Permeabilities Inferred from Poroelastic Modeling. of InSAR-Determined Land Surface Deformation in

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1 submitted to Geophys. J. Int. Aquifer and Shallow San Andreas Fault Permeabilities Inferred from Poroelastic Modeling of InSAR-Determined Land Surface Deformation in Coachella Valley, California Ravi Appana 1, Martin O. Saar 1, Beth A. Wisely 2, David A. Schmidt 2 1 Department of Geology and Geophysics, University of Minnesota, Twin Cities 55455, USA 2 Department of Geological Sciences, University of Oregon, Eugene 97403, USA SUMMARY The Coachella Valley groundwater aquifer in southern California, USA, is a major agricultural and municipal water resource. Groundwater overdraft has led to significant reductions of water levels and subsequent land subsidence in some areas of this alluvial basin. Recharge efforts in the Upper Coachella Valley have partially restored groundwater levels and presumably slowed long-term land subsidence. Interferometric Synthetic Aperture Radar (InSAR) between late-1993 through 2000 reveals differential uplift of land surface across two strands of the southern San Andreas Fault (the Garnet Hill and the Banning Faults) in the northwest of the basin, associated with episodes of artificial groundwater recharge at the White Water Recharge Facility. Using InSAR data of land-surface displacement as well as groundwater levels as constraints, we model pore-fluid pressure diffusion and groundwater flow across these two strands of the San Andreas Fault system. Numerical models yield estimates of subsurface hydraulic properties, representing averages over a few kilometers, useful for groundwater management. We constrain the horizontal permeability

2 2 Appana et al. of the White Water sub-basin (WWB) to m 2 k wwb x m 2 and the permeability anisotropy, a = (k z /k x ), of the White Water and the Garnet Hill sub-basins (GHB) to 0.04 a wwb and a ghb 0.016, respectively. In addition, our model suggests permeabilities of m 2 k ghf m 2 and k bf m 2 for the Garnet Hill Fault (GHF) and the Banning Fault (BF), respectively. These results indicate that both faults act as semi-permeable barriers to pore-fluid pressure diffusion and groundwater flow due to a low-permeability fault core. Preliminary calculations result in permeabilities of m 2 k ghf c m 2 for the Garnet Hill Fault core and k bf c m 2 for the Banning Fault core at depths 2 km. Therefore, our study provides estimates for the shallow San Andreas Fault zone permeability field which can serve as an upper limit for fault-zone permeabilities at greater depths and may thus help constrain conceptual and numerical models of active faulting in general and of San Andreas Fault slip dynamics in particular. Key words: Numerical Modeling Permeability Coachella Valley San Andreas Fault Land subsidence Groundwater overdraft. 1 INTRODUCTION Formation permeability is arguably the most important parameter in geological porous media flow as it largely determines fluid flow rates and varies over 15 orders of magnitude in natural settings (e.g., Freeze & Cherry 1979; Saar & Manga 2004; Ingebritsen & Manning 2010). In contrast, other porous media flow parameters, such as hydraulic head gradient, water density, or water viscosity vary much less (e.g., Saar & Manga corresponding author: appan002@umn.edu

3 Poroelastic Modeling in Coachella Valley, CA, USA ; Ingebritsen et al. 2006). In addition to the bulk permeability of the sediment matrix or geologic formations, faults in unconsolidated sediments, bounding or disecting basin aquifers, can act as flow barriers (e.g., Antonellini & Aydin 1994; Rawling et al. 2001; Eichhubl et al. 2005; Mayer et al. 2007), conduits, or combined conduit-barrier systems (e.g., Bredehoeft et al. 1992; Caine et al. 1996; Bense & Person 2006; Bense et al. 2008), depending on their permeability field. Therefore, the permeability of the faults can dictate local to regional groundwater flow paths and rates and potentially affect recharge to groundwater basins (e.g., Marler & Ge 2002; Folch & Mas-Pla 2008). Faults can thus strongly influence the subsurface hydraulic head distribution in faulted aquifer systems (e.g., Haneberg 1995; Mayer et al. 2007). As a result, determination of fault permeabilities is an important component of hydrogeologic investigations. Moreover, improved knowledge of subsurface hydraulic properties can aid with groundwater management, for example to prevent groundwater overdraft and its associated adverse effects such as groundwater storage reduction, land-surface subsidence, and water quality degradation (e.g., Galloway et al. 1999). While faults associated with aquifer systems can affect groundwater flow and storage processes, hydrogeologic conditions can conversely influence fault-slip behavior. For example, many plate-boundary faults, like the San Andreas Fault (SAF), have been interpreted to slip at lower shear stresses than expected for rocks and for faults with similar friction coefficients (e.g., Lachenbruch & Sass 1980; Zoback et al. 1987; Hickman 1991). One possible explanation for this weakness is existence of (large) pore-fluid over-pressures within the fault zones (e.g., Byerlee 1990, 1992; Rice 1992), resulting in the reduction of effective stresses causing fault weakening (e.g., Raleigh et al. 1976; Simpson et al. 1988; Gupta 1992; Saar & Manga 2003; Fulton & Saffer 2009). Furthermore, frictional heating during fault slip can lead to thermal pressurization of the fluids trapped in the low-permeability fault core and resultant reductions in effective stresses, causing dynamic fault weakening (Vredevoogd et al. 2007). Therefore, determining the

4 4 Appana et al. permeability field given by a fault-zone s architecture (dimensions of damage zone vs. fault core as discussed in Sec. 7) can provide insights into the role played by pore-fluid pressures during fault slip. In this paper, we present a case study illustrating the influence of low-permeability faults on the groundwater flow within an unconfined aquifer system in Coachella Valley, California, USA. The three branches of the southern SAF, the Garnet Hill Fault (GHF), the Banning Fault (BF), and the Mission Creek Fault (MCF), are sub-vertical, exhibit dextral strike-slip motion (Yule & Sieh 2003), and comprise the main tectonic features of the upper valley region (Fig. 1). We develop numerical models of pore-fluid pressure diffusion, groundwater recharge and flow, and associated poroelastic land-surface uplift in the Upper Coachella Valley. The models are constrained by both Interferometric Synthetic Aperture Radar (InSAR) data of land-surface uplift and groundwater level measurements in wells (Sec. 3). Our models provide estimates for both basin and fault permeabilities and thus have implications for groundwater and tectonic studies. Most estimates of fault-zone permeability come from laboratory experiments on fault samples from surface outcrops or drill cores (e.g., Chu et al. 1981; Morrow & Lockner 1994; Zhang et al. 1999; Faulkner 2004; Tsutsumi et al. 2004; Mizoguchi et al. 2008; Wibberley et al. 2008; Lockner et al. 2009). Here, we infer permeabilties at regional aquifer scales by modeling pore-fluid pressure changes across fault zones. Our approach yields a range of relatively shallow fault permeabilities, applicable only to basin depths or depths of 2 km at most. However, these values likely serve as upper bounds for deeper fault permeabilities and have thus implications for slip dynamics of faults in general and of the San Andreas Fault (SAF) in particular.

5 Poroelastic Modeling in Coachella Valley, CA, USA 5 2 BACKGROUND In the following sections we introduce the equations governing fluid flow through, and deformation of, porous media. We also provide background information on the hydrogeologic and poroelastic setting of the study region. 2.1 Fluid flow and poroelasticity Laminar, low-inertia fluid flow through porous media under unconfined aquifer conditions is governed by the here linearized Boussinesq equation, S h h 1 t (K h ) = Q s + α ( s), (1) t where S = S y + DS s is storativity with S y, D, and S s denoting specific yield, thickness, and specific storage of the aquifer, respectively. Furthermore, K is the hydraulic conductivity tensor, Q s is a fluid source or sink, and are the gradient and the divergence operators, respectively, α is the Biot-Willis coefficient defined as the ratio of increment in fluid content to volumetric strain while maintaining constant fluid pressure conditions (e.g., Wang 2000), s is the displacement vector (see Equation (10), defined for solid displacement), t ( s) is the temporal change in strain, and h 1 and h are the constant and spatially varying terms of the hydraulic head, h, respectively. Neglecting kinematic energy due to assumption of low groundwater flow velocities, hydraulic head is defined as h = p ρ f g + h z = h + h 1, (2) where h z is elevation head and pρ f 1 g 1 is pressure head with p representing porefluid pressure, ρ f fluid density, and g (vertical) acceleration due to Earth s gravity. Linearization implies that Equation (1) is only valid for small h /h 1 ratios, as given in many settings, including the basins in the study region (see Fig. 5 introduced in Sec. 4). Under steady-state conditions, Equation (1) simplifies to (K h ) = Q s, (3)

6 6 Appana et al. which is solved for h in our fluid-flow models. Darcy s law (Darcy 1886) is then applied to yield specific discharge or Darcy velocity, q, given as q = K h, (4) where the hydraulic conductivity tensor is defined as K = ρ f gk/η, (5) where k is the second-rank intrinsic permeability tensor and η is the fluid s dynamic viscosity. In our two-dimensional models, k is reduced to a horizontal, k x, and a vertical, k z, component (ignoring minor off-diagonal terms) which are related by an anisotropy parameter, a = k z /k x. (6) Under hydrostatic conditions, the pore-fluid pressure, p, is related to the hydraulic head, h, by p = ρ f gh. (7) Therefore, the steady-state groundwater flow or hydraulic head diffusion equation (Equation 3) can also be written in terms of the pore-fluid pressure gradient, p = ρ f g h, then denoting pore-fluid pressure diffusion. Hydraulic diffusivity is given by D u = hk S y = hρ fgk ηs y (8) in unconfined aquifers. Consequently, the subsurface pore-fluid pressure distribution is largely determined by the hydraulic conductivity or the permeability of the porous medium. The effective stress describes the relation between pore-fluid pressure, p, and the stress state as σ t = σ e + αpδ ij, (9)

7 Poroelastic Modeling in Coachella Valley, CA, USA 7 where σ t are the total stresses acting on the porous material, σ e are the effective stresses, and δ ij is the Kronecker delta. Furthermore, plane-strain theory relates changes in pore-fluid pressure to displacement of the porous medium matrix by Y Y 2(1 + ν) 2 s + s = α p, (10) 2(1 + ν)(1 2ν) where Y is the Young s modulus of the aquifer material (porous medium) and ν is its Poisson s ratio (Wang 2000). The numerical model introduced in Section 5, solves Equations (3), (9), and (10) and applies Equation (4) to determine fluid flow lines when desired. 2.2 Hydrogeologic setting The study region is located in the Upper Coachella Valley in southern California, USA (Fig. 1), an area enclosed between Little San Bernardino, San Bernardino, and San Jacinto Mountains. The southern San Andreas Fault (SAF) system branches into several strands in the upper valley region, dividing the basin into sub-basins and respective aquifers. Regional groundwater flow paths extend through the valley along its long-axis from the NW to the SE and drain into the Salton Sea. A much smaller but significant cross-valley component to groundwater flow also exists in the upper valley region due to artificial groundwater recharge at the White Water Recharge Facility as shown later. Runoff from the mountains in the NE, NW, and SW of the study region and baseflow from the San Gorgonio Pass form the main sources of natural groundwater recharge. Evapotranspiration, groundwater pumpage through wells, and outflow to the lower valley contribute to groundwater discharge (CVWD 2002). The sediments of the Upper Coachella Valley basin include unconsolidated, semiconsolidated, and consolidated deposits (Tyley 1974). The main water-bearing sediment units are Pleistocene and Holocene unconsolidated deposits. These are poorly sorted heterogeneous alluvial fan deposits with few fine sediments, forming unconfined aquifers (CVWD 2002). Furthermore, the foothills of the mountains are formed by partly consolidated deposits of Pliocene and Pleistocene age that yield little water.

8 8 Appana et al. Similarly, the pre-tertiary and Tertiary rocks of the basement and the San Jacinto Mountains do not yield any significant amount of water and thus act as groundwater flow barriers (CDWR 1964). The White Water sub-basin (WWB), southwest of the Garnet Hill Fault, hosts the groundwater recharge facility (Fig. 1). This basin has the most permeable deposits in the Upper Coachella Valley, allowing the most direct recharge of the unconfined aquifer below. 2.3 Poroelastic deformation Sneed & Brandt (2007) report aquifer deformation and related land-surface subsidence associated with groundwater overdraft in the Lower Coachella Valley ranging from about 35 to 150 mm in These studies further report an increase in subsidence of as much as 75 to 180 mm in Such deformation can be elastic and/or inelastic. Elastic deformation occurs when decreases in pore-fluid pressures due to groundwater discharge or withdrawal increase effective stresses, σ e, causing aquifer skeleton contraction (e.g., Poland 1981; Wang 2000; Hoffmann et al. 2001). However, if this decrease in pore-fluid pressure causes the effective stresses to increase beyond their pre-consolidation values, deformation is not recoverable, i.e., it is inelastic and results in a permanent loss of aquifer storage capacity (e.g., Poland 1981, 1984; Galloway et al. 1998). In addition, compaction of the clay-rich sediments present in the Lower Coachella Valley may contribute to inelastic deformation in that region (Galloway et al. 1999). Therefore, the recorded decrease in groundwater levels in the Lower Coachella Valley between 1996 and 2005 suggests that part of the observed land-surface subsidence might be permanent, resulting in loss of aquifer storage. To counteract land-surface subsidence, the Coachella Valley Water District (CVWD) has introduced artificial groundwater recharge in the upper valley since 1973 (CVWD 2002). Due to an increase in the amount of artificial groundwater recharge, satellite interferometric methods have registered ground-surface uplift in the upper valley during recent years (late-1993 to 2000). The InSAR data further shows differential land-surface uplift between the sub-basins separated by the BF and the GHF (Fig. 2). We suggest

9 Poroelastic Modeling in Coachella Valley, CA, USA 9 that such land-surface uplift may potentially be interpreted as the combined response of the aquifer-fault system to 1) artificial groundwater recharge and 2) tectonic stresses acting on the basin, with a strong preference toward the former as discussed later. 3 DATA We use both geophysical and hydrologic data to develop a coupled hydrologic and poroelastic model of the Upper Coachella Valley. The rectangular region stretching SW- NE in Figure 1 shows the area of interest which is primarily chosen for its proximity to wells where groundwater levels are available during late-1993 through 2000 (Sec. 3.3). In addition, this region is down-dip from the groundwater recharge area where groundwater levels are elevated due to the artificial groundwater recharge. Finally, the cross-sectional profile is drawn perpendicular to the main hydraulic head gradient, oriented down the axis of the valley. Table 1 lists the parameters used in this study. 3.1 Digital Elevation Model (DEM) data The topography across the actual basin is relatively flat with only about 60 m variation in elevation over a distance of 12 km (Fig. 1). We represent this topography in a two-dimensional (2D) vertical model by averaging land-surface elevations over a series of parallel SW-NE-trending cross-sections within the rectangular region ( km 2 ) shown in Figure 1 (i.e., averaging perpendicular to the cross-sections). Advantages of using such an average surface elevation are that 1) it includes topography information from the region immediately surrounding the model cross-section and 2) any local features deviating from the average topography are subdued, similar to the underlying groundwater-table topography. This averaged land-surface topography does not have a precise physical location on the map and is thus represented by the dashed line passing

10 10 Appana et al. through the mid-point of the rectangular region (Fig. 1), hereafter referred to as the model cross-section. 3.2 InSAR data Interferometric Synthetic Aperture Radar (InSAR) is a repeat-pass satellite data acquisition tool that can be effectively used for monitoring surface deformation due to groundwater extraction and recharge (e.g., Galloway et al. 1998; Amelung et al. 1999; Bawden et al. 2001; Lu & Danskin 2001; Schmidt & Bürgmann 2003; Bell et al. 2008; Wisely & Schmidt 2010). SAR data from the ERS1/2 satellite of the European Space Agency is used to measure surface deformation in the study region. This type of data is most useful in areas with little vegetative cover and in urban areas, and therefore is well suited for the semi-arid Coachella Valley. Differential interferograms can be constructed to span months, even years, depending on the suitability of SAR pairs regarding interferometry and coherence of each scene, and are processed to a spatial resolution of 30 m using the ROI PAC software package (Rosen et al. 2004). Flattening the interferometric phase removes 1) any gradient caused by orbital errors and 2) the horizontal displacement signal associated with plate boundary deformation. Because the perpendicular baseline between the orbital passes is greater than zero, there is a topographic contribution to the phase difference (Bürgmann et al. 2000). This is removed using a 30 m Digital Elevation Model (Fig. 1) from the Shuttle Radar Topography Mission (SRTM). The phase difference is then unwrapped to estimate range change in the satellite s line-of-sight (LOS) or look direction. Stacking differential interferograms estimates an average rate of deformation for each pixel and dampens the effect of atmospheric noise. We stack 23 interferograms (processed from 24 independent SAR scenes) by summing the LOS range change for a given pixel and dividing by the cumulative time spanned by all of the interferograms (Table 2). All 23 differential interferograms used in the analysis span intervals within late-1993 through 2000 and have a perpendicular baseline of < 277 m, averaging 77 m.

11 Poroelastic Modeling in Coachella Valley, CA, USA 11 These short distances in satellite positioning between acquisitions maximize coherence and minimize topographic errors. A phase step in an interferogram across a fault in this region (Fig. 2a) could be caused by subsurface fault slip for which we would expect predominantly horizontal surface displacement. Alternatively, natural or artificial groundwater recharge can cause differential uplift when subsurface hydraulic properties, for example, permeability or storage coefficients, are heterogeneously distributed causing non-uniform pore-fluid pressure and effective stress fields (e.g., Haneberg 1995; Bense & Balen 2004; Mayer et al. 2007). Therefore, a sharp contrast between fault and/or basin aquifer permeabilities can give rise to relatively sharp pore-fluid pressure changes and related uplift step functions across faults resulting in such a phase step in an interferogram. InSAR does not determine the full 3D displacement vector unless multiple satellite look directions can be employed in the analysis. However, we find that the ascending track data, although limited, is consistent in magnitude and direction to the more abundant descending data, thereby suggesting that the vertical direction is the dominant mode of deformation for this hydrogeologic basin (Bawden et al. 2001; Hoffman & Zebker 2003; Wisely & Schmidt 2010). This also suggests that most of the land-surface uplift during late-1993 to 2000 is caused by groundwater recharge. Hereafter, we refer to this poroelastic response of the aquifer simply as uplift. While tectonic causes of, or at least contributions to, the observed uplift pattern cannot be completely excluded, they are likely minor and thus beyond the scope of the present study. Furthermore, since the look vector is nearly vertical (Fig. 2a), we assume that the LOS range change observation is representative of the vertical deformation. The actual vertical deformation is 6% more than the LOS observations once the LOS is back-projected onto a vertical unit vector. However, the spatial averaging of the LOS observations perpendicular to the profile across the basin (discussed below) and the likelihood of only a small horizontal deformation component, means that the uncertainty in vertical deformation is greater than the 6% LOS correction. The patterns of time-dependent surface displacement may also be assessed by time-

12 12 Appana et al. series analysis (Fig. 3). In regions like Coachella Valley, where surface deformation may be due to more than one process, high temporal resolution of a time-series analysis is a method used to separate transient seasonal deformation from long-term deformation. Therefore, we produce a pixel-by-pixel time-series of vertical displacement using an inversion method developed by Schmidt & Bürgmann (2003). The method solves for the incremental range change between SAR scene acquisitions employing a linear inversion which translates the set of interferograms into a range-change time-series. The same interferograms used in stacking are used in the time-series construction (Table 2). Scenes used in multiple interferograms are down-weighted in the time-series inversion process, so that artifacts in repeated scenes do not dominate the time-series of deformation. The resultant time-series is a pixel-by-pixel deformation map sequence from late-1993 to 2000, showing vertical deformation accumulating from scene acquisition date to acquisition date. Analogously to averaging multiple topographic cross-sections (Sec. 3.1), we calculate averages along the model cross-section from the stacked interferogram showing uplift rates (Fig. 2b) and from the time-series data showing cumulative uplift (Fig. 3a). Such averaging provides a more representative uplift profile for the model cross-section and allows for better predictions of average permeabilities for the aquifer-fault system. In part due to this approximation, our estimates of permeability and other parameters along the cross-section are not exact but rather first-order approximations of plausible parameter ranges. Reporting such parameter ranges is, however, consistent with the notion that natural geologic parameters over large spatial scales are likely heterogeneous and/or anisotropic. From the time-series of average uplift (Fig. 3a), we calculate a sub-basin spatial average of the land-surface uplift (Fig. 3b) for all three sub-basins in the upper valley. The uncertainties in these averages are estimated using standard error propogation. Excluding negligible tectonic effects discussed previously (Sec. 3.2), the total uplift recorded in the upper valley sub-basins from late-1993 to 2000 is caused by a convolution of seasonal recharge/discharge and artificial recharge of groundwater at the White Water

13 Poroelastic Modeling in Coachella Valley, CA, USA 13 Recharge Facility. We assume that artificially recharged groundwater does not reach the Mission Creek sub-basin (MCB) due to its distal location to the White Water Recharge Facility as may be inferred from Figure 1. Thus, we attribute the temporal variations in spatially averaged MCB uplift (MCB-curve in Fig. 3b) solely to natural seasonal changes in groundwater content and related pore-fluid pressures. Furthermore, assuming that seasonal groundwater recharge/discharge effects in the White Water subbasin (WWB) and the Garnet Hill sub-basin (GHB) are similar to those in the MCB, we approximately remove the natural seasonal land-surface uplift/subsidence from the total uplift (Fig. 3a) by subtracting the spatially averaged MCB uplift from that of the WWB and the GHB, resulting in a relative land-surface uplift (Fig. 3c). This relative uplift of the WWB and the GHB should thus largely reflect cumulative uplift that is solely caused by the increase in artificial groundwater recharge in the WWB during late to 2000 (Fig. 4), compared to that during 1987 to 1993, as discussed in Section 3.3. Moreover, we observe that the relative uplift in the WWB and the GHB from late-1993 to 2000 (Fig. 3c) is significantly larger than 1) the uncertainties introduced by averaging uplift as discussed above and 2) the seasonal variations in land-surface uplift, indicating that the majority of the uplift is due to groundwater recharge. Therefore, the average uplift rate (Fig. 2b) calculated from the stacked interferogram along the model crosssection is adjusted such that the uplift rate from late-1993 to 2000 is zero throughout the MCB. 3.3 Hydrologic data Figure 4a shows temporal variations in water-table depth below ground-surface elevation (GSE) at nine monitoring wells (Fig. 1) projected onto the model cross-section. The peaks in the water levels of Wells W6, W7, W8, and W9 in the WWB appear to indicate responses to episodes of artificial groundwater recharge (Fig. 4b). In contrast, Wells W1, W2, W3, as well as W4 and W5 in the MCB and the GHB, respectively, are farther away from the artificial groundwater recharge area and thus show approximately constant groundwater levels during the same time period. Although these wells are at

14 14 Appana et al. different topographic elevations (Appendix C), the depth to the water in wells of a given sub-basin are approximately identical. Therefore, we assume that the groundwater-table elevation is a subdued replica of the topography within a sub-basin and is offset across different sub-basins with higher groundwater levels in the NE than in the SW of the cross-section (Fig. 5). The amount of artificial groundwater recharge, Q [m 3 /yr], introduced at the White Water Recharge Facility in the WWB from late-1993 to 1999 is shown in Figure 4b. The horizontal dashed and solid lines represent the average annual artificial groundwater recharge added from 1987 through 1993 ( m 3 /yr) and from late-1993 through 1999 ( m 3 /yr), respectively (CVWD 2002). The net change in artificial groundwater recharge, Q [m 3 /yr], is defined as the difference between the amount of average annual artificial groundwater recharge from late-1993 through 1999 and that from 1987 through However, only a portion of Q, hereafter denoted Q c [m 3 /yr/m], reaches the model cross-section where it causes poroelastic land-surface uplift (Fig. 2). Therefore, the actual value of Q c [m 2 /yr] is estimated as a plausible range. Hence, we consider two scenarios with minimum and maximum extent of alongvalley pore-fluid pressure diffusion of 3 and 9 km, respectively, represented by the two triangles (with bold and thin lines) in Figure 2a. The portion of the artificial groundwater recharge entering the rectangular region in the WWB is estimated to be proportional to the ratio of its area (trapezoid) to the areal extent of groundwater diffusion (the two triangles). This results in plausible Q c values of m 2 /yr Q c m 2 /yr. All simulations are thus conducted for Q c values of (min), (mean), and (max) m 2 /yr.

15 Poroelastic Modeling in Coachella Valley, CA, USA 15 4 CONCEPTUAL MODEL A cross-section across the Upper Coachella Valley, showing our conceptual two-dimensional model, is given in Figure 5. The cross-section extends from the foothills of the San Jacinto mountains in the SW to a distance of 11.5 km toward the NE into the Mission Creek sub-basin (MCB) where the effects of artificial groundwater recharge in the White Water sub-basin (WWB), and the runoff from the Little San Bernardino Mountains, are negligible. The permeability and its anisotropy, hereafter referred to as permeability structure, can be different for different sub-basins. Adjacent domains are linked by requiring continuity of hydraulic head and groundwater flux across the internal boundaries. The faults are modeled as vertical features (Yule & Sieh 2003), as a small deviation in actual fault orientation from vertical does not substantially modify the regional groundwater flow system (Folch & Mas-Pla 2008). Furthermore, we do not model the permeability structure of the MCB as there is no observed uplift across that sub-basin in the region of interest (Fig. 2). Instead, we use permeability estimates of m 2 k mcb x m 2 from previous studies (Tyley 1974; Swain 1978; Mayer et al. 2007) for the MCB. No aquitards are modeled as the clay content of the aquifer sediments is minor in the upper valley region (CVWD 2002). The San Jacinto Mountains toward the SW end of the model cross-section and the low-permeability basement rocks act as barriers to groundwater flow restricting the active groundwater flow zone to the upper 450 m of the basin, which corresponds to a water-saturated sediment thickness of about 300 m (Tyley 1974; Swain 1978). There is no cross-valley flow across the NE boundary of the cross-section, as it is far away from both the groundwater recharge area and the runoff from the mountains to the NE. In our model, increase in pore-fluid pressures can induce poroelastic land-surface uplift in two ways: 1) by increasing the water pressure in saturated pores and 2) by raising the water table into previously unsaturated zones which increases pore-fluid pressures from atmospheric, or sub-atmospheric, to (approximately) hydrostatic conditions. In order to constrain hydrogeologic parameters, we conduct simulations to explore parameter space. To reduce the number of unknowns to a tractable value, we make

16 16 Appana et al. the following assumptions: 1) All uplift is caused by poroelastic deformation of the sediment matrix, i.e., there is no tectonic uplift (Sec. 3.2). 2) The main along-valley groundwater flow, perpendicular to the cross-section, does not affect water-table elevations or pore-fluid pressures, as this flow into and out of the cross-section is equal. 3) Groundwater recharge rates to valley aquifers through the mountains are negligible in comparison to both along-valley and across-valley components of groundwater flow (CDWR 1964). 4) Groundwater flow in the aquifer is assumed to be isothermal due to the small topographic relief and groundwater flow depths encountered within the sedimentary basin and negligible groundwater flow within the adjacent mountains (see Point 3). 5) Artificial groundwater recharge at the surface enters the aquifer system instantaneously due to the large proportion of coarse, high-permeability sediments present in the WWB (CVWD 2002). Therefore, flow in the unsaturated zone is not explicitly simulated. 6) The water table is a subdued replica of the topography within fault-bounded sub-basins (Sec. 3.3). 7) Equilibrium conditions for poroelastic deformation are reached instantaneously whenever subsurface pore-fluid pressures change. This implies that a) diffusion of pore-fluid pressure in the sub-surface is a relatively fast process so that water levels at any instant determine groundwater flow velocity vectors and b) the coupling between pore-fluid pressures and stresses in the sediment matrix is instantaneous. 8) Fault-zones are simulated as isotropic porous media, with a uniform width of 50 m throughout the entire depth of the basin (Mayer et al. 2007), although permeability anisotropy and a different width (of 10 m) are considered later by employing a heterogeneous fault-zone architecture. 9) The permeability structures of all formations (three sub-basins and two faults in Fig. 5) are homogeneous. However, different formations may have different permeabilities, so that the aquifer-fault system as a whole can be heterogeneous. 10) The effect of net artificial groundwater recharge on uplift is negligible in the Mission Creek sub-basin (Sec. 3.2).

17 Poroelastic Modeling in Coachella Valley, CA, USA 17 5 NUMERICAL MODEL We develop a two-dimensional, vertical numerical model, employing the finite-element simulator COMSOL Multiphysics (R), to constrain the permeability structure of the subsurface. Our model simulates instantaneous artificial groundwater recharge causing pore-fluid pressure diffusion and groundwater flow and associated poroelastic stress redistribution leading to deformation of porous media in both horizontal and vertical directions along the model cross-section. The numerical model grid has triangular mesh elements with quadratic shape functions that interpolate parameter values in-between element corners. The triangular elements are of varied sizes with coarser element resolutions in the center of the model sub-domains and finer element resolutions toward subdomain edges. The total number of elements used in the model cross-section ( km 2 ) is The simulation procedure is discussed in the following sections. 5.1 Initial state (late-1993) The initial pore-fluid pressure distribution (Fig. 6a) and the state of stresses (Fig. 6e) in the aquifer are defined by conducting steady-state simulations of fluid flow and planestrain deformation for a baseline set of parameter values. For the 2D fluid-flow model, the water table is approximated from observed groundwater levels during late-1993 (Sec. 3.3). The left, right, and bottom edges of the model cross-section are no-flow boundaries (Table 3). For the 2D plane-strain model, the boundary conditions defining the horizontal and vertical movement of the porous sediment matrix are described in Table 3. The flow lines and the z-displacements of the porous sediment matrix modeled for late-1993 are shown in Figures 6b and 6f, respectively. 5.2 Final State (2000) The final state of the aquifer is modeled by introducing artificial groundwater recharge, i.e., by adding a fluid source term. An integrated constant-flux term, Q c [m 2 /yr],

18 18 Appana et al. representing the net change in artificial groundwater recharge entering the cross-section (Sec. 3.3), is introduced in the White Water sub-basin along a line source. The line source is centered at R(x, z) = (2600, 120) m, approximately at the location of the peak uplift rate along the model cross-section (Fig. 2), and has a horizontal extent of L = 2500 m. Both R and L are constant parameters in the steady-state simulation. The fluid-flow model estimates the resultant pore-fluid pressure redistribution in the subsurface (Fig. 6c). These pore-fluid pressure changes lead to modifications in the Darcy velocity field and associated groundwater flow lines (Fig. 6d). The plane-strain model in turn calculates the resultant stresses (Fig. 6g) and displacements (Fig. 6h) for the new hydrogeologic conditions. Although we show only the vertical displacements in our illustrations, we consider the total two-dimensional displacement vector when calculating the misfit, M [mm/yr], discussed below. The rate of uplift is shown as a function of position, x, along the model crosssection (e.g., Fig. 7b). We explore parameter space of basin and fault permeabilities (as discussed in Sec. 6), minimizing the misfit between modeled and measured uplift rates. The misfit, M [mm/yr], is defined as a root-mean-squared error along the model cross-section, where M = 1 n n ( u(x i )) 2, (11) i=1 u(x i ) u obs (x i ) if u(x i ) u obs (x i ) ū obs (x i ) u(x i ) = 0 if u(x i ) u obs (x i ) < ū obs (x i ). In Equations (11) and (12), x i [km] are distances along the cross-section, u(x i ) [mm/yr] and u obs (x i ) [mm/yr] are the simulated and observed uplift rates at x i, respectively, ū obs (x i ) [mm/yr] are the standard deviations of u obs (x i ) at x i, and n is the number of measurements along the model cross-section. (12)

19 Poroelastic Modeling in Coachella Valley, CA, USA 19 6 RESULTS We employ numerical models (Secs 4 and 5), simulating pore-fluid pressure diffusion, groundwater flow, and land-surface uplift to explore parameter space (Table 4) of k wwb x, a wwb, k ghf (k ghf x = k ghf z ), k ghb, a ghb, and k bf (k bf x x = k bf z ). Other parameters, D, L, R(x, z), b, Y, α, η, ν, and ρ s, described in Table 1, are held constant and assigned typical values for the Upper Coachella Valley, as variations in these parameters are small compared to the variable parameters (numbered in square brackets throughout this paper) listed in Table 4. Appendix A provides detail regarding the interdependence of some model parameters. In the following, sub-basins and faults are discussed in order of appearance along the modeled cross-section from the SW (near the White Water Recharge Facility) to the NE (Fig. 5). As mentioned before, uplift in the MCB beyond that caused by natural grounwater recharge is not observed (Fig. 3c), so that the BF is the last feature discussed along the cross-section. 6.1 White Water sub-basin (WWB) We use a contour plot of misfit (Fig. 7a) to analyze the simulations conducted by varying parameters k wwb x [1] versus a wwb [2] at constant Q c [3] = m 2 /yr, k ghf [4], kx ghb [5], a ghb [6], and k bf [7] as shown in Table 4. The dots in the figure represent parameter combinations of kx wwb [1] and a wwb [2]=(k z /k x ) wwb at which simulations are run. Contours with lower misfit numbers, M, represent regions with better matches between observed and simulated uplift rates. For these simulations, the bold solid line in Figure 7a represents the contour with minimized misfit values of M 0.14 mm/yr. The dashed and dot-dashed curves in Figure 7a are contours with minimized misfit values of M 0.14 mm/yr for simulations conducted at Q c [3] values of and m 2 /yr, respectively, and constant [4]-[7]. However, the best match is obtained only after optimizing all parameters considered, as discussed further in the following sections. As expected, an increase in kx wwb [1], at constant values for parameters [2]-[7], results

20 20 Appana et al. in a decrease in simulated uplift rates in the WWB (Fig. 7b). Similarly, an increase in a wwb = (k z /k x ) wwb [2], at constant [1] and [3]-[7], results in a decrease in simulated uplift rates in the WWB (Fig. 7c). It is important to note that variations in k wwb x [1] and a wwb [2] also affect simulated uplift rates in the adjacent Garnet Hill sub-basin (GHB) but not the Mission Creek sub-basin (MCB). Furthermore, these simulations show that estimates of kx wwb [1] at constant [2] and [4]-[7], depend on parameter values for Q c [3]. Therefore, by considering a plausible range of values for Q c [3] (Sec. 3.3), we constrain the permeability structure of the WWB near the model cross-section (Fig. 1) to m 2 k wwb x m 2 and 0.04 a wwb In summary, the WWB aquifer appears to be anisotropic, with higher horizontal permeability values, kx wwb [1], associated with larger permeability anisotropies, where the latter are indicated by decreasing values of a wwb [2] further away from Garnet Hill Fault (GHF) To estimate the permeability of the Garnet Hill Fault (GHF), we explore the parameter space of k ghf [4] versus a ghb [6], at constant k wwb x [1], a wwb [2], Q c [3], kx ghb [5], and k bf [7] (Table 4). Simulation results suggest that increasing values of a ghb [6]=(k z /k x ) ghb at constant [1]-[3], [5], and [7] requires a corresponding increase in k ghf [4] to maintain minimized misfit values (Fig. 8a). However, this trend is finite so that a bounded elliptical region with minimized misfit, M, exists. The effect of variations in kx ghb [5], the parameter representing the horizontal permeability of the GHB on the permeability, k ghf [4], of the GHF is illustrated by comparing Figures 8a and 8b. Figures 8a and 8b show contour plots of misfit, M, corresponding to simulations conducted with values of kx ghb [5] equal to (minimum) and m 2 (maximum), respectively (Reichard & Meadows 1992), at constant [1]-[3] and [7]. Furthermore, the effect of variations in parameter values of Q c [3] is also explored (Appendix A). In summary, our simulations suggest a permeability range for the GHF of m 2 k ghf m 2. As expected, an increase in Garnet Hill Fault permeability, k ghf [4], at constant values for all other parameters considered, re-

21 Poroelastic Modeling in Coachella Valley, CA, USA 21 sults in an increase in simulated uplift rates in the adjacent GHB (Fig. 8c), as pore-fluid pressure diffusion from the WWB to the GHB is facilitated. However, it is important to note that these variations in k ghf [4] do not appear to influence the simulated uplift in the WWB, where the artificial groundwater recharge occurs. 6.3 Garnet Hill sub-basin (GHB) We use estimates of the horizontal permeability of the GHB from previous studies (Tyley 1974; Swain 1978) as input values for kx ghb [5] in our simulations (for justification, see Appendix A) but do constrain the permeability anisotropy of the GHB to a ghb [6] (Figs 8a-b). As expected, an increase in k ghb x [5], at constant values for parameters [1]-[4], [6], and [7] (Table 4), results in a decrease in simulated uplift rates in the GHB (Fig. 9a). Similarly, an increase in a ghb [6] = (k z /k x ) ghb, at constant [1]-[5] and [7] (Table 4), results in a decrease in uplift rates in the GHB as well (Fig. 9b). However, we note that the variations of kx ghb [5] and a ghb [6] do not affect uplift rates in the adjacent sub-basins, i.e., the WWB or the MCB, as shown in Figures 9a-b. 6.4 Banning Fault (BF) In order to conclusively constrain the permeability of the BF it would be necessary to conduct a 5-dimensional parameter analysis, i.e., a wwb [2] versus Q c [3] versus k ghf [4] versus a ghb [6] versus k bf [7], at constant k wwb x [1] and kx ghb [5], which is beyond the scope of this study (Secs 6.1, 6.2, and 6.3). However, we conduct simulations of land-surface uplift considering six plausible combinations of parameter values for [1]-[6] (Table 4) within their likely variability as determined elsewhere in this study. Figure 10 shows the reduced misfits, δm = M M i min, as a function of the permeability of the BF, where M i min, with i = 1 to 6, are the minimum misfit values corresponding to the simulations run with the six different combinations of parameters [1]-[6], respectively. We observe that irrespective of the parameter values used for [1] to [6], the reduced misfit increases with increasing values for k bf [7] above m 2 (Fig. 10). There-

22 22 Appana et al. fore, we consider that this value represents a maximum permeability for the BF. That only an upper bound can be established for k bf [7] is not surprising, as the fault permeability needs to be just low enough to prevent land-surface uplift in the adjacent MCB (as observed - see Fig. 3c) by sufficiently limiting pore-fluid pressure diffusion and groundwater flow across the BF. 7 DISCUSSION Estimates of permeability are often scale-dependent (e.g., Zlotnick et al. 2000; Ingebritsen et al. 2006). Our study provides additional insights into the subsurface hydrogeology of the Upper Coachella Valley when combined with previous permeability estimates determined on local scales using well logs (Tyley 1974) and regional scales (few km) using steady-state groundwater flow models (Tyley 1974; Swain 1978). Figure 11a shows a summary of the permeability estimates in the Upper Coachella Valley from this study in comparison to previous work. Figure 11b shows the uplift rate along the model cross-section for one plausible combination of parameter values (listed under Fig. 11b in Table 4) giving a close-to optimal fit between simulated and observed uplift rates. However, the model seems to slightly underpredict the observed uplift rates on the left side of the profile (in the WWB) and a better fit may be obtained by changing the position, R(x, z), and/or length, L, of the recharge zone (Sec. 5.2). Since the simulated uplift rates shown are within the zone of acceptable values indicated by the standard deviation of observed uplift rates and given how the misfit, M, is determined (Equations 11 and 12), we do not expect significant changes in the estimated permeabilities resulting from variations in R and L. Therefore we keep these secondary parameters fixed.

23 7.1 Permeability structure of the sub-basins Poroelastic Modeling in Coachella Valley, CA, USA 23 The estimates for the horizontal permeability of the WWB (Fig. 11a) in the Upper Coachella Valley are well within the range of values representative of clean unconsolidated sand deposits (Freeze & Cherry 1979) present in the study region (Proctor 1968). Furthermore, our large-scale (several km) permeability estimates for the WWB of m 2 k wwb x m 2 match closely values of m 2 k wwb x m 2 from previous studies (Tyley 1974; Swain 1978). Our permeability anisotropy estimates of 0.04 a wwb = (k z /k x ) wwb for the WWB (Sec. 6.1) predict higher horizontal permeabilities and may indicate stratification due to alternation of coarse- and fine-grained sediment deposits, resulting from variations in stream power from wet to dry years (CDWR 1964). A possible explanation is that horizontal layers in parallel, formed by such stream processes, provide overall horizontal permeabilities given by the arithmetic mean, which is dominated by the highest-permeability layer (e.g., Saar & Manga 2004; Ingebritsen et al. 2006). Our analysis also suggests that the permeability anisotropy of the GHB of a ghb is approximately an order of magnitude smaller than that of the WWB (Fig. 11a). Furthermore, the horizontal permeabilities of m 2 k ghb x m 2 considered for the GHB in model simulations from a previous study (Reichard & Meadows 1992) are an order of magnitude less than those predicted here for the adjacent WWB (Sec. 6.1). This is expected, as basic sedimentological principles suggest that sediments deposited farther away from the mountains, for example, in the GHB, tend to be relatively finer-grained, and thus less permeable, than those deposited closer to the sediment source, for example, in the WWB (CDWR 1964). We thus suggest that this contrast in the average permeability structure of the WWB and the GHB can be caused by differing sediment types.

24 24 Appana et al. 7.2 Fault permeabilities Our study suggests that the inferred permeability of the GHF of m 2 k ghf m 2 is an important hydrogeologic parameter to consider when managing groundwater resources and related processes in the region, for example, to reverse landsurface subsidence in the GHB (e.g., Fig. 8c). Furthermore, our estimates for k ghf result in permeability contrasts of 10 2 kx wwb /k ghf 10 4 between the GHF and the WWB and 10 1 kx ghb /k ghf 10 3 between the GHF and the GHB. Such permeability contrasts suggest that the GHF acts as a semi-permeable barrier to groundwater flow. In addition, we establish a maximum permeability value for the BF of k bf m 2 (Fig. 11a). This maximum likely permeability is of particular interest when determining the permeability contrast between the sub-basins and the faults as the basins have much higher permeabilities. We calculate a permeability contrast of kx ghb /k bf 10 3 between the GHB and the BF and kx mcb /k bf 10 2 between the MCB and the BF. However, these inferred permeability contrasts are only a conservative minimum estimate. Analogously to the GHF discussed above, these permeability contrasts suggest that the BF also acts as a semi-permeable barrier to groundwater flow. Figure 11a summarizes all results. The permeability structure of a fault zone is often complex, affecting groundwater movement or trapping within the fault zone. For example, field observations suggest that fault zones are generally composed of two main components (e.g., Chester & Logan 1986; Caine et al. 1996): 1) a fault core where comminution produces fine-grained fault gouge or cataclasite, and 2) an adjacent damage zone with enhanced fractures and veins. The permeability structure of faults is strongly determined by the distribution of cross-cutting fractures and the grain size within these fault components. Furthermore, the proportion of fault core to damage zone depends on the type of basin sediments and the geologic setting of the fault (Caine et al. 1996). Faults can act as barriers when 1) they contain finer-grained, and thus low-permeability, fault gouge (Caine et al. 1996), 2) their permeabilities are reduced as a result of mineral precipitation from circulating fluids during fault diagenesis (Ingebritsen et al. 2006), 3) they juxtapose hydrogeologic

25 Poroelastic Modeling in Coachella Valley, CA, USA 25 units of contrasting permeability structures (Maclay & Small 1983; Galloway & Hoffmann 2007), and 4) realigned elongated clasts reduce fault-normal permeability and increase fault-parallel permeability (Davis & DeWeist 1966). Although some permeability contrast exists between the WWB and the GHB as well as between the GHB and the MCB (Fig. 11a), we do not expect this to result from juxtaposition of hydrogeologic units across the GHF and the BF, respectively, because both faults are relatively young (Langenheim et al. 2005) and such a scenario would require significant displacement history. Additionally, the here-inferred bulk fault-zone permeability is two to three orders of magnitude smaller than those of the nearby sub-basins, which argues against Point (3) above, because in such a case, fault-zone permeability would be expected to be on the same order of magnitude as the two sub-basin permeabilities. In contrast, the displacement along both of these faults, although small, is likely sufficient to cause wear and gouge formation, arguing for Points (1) and (4) above. We use a simplified fault-zone model for both the GHF and the BF as shown in Figure 12, to constrain the horizontal permeabilities of the corresponding fault cores (Table 5). We vary the damage-zone permeabilities in our model to consider the possibility of faults acting either as barriers to fluid flow (e.g., Sand Hill Fault, Albuquerque basin, USA; Rawling et al. (2001)) or combined conduit-barrier systems (e.g., Lower Rhine Embayment, Germany; Bense et al. (2008); Baton Rouge Fault, Louisiana, USA; Bense & Person (2006)) in sedimentary basins. In the latter case, the fault zone as a whole is modeled with a large permeability anisotropy (vertical permeability horizontal permeability) such that the majority of fluid flow occurs within the damage zone and along the fault plane while a considerable hydraulic head drop across the fault core is maintained. Therefore, (vertical) layers of the fault-adjacent damage zones and the fault core are located in-series with respect to horizontal groundwater flow. Hence, the bulk horizontal permeability of the fault zone is given by the harmonic mean of the permeabilities of the individual layers as b k b = d k dl + c k c + d k dr, (13)

26 26 Appana et al. where, b [m] is the width of the fault zone considered, k b [m 2 ] is the bulk permeability of the fault zone, c [m] is the width of the fault core, k c [m 2 ] is the (unknown) permeability of the fault core, d = (b c)/2 [m] is the width of the damage zones and k d = k dl = k dr [m 2 ] is the permeability of the damage zone on either side of the fault core. We estimate the fault-core permeabilities using a range of fault-core widths, c, a range of values for the bulk permeabilities of fault zones, k b, established from our numerical simulations, and two different fault-zone widths, b (Table 5). Since our simulations are conducted for a constant fault-zone width, the k b values used in Equation (13) are only valid for b = 50 m. For any other value of b, the bulk permeability of the fault zone, k b, is recalculated as shown in Appendix B. These considerations constrain the fault-core permeabilities of the GHF and the BF to m 2 k ghf c k bf c m 2, respectively m 2 and Direct observations of fault permeabilities at major plate-boundary faults are not readily available in the literature. Chu et al. (1981) found that fault-gouge samples from the SAF exhibit permeabilities between and m 2. Similarly, Mizoguchi et al. (2008) report fault-core permeabilities between and m 2 at the Nojima fault in Japan. Both of these permeability ranges are very low with respect to fluid flow as they are comparable to unfractured metamorphic and igneous rocks and shale (e.g., Freeze & Cherry 1979) and to geologic materials more typically found at depths of approximately 10 km or more (e.g., Manning & Ingebritsen 1999; Saar & Manga 2004). In contrast, our estimates for fault-core permeability are one to two orders of magnitude higher. It is important to note, however, that our fault permeability estimates apply only to the shallow depths of the investigated basins (Secs 6.2 and 6.4). Thus, our fault-core and fault-zone permeabilities may serve as upper limits for permeabilities likely present at greater depths, as permeability is expected to decrease with depth (e.g., Manning & Ingebritsen 1999; Faulkner 2004; Saar & Manga 2004).Furthermore, Mizoguchi et al. (2008) found that permeability values estimated from surface samples compare well

27 Poroelastic Modeling in Coachella Valley, CA, USA 27 with borehole samples down to 2 km depth. Thus, our constraints for fault-core and fault-zone permeabilities may also be applicable for the uppermost 2 km of the SAF in the Coachella Valley region. Quantitative estimates of fault-zone permeabilities provide important constraints for understanding the static and dynamic weakening of faults. Lower fault-core permeabilities can cause elevated pore-fluid pressures within the fault core and lead to reduction of normal stresses across the fault (e.g., Byerlee 1990; Rice 1992). Consequently, lower shear-driving stresses are sufficient to cause fault slip at seismogenic depths (Raleigh et al. 1972, 1976; Talwani & Acree 1984; Simpson et al. 1988; Gupta 1992; Saar & Manga 2003). By considering the SAF as a hydrologic barrier, Fulton & Saffer (2009) show that such elevated pore-fluid pressures can be localized within the faults at depths greater than 5 km when horizontal permeabilities of k x m 2, at a depth of 500 m, are considered for the fault zone. Dynamic rupture is also affected by low permeabilities within the fault core relative to the damage zone or surrounding country rock. For example, several studies have explored thermal pressurization as a dynamic weakening mechanism (e.g., Sibson 1973; Vredevoogd et al. 2007). Finally, through numerical simulations, Bizzarri & Cocco (2006) show that source parameters such as stress drop, slip-weakening distance, and fracture energy all decrease systematically as permeability increases within the fault. Thus, estimates of fault-core and fault-zone permeabilities, as presented here, provide important constraints for conceptual and numerical models of active faulting. 8 CONCLUSIONS Our study suggests that the subsurface permeability structure (i.e., permeability and permeability anisotropy) in the Upper Coachella Valley region is heterogeneous over

28 28 Appana et al. basin scales, with the White Water (WWB), the Garnet Hill (GHB), and the Mission Creek (MCB) sub-basins having permeabilities typical for groundwater aquifers. Furthermore, we infer that the permeability anisotropy of the GHB and the WWB are significantly different, with at least an order of magnitude variability (Fig. 11a), likely caused by different sediment types existing in these sub-basins. In addition, simulations suggest that the permeability of the Garnet Hill Fault (GHF) is an important hydrogeologic parameter to consider when managing groundwater in the region, for example, to reverse land-surface subsidence in the GHB. InSAR observations in conjunction with numerical modeling suggest that the GHF and the Banning Fault (BF) act as semi-permeable barriers to groundwater flow in this region. We calculate a permeability contrast of between the GHF and the surrounding sub-basins and at least 10 2 between the BF and the surrounding sub-basins, with the faults having lower permeabilities in either case. Moreover, our calculations suggest fault-core permeabilities of k ghf c m 2 and k bf c m 2 for the GHF and the BF, respectively, which are one to two orders of magnitude higher than previous estimates for the San Andreas Fault (SAF). However, our estimates of fault-core permeabilities are only valid down to a maximum depth of 2 km, but may thus serve as an upper limit for fault-core permeabilities at greater depths. Therefore, our study provides estimates for the SAF-zone permeability structure and architecture which can potentially be used to constrain conceptual and numerical models of active faulting in general and SAF slip dynamics in particular. 9 ACKNOWLEDGEMENTS We thank Stuart Walsh for help with the numerical analysis, John Boggs for computational support and the reviewers for their helpful comments and suggestions. We also thank the George and Orpha Gibson endowment for its generous support of the Hydro-

29 Poroelastic Modeling in Coachella Valley, CA, USA 29 geology and Geofluids group. This research was supported by NSF grants EAR and EAR , as well as a grant by the Institute for Renewable Energy and the Environment (IREE) at the University of Minnesota. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the NSF or the IREE. REFERENCES Amelung, F., Galloway, D. L., Bell, J. W., Zebker, H. A., & Laczniak, R., Sensing the ups and downs of Las Vegas: InSAR reveals structural control of land subsidence and aquifer-system deformation, Geology, 27(6), Antonellini, M. & Aydin, A., Effect of faulting on fluid flow in porous sandstone: Petrophysical properties, Am. Assoc. Petrol. Geol. Bull., 78, Bawden, G. W., Thatcher, W., Stein, R. S., Hudnut, K. W., & Peltzer, G., Tectonic contraction across Los Angeles after removal of groundwater pumping effects, Nature, 412, Bell, J. W., Amelung, F., Ferretti, A., Bianchi, M., & Novali, F., Permanent scatterer In- SAR reveals seasonal and long-term aquifer-system response to groundwater pumping and artificial recharge, Water Resour. Res., 44. Bense, V. F. & Balen, R. V., The effect of fault relay and clay smearing on groundwater flow patterns in the Lower Rhine Embayment, Basin Res., 16, Bense, V. F. & Person, M. A., Faults as conduit-barrier systems in siliciclastic sedimentary aquifers, Water Resour. Res., 42(W05421), 18 pp. Bense, V. F., Person, M. A., Chaudhary, K., You, Y., Cremer, N., & Simon, S., Thermal anomalies indicate preferential flow along faults in unconsolidated sedimentary aquifers, Geophys. Res. Lett., 35(L24406), 6 pp. Bizzarri, A. & Cocco, M., A thermal pressurization model for the spontaneous dynamic rupture propagation on a three-dimensional fault: 2. Traction evolution and dynamic parameters, J. Geophys. Res., 111(B05304). Bredehoeft, J. D., Belitz, K., & Sharp-Hansen, S., The hydrodynamics of the Big Horn basin: the study of the role of faults, Am. Assoc. Petrol. Geol. Bull., 76, Bürgmann, R., Rosen, P. A., & Fielding, E. J., Synthetic aperture radar interferometry to measure Earth s surface topography and its deformation, Annu. Rev. Earth Planet. Sci., 28, Byerlee, J., Friction, overpressure, and fault normal compression, Geophys. Res. Lett., 17(12), Byerlee, J., The change in orientation of subsidiary shears near faults containing pore fluid under high pressure, Tectonophysics, 211,

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33 Poroelastic Modeling in Coachella Valley, CA, USA 33 Southwest Japan, Tectonophysics, 379, Tyley, S., Analog model study of the ground-water basin of the upper Coachella Valley, California, United States Geological Survey, Water-Supply Paper, 2027, 77 pp. Vredevoogd, M. C., Oglesby, D. D., & Park, S. K., Fluid pressurization due to frictional heating on a fault at a permeability contrast, Geophys. Res. Lett., 34, 4 pp. Wang, H. F., Theory of Linear Poroelasticity with Applications to Geomechanics and Hydrogeology, Princeton University Press, Princeton, N.J. Wibberley, C. A. J., Yielding, G., & Toro, G. D., Recent advances in the understanding of fault zone internal structure: a review, Geol. Soc. Spec. Pub., London, 299, Wisely, B. A. & Schmidt, D. A., Deciphering vertical deformation and poroelastic parameters in a tectonically active fault-bound aquifer using InSAR and well level data, San Bernardino basin, California, Geophys. J. Int.. Yule, D. & Sieh, K., Complexities of the San Andreas fault near San Gorgonio Pass: Implications for large earthquakes, J. Geophys. Res., 108(B11), Zhang, S., Tullis, T. E., & Scruggs, V. J., Permeability anisotropy and pressure dependency of permeability in experimentally sheared gouge materials, J. Struc. Geo., 21, Zlotnick, V. A., Zurbuchen, B. R., Ptak, T., & Teutsch, G., Support volume and scale effect in hydraulic conductivity: experimental aspects. in Theory, Modeling, and Field Investigation in Hydrogeology: A Special Volume in Honor of Shlomo P. Neuman s 60th Birthday, Zhang, D., and Winter, C. L., Geol. Soc. Am. Special Paper, 348, Zoback, M. D., Zoback, M. L., Eaton, J. P., Mount, V. S., & Suppe, J., New evidence on the state of stress of the San Andreas Fault, Science, 238,

34 34 Appana et al. FIGURE LEGENDS Fig. 1: The shaded relief map of Upper Coachella Valley in southern California, USA, produced using a 30 m Digital Elevation Model (DEM) from the Shuttle Radar Topography Mission (SRTM). The Banning and Garnet Hill faults represent active strands of the San Andreas Fault. Squares represent monitoring wells close to the rectangular region of interest. The model cross-section is chosen along the dashed line. Artificial groundwater recharge occurs at the White Water Recharge Facility (diamond). Fig. 2: a) Stacked differential interferogram using Synthetic Aperture Radar (SAR) data from late-1993 to 2000 indicating line-of-sight (LOS) range change in the Upper Coachella Valley. Negative values (blue) indicates motion towards the satellite and positive values (red) indicates motion away from the satellite. White regions are decorrelated, i.e., uplift data is not available. Black lines are regional faults. Also shown are the locations of the White Water Recharge Facility (diamond), the study region (rectangle), and a triangular region representing the assumed maximum extent of pore-fluid pressure diffusion down-stream from the White Water Recharge Facility. b) Average land-surface uplift rate calculated across the model cross-section, which is chosen along the dashed line in (a). Fig. 3: Variously averaged (see text for explanation) land-surface uplift along the model cross-section in the Upper Coachella Valley spanning late-1993 to 2000: a) Average cumulative uplift profiles from InSAR time-series data plotted as a function of time. b) Temporal variations of sub-basin-wide spatial averages for cumulative land-surface uplift with standard error bars for each of the three sub-basins. c) Temporal variations of sub-basin-wide spatial averages for relative uplift with standard error bars for each of the three sub-basins estimated by subtracting the corresponding uplift of the Mission Creek sub-basin (MCB) from that of each sub-basin at each time step to remove/reduce seasonal variations.

35 Poroelastic Modeling in Coachella Valley, CA, USA 35 Fig. 4: a) Depth to groundwater, recorded by the Coachella Vally Water District, at wells near the model cross-section (Fig. 1) during late-1993 through 2000, i.e., the period over which InSAR data is measured (Sec. 3.2). W1 through W4 are wells located in the Mission Creek sub-basin (MCB), W5 is the well in the Garnet Hill sub-basin (GHB), and W5 through W9 are wells located in the White Water sub-basin (WWB). b) Artificial groundwater recharge, Q [m 3 /yr], introduced into Upper Coachella Valley from late-1993 to 1999 (CVWD 2002). Data for the year 2000 is not available. The horizontal dashed and solid lines represent average annual artificial groundwater recharge values, Q mean, during 1987 through 1993 and late-1993 through 1999, respectively. Q mean represents the net change in mean annual artificial groundwater recharge between the two time periods considered. Fig. 5: Illustration showing the model cross-section ( 10 vertically exaggerated) from SW to NE across the Upper Coachella Valley. The bottom, left, and right sides of the model cross-section are no-flow boundaries. The Garnet Hill Fault (GHF) and the Banning Fault (BF) mark the boundaries between the White Water sub-basin (WWB) and the Garnet Hill sub-baisn (GHB) and the GHB and the Mission Creek sub-basin (MCB), respectively. The diamond marks the approximate projection of the White Water spreading facility onto the model cross-section, where artificial groundwater recharge, Q, occurs. Fig. 6: Example simulations conducted using steady-state conditions. The water table (black line) is continuous within sub-basins and offset across faults: a) Simulated pore-fluid pressure distribution in the aquifer in late-1993 (initial state). b) Simulated groundwater flow lines in the aquifer in late c) Simulated pore-fluid pressure redistribution in the aquifer in 2000 (final state) resulting from the increase in the artificial groundwater recharge, Q c. d) Simulated groundwater flow lines in the aquifer in e) Modeled vertical stress field in the aquifer in late-1993 (initial state). f) Modeled z- displacement in the aquifer during late g) Modeled vertical stress field in the

36 36 Appana et al. aquifer in 2000 (final state). h) Modeled z-displacement in the aquifer in Fig. 7: a) Contour plot of misfit, M [mm/yr], from simulations exploring the parameter space of k wwb x [1] versus a wwb [2], where values of a wwb [2] decreasing further away from 1 indicate larger permeability anisotropies for the White Water sub-basin (WWB). The dots represent parameter combinations of kx wwb [1] and a wwb [2] at which simulations are run, keeping parameters [3]-[7] fixed (Table 4). The solid, dashed, and dot-dashed lines represent contours with minimized misfit (M 0.14 mm/yr) corresponding to simulation runs using Q c [3] [m 2 /yr] values of 22500, 35000, and 10000, respectively. b) Simulated land-surface uplift rate, u(x), as a function of k wwb x [1] at constant [2]-[7]. c) Simulated uplift rate, u(x), as a function of a wwb [2]=(k z /k x ) wwb at constant [1] and [3]-[7]. Fig. 8: a) Contour plot of misfit, M [mm/yr], from simulations exploring the parameter space of k ghf = k ghf x = kz ghf [4] versus a ghb [6], where values of a ghb [6] decreasing further away from 1 represent larger permeability anisotropies for the Garnet Hill subbasin (GHB). The dots represent parameter combinations of k ghf [4] and a ghb [6] for which simulations are run, keeping values of parameters [1]-[3], [5], and [7] fixed (Table 4). b) Contour plot of misfit, M, from simulations exploring the parameter space of k ghf [4] versus a ghb [6] at kx ghb [5] = m 2 and constant [1]-[3] and [7]. c) Simulated land-surface uplift rate, u(x), as a function of k ghf [4] at constant [1]-[3] and [5]-[7]. Fig. 9: Simulated land-surface uplift rate, u(x), as a function of a) kx ghb [5] at constant [1]-[4], [6], and [7] and b) a ghb [5]=(k z /k x ) ghb at constant [1]-[5] and [7] (Table 4). Fig. 10: Reduced misfit, δm = M M min, as a function of the permeability of the Banning Fault (BF), for simulations conducted at constant parameter values for [1]- [6] (Table 4). Six different sets of values are used for the constants. For simulations conducted with each of these sets, the corresponding minimum misfit is designated as

37 Poroelastic Modeling in Coachella Valley, CA, USA 37 M i min, where i=1 to 6. Fig. 11: a) Summary of parameter estimates from the present study, subscripted one (1), and comparison with values from previous studies; subscript two (2): Tyley (1974); Swain (1978); subscript three (3): Mayer et al. (2007). Note, only an upper limit is found for the permeability of the BF. b) Curve showing simulated uplift rate, u(x), using an optimal parameter set (Table 4). Fig. 12: Illustration showing an idealized cross-section of a fault zone with its two components, the fault core and the damage zone. We assume that 1) the fault core is of uniform width, c [m], along the length of the fault zone and 2) the damage zones, with a width of d [m] around the fault core, are symmetric. Variables are defined in Table 5. The width of the fault zone is b [m]. Fig. 13: The dots represent parameter combinations of k ghf [4] and a ghb [6] for which simulations are run, keeping values of parameters [1]-[2], [5], and [7] fixed (Table 4). Contour plots of misfit, M, from simulations exploring the parameter space of k ghf [4] versus a ghb [6] for Q c [3] values of a) m 2 /yr and b) m 2 /yr. Fig. 14: Contour plot of misfit, M [mm/yr], from simulations exploring the parameter space of kx ghb [5] versus a ghb [6], where values of a ghb [5] decreasing further away from 1 indicate larger permeability anisotropies. The dots represent parameter combinations of k ghb x [5] and a ghb [6] at which simulations are run, keeping parameters [1]-[4] and [7] fixed (Table 4).

38 38 Appana et al. Table 1. Definition of parameters used in this study. Symbol Units Value Definition a permeability anisotropy (k z /k x ) a mcb a ghb permeability anisotropy of the MCB b m 50 width of the faults (in simulations) D m 450 depth of the basin g m/s gravitational acceleration h m hydraulic head h o m initial hydraulic head k m 2 permeability tensor kx mcb m horizontal permeability of MCB K m/s hydraulic conductivity tensor L m 2500 length of the line source for groundwater recharge M mm/yr root mean-squared error (misfit) δm mm/yr reduced misfit n 73 number of observation points Q m 3 /yr amount of artificialgroundwater recharge Q s 1/s fluid source or sink per unit volume Q m 3 /yr net artificial groundwater recharge Q c m 2 /yr Q entering the model cross-section R(x, z) m (2600, 120) co-ordinates of the center of the line source (see L) s m displacement vector u mm/yr land-surface uplift rate ū mm/yr standard deviation of u Y GPa 1 Young s modulus α 0.75 Biot-Willis coefficient η Pa s dynamic viscosity of fluid ν 0.2 Poisson s ratio ρ f kg/m density of the fluid ρ s σ e kg/m 3 Pa 2500 density of the sediment effective stress tensor σ t Pa total stress tensor subscripts/ superscripts c fault core d damage zone of fault bf Banning Fault ghb Garnet Hill sub-basin ghf Garnet Hill Fault mcb Mission Creek sub-basin min minimum obs observed wwb White Water sub-basin x m horizontal dimension z m elevation (vertical)

39 Poroelastic Modeling in Coachella Valley, CA, USA 39 Table 2. Temporal and perpendicular baselines for interferometric pairs (columns 1 and 2) used in both stacking and time-series analysis of surface displacement. Master Slave b-perp yyyymmdd yyyymmdd [m] Table 3. Boundary conditions used in the 2D fluid-flow and displacement model across the Upper Coachella Valley. Here, h is the hydraulic head potential, h o is the water table elevation in late-1993, s is the displacement vector, and x and z indicate horizontal and vertical dimensions of the model cross-section, respectively. The surface, i.e., the top boundary, is free to move in both directions. Condition h/ x = 0 (no-flow) δs x = 0 h/ z = 0 (no-flow) δs x = δs z = 0 h o = h o (x) free δs x and δs z Boundary left/right left/right base base surface surface

40 40 Appana et al. Table 4. Values assigned to the seven parameters [numbered in square brackets] in different simulation runs as discussed in the main text. Both faults are considered to be isotropic, i.e., kx ghf = kz ghf = k ghf and kx bf = kz bf = k bf. Minimum misfit values, M min, achieved are also shown. [1] [2] [3] [4] [5] [6] [7] kx wwb a wwb Q c k ghf kx ghb a ghb k bf M min Fig. [m 2 ] [m 2 /yr] [m 2 ] [m 2 ] [m 2 ] [mm/yr] 7a b c a b c a b b a b

41 Poroelastic Modeling in Coachella Valley, CA, USA 41 Table 5. Estimates of fault core permeabilities of the GHF and the BF. Variables are: b is the width of the fault zone, k b is the bulk permeability of the fault zone (estimated from numerical simulations), c is the width of the fault core, k c is the permeability of the fault core, and k dl = k dr (denoted by k d ) are the permeabilities of the damage zones to the left and the right of the fault core. For the above calculations we consider the following values for k left and k right (see Fig. 12). GHF: k left = kx wwb = m 2 and k right = kx ghb = m 2. BF: k left = k ghb x = m 2 and k right = k mcb x = m 2 k b [m 2 ] k d [m 2 ] b [m] c [m] k c [m 2 ] comments GHF upper limit for k c k c does not depend on k d lower limit for k c see Appedix B k c does not depend on b BF upper limit for k c see Appendix B Table 6. Well number as used in this paper, official well identification number (CVWD), latitude, and longitude of the wells used in this study. Water level depths are shown in Figure 4a. Well No. Well ID Latitude Longitude 1 03S04E12B001S S04E12C001S S04E12F001S S04E12H002S S04E13N001S S04E20F001S S04E20J001S S04E29F001S S04E29R001S

42 42 Appana et al. Figure 1.

43 Poroelastic Modeling in Coachella Valley, CA, USA 43 a) Land surface uplift rate, u [mm/year] WWB GHF GHB b) x [km] Figure 2. BF Observed uplift, u obs Standard deviation MCB

44 44 Appana et al. a) Average land surface uplift [mm] WWB GHB MCB With seasonal variations 5 b) c) Relative land surface uplift, u [mm] Year WWB GHB MCB Reduced/no seasonal variations Year Figure 3.

45 Poroelastic Modeling in Coachella Valley, CA, USA 45 Depth to groundwater [m] W5 W1 W2 W3 W4 W6 W7 W8 W9 a) b) Q [m 3 /year] 2.5 x Net change, Q mean Total Recharge, Q Q mean ( ) Q mean ( ) 0.5? Year Figure 4. Figure 5.

46 46 Appana et al. a) b) c) d) e) f) g) h) Figure 6.