustal dynamics and deformation because system, that if more active and connected with the the influence in actively deforming regions may be Cerro Prieto fault (Figure 1), would allow relative overprinted by other processes such as plate inter- Pacific-North American motion on a more through- action. Actively deforming regions have a distinct going transform system and largely bypass the Big advantage, however, in that they provide the nec- Bend geometry. Numerical modeling has shown essary observables to allow discrimination of that an effect of the present-day geometry of the superimposed sources of driving forces. In this San Andreas fault is to promote slip on other slip paper we aim to resolve the role of small-scale systems such as the Eastern California Shear Zone convection of the upper mantle in driving defor- and offshore faults [Li and Liu, 2006], indicating mation of the overlying crust in southern Califor- the current San Andreas geometry should not be nia. It is clear that present-day deformation in stable. southern California is strongly influenced by plate interaction stresses; we show that much of the [5] However, the San Andreas fault appears to be deformation that cannot be explained by plate the dominant plate boundary fault at present interaction derives from small-scale convection of throughout most of southern California slipping the underlying upper mantle. 20–35 mm/yr [e.g., Sieh and Jahns, 1984; Weldon and Sieh, 1985; Meade and Hager, [3] Approximately 50 mm/yr of relative motion 2005; Bennett et al., 2004; Becker et al., 2005; between the Pacific and North American plates Fay and Humphreys, 2005]. The Big Bend geom- [DeMets and Dixon, 1999] is accommodated largely etry of the San Andreas fault system has existed by strike-slip deformation. The most active struc- since the opening of the Gulf of California ( 6 Ma) ture, the San Andreas fault, accommodates half or and likely longer [Wilson et al., 2005], indicating more of the present-day slip budget [e.g., Meade today’s transpressive geometry is a persistent tec- and Hager, 2005], although its rate depends on tonic feature of the plate boundary at least over the location. In addition to strike-slip deformation past few million years. One possible explanation is there is a nontrivial component of nonsimple shear that the San Andreas fault is extremely weak com- deformation such as block rotation, shortening and pared to the surrounding crust and nearby faults uplift in the Transverse Ranges [e.g., Dibblee, [Zoback et al., 1987; Townend and Zoback, 2000, 1975; Yeats et al., 1988; Jackson and Molnar, 2004], perhaps owing to its greater accumulated 1990; Luyendyk, 1991; Donnellan et al., 1993; offset and structural maturity [Wesnousky, 1988, Morton and Matti, 1993; Spotila et al., 1998; 2005], and the work required to generate a new, Onderdonk, 2005; Spotila et al., 2007]. Kinemat- straighter fault system is greater than that to drive ically, the transpressive deformation in the Trans- shortening and mountain building in the Transverse verse Ranges can be considered a consequence of Ranges. the ‘‘Big Bend’’ in the San Andreas fault (here defined as the segment of the San Andreas fault [6] Alternatively, upper mantle processes, namely between the San Emigdio Bend and San Gorgonio downwelling beneath the Transverse Ranges, may

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Figure 1. Map showing study area and geographic features discussed in the text. Solid lines show fault traces, and the San Andreas fault (SAF) is indicated with a thick line. The Walker Lane Belt (WLB) extends from the Garlock fault (GAR) to the northwest along the eastern side of the Sierra Nevada Mountains. The Eastern California Shear Zone (ECSZ) extends from the Garlock to the southeast. The western Transverse Ranges (WTR) and central Transverse Ranges (CTR) lie to the west of the SAF, and the eastern Transverse Ranges (ETR) lie to its east. Approximately NW motion of 50 mm/a of the Pacific plate relative to North America [DeMets and Dixon, 1999] is shown. Dashed line shows the approximate projection of the southernmost San Andreas fault into the Great Valley to illustrate the 120 km offset with respect to its central California location. Gray scale gives smoothed elevation above sea level. SJF, San Jacinto fault; ELS, Elsinore fault; LSF, Laguna Salada fault; CPR, Cerro Prieto fault; SEB, San Emigdio Bend; SBG, San Gorgonio Bend; SS, Salton Sea. act to draw in the overlying crust and cause al., 1985], and (3) high-velocity anomalies beneath shortening superimposed on the shear deformation the Transverse Ranges. This latter feature is the related to plate motion. A number of seismic most important for this paper and has previously studies have shown that the upper mantle velocity been interpreted as a slab-like feature extending to structure beneath southern California is rather at least 200 km [Humphreys and Clayton, 1990; heterogeneous [Raikes, 1980; Humphreys and Kohler et al., 2003]. Recently, Yang and Forsyth Clayton, 1990; Jones et al., 1994; Kohler et al., [2006a] have argued that the Transverse Range 2003; Boyd et al., 2004; Yang and Forsyth, 2006a; velocity anomalies extend to only 150 km and Tian et al., 2007]. The dominant upper mantle are separated into two nearly distinct anomalies seismic features are (1) a roughly circular high- centered beneath the eastern Transverse Ranges velocity body beneath the southern Great Valley and offshore near the Channel Islands (Figure 2). and Sierran foothills adjacent to a low-velocity region beneath the high elevation of the Sierra [7] If these velocity anomalies derive largely from Nevada and southern Walker Lane Belt, (2) low temperature variations, the velocity structure pro- velocities beneath the greater Salton Sea area, vides a proxy for the temperature heterogeneity in likely associated with extension and mantle up- the upper mantle and its associated density structure. welling [e.g., Elders et al., 1972; Lachenbruch et The high-velocity body beneath the Transverse

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Ranges has been interpreted as downwelling of cool, and relatively dense, mantle lithosphere [Bird and Rosenstock, 1984; Sheffels and McNutt, 1986; Humphreys and Hager, 1990]. Houseman et al. [2000] and Billen and Houseman [2004] suggest the velocity anomalies are a result of a gravity- driven lithospheric instability to account for their drip-like structure. Whatever the mechanism of formation, the forces associated with a heterogeneous distribution of density in the upper mantle must be balanced by viscous stresses associated with gravity-driven flow, or by displacing a horizontal density interface such as the Earth’s surface (dynamic topography).

[8] The focus of this paper is to quantify the three- dimensional anomalous upper mantle density structure, the viscous flow induced by this density structure, and the effect on the dynamics and deformation of the overlying crust. We calculate the instantaneous viscous flow of the uppermost mantle with respect to a rigid crust; this approach allows us to isolate the stresses on the base of the crust. Three-dimensional upper mantle density structure is derived from the seismic tomography model of Yang and Forsyth [2006a]. We do not attempt to include any large-scale shear in the upper mantle potentially induced by relative plate motion [e.g., Bourne et al., 1998; Molnar et al., 1999]; our study is restricted to the largely poloidal flow caused by gravity acting on a heterogeneous distribution of density. The influence of upper mantle flow on crustal dynamics is evaluated by comparison with regional deformation patterns determined from geodetic observations and torque balance on a crustal block.

2. Three-Dimensional Seismic Velocity and Density Structure of the Uppermost Mantle

[9] We use the shear wave velocity model derived from surface (Rayleigh) wave tomography of Yang

Figure 2. Upper mantle seismic velocity and density structure in southern California. Shear wave velocity (Vs) anomalies from the Yang and Forsyth [2006a] tomography model and inferred density are shown at depth slices at (a) 70–90 km, (b) 110–130 km, and (c) 150–170 km. The area without stipple, in this and subsequent figures, shows the well-resolved region of the seismic velocity model as defined by Yang and Forsyth [2006a]. We use the entire velocity model (which extends beyond the limits of these maps) in our modeling as discussed in the text.

4 of 23 Geochemistry Geophysics 3 fay et al.: upper mantle convection and crustal dynamics 10.1029/2008GC001988 Geosystems G and Forsyth [2006a] to estimate the three-dimensional with continental cratons and the tectosphere [e.g., upper mantle density structure in southern California. Lithgow-Bertelloni and Silver, 1998; Becker and Here we only briefly discuss the velocity model. O’Connell, 2001; Steinberger et al., 2001]. It is Readers interested in the details of the seismic data, unlikely, however, that the velocity variations in results, and methodology should refer to Yang and the shallow upper mantle in southern California Forsyth [2006a, 2006b] and Forsyth and Li [2005]. imaged by Yang and Forsyth [2006a] and others We choose the Yang and Forsyth [2006a] model are dominated by compositional variations because because (1) Rayleigh waves are most sensitive to the magnitude of the velocity anomalies are much the depth range we are most interested in here (e.g., greater ( 3 times) than that produced by chemical 50–250 km), (2) they incorporate finite-frequency segregation of the upper mantle [Humphreys and effects in their inversions, and (3) the velocity Hager, 1990; Jordan, 1975]. Anisotropy and par- structure they find is quite similar to that reported tial melt can also be excluded leaving temperature in previous studies, giving us some confidence it is variations as the most likely cause of the velocity likely real. anomalies [Humphreys and Hager, 1990]. Our modeling results (traction and stress magnitudes, [10] Figures 2a, 2b, and 2c present three represen- see sections 3 and 4) scale linearly with g and tative depth slices through the Yang and Forsyth therefore if any fraction of the seismic velocity [2006a] model at depths of 70–90, 110–130 and anomalies do in fact represent compositional var- 150–170 km, respectively. Velocity anomalies, iations that are isostatically compensated, we will dVs, are shown as percent deviations from a 1-D overestimate their influence on mantle flow. We average velocity model. Three major fast (blue) have, however, chosen g conservatively to mini- structures beneath the southern Great Valley and mize this effect. In section 4.2 we show that the Transverse Ranges are clear. Slow velocities (red) influence on crustal dynamics of mantle flow (with are strongest at shallowest depths in the southern g = 0.2) is of similar magnitude to tectonic plate Walker Lane and at all depths near the Salton Sea. interaction, indicating 0.2 is a reasonable value for The three dominant fast bodies, and the stresses g in the southern California upper mantle. they induce on the overlying crust (discussed in section 3) are hereafter referred to as the Sierra [13] Our reference one-dimensional density struc- Nevada anomaly, western Transverse Ranges ture (from iasp91 [Kennett and Engdahl, 1991]) anomaly, and eastern Transverse Ranges anomaly increases linearly from 3320 kg/m3 at 35 km to (see Figure 2). 3 @ dr 3490 kg/m at 310 km and thus ð@z Þ is g;dVs [11] Seismic velocity variations depend primarily positive though typically very small compared to on composition, temperature, partial melt, and dr itself. The corresponding density anomaly struc- anisotropy. In this paper we effectively assume ture is shown in Figure 2 with the same color scale that the velocity variations are entirely thermal in as the seismic velocity anomalies. Density anoma- origin and adopt a constant scaling factor, g, lies are typically ±10–30 kg/m3, with the largest relating density (r) variations to velocity varia- anomalies in our study area at depths of 50– tions, given by 100 km. The choice of reference density model is not particularly critical because the numerical modeling results scale with respect to variations g @ ln r=@ ln Vs; 1 ¼ ð Þ in background density in the same way as with [Karato, 1993]. In the upper mantle g is estimated variations in g, and the former is likely better to be 0.2–0.3 [Karato, 1993; Steinberger and constrained than the latter. Calderwood, 2006]. We choose g = 0.2 such that, [14] The density anomaly structure shown in for example, a 5% velocity anomaly maps into a Figure 2 is used as input to our viscous flow 1% density anomaly (dr). calculations, discussed in the next section. The background density model is not included as it [12] This method of scaling velocity to density is commonly used in global studies of mantle would create only a lithostatic pressure that does dynamics [e.g., Lithgow-Bertelloni and Silver, not drive differential flow. The nonstippled area in 1998; Becker and Boschi, 2002; Conrad et al., Figure 2 shows the region of the seismic velocity 2004], although shallow (above 325 km) upper model that is well resolved and most reliable [Yang mantle seismic velocity anomalies are often and Forsyth, 2006a]. We use the entire velocity excluded because they may derive from isostatically model (and inferred anomalous density structure), compensated compositional variations associated so as to avoid artificial truncation effects. We

5 of 23 Geochemistry Geophysics 3 fay et al.: upper mantle convection and crustal dynamics 10.1029/2008GC001988 Geosystems G demonstrate later that restricting the density model Therefore, the modeling results we present here are to within the resolved region produces very similar independent of the absolute value of the viscosity results. chosen for the upper mantle. This is because we prescribe density and compute the flow response 3. Numerical Modeling and associated stresses; the stresses necessary to support the forces of the density anomalies are [15] Our primary objective is to resolve the forces dictated by the densities and their spatial distribu- created by upper mantle density structure that tion. We model cases of a uniform upper mantle contribute to loading the southern California crust. viscosity with and without a high-viscosity lid, an To that end, we calculate the viscous flow of the upper mantle in which viscosity depends on tem- upper mantle and concomitant tractions on the base perature, and a relatively weak lower crust. of the crust. Importantly, by driving the flow with gravitational body forces acting on density anoma- 3.1. Uniform Upper Mantle Viscosity lies, their geometry and magnitude known in [18] Figures 3 and 4 present the vertical and absolute value, we are able to predict absolute horizontal tractions on the base of the crust for a levels of stress in the upper mantle and crust. We uniform viscosity upper mantle. Figure 3 gives the solve the three-dimensional equations of conserva- vertical normal stress at element centroids. Above tion of mass and momentum for incompressible the three major positive density (negatively buoy- Newtonian viscous flow using the finite element ant) bodies, the western Transverse Ranges, eastern code Gale [Moresi et al., 2003; Landry and Transverse Ranges and Great Valley anomalies, Hodkinson, 2007; Landry et al., 2008]. We restrict vertical stresses are negative (act to pull the crust our analysis to very small strains, essentially down) with a maximum magnitude of 9 MPa instantaneous flow, because the seismic tomogra- offshore. The slowest seismic velocities and largest phy model provides us with only the present-day positive vertical stresses ( 14 MPa) occur in the velocity and density structure and we wish to southern Walker Lane Belt, just to the east of the isolate the contribution of sub-crustal density Sierra Nevada anomaly. dVs of 5 to 6% at 50– structure on crustal stress. 70 km depth indicates a likely completeÀ Àabsence of [16] The model domain is a Cartesian grid 1600 km lithospheric mantle there [Yang and Forsyth, 1600 km in map view and extends to 1000 km 2006a]. Relatively warm asthenosphere is thought depth.Â The model is centered on southern California to have passively upwelled to fill the region that is represented as an oblique-Mercator projec- vacated by delaminating lithospheric mantle [Zandt tion about the Pacific-North American Euler pole et al., 2004; Le Pourhiet et al., 2006]. Yang and [DeMets and Dixon, 1999]. Element spacing is Forsyth [2006a] show that the region of lowest 25 km horizontally and 10 km vertically; this seismic velocities corresponds well with the locus element resolution was chosen on the basis of the of Pliocene and Quaternary volcanism. If any resolution of the seismic tomography model and partial melt, which can have strong retarding finer mesh resolution produces indistinguishable effects on shear wave velocities [Hammond and results. The sides and bottom are held fixed. We Humphreys, 2000], is retained in the upper mantle, model the crust as a highly viscous layer 30 km we may be over estimating the inferred density deep that is fixed vertically and unconstrained anomaly and vertical stresses. horizontally. This allows the mantle flow to load [19] These vertical stresses should vertically de- the crust permitting us to monitor crustal stress. flect the crust. The predicted dynamic topography Density is assigned to the model by interpolating can be estimated by dividing the radial stresses by the three-dimensional density structure (Figure 2) the deflected density contrast (e.g., 3300 kg/m3) to element centroids. The seismic velocity model is and gravitational acceleration. This gives a maxi- given in depth slices, each 20 km thick. Thus the mum upward static deflection of 0.4 km in the density structure input into the modeling resembles eastern Sierra Nevada and southern Walker Lane, a slightly coarser version of Figure 2. Outside the and maximum downward deflection of 0.3 km extent of the seismic velocity model (e.g., below offshore in the vicinity of the Channel Islands. This 250 km), no density anomaly is assigned. simple isostatic calculation overestimates the actual [17] In this paper we are concerned with the dynamic topography because these relatively short stresses acting on the crust from density-driven horizontal wavelength vertical loads will be partly upper mantle flow, not the strain in mantle itself. supported by flexure of the elastic crust. While the

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Figure 3. Vertical normal stresses (colored dots) on the base of crust caused by viscous flow of the upper mantle driven by the three-dimensional density structure in Figure 2. Results are shown at element centroids, and positive/ negative indicates upward/downward directed vertical normal stress. The largest positive vertical stress occurs in the Walker Lane Belt above the positively buoyant, slow velocity anomaly there. The largest negative vertical stress occurs offshore above the negatively buoyant fast anomaly. As in Figure 2, the nonstippled area shows the region of seismic velocity model that is best constrained, and therefore we focus on this area in our interpretation. total deflected mass must be conserved, flexure of Tractions beneath the Eastern California Shear an elastic plate should broaden and smooth any Zone and western Mojave Desert are converging subsidence or uplift and thereby decrease local on the eastern Transverse Ranges (San Bernardino amplitudes. Nonetheless, in the southern Sierra Mountains) and Mojave segment of the SAF. The Nevada active subsidence and sedimentation pattern here is asymmetric with tractions much appears to be burying mountainous topography larger to the northeast of the San Andreas fault [Saleeby and Foster, 2004], suggesting at least than to the south. To the north of the San Andreas some of the negative dynamic topography pre- fault tractions have an approximately SW orienta- dicted by our models may be real, and possibly tion and magnitude of 2.5 MPa with a maximum increasing with time. In the remainder of this paper of 3.2 MPa. Horizontaltractions north of 33.5°N we focus on the horizontal tractions. and within the Salton block, between the SanJacinto and San Andreas faults, are nearly parallel to those [20] The horizontal tractions at the Moho are two faults and directed toward the San Bernardino shown in Figure 4. Downwelling of the dense Mountains, and provide some of the force driving material offshore of the western Transverse Ranges convergence there [Fay and Humphreys, 2006]. produces a nearly radial pattern of convergent Within 100 km of the Salton Sea, horizontal tractions. Traction magnitudes are typically 1– tractionsare typically less than 2 MPa and show a 2 MPa and strongest ( 2.7 MPa) onshore to the clear radial pattern, consistent with horizontal di- north of the center of the downwelling region. vergence of buoyant upwelling.

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Figure 4. Horizontal tractions at the base of the crust, complement to the vertical tractions in Figure 3, for the case of a uniform viscosity upper mantle. Traction vectors are shown with their tails located at the finite element mesh nodes (25 km spacing). Tractions are convergent in the southern Great Valley and Transverse Ranges and generally divergent in the southern Walker Lane Belt near the intersection with the Garlock fault and near the Salton Sea. Traction magnitudes are typically 3–4 MPa (scale in bottom left corner) and largest near the California-Nevada border and in the western MojaveDesert.

[21] The horizontal tractions along the California- sNN, sNE) of the three-dimensional stress tensor at Nevada border have a maximum magnitude of 20 km depth. At this depth, the stress field is nearly 3.5 MPa and are directed to the NE. These are ‘‘horizontal’’ in that one of the principal stresses is caused by a combination of strong upwelling and typically within 15° from vertical. This is divergence of the buoyant material beneath the expected as at theEarth’s surface one principal southern Sierra Nevada and southern Walker Lane stress must be vertical and the thickness of the Belt, and a relatively deep downwelling in south- crustal layer (30 km) is small compared to the eastern Nevada. This latter velocity anomaly lies wavelength of the tractions acting on its base. outside the well-resolved region of the Yang and Figure 6 portrays the same stress tensor as the Forsyth [2006a] velocity model, although a high- orientation of maximum horizontal compressive velocity body at similar depths in south central stress (sHmax, long axis of the bars) and stress Nevada has been previously imaged [Biasi and regime parameter AY [Simpson, 1997]. Humphreys, 1992] and therefore may be real. [23] It is important to recall that the stress fields in [22] The horizontal and vertical tractions in Figures 3 Figures 5 and 6 represent the stress caused only by and 4 stress the overlying crust and the resulting the tractions on the base of the crust and not the crustal stress field is shown in Figures 5 and 6. In entire state of stress. To estimate the complete Figure 5 we show the principal stresses derived stress tensor, as done by Sonder [1990], we may from the horizontal (map view) components (sEE, add a stress field dominated by approximately

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Figure 5. State of stress in the crust caused by the vertical and horizontal tractions of Figures 3 and 4. The stress tensor is represented as principal stresses (bars) determined from the stress tensor at 20 km depth. Solid bars indicate compression, and open bars indicate tension. The length of the bar indicates magnitude, and the scale is given in the bottom left corner. Approximately NE–SW tensional stress dominates in the southern Walker Lane Belt and Salton Sea region. Approximately radial compression (horizontal principal stresses both compressive and approximately equal magnitude) exists in the southern Great Valley and the western Transverse Ranges. Approximately NNW–SSE uniaxial compression (one principal stress compressive and much larger in magnitude than the other) dominates in the central and eastern Transverse Ranges in the vicinity of the Big Bend segment of the San Andreas fault. The stress state producing maximum right-lateral shear stress on planes oriented N45W (the approximate orientation of the San Andreas fault in central California) is shown by the scale in the bottom left corner.

NW–SE shear stress parallel to the relative Pacific- in the southern Great Valley and as much as North American plate direction. The 5 MPa scale 11.5 MPa in the eastern Sierra Nevada and south- in the bottom left corner of Figure 5 shows the ern Walker Lane Belt. These crustal stress magni- principal stress for such a NW–SE shear-dominated tudes are comparable in magnitude to the vertical stress field. Detailed analysis of the total stress field tractions and generally larger than the horizontal in the crust and comparison to stress observations tractions acting at the Moho. This is expected as [e.g., Townend and Zoback, 2001, 2004; Hardebeck the horizontal basal tractions integrate over a much and Michael, 2004, 2006] is forthcoming in a future larger area than the unit cross-sectional area of the publication. Here we concentrate on the crustal crust and therefore stress magnitudes in the crust stress field caused only by small-scale upper mantle must be larger to balance the applied force of the convection. basal tractions. Similar to the basal tractions (Figures 3 and 4), the principal stress magnitudes [24] Principal stress magnitudes in the crust are are linearly dependent on g, the velocity-density typically 5 MPa in the Transverse Ranges, 3 MPa scaling parameter.

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Figure 6. Crustal stress state (same as Figure 5) shown as the orientation of maximum horizontal compressive stress (sHmax) and stress regime parameter AY, a continuous function of the relative magnitudes of the components of the stress tensor [Simpson, 1997]. As shown by the accompanying arrows, AY = 0 indicates radial tension, AY = 30 indicates uniaxial tension, AY = 60 indicates transtension, AY = 90 indicates strike-slip, AY = 120 indicates transpression, AY = 150 indicates uniaxial compression, and AY = 180 indicates radial compression. The length of the bar represents the magnitude of the horizontal principal stresses as their vector sum ( s2 s2 ). The stress qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiH max þ H minffiffiffiffiffiffi state is dominated by tension (AY 60) and compression (AY 120), consistent with largely vertical upwellings and downwellings in the underlying upper mantle.

[25] Radial tension to pure normal stress is pre- pressure in the crust owing to the large upper dicted in the Sierra Nevada Mountains and south- mantle buoyancy (Figure 2) and induced vertical ern Walker Lane Belt. Magnitudes are largest in the tractions on the base of the crust (Figure 3), and the north ( 11 MPa) and gradually decrease to the approximately NE–SW divergent horizontal trac- southeast. Southeast of the Garlock fault the state tions directed toward the downwelling in the Great of stress transitions to uniaxial tension and strike Valley, the Transverse Ranges, and southern slip in the Mojave Desert. This dominantly ten- Nevada (see Figure 4). Deviatoric tension super- sional horizontal stress field in the eastern Sierra imposed on right lateral shear is consistent with the Nevada, Walker Lane Belt and Eastern California occurrence of normal fault earthquakes in the Shear Zone is a consequence of the positive southern Sierra Nevada Mountains [Jones and

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Dollar, 1986], oblique normal-right lateral slip on 1993; Spotila and Sieh, 2000], and N–S contraction the Owens Valley fault [e.g., Beanland and Clark, throughout the Mojave [Bartley et al., 1990]. NW– 1994] and regional transtension along the eastern SE compressive stress along the Big Bend of the San margin of the Sierra Nevada range [Unruh et al., Andreas fault also has the effect of rotating the plane 2003]. A similar system of approximately E–W of maximum right-lateral shear stress counterclock- oriented, essentially uniaxial tension is seen in the wise with respect to a background stress state caused Salton Trough region caused by positive (tensional) by plate motions [Sonder, 1990]. pressure in the crust and approximately radial divergence of horizontal tractions (Figure 4). [29] We use the entire Yang and Forsyth [2006a] velocity model in the calculations leading to Fig- [26] Uniaxial to radial horizontal compression is ures 3–6, including that which falls outside the seen in the central southern Great Valley, above the polygon defining the well-resolved velocity struc- negatively buoyant upper mantle anomaly. This ture (e.g., Figure 2). To test whether possibly stress is a result of the negative pressure in the erroneous velocity and inferred density structure crust caused by the downward directed vertical outside the well-resolved region strongly influen- Moho stress and convergent horizontal tractions. ces our results, we have performed the same The locus of maximum compressive stress (approx. viscous flow calculations with the density structure 240°E, 36.5°N, 3 MPa) is shifted slightly to the restricted to the well-defined polygonal region of WSW of the center of the upper mantle velocity Figure 2. Figure 7 shows the resulting horizontal anomaly indicating that to some degree compres- tractions and crustal stress field. Except along the sion of crust directly overlying and along the E– California-Nevada border, where traction magni- NE side of the downwelling is overprinted by the tudes decrease by 50% or more, the results are tension induced by approximately NE directed largely unchanged. Compared to the results horizontal tractions along the California-Nevada in Figure 4, horizontal traction orientations are border. virtually identical. Magnitudes increase slightly ( 0.2 MPa) northeast of the San Andreas fault in [27] The largest compressive principal stresses the vicinity of the eastern Transverse Ranges ( 5.7 MPa) occur offshore above the western downwelling, decrease slightly ( 0.1 MPa) near Transverse Ranges anomaly and are a result of the offshore downwelling region, and increase the relatively large negative vertical tractions and ( 0.5 MPa) along the eastern side of the Sierra convergent horizontal tractions there. Maximum Nevada anomaly. The crustal stress field (Figure 7b) compression direction (Figure 6) is on average is also nearly the same with only minor differences. N–S, approximately perpendicular to the numer- We conclude from this analysis that the computed ous E–W trending reverse and oblique reverse/left- basal tractions and crustal stress field in our study lateral faults such as those that are exposed in the area are dominated by local, relatively shallow, northern Channel Islands (Santa Rosa Island fault, density structure and not strongly influenced by Santa Cruz Island fault) and on the mainland (e.g., structure outside the well-resolved region of the Santa Ynez fault, Oak Ridge fault, San Cayetano velocity model. For the remainder of this paper, all fault, etc.). model comparisons and discussion will refer to the [28] In the central and eastern Transverse Ranges results shown in Figures 3–6 utilizing the entire the stress state is dominated by approximately velocity model. uniaxial compression oriented approximately NW–SE in the central Transverse Ranges (San 3.2. High-Viscosity Lithospheric Lid Gabriel Mountains) and approximately NNW– [30] Average lithospheric thickness in southern SSE in the eastern Transverse Ranges and Mojave California has been estimated to be approximately Desert. These stresses are clearly a consequence of 90 km [Humphreys and Hager, 1990; Yang and the negative vertical tractions and the approximately Forsyth, 2006a], although this does not apply to SSW oriented horizontal tractions, strongest in the the southern Sierra Nevada where lithospheric Mojave Desert. NNW–SSE compressive stress is mantle is likely absent [Yang and Forsyth, 2006a; consistent with the many approximately E–W Savage et al., 2003]. Here we test whether the striking thrust and oblique slip faults accommodat- presence of a high-viscosity mantle lithosphere lid ing approximately N–S shortening such as the 60 km thick (90 minus average crustal thickness of Cucamonga fault, Sierra Madre fault, San Gorgo- 30 km) significantly changes the predicted stresses nio fault zone, North Frontal fault zone, etc. [e.g., compared to the uniform viscosity case in Figure 4. Meisling and Weldon, 1989; Morton and Matti,

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Figure 7. (a) Horizontal tractions on the base of the crust (as in Figure 4) and (b) principal stresses in the crust (as in Figure 5) resulting from upper mantle flow driven by density structure restricted to within the well-resolved region of the seismic velocity model (nonstippled area). The basal tractions and crustal stress field are very similar in orientation and magnitude to those based on the entire velocity model (Figure 4), implying our results are not strongly dependent upon the velocity and density structure outside the study area.

All else being equal, a higher viscosity lid should magnitude higher viscosity than the underlying support a larger fraction of the shallow load, thereby mantle. Traction orientations do not change appre- increasing the tractions on the overlying crust. ciably whereas magnitudes increase nearly every- where with maximum increase of 1.2 MPa. The [31] Figure 8 shows that this is in fact the case. We largest increase occurs onshore and just offshore show the horizontal tractions and crustal stress near the western Transverse Ranges anomaly and field for the case of a lithospheric lid 2 orders of

Figure 8. (a) Horizontal tractions and (b) crustal principal stresses for the case of a high-viscosity lithosphere 90 km thick and 100 times as viscous as the underlying mantle. The resulting basal tractions (as compared with Figure 4) are virtually unchanged in orientation and increase in magnitude by 25%. 12 of 23 Geochemistry Geophysics 3 fay et al.: upper mantle convection and crustal dynamics 10.1029/2008GC001988 Geosystems G

Figure 9. (a) Horizontal tractions and (b) crustal principal stresses for the case of density-dependent (as a proxy for temperature-dependent) viscosity. Here r = 5 in equation (2), indicating 1/2 order of magnitude increase/decrease in viscosity for every 0.1 km/s increase/decrease in shear wave velocity relative to the layer average. Traction orientations change little though magnitudes decrease (compared to Figure 4) in the Sierra Nevada, Walker Lane Belt, and western Transverse Ranges. Magnitudes increase in the western Mojave and Eastern California Shear Zone area. The corresponding vertical stresses (not shown) generally increase in magnitude compared to Figure 3, and this is most pronounced above the dense bodies in the Great Valley and Transverse Ranges. in the Mojave Desert near the eastern Transverse mensional viscosity variations influence our esti- Ranges anomaly to a maximum magnitude of 3.9 mates of tractions on the base of the crust, we have MPa. The crustal stress field (Figure 8b) is also devised an ad hoc relationship between seismic largely unchanged in principal stress orientations velocity and viscosity that mimics the strong de- although magnitudes increase from 20–50% pendence of viscosity on temperature as in the depending upon location. A similar mo del (not Arrhenius relationship, and avoids the need to shown) with only 10 times higher lithospheric lid estimate temperature anomalies from seismic ve- viscosity produces very similar results indicating 1 locity anomalies. Viscosity (h) is given as order of magnitude may be sufficient to signifi- dVs r cantly modify how density anomalies are sup- h h010ð Á Þ 2 ported in the lithosphere. ¼ ð Þ where h0 is the reference viscosity, dVs is the 3.3. Three-Dimensional Viscosity velocity anomaly (expressed in km/s) and r is a Variations constant. Figure 9 shows the tractions and crustal principal stresses for the case of r = 5, i.e., every [32] The viscosity of the Earth’s mantle is thought 0.1 km/s variation in seismic velocity produces a to be highly temperature dependent, often assumed factor of 3.16 (1/2 order of magnitude) change in to follow the Arrhenius relationship where viscos- viscosity,resulting in 2.9 orders of magnitude ity is proportional to exp(Q/RT), where Q is the total viscosity variation throughout the entire activation energy, R is the universal gas constant model. Figure 10 shows the case of r = 10, i.e., and T is absolute temperature [e.g., Ranalli, 1995]. every 0.1 km/s variation in seismic velocity We assume that the velocity and density anomalies produces a factor of 10 change in viscosity, in the southern California upper mantle arise from resulting in over 5 orders of magnitude variation temperature variations, and therefore should also in viscosity throughout the model. reflect viscosity variations; fast/dense regions are relatively cool and therefore more viscous, and [33] As in the lithospheric lid example in the slow/buoyant regions are relatively warm and previous section, horizontal traction orientations therefore less viscous. To test whether three-di- are largely unchanged and only magnitudes depend

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Figure 10. (a) Horizontal tractions and (b) crustal principal stresses for a heterogeneous viscosity upper mantle with r = 10 in equation (2) (1 order of magnitude increase/decrease in viscosity for every 0.1 km/s increase/decrease in shear wave velocity relative to the layer average).

on the viscosity distribution, although here the basal tractions on the Moho and crustal stress state effect is somewhat less homogeneous. Horizontal change little in orientation and sometimes appre- tractions on the eastern side of the Sierra Nevada ciably in magnitude. This effect is strongest to the anomaly decrease in magnitude, owing to the east of the downwelling in the southern Great particularly slow upper mantle seismic velocity Valley, where tractions and crustal stresses de- and inferred low viscosity. Tractions along the crease in magnitude, and in the Mojave Desert to California-Nevada border directed toward the the northeast of the SAF, where tractions and downwelling region in southeast Nevada decrease crustal stresses increase in magnitude. for the same reason. Traction magnitudes also decrease to the north of the offshore downwelling 3.4. Weak Lower Crust in the western Transverse Ranges, owing to the [35] Thus far we have treated the entire crust as shallow slow velocities (Figure 2a) and inferred essentially rigid in order to isolate the stresses low viscosity there. Magnitudes generally increase transmitted across the Moho. This effectively in the Mojave because it is underlain by high assumes the viscosity of the lower crust is (much) velocities (Figure 2a). For r = 5 (Figure 9), trac- greater than the upper mantle, generally consistent tions increase in the Mojave by 1 MPa to a with geodetically inferred estimates of lithospheric maximum of 3.3 MPa, and for r= 10 (Figure viscosity [e.g., Freed et al., 2007; Thatcher and 10), tractions increase by 2.3 MPa to a maximum Pollitz, 2008]. Nonetheless, it is useful to consider of 4.5 MPa with typical magnitudes of 2–3.5 the case of the lower crust with a reduced viscosity. MPa. The crustal stress fields in Figures 9b and We have calculated the stresses for the case of the 10b change in much the same way with orienta- lower crust viscosity an order of magnitude lower tions of principal stress largely the same and local than the upper mantle. The resulting stress orienta- variations in magnitude. tions in the crust are very similar to the case of a rigid [34] The viscosity-velocity relationship is equation lower crust (Figure 5). Principal stress magnitudes (2), and associated model calculations (Figures 9 (vector sum of the horizontal principal stresses) and 10), are meant only to demonstrate the trend in decrease by an average of 0.5 MPa (within the predicted stresses if upper mantle viscosity and nonstippled area of Figure 5), corresponding to an density are both related via temperature; as the average percent decrease of 12. The relatively viscosity dependence on temperature increases, small decrease in principalstress magnitudes

14 of 23 Geochemistry Geophysics 3 fay et al.: upper mantle convection and crustal dynamics 10.1029/2008GC001988 Geosystems G reflects the fact that while the relatively low viscos- ing, and results, are described by Bennett et al. ity of the lower crust somewhat decreases its ability [2006] and a forthcoming publication (J. C. Spinler to support horizontal shear stresses, the vertical et al., manuscript in preparation, 2008). The three normal stresses transmitted across the Moho are data sets were rotated onto a common stable North decreased by an even smaller amount, resulting American reference frame [Blewitt et al., 2005] in similar stress orientations and only slightly using common velocities at continuous GPS sites decreased magnitudes. and the average was taken when more than one velocity estimate existed at a single point.

4. Comparison With Observations and [38] To estimate dilatation rate, velocities were Discussion interpolated to a uniform grid using piecewise continuous tri-linear (Delaunay triangulation) in- [36] Do the tractions and crustal stresses in Figures 3– terpolation, smoothed with a moving-window 10 contribute in a significant way in driving crustal Gaussian filter (full width half maximum of 120 km) deformation in southern California? Unfortunately to retain only the relatively long wavelength signal, it is not possible to directly answer that question as and differentiated using the finite element method. we have no means of observing tractions at Moho The results in Figure 11a are similar to those of depths and only sparse quantitative measurements Hernandez et al. [2005, 2007] who use a different of the shallow state of stress in the crust [e.g., interpolation and differentiation scheme. This is Zoback and Healy, 1992]. We must therefore use not surprising in that we consider dilatation rate at other measures as proxies. In this section we a wavelength much greater than typical geodetic discuss two independent measures of crustal dy- station spacing and therefore it is not particularly namics: (1) active deformation patterns as revealed important how velocity is interpolated between by geodetic data and (2) an estimate of the sum of stations. forces acting on a crustal block. Both seem to indicate the stresses on the base of the crust may [39] Figure 11a shows two dominant lobes of be an important contribution to the sum of forces negative dilatation (net area loss) in the western driving crustal deformation. For the remainder of Great Valley. The northern lobe may be an artifact this paper, we focus on the tractions and crustal of relatively sparse station coverage, although stress field for the case of a uniform viscosity upper some shortening at high angle to the San Andreas mantle, shown in Figures 3–6. fault is expected in the California Coast Ranges [Wentworth and Zoback, 1989; Argus and Gordon, 2001] and very little (and even net extension) is 4.1. Active Deformation Patterns seen along the San Andreas itself (Figure 11a). The [37] An idealized transform plate boundary expe- southern lobe of negative dilatation is likely real riences only shear deformation and therefore no and consistent with contractional structures in the change in surface area with time. Transpression in southern San Joaquin Valley such as the Pleito and the Transverse Ranges and transtension in the White Wolf fault systems [e.g., Keller et al., 1998, Walker Lane Belt and Salton Trough suggests that 2000; Stein and Thatcher, 1981]. In the southeast- the San Andreas fault system in southern California ern Great Valley and southern Sierra Nevada, we is not such an ideal plate boundary. We illustrate predict a minor amount of positive dilatation, this nonideal plate boundary behavior in active consistent with observed extensional faulting deformation patterns by estimating the dilatation [Jones and Dollar, 1986]. rate, or rate of increase in surface area, from the dense geodetic velocity field in southern California [40] Positive dilatation is seen in the southern (Figure 11a). Dilatation rate is the trace of the Walker Lane Belt consistent with active transtension along the eastern margin of the Sierra Nevada strain rate (e_v) tensor and is coordinate system invariant making it a useful measure to compare [Unruh et al., 2003], effectively the western with the frame invariant tractions and crustal boundary of the extensional Basin and Range stresses predicted by our model. We have com- province [Wernicke, 1992; Wernicke and Snow, bined the published data sets of Shen et al. [2003] 1998]. Net area gain is seen in the Mojave Desert and Kreemer and Hammond [2007] with a new east of the Eastern California Shear Zone and in the velocity solution processed at the University of eastern Transverse Ranges; the latter is broadly Arizona consisting of existing and new data col- consistent with a right step in the transfer of right- lected in the eastern Transverse Ranges; the latter lateral slip between the southernmost San Andreas data set, including monumentation, data process- and Eastern California Shear Zone [Savage et al., 15 of 23 Geochemistry Geophysics 3 fay et al.: upper mantle convection and crustal dynamics 10.1029/2008GC001988 Geosystems G

Figure 11. (a) Observed surface dilatation derived from geodetic velocities (black triangles) in southern California. Velocities were interpolated to a grid and smoothed with a moving-window Gaussian filter with wavelength of 120 km and differentiated to obtain strain and dilatation rates. Anywhere more than 60 km from a geodetic station is not shown. Positive dilatation indicates net extension (increase in surface area), and negative dilatation indicates net compression (decrease in surface area). (b) Predicted relative rates of vertical thinning and horizontal dilatation, determined from the model strain rate tensor at 20 km depth. Results were interpolated from finite element mesh nodes to the continuous field shown here. Extension is reckoned positive, and rates are normalized by the maximum. The greatest dilatation rate in both the observed (Figure 11a) and predicted (Figure 11b) fields is at approximately the same location as Long Valley Caldera (LVC), implying the possibility of a causal relationship between crustal extension, thinning, and volcanism.

1993; Johnson et al., 1994; Hudnut et al., 2002]. on data collected before and after these events, is Areal extension is seen near the southern termina- not yet clear. The broad agreement between pre- tion of the San Andreas fault, curiously offset to dicted dilatation rates and geologic deformation, the NE of the Salton Sea. Negative dilatation is and the lack of evidence for postseismic relaxation evident in the western Mojave, and central and throughout all of southern California [Meade and western Transverse Ranges, consistent with geo- Hager, 2005; Argus et al., 2005] allows us to logic and active shortening in this region [e.g., proceed with some confidence that the geodetically Bartley et al., 1990; Donnellan et al., 1993; derived dilatation estimate is generally representa- Hauksson et al., 1995; Argus et al., 2005]. tive of relatively long wavelength permanent crustal deformation. [41] Some of the dilatation shown in Figure 11a may be a transient effect of postseismic relaxation [42] The predicted crustal deformation from our following major earthquakes [e.g., Nur and Mavko, model with a uniform viscosity upper mantle 1974]. Transient surface deformation in the years (Figures 3–6) is given in Figure 11b. We calculate following the 1992 and 1999 Mojave Desert earth- the horizontal dilatation rate from the strain rate quakes was clearly seen in geodetic data [Pollitz et tensor at 20 km depth. Extension is reckoned al., 2001; Freed and Bu¨rgmann, 2004; Fialko, positive and dilatation rate is equal and opposite 2004; Freed et al., 2007], but whether this influ- to the vertical strain rate (e_v) because the crust is ences our steady state dilatation estimates, based treated as an incompressible fluid. Here strain rates

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the approximately radially compressive stress in the offshore/western Transverse Ranges region and uniaxial compressive stress in the Mojave and eastern Transverse Ranges (Figure 5).

[45] Overall, the comparison of observed (Figure 11a) and predicted (Figure 11b) dilatation rate is com- pelling; the model is generally successful in predicting the style and relative rate of crustal dilatation. Negative dilatation is correctly predicted in part of the southern Great Valley and in the western Mojave and Transverse Ranges, and positive dilatation is predicted and observed in the Walker Lane Belt, eastern Mojave and Salton Sea Figure 12. A simplified Mojave block (double solid regions. Notably, the model and observed dilatation line) and the forces acting on it. Basal tractions from fields both show the strongest crustal dilatation and Figure 4 within the block were interpolated to a finer thinning along the eastern margin of the Sierra grid. These tractions impart a counterclockwise torque Nevada at 241°E, 37.5°N, the location of Long on the block. Shear stress supported by the left lateral Valley Caldera. The observed dilatation could be a Garlock fault (GAR) also imparts a counterclockwise result of a recent shallow magmatic intrusion or torque. Shear stress supported by the right lateral San expansion event causing surface uplift and exten- Andreas fault (SAF) and Eastern California Shear Zone sion [e.g., Newman et al., 2006]. However, our (ECSZ) impart clockwise torque and may balance the model contains no such mechanism and therefore basal traction and Garlock loads, although we have not the spatial coincidence of observed and predicted included stresses acting normal to the block boundaries such as the excess pressure at depth caused by the dilatation implies a possible causal relationship elevated San Bernardino Mountains. The torque form between upper mantle upwelling and crustal exten- these loads is quantified in the text. sion and thinning, and the voluminous volcanism and historic seismicity [e.g., Hill, 2006] at Long Valley Caldera.

[46] To quantify the correlation between observed are only relative because absolute value depends and predicted dilatational deformation, we compare on the absolute value of viscosity and this does not the predicted and observed sign (positive or nega- enter into our calculations. tive) of dilatation rate at model nodes within our [43] Negative dilatation is predicted in the southern study area (polygon in Figure 11). We find that Great Valley resulting from crustal convergence 70% of the model nodes (25 km spacing) predict over the downwelling there. Positive dilatation is the same sign as observed dilatation at the same seen in the eastern Sierra Nevada and Walker Lane point, and therefore 70% of the surface area of Belt and extends south of the Garlock fault into the southern California experiencing significant dilata- eastern Mojave region as well. This is a conse- tion is correctly predicted by the model. Dilatation quence of the upwelling and divergent flow of rate less than 10 nanostrain/yr is considered insig- buoyant upper mantle, with the largest divergence nificant and excluded in this calculation. Compar- approximately at the intersection of the Walker ing dilatation rates is more difficult because our Lane Belt, Garlock fault and Eastern California model does not consider absolute strain rates. Shear Zone. Areal extension is also predicted in the Salton Sea area, a result of upwelling in the upper 4.2. Forces Acting on the Mojave Block mantle and divergent crustal strain. [47] Thus far we have considered model predic- [44] Crustal convergence and negative dilatation is tions based largely on the orientation of the mantle seen throughout the Transverse Ranges. The stron- tractions and crustal stress field. Here we consider gest area loss is offshore because the upper mantle magnitude by estimating the sum of torques acting density anomaly is largest there and because the on a crustal block. Because the vector sum of induced horizontal basal tractions are more con- torques on any plate on the surface of the Earth vergent than in the Mojave and eastern Transverse must be zero, it is useful to consider the set of Ranges (see Figure 4), resulting in greater net forces acting on a piece of crust to compare their crustal strain and area loss. This is consistent with relative magnitudes. Figure 12 shows the Mojave

17 of 23 Geochemistry Geophysics 3 fay et al.: upper mantle convection and crustal dynamics 10.1029/2008GC001988 Geosystems G block, bounded by the dextral San Andreas fault dynamics and basal tractions on horizontal planes and Eastern California Shear Zone, the sinistral typically act over a large area. Garlock fault, and the San Bernardino Mountains. For the following simple calculation, it is not 5. Summary and Conclusions necessary to consider the details of the bounding faults orientation and the Mojave block is defined [50] Crustal deformation in southern California is as a simple, four-sided polygon. In Figure 12 it can clearly strongly influenced by shear stress owing to be seen that the San Andreas fault and Eastern relative motion of the Pacific and North American California Shear Zone shear loads impart clock- plates. Superimposed on shear deformation is a wise torque (about a hypothetical vertical pole in significant amount of crustal shortening and moun- the center of the block), and the Garlock shear load tain building in the Transverse Ranges. We have and the basal traction field both impart a counter- shown through numerical modeling of the stresses clockwise torque, and, qualitatively, their sum is on the crust induced by upper mantle flow, that zero. much of this ‘‘nonideal’’ plate boundary behavior

[48] To quantify these loads, we estimate the torque may be explained by being driven from below by on the block from each load by calculating (*r small-scale convection of the southern California * F)dA, where *r is the radial vector from theRcenterÂ upper mantle. Favorable comparison with active * deformation determined from geodetic data and the of the Earth and F is the force vector (stress area) acting on an area element dA. The horizontalÂ sum of forces acting on crustal blocks suggest the basal tractions were interpolated to a denser grid stresses exerted on the crust from small-scale (10 km spacing) so as to avoid biasing the calcu- downwellings and upwellings in the upper mantle lation by a nonuniform distribution of integration are an important component of the sum of forces points. For the uniform mantle viscosity case in driving crustal deformation in southern California. Figure 4, the basal tractions produce a net torque of 1.9 1023 mN (magnitude of the torque vector). [51] Figures 3–10 show the computed tractions on This valueÂ is likely an underestimate because the the base of the crust and the resulting stress fields basal tractions in the vicinity of the Mojave block within the crust. Horizontal tractions are typically increase, as compared to the uniform viscosity 3–4 MPa or less in magnitude (for the chosen case, for all scenarios of variable upper mantle seismic velocity to density scaling relationship). viscosity that we have explored. For example, if we Traction orientations are largely determined by the use the traction field from Figure 7a, calculated for distribution of seismic velocity anomalies [Yang a lithospheric lid 2 orders of magnitude higher and Forsyth, 2006a] and inferred density structure viscosity than the underlying mantle, the total in the upper mantle, and are largely independent of torque is 2.6 1023 mN, 25% larger. Â viscosity distribution. Three nearly distinct down- [49] To compare with other loads acting on the welling zones in the southern Great Valley, western block, we use 30 MPa as the depth-averaged, long- Transverse Ranges and eastern Transverse ranges term shear stresses supported by block-bounding create negative vertical tractions and convergent faults in southern California [Fay and Humphreys, horizontal shear tractions on the base of the crust. 2006] and assume this stress acts over the approx- In the southern Great Valley, mantle lithosphere imate seismic depth of 15 km. This results in torque formerly beneath the Sierra Nevada is now sinking magnitudes of 4.4 1023 mN, 5.4 1023 mN, and beneath the southern Great Valley, causing active 3.9 1023 mN forÂthe San AndreasÂ fault, Eastern surface subsidence [Saleeby and Foster, 2004] and CaliforniaÂ Shear Zone, and Garlock fault respec- approximately radially convergent shear tractions tively. These torques are approximately a factor of on the base of the crust. In the Transverse Ranges, 2 larger than the basal traction torque, but clearly of two dominant downwelling zones centered off- the same order of magnitude and thus the basal shore and beneath the western San Bernardino tractions are likely as relevant to the dynamics of Mountains act to draw in the overlying crust and the Mojave block as plate interaction stresses cause approximately N–S compressive stress supported by active faults. Stresses acting on (Figure 5), and active shortening (Figure 11). horizontal planes such as our basal traction esti- [52] Crustal deformation driven by small-scale mates (e.g., 3 MPa) may seem small, but it is the convection helps to explain the obliquity of the integrated force and torque that influences crustal Mojave segment of the San Andreas fault with

18 of 23 Geochemistry Geophysics 3 fay et al.: upper mantle convection and crustal dynamics 10.1029/2008GC001988 Geosystems G respect to plate motions. Shortening in the Trans- 2005]. Second, the stress field associated with the verse Ranges as a consequence of a bend in the San excess density beneath the Transverse Ranges Andreas fault is a plausible kinematic interpreta- (Figures 5 and 6) tends to rotate the plane of tion, but provides no dynamic explanation for why maximum right lateral shear stress counterclock- the lithosphere maintains this apparently energeti- wise with respect to the background stress field cally unfavorable plate boundary geometry. Fur- (caused by plate motions), thereby promoting slip thermore, there does not appear to be any clear on faults such as the San Andreas oriented coun- relationship between rock uplift, horizontal short- terclockwise of the plate motion direction [Sonder, ening and the obliquity of the San Andreas fault 1990]. [Spotila et al., 2007]. Our model, which successfully predicts the majority of the dilatational deformation Acknowledgments in southern California without incorporating any shear strain and oblique geometry of the San [54] We thank Y. Yang and D. Forsyth for sharing their Andreas fault (Figure 11), provides an alternative tomography model, Walter Landry and the Computational kinematic interpretation that the bend in the fault is Infrastructure for Geodynamics for developing and maintain- not a cause but rather a consequence of contraction ing Gale, C. Kreemer for sharing his GPS data set prior to publication, and two anonymous reviewers for their con- in the adjacent crust. In this view the fault does not structive reviews. The figures were prepared with GMT act as a fixed barrier to crustal flow but simply a [Wessel and Smith, 1998]. This research was supported by geographic point attached to the adjacent, deform- NSF grant EAR-0510484 to R.B. ing crust. With respect to a fixed Pacific plate, approximately N–S shortening southwest of the References San Andreas fault in the western Transverse Ranges [e.g., Yeats et al., 1988] requires that the Argus, D. F., and R. G. Gordon (2001), Present tectonic mo- trace of the San Andreas fault move to the south- tion across the Coast Ranges and San Andreas fault system in central California, Geol. Soc. Am. Bull., 113(12), 1580– west. Shortening on the northern side of the San 1592, doi:10.1130/0016-7606(2001)113<1580:PTMATC> Andreas fault in the San Bernardino Mountains 2.0.CO;2. [e.g., Dibblee, 1975; Spotila and Sieh, 2000] Argus, D. F., M. B. Heflin, G. Peltzer, F. Crampe, and F. H. requires that the trace of the San Andreas there Webb (2005), Interseismic strain accumulation and anthro- move to the NNE. Both process tend to rotate the pogenic motion in metropolitan Los Angeles, J. Geophys. Res., 110(B4), B04401, doi:10.1029/2003JB002934. trace of the San Andreas fault counterclockwise Artyushkov, E. (1973), Stresses in lithosphere caused by crus- with respect to its previous orientation, and in- tal thickness inhomogeneities, J. Geophys. Res., 78(32), crease the obliquity with respect to plate motion 7675–7708, doi:10.1029/JB078i032p07675. direction. Atwater, T. (1970), Implications of plate tectonics for the Cen- ozoic evolution of western North America, Geol. Soc. Am. [53] Thus the dynamic effect of heterogeneous Bull., 81, 3513 –3536, doi:10.1130/0016-7606(1970)81 upper mantle density structure and induced flow [3513:IOPTFT]2.0.CO;2. on crustal deformation in southern California is Bartley, J. M., J. M. Fletcher, and A. F. Glazner (1990), Tertiary extension and contraction of lower-plate rocks in the central twofold. First, upper mantle downwelling, stron- Mojave metamorphic core complex, southern California, gest beneath the Transverse Ranges, drives short- Tectonics, 9(3), 521–534, doi:10.1029/TC009i003p00521. ening of the overlying crust to the southwest and Beanland, S., and M. M. Clark (1994), The Owens Valley northeast of the present-day location of the Big Fault Zone, eastern California, and surface faulting asso- Bend segment of the San Andreas fault. This has the ciated with the 1872 earthquake, U.S. Geol. Surv. Bull., 1982, 29 pp. kinematic consequence of rotating the San Andreas Becker, T., and L. Boschi (2002), A comparison of tomo- counterclockwise, thereby increasing its obliquity graphic and geodynamic mantle models, Geochem. Geophys. with respect to plate motions, possibly inducing Geosyst., 3(1), 1003, doi:10.1029/2001GC000168. additional downwelling of lower crust or mantle Becker, T. W., and R. J. O’Connell (2001), Predicting plate velocities with mantle circulation models, Geochem. Geo- lithosphere during convergence. There must be a phys. Geosyst., 2(12), 1060, doi:10.1029/2001GC000171. limit to this positive feedback in that the elevation Becker, T. W., J. L. Hardebeck, and G. Anderson (2005), of the Transverse Ranges is finite and therefore Constraints on fault slip rates of the southern California plate provides an independent means of estimating the boundary from GPS velocity and stress inversions, Geophys. magnitude of the mantle tractions [Humphreys and J. Int., 160(2), 634–650, doi:10.1111/j.1365-246X.2004. 02528.x. Hager, 1990; Fay and Humphreys, 2006]. Analysis Bennett, R. A., A. M. Friedrich, and K. P. Furlong (2004), of a similar feedback process of fault orientation Codependent histories of the San Andreas and San Jacinto and local topography has also provided constraint fault zones from inversion of fault displacement rates, Geol- on the state of stress within the crust [Fialko et al., ogy, 32(11), 961–964, doi:10.1130/G20806.1.

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