A THESIS SUBMITTED TO THE FACULTY OF THE GRADUATE SCHOOL OF THE UNIVERSITY OF MINNESOTA BY. Ravi Appana

Transcription

1 Aquifer and Shallow San Andreas Fault Permeabilities Inferred from Poroelastic Modeling of InSAR Measurements of Land Surface Deformation in Coachella Valley, California A THESIS SUBMITTED TO THE FACULTY OF THE GRADUATE SCHOOL OF THE UNIVERSITY OF MINNESOTA BY Ravi Appana IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF Master Of Science August, 2009

2 c Ravi Appana 2009 ALL RIGHTS RESERVED

3 Aquifer and Shallow San Andreas Fault Permeabilities Inferred from Poroelastic Modeling of InSAR Measurements of Land Surface Deformation in Coachella Valley, California by Ravi Appana ABSTRACT Coachella Valley, in southern California, is located between Little Bernardino, San Jacinto, Santa Rosa, and San Bernardino Mountains. The southern part of the San Andreas Fault system, comprising three main faults, cuts through the upper valley aquifer dividing it into four sub-basins. Satellite interferometry (InSAR) has revealed a differential uplift of the land surface across two of these faults, the Banning Strand - San Andreas Fault (BSF) and the Garnet Hill Fault (GHF), in the upper Coachella Valley region. This uplift is suggested to be caused by i) the elastic response of the aquifer to artificial groundwater recharge and ii) the tectonic stresses acting in this region. However, the differential uplift appears to be caused by the semi-permeable faults which partially restrict pore-fluid pressure diffusion and related groundwater flow. Hence, by employing numerical models of coupled groundwater flow and poroelastic deformation of the sediments constituting the aquifer, the land surface uplift can be utilized to constrain a large-scale hydrologic model of the region that includes hydraulic representations of the faults and the sub-basins. Such a regional model can aide in developing better groundwater management strategies that aim at uniform restorations of ground surface elevations and groundwater levels in the aquifer. In addition, the proposed model would better constrain fault permeabilities with implications for research related to earthquake dynamics and assessment of potential slip along segments of the southern San Andreas Fault system. Therefore, a finite element code is used to implement a coupled poroelastic groundwater flow model. i

4 InSAR data of regional land surface elevation change and well data of water table elevations, collected in this region, are used to constrain the model yielding parameters such as the permeability and permeability anisotropy fields of the aquifer and the fault system. My results suggest that the horizontal permeability of the White Water sub-basin (WWB), k wwb, and its permeability anisotropy, a wwb, are on the order of m 2 k wwb m 2 and 0.04 a wwb 0.085, respectively. Furthermore, the model suggests permeabilities of the GHF and the BSF of m 2 k ghf m 2 and k bsf m 2, respectively, for a given horizontal permeability of m 2 k ghb m 2 for the Garnet Hill sub-basin (GHB) taken from previous studies. These results also suggest that values of k ghb considered and estimates of a ghb made (0.002 a ghb 0.016) are approximately one order of magnitude less than k wwb and a wwb, respectively. Further analysis indicates that estimates of k ghf are important to consider when managing groundwater levels and land surface deformation in the WWB and the GHB. Finally, these results imply a permeability contrast of between the GHF and the surrounding sub-basins and at least 10 2 between the BSF and the surrounding sub-basins, with the faults having the lower permeabilities in either case. Therefore, as qualitatively indicated by the differential land surface uplift across the faults in Coachella Valley, the model I present here confirms quantitatively that the faults act as semi-permeable barriers to pore-fluid pressure diffusion and groundwater flow due to their low permeabilities. Low permeabilities, in turn, tend to promote elevated pore-fluid pressures and reduce effective stresses within faults, thereby increasing the likelihood of fault slip. While the study presented here can only shed light on shallow fault permeabilities, which, however, may serve as upper limits to deep fault permeabilities, such maximum fault permeabilities may help explain why San Andreas Fault system tends to have weak faults. i

5 Acknowledgements First and foremost I offer my gratitude to my advisor, Dr Martin Saar, who has supported me throughout my thesis with his enthusiasm, patience, and knowledge whilst allowing me the room to work in my own way. I attribute the level of my Masters degree to his encouragement and effort. One simply could not wish for a friendlier advisor. I thank my collaborators Ann beth Wisely and Dr David Schmidt from the University of Oregon at Eugene for sharing their ideas about their future work, out of which this project came into place. I am fortunate to work with Ann beth and thank her for helping me in getting started with the project. Special thanks to Dr Stuart Walsh for helping with the implementation of the numerical model and Dr Calvin Alexander Jr. and Dr David Kohlstedt for critically reviewing the thesis. In my daily work I have enjoyed the company of working with a friendly and cheerful group of fellow students in the Gibson computational lab. They have always found the time to listen and share their ideas and have been helpful in many occasions. I also appreciate the help provided by the staff in the Geology and Geophysics department in making my administrative responsibilities easier to handle. Special thanks to John boggs for keeping the lab computers at their best and taking the time to answer all my computing questions. In this regard, I also thank COMSOL support group for their willingness to help find solutions to problems encountered during modeling. Finally, I would like to thank my family and friends whose care and support has made it possible to realize a home away from home. ii

6 Dedication To those who held me up over the years and have taught me the art of living! iii

7 Contents Abstract Acknowledgements Dedication List of Tables List of Figures i ii iii vii ix 1 Introduction 1 2 Background Fluid flow and poroelasticity Study region Tectonic setting Hydrogeology Model Conceptual model Model assumptions Numerical analysis Data sets Topography iv

8 4.1.2 InSAR data of land surface deformation Groundwater table depths and artificial groundwater recharge Poroelastic model Initial state (time = late 1993) Final state (time = mid 2000) Variable and constant parameters Results Permeability structure of the White Water sub-basin (WWB) Permeability of the Garnet Hill Fault (GHF) Permeability structure of the Garnet Hill sub-basin (GHB) Permeability of the Banning Strand - San Andreas Fault (BSF) Pore-fluid pressures Discussion and Implications Discussion Implications Conclusions 52 Appendix A. Glossary and Acronyms 55 A.1 Glossary A.2 Acronyms Appendix B. Groundwater well locations 57 Appendix C. Definition of parameters 58 Appendix D. COMSOL model details 61 D.1 User defined constants D.2 Geometry v

9 D.2.1 Application mode: Darcy s law (esdl) D.2.2 Application mode: Plane strain (smpn) D.3 Interpolation functions D.4 Solver settings D.4.1 Stationary D.4.2 Parametric vi

10 List of Tables 4.1 Boundary conditions used in the 2D fluid flow model for the upper Coachella Valley Boundary conditions used in the 2D plane-strain model for the upper Coachella Valley Variable parameters in the numerical model Constant parameter values in the numerical model List of parameter values considered in conducting simulations used for estimating the permeability structure of the White Water sub-basin (WWB) List of parameter values considered in conducting simulations used for estimating the permeability structure of the Garnet Hill Fault (GHF) List of parameter values considered in conducting simulations used for estimating the permeability structure of the Garnet Hill sub-basin (GHB) Values assigned to parameters in simulations representing different permeabilities for the Banning Strand - San Andreas Fault (BSF) Parameter values considered in conducting simulations used for estimating the permeability of the Banning Strand - San Andreas Fault (BSF) List of parameter values considered in the best-fit simulation A.1 Acronyms used in this thesis B.1 Well IDs and their locations vii

11 C.1 Summary of parameters used in this thesis along with their units and definitions viii

12 List of Figures 2.1 Shaded relief map of the Coachella Valley, California Sketch showing the cross-sectional region of interest in the upper Coachella Valley DEM, InSAR, and cross-sectional profiles of elevation and inflation along the averaged cross-section of interest in the upper Coachella Valley Groundwater table depths and the amount of artificial groundwater recharge introduced into the aquifer from 1993 to 2000 in upper Coachella Valley Simulated pore fluid pressures and flow lines in the aquifer during i) 1993 and ii) Vertical stress field and z-displacement field in the aquifer during i) 1993 and ii) Contour plot of misfit, M, and cross-sectional plots of uplift, u(x), from simulations conducted with different permeability structures for White Water sub-basin (WWB) Contour plots of misfit, M, from simulations conducted with different permeabilities for Garnet Hill Fault (GHF) Contour plots of misfit, M, and cross-sectional plot of uplift, u(x), from simulations conducted with different permeabilities for Garnet Hill Fault (GHF) ix

13 5.4 Contour plot of misfit, M, and cross-sectional plots of uplift, u(x), from simulations conducted with different permeability structures for Garnet Hill sub-basin Contour plot of misfit, M, and plot of δm vs. k bsf from simulations conducted with different permeabilities for Banning Strand - San Andreas Fault (BSF) Simulated pore-fluid pressure change as a function of depth in the GHF and BSF Summary of results from the present study D.1 Geometry of the numerical model x

14 Chapter 1 Introduction Land surface deformation, due to groundwater withdrawal, is a common phenomenon above aquifer systems (e.g., Poland, 1981, 1984; Hanson, 1989; Galloway et al., 1998; Amelung et al., 1999; Galloway et al., 1999; Hoffmann et al., 2001; Watson et al., 2002; Mellors and Boisvert, 2003; Teatini et al., 2006; Sneed and Brandt, 2007; Bell et al., 2008). In recent years, satellite interferometry techniques (Appendix A.1) have been increasingly used in mapping land surface deformation over large spatial and temporal scales (e.g., Galloway et al., 1998; Amelung et al., 1999; Bawden et al., 2001; Lu and Danskin, 2001; Sneed et al., 2002; Watson et al., 2002; Schmidt and Burgmann, 2003). Furthermore, Interferometric Synthetic Aperture Radar (InSAR) studies have been used to characterize macroscopic subsurface properties such as hydraulic conductivity, or related permeability, and storage properties of aquifers (e.g., Hoffmann et al., 2001, 2003a; Halford et al., 2005) and to constrain numerical models of groundwater flow and land surface subsidence (e.g., Hoffmann et al., 2003a; Hanson et al., 2004; Halford et al., 2005). Aquifer permeability, as suggested by Saar and Manga (2004) and Ingebritsen et al. (2006), is arguably the most important parameter in hydrogeologic studies in cases where fluids flow through porous media under predominantly laminar flow conditions. This is because knowledge of subsurface permeability fields can greatly 1

15 2 aid in groundwater management, for example to prevent groundwater overdraft (Appendix A.1) and its associated adverse effects including land subsidence, groundwater storage reductions, and water quality degradations (Galloway et al., 1999). Furthermore, subsurface fault permeabilities may significantly affect groundwater flow patterns over local to regional scales (Smith et al., 1990; Lopez and Smith, 1996). In addition, flow across faults may determine the amount of groundwater recharge into local sub-basins (Marler and Ge, 2002; Mayer et al., 2007; Folch and Mas-Pla, 2008) depending on whether they act as conduits, barriers, or combined conduit-barrier systems (Bredehoeft et al., 1992; Caine et al., 1996). Lastly, changes in pore-fluid pressures in pre-existing faults may reduce effective stresses in the faults, potentially affecting fault rupture dynamics (Raleigh et al., 1972, 1976; Talwani and Acree, 1984/85; Simpson et al., 1988; Gupta, 1992; Saar and Manga, 2003). Therefore, knowledge of fault permeabilities is essential to improve our understanding of the interactions between groundwater and aquifer-fault systems. Determining the Coachella Valley aquifer-fault system permeability field is important for a) groundwater management and b) understanding fault rupture dynamics of the southern San Andreas Fault system. Groundwater management in Coachella Valley is critical because i) the upper valley contains a resort- and recreation-based economy that relies on groundwater and the lower valley is an agricultural-based economy requiring irrigation water, ii) land surface subsidence needs restoration and management, and iii) groundwater serves as the drinking water resource to a large growing population in the region (CVWD, 2002). These groundwater management related issues are discussed in more detail next, while more background information on fault rupture dynamics is provided thereafter. Over the last century increasing demands and limited supplies in Coachella Valley have resulted in groundwater overdraft, reaching a maximum in the late 1940s when water levels declined by as much as 15 meters in some parts of the valley (CVWD, 2002), causing land surface subsidence. Furthermore, recent studies (e.g., Sneed and

16 3 Brandt, 2007) have measured land surface subsidence over regional scales in Coachella Valley ranging from about 35 to 150 mm from 1996 to 2000 and 75 to 180 mm from 2003 to Land surface deformation also causes damage to surface infrastructure such as roads, buildings, and rail road tracks. In addition, aquifer deformation associated with inelastic compaction of clay-rich sediments typically causes permanent reduction of land surface elevation (Galloway et al., 1999). This, accompanied with lower groundwater levels, i.e., reduced porefluid pressures, has the potential to cause salt water intrusion from the Salton Sea into the groundwater aquifers in the lower Coachella Valley (CVWD, 2002). Furthermore, stresses caused by historically low groundwater levels may exceed preconsolidation values causing permanent inelastic deformation of aquifer sediments resulting in permanent loss of groundwater storage capabilities, further illustrating the need for groundwater management. Therefore, to compensate for the groundwater overdraft and related land surface subsidence, the Coachella Valley Water District (CVWD) has artificially recharged groundwater at the White Water spreading facility in the upper valley since 1973 (CVWD, 2002) using Colorado River water. In later chapters, I discuss the effects of this artificial groundwater recharge on land surface elevation and how I use these land surface elevation changes to constrain hydraulic aquifer properties in the region. The southern San Andreas Fault, extending through Coachella Valley, with observed strain rates indicating large slip deficit (Fialko, 2006), has been suggested to pose the largest seismic risk in California (Weldon et al., 2005). Furthermore, many plate boundary faults, including the San Andreas Fault, have been interpreted to slip at much lower shear stresses than expected for rocks and faults with similar friction co-efficients, at hydrostatic pressure conditions (e.g., Lachenbruch and Sass, 1980; Zoback et al., 1987; Hickman, 1991). Elevated pore-fluid pressures in faults can potentially explain this phenomenon (Rice, 1990; Byerlee, 1990, 1992). Furthermore, Fulton and Saffer (2009) use models, with realistic permeability and permeabiity anisotropies

17 4 for the country rock, to show that large localized fluid pressures can be focused within a San Andreas Fault acting as a hydrologic barrier. Therefore, estimating permeabilities of faults and surrounding rocks, and the amount of pore-fluid pressure changes in segments of the southern San Andreas Fault in Coachella Valley can provide insights into fault rupture dynamics and associated seismic hazards. Interferometric Synthetic Aperture Radar (InSAR) data has revealed a differential land surface uplift (Wisely and Schmidt, 2005) across two basin-cutting faults, the Banning Strand - San Andreas Fault (BSF) and the Garnet Hill Fault (GHF), in the upper Coachella Valley region. Wisely and Schmidt (2006) suggest that this uplift may be interpreted as the combined response of the aquifer-fault system to i) artificial groundwater recharge and ii) tectonic stresses acting on the basin. Tectonic stresses may cause differential land surface uplift along faults with some vertical slip component. This process, however, tends to produce more or less sharp step functions of uplift across faults and not the fairly smooth uplift profile observed in the upper Coachella Valley (discussed later). However, tectonic causes of, or at least contributions to the observed land surface uplift pattern cannot be excluded, but are beyond the scope of the present study. Furthermore, Yule and Sieh (2003) suggest that the vertical slip component along the sections of the San Andreas Fault in the Coachella Valley are minor. Groundwater recharge - artificial or natural - can cause differential land surface uplift when subsurface hydraulic properties (mainly permeability and porosity but potentially also storage coefficients) are heterogeneously distributed, causing heterogeneous pore-fluid pressure fields and related poroelastic rock deformation patterns. In addition, the diffusive nature of pore-fluid pressure propagation would likely result in a smoother land surface uplift profile than those generated by slip along faults. However, in the study region, subsurface heterogeneity is mainly caused by the basin-cutting faults which exhibit (as shown in this study) permeabilities that are significantly different from those of the basin aquifers. The sharp contrast between fault and basin aquifer properties (e.g., permeability, porosity) can

18 give rise to relatively sharp pore-fluid pressure and related land surface uplift step functions despite pore-fluid pressure propagation being a diffusive process. 5 The objective of this study is to use InSAR observations of land surface deformation and changes in local groundwater table levels, recorded in wells, during the years from 1993 to 2000, to characterize i) the permeability field of the aquifer sediments in the sub-basins divided by the faults and ii) the permeabilities of the basin cutting faults of the San Andreas Fault system in the upper Coachella Valley region. The following chapter briefly presents background information relevant to fluid flow and poroelasticity and also describes the study region in more detail. In Chapter 3, I describe the conceptual model of coupled fluid flow and poroelastic land surface deformation I developed for the upper Coachella Valley. Chapter 4 lists the data sets used in the numerical analyses along with details regarding the modeling procedure. Chapter 5 presents simulation results, Chapter 6 discusses the results and implications, and Chapter 7 provides conclusions.

19 Chapter 2 Background This chapter provides some background information about the principles of coupled fluid flow and poroelastic deformation of sediment in porous media. The study region is also discussed in more detail. Appendix C provides a table with definitions of parameters. 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 y h c h t (K h ) = Q s, (2.1) where S y is the specific yield of the aquifer material, K is the hydraulic conductivity, Q s is a fluid source or sink, and h c and h are the constant and varying terms of the hydraulic head, h, respectively, defined as h + h c = h = p ρ f g + h e, (2.2) where h e is the elevation head and pρ f 1 g 1 is the pressure head with p as the porefluid pressure, ρ f the fluid density, and g acceleration due to gravity. As mentioned, Equation (2.1) is linearized and thus only valid for small h, compared to large h c. 6

20 Further, laminar fluid flow through porous media under confined conditions is governed by the standard groundwater flow equation, S s h t (K h) = Q s, (2.3) where S s is the specific storage of the medium. For steady-state conditions, h/ t = 0 in Equations (2.1) and (2.3). The hydraulic conductivity, K, is a second-rank tensor representing both fluid and solid material properties and describes how easily the specific fluid is transmitted through the porous medium. Hydraulic conductivity is defined as K = ρ f gk/η, (2.4) 7 where k is the intrinsic permeability and η is the fluid s dynamic viscosity. Permeability, k, is also a second-rank tensor but depends only on the following porous medium properties: porosity, pore connectivity, specific surface area, and pore space tortuosity. In my wo-dimensional model, k is reduced to a horizontal, k x, and a vertical, k z, component (ignoring minor off-diagonal terms) and are related by an anisotropy parameter, a = k z /k x. (2.5) The Darcy velocity, q, for groundwater flow is given by Darcy s Law (from the hydraulic head field) as q = K h. (2.6) Under hydrostatic conditions, the pore-fluid pressure, p, is related to the hydraulic head, h, by p = ρ f gh. (2.7) Therefore, the groundwater flow equation in both unconfined (Equation 2.1) and confined (Equation 2.3) systems can also be written in terms of the pore-fluid pressure gradient, p = ρ f g h, thus representing a pore-fluid pressure or hydraulic head

21 8 diffusion equation with a hydraulic diffusivity of in unconfined aquifers and D u = h c K/S y = h cρ f gk ηs y (2.8) D c = K/S s = ρ fgk ηs s (2.9) in confined aquifers. Consequently, the subsurface pore-fluid pressure or hydraulic head distribution is largely determined by the hydraulic conductivity or the permeability structure of the porous medium. The principle of effective stress describes the relation among changes in pore-fluid pressures and the stress state as follows: For any arbitrary plane below the water table, the total stress represented by the weight of the overlying rock and water is balanced by the pore-fluid pressure and the intergranular effective stress (Galloway et al., 1999). This is explained in mathematical form as σ t = σ e + αpδ ij, (2.10) where σ t are the total principal stresses acting on a porous material, σ e are the effective principal stresses, p is the pore-fluid pressure, α is the Biot-Willis coefficient given by the ratio of increment of fluid content to volumetric strain while maintaining constant fluid pressure conditions (Wang, 2000), and δ ij is the Kronecker delta. Furthermore, plane strain theory relates changes in the pore-fluid pressures to displacement in the porous medium by using the following equation: Y Y 2(1 + ν) 2 s + s = α p, (2.11) 2(1 + ν)(1 2ν) where Y is the Young s modulus of the aquifer material (porous medium), ν is the Poisson s ratio, and s is the displacement vector with components s x and s z in two dimensions.

22 9 Elastic deformation in aquifers is common due to changes in groundwater storage. However, if decreases in pore-fluid pressures cause the effective stresses to increase beyond preconsolidation stresses, deformation is not recoverable and thus often permanent land surface subsidence and loss of aquifer storage capacity results (Poland, 1981, 1984; Galloway et al., 1998). Finally, increase in pore fluid pressures due to groundwater recharge results in a reduction of effective stresses, σ e, and results in ground surface uplift as the granular skeleton expands (Poland, 1981; Hoffmann et al., 2001). 2.2 Study region The study region for this work is located in Coachella Valley (Figure 2.1), an area enclosed between Little Bernardino, San Jacinto and Santa Rosa Mountains in Southern California. The San Andreas Fault Zone (SAFZ) passes through the valley and includes a restraining bend immediately to the NW of the region, resulting in a geologically complex region (Yule and Sieh, 2003) Tectonic setting The upper Coachella Valley is located in a region of compression formed by the oblique collision of the San Jacinto Mountains with the San Bernardino Mountains (Yule and Sieh, 2003). In this region, the SAFZ comprises three main active faults, the Garnet Hill Fault (GHF), the Banning Strand - San Andreas Fault (BSF), and the Coachella Strand - San Andreas Fault (CSF). These faults are basin-cutting and divide the upper Coachella Valley into sub-basins. CSF and BSF are sub-vertical dextral strikeslip faults (Proctor, 1968) and comprise the main tectonic features of this region. The GHF is a dextral reverse fault (Yule and Sieh, 2003) with a poorly constrained dip to the NE.

23 Hydrogeology The sediments of the upper Coachella Valley basin are divided into consolidated, semiconsolidated, and unconsolidated deposits (Tyley, 1974). The main water-bearing rock units are Pleistocene and Holocene unconsolidated deposits. Pre-Tertiary to Tertiary rocks of the basement and the San Jacinto mountain do not yield any significant amount of water and thus act as groundwater barriers (CDWR, 1964). The foothills of the mountains are formed by partly consolidated deposits of Pliocene and Pleistocene age yielding little water N San Bernardino Mtns S BSA F SGP Mission Creek sub basin (MCB) GHF BSF 33.9 White water spreading facility EF Latitude Santa Rosa Mtns Va CVS lle AF y Salton Sea SJF Garnet Hill sub basin (GHB) White Water sub basin (WWB) Ca SA F C San Jacinto oac he Mtns lla MCF CV Little San Bernardino Mtns Longitude km Figure 2.1: Coachella Valley is located in the southern part of California (inset in top-right), stretching from SE of the San Bernardino Mountains to the Salton Sea, and is surrounded by Little San Bernardino Mountains in the NE and San Jacinto and Santa Rosa Mountains in the SE. The inset in the bottom-left shows the study region in detail. Abbrevations are: CVSAF - Coachella Valley segment of the San Andreas Fault; EF - Elsinore Fault; SBSAF - San Bernardino segment of the San Andreas Fault; SGP - San Gorgonio Pass; SJF - San Jacinto Fault system. The upper Coachella Valley consists of poorly sorted heterogeneous alluvial fan

24 11 deposits that contain few fine sediments, thus forming an unconfined aquifer (CVWD, 2002). The White Water sub-basin (WWB), southwest of the GHF (Figure 2.1), hosts the artificial groundwater recharge facility as the basin has the most permeable deposits in the upper valley, allowing the most direct recharge of the unconfined aquifer below. Runoff from the mountains in the north and west, where precipitation is approximately inches per year (Reichard and Meadows, 1992), and baseflow from the San Gorgonio Pass, northwest of the study region, are the main sources of natural groundwater recharge. Evapotranspiration, groundwater pumpage through wells, and outflow to the lower valley are the main causes of groundwater discharge. The regional groundwater flow within the basin is from the mountains in the NW toward the SE and into the Salton Sea, which forms the only natural groundwater outlet.

25 Chapter 3 Model In this chapter, I discuss my conceptual model for groundwater flow and poroelastic deformation considered for numerical analysis (Chapter 4.2) in the upper Coachella Valley. Following this, I present the assumptions made and discuss their validity. 3.1 Conceptual model Figure 3.1 shows the conceptual model along a cross-section within the upper Coachella Valley (for map view see Figure 4.1a). Two main faults, i.e., the Garnet Hill Fault and the Banning Strand - San Andreas Fault, divide the aquifer into three subbasins namely the White Water sub-basin, the Garnet Hill sub-basin and the Mission Creek sub-basin. The faults and the sub-basins are modeled as five distinct hydrogeologic units. The cross-section shown extends from the foothills of the San Jacinto Mountains in the SW up to a distance of 11.5 km toward the NE into the Mission Creek sub-basin where effects of both, the artificial groundwater recharge from the White Water sub-basin and the natural groundwater recharge from the Little San Bernardino Mountains, appear to be negligible. Although Proctor (1968) and Yule and Sieh (2003) suggest that both faults are sub-vertical, I model them as vertically oriented, assuming that a small deviation in fault orientation from vertical does not substantially modify the regional groundwater flow system (Folch and Mas-Pla, 2008). 12

26 13 SW NE SW NE Sedimentary basins artificial recharge, Q GHF BSF 3 K m San Jacinto Mountains Q WWB Faults GHB MCB Little San Bernardino Mountains Elevation [m] N O F L O W White Water sub-basin (WWB) Garnet Hill subbasin (GHB) Mission Creek sub-basin (MCB) N O F L O W area of panel b NO FLOW a) 35 K m b) x [m] Figure 3.1: a) Sketch showing the cross-section (vertically exaggerated) from SW to NE across the upper Coachella Valley (Figure 4.1a) used for this study. b) Vertically exaggerated sketch showing model boundaries within the cross-section of interest. Toward the left, the Garnet Hill Fault (GHF) marks the boundary between the WWB and the GHB. Toward the right, the Banning Stand - San Andreas Fault (BSF) divides the MCB from the GHB. The approximate location of the white water spreading facility, where artificial groundwater recharge, Q, occurs is marked by a diamond. In the upper valley, the aquifer is unconfined and contains poorly sorted, heterogeneous, unconsolidated alluvial fan deposits (CDWR, 1964). As a result, the sediments deposited closer to the foot-hills of the mountains are coarser than those deposited far away from the mountains, i.e., in the center of the valley. In addition, large relative displacements of rocks and sediments along faults can juxtapose terrains with dissimilar compositions and hydromechanical properties (Thatcher, 1983). Therefore, my models exhibit homogeneous and anisotropic hydraulic properties within individual sub-basins while hydraulic properties can vary from sub-basin to sub-basin. Similarly, faults are modeled as homogeneous and isotropic media but permeabilities of different faults are considered as independent parameters, i.e., different faults can have different permeabilities. However, as there is no observed land surface uplift across the

27 14 Mission Creek sub-basin (MCB) within the extent of my cross-section, I do not consider variations in permeability for the MCB and instead use permeability estimates from previous studies which report k mcb m 2 (Tyley, 1974; Swain, 1978; Mayer et al., 2007). Furthermore, the active groundwater flow zone is restricted to the top 450 m (saturated thickness of about 300 m) in my model as suggested by Tyley (1974) and Swain (1978). The clay content of the aquifer sediments is minor (CVWD, 2002) and thus no aquitards are modeled in this region. To compensate for groundwater overdraft and related land surface subsidence, the Coachella Valley Water District (CVWD) has artificially recharged groundwater through percolation ponds in the White Water sub-basin (WWB) since 1973 (CVWD, 2002). The large proportion of the coarse, high-permeability sediments present in the WWB, allows the added water to percolate easily into the underlying (unconfined) aquifer (CVWD, 2002). As a result, the pore-fluid pressure increases in the valley aquifer causing poroelastic land surface uplift, thereby countering, in part, previous land surface subsidence. However, InSAR data (Section 4.1.2) shows that in the region near the artificial groundwater recharge site, land surface uplift is non-uniform. In particular, land surface uplift changes step-wise across faults, suggesting that these faults act as semi-permeable barriers to pore-fluid pressure diffusion and thus groundwater flow (Wisely and Schmidt, 2005). 3.2 Model assumptions In order to constrain important hydrologic parameters (discussed further in the following chapter), I explore their parameter space by conducting numerical analyses. To reduce the number of unknowns so that exploration of the parameter space becomes tractable, I make the following assumptions: 1. All uplift is caused by poroelastic deformation of the sediment matrix, i.e., there is no tectonic uplift. Studies (e.g., Yule and Sieh, 2003) indicate that the sections

28 15 of the San Andreas Fault in the Coachella Valley show mainly strike-slip motion, suggesting that tectonic uplift rates are relatively small in the region. Including tectonic uplift may change the parameter estimates somewhat, but is beyond the scope of this study. 2. The net change in pore-fluid pressures in the study region during late 1993 to mid 2000 is due only to net artificial groundwater recharge (Section 4.1.3), i.e., the water table elevation would not have changed, for example, due to natural groundwater recharge, if there had been no net artificial groundwater recharge. This is assumed because i) runoff from the mountains, forming the main source of natural groundwater recharge in the region (CVWD, 2002), is restricted to the valley regions that are adjacent to the mountain edges (Figure 4.1c) and do not reach the region of interest, ii) groundwater pumpage in the study region is assumed to be constant for the period before 1993 and during 1993 to 2000 as indicated by approximately constant groundwater levels in wells located away from the white water spreading facility (Figure 4.2a), and iii) the component of natural groundwater recharge entering the study region as baseflow is considered constant for the period before 1993 and during 1993 to Groundwater flow rates, i.e., groundwater recharge rates to the valley aquifers, through the mountains are negligible compared to both along-valley groundwater flow and groundwater flow induced by the artificial groundwater recharge, due to the low permeabilities of the crystalline basement rocks of the mountains (CDWR, 1964). 4. Groundwater flow is assumed to be isothermal. High-relief terrains can cause groundwater to reach depths where thermal effects may influence flow rates and patterns (Forster and Smith, 1988). As I model groundwater flow only in the Coachella Valley where the active groundwater flow zone is restricted to the top 450 m and not the surrounding mountains from where groundwater flow is likely negligible (see point 3), the assumption of isothermal flow is likely justified.

29 16 5. Artificial groundwater recharge at the surface enters the aquifer system instantaneously, i.e., flow in the unsaturated zone is not explicitly simulated. 6. The basal boundary of the sedimentary basin marks the end of the active groundwater flow zone and is impermeable to groundwater flow across it. 7. The water table is a subdued replica of the topography within fault-bounded sub-basins. The groundwater level data, monitored by the CVWD, in the wells near the study region support this assumption (Figure 4.2a). However, groundwater table elevations, as constrained by well data, are discontinuous across fault zones. 8. I assume that equilibrium conditions for poroelastic deformation are reached instantaneously whenever pore-fluid pressure changes occur. This implies that i) the diffusion of pore-fluid pressure in the sub-surface is a relatively fast process, so that water levels at any instant determine groundwater flow directions and ii) the coupling between pore-fluid pressures and stresses in the sediment matrix is instantaneous. This is likely a good first-order approximation, but might not be entirely valid. Thus, transient simulations may provide insights into the validity of this assumption by comparing permeability fields estimated using both analysis types. However, investigating delayed fluid flow and delayed rock matrix deformation is beyond the scope of this study. 9. Faults are simulated as isotropic porous media, with a uniform width of 50 m for the entire depth of the basin (Mayer et al., 2007). 10. All rock units (sub-basins and fault zones in Figure 3.1b) are homogeneous within themselves. However, different units may have different hydraulic properties, e.g., permeability, so that the aquifer-fault system as a whole can be heterogeneous. 11. The effect of net artificial groundwater recharge on land surface uplift is negligible in the Mission Creek sub-basin (as suggested by InSAR data). In my model, changes in pore-fluid pressures can induce deformation in two ways: a) by changing effective stresses in water-filled sediments and b) by raising the water

30 table level into previously unsaturated zones (which changes pore-fluid pressures from atmospheric or sub-atmospheric to hydrostatic pressure conditions). 17

31 Chapter 4 Numerical analysis In this chapter, I present the data sets used to set up and constrain the numerical models of groundwater flow and associated poroelastic deformation in the upper Coachella Valley. Thereafter, the numerical procedure followed in this study is presented. 4.1 Data sets To set up and constrain the model, I use three data sets: i) topography from Digital Elevation Models (DEM), ii) InSAR (Interferometric Synthetic Aperture Radar) data showing land surface deformation, and iii) groundwater table depth data as measured in wells Topography The topographic relief between Coachella Valley and surrounding mountains is large, ranging from 3000 m at the peaks of the mountains to 60 m below sea level near the Salton Sea (Figures 2.1 and 4.1a). I calculate the average land surface elevation of a 2D cross-section by averaging elevations over a series of parallel cross-sections within the rectangular region ( km 2 ) shown in Figure 4.1a (i.e., averaging 18

32 Avg Elevation Stan. Dev. 300 Elevation [m] a) b) Latitude Land surface uplift, u o [mm] ( ) GHF MCF Mission Creek sub basin (MCB) BSF White Water sub basin (WWB) Garnet Hill sub basin (GHB) 42 mm 28 mm 14 mm 0 mm 14 mm 28 mm Land surface uplift, u o [mm] x [km] GHF BSF WWB GHB MCB Stan. Dev. Average Uplift c) Longitude d) x [km] Figure 4.1: a) Digital Elevation Model (DEM) of the upper Coachella Valley showing the locations of the wells (Appendix B) near the rectangular region of interest. Groundwater flow direction is from NW to SE. b) The average elevation (solid line) and its standard deviation (dashed line) of the ground surface calculated along a cross-section (dashed line) (see main text for explanation). c) Land surface uplift in upper Coachella Valley during 1993 to 2000 (Wisely and Schmidt, 2006). Positive range change indicates land surface motion away from the satellite (subsidence) and negative range change indicates land surface motion toward the satellite (uplift, u). White regions are uncorrelated, i.e., uplift data is not available. Also shown are i) the White Water Recharge Facility location (red diamond) and ii) the rectangular region of interest from Figure 4.1a. d) Averaged (spatial) land surface uplift, u (solid line), calculated along the cross-section and its standard deviation (gray shaded area) over the period from 1993 through The discontinuities in the profile shown, marked by small gaps across the faults, are due to the absence of uplift data.

33 20 perpendicular to the cross-sections). Advantages of using such an average are that 1) the average surface elevation includes topography information from the region immediately surrounding the cross-section and 2) any local features deviating significantly from the average topography are subdued similar to underlying groundwater table topographies. However, this averaged topography does not have a unique physical location on the map and, as a first-order approximation, is thus represented by the dashed line passing through the mid-point of the rectangular region used for averaging topography (Figure 4.1a). This approach also allows me to report a standard deviation from the average elevation (Figure 4.1b) InSAR data of land surface deformation Synthetic-aperture radar (SAR) is a form of radar in which multiple radar images of a satellite s distance to the Earth s surface are processed to yield higher resolution elevation images than would be possible by conventional means. An interferogram is a phase difference image between two SAR acquisitions taken at different times but having very similar imaging geometries. The temporal land displacement, along with the measurement error, for a large region of 100 km 2, is encoded in the interferograms. Under optimal conditions, the resolution of InSAR at an areal pixel size of m 2 is currently 1-10 mm (Galloway and Hoffmann, 2007). InSAR techniques are best suited for regions with minor vegetation, like the arid, metropolitan upper Coachella Valley. The InSAR (abbreviations are defined in Appendix A.2) data used in this study was processed by Wisely and Schmidt (2005) and contains twenty-three individual interferograms stacked on one another to reduce atmospheric noise. Figure 4.1c shows a stacked differential interferogram of the upper Coachella Valley measuring line-of-sight range change (Appendix A.1). Most of the observed deformation is vertically upwards (negative deformation values), as the sign of range changes and magnitudes of signals for both ascending and descending satellite tracks match closely (Wisely and Schmidt, 2005).

34 21 Averaged total land surface uplift, u (Figure 4.1d), along the averaged crosssection of topography (Figure 4.1b) is calculated using the same approach as described in Section for averaging topography data. The reason for averaging observed land surface uplift data perpendicular to the cross-section is to obtain a more representative land surface deformation profile along the cross-section of interest which in turn will likely allow better predictions of average permeabilities of the aquifer-fault system. In part due to this approximation, the estimates of permeability and other parameters along the cross-section are not exact but rather provide a first-order estimate of plausible parameter value 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 and that I am mainly interested in the permeability contrast between the sub-basins and the faults Groundwater table depths and artificial groundwater recharge Figure 4.2a shows time-series data of groundwater depths below averaged ground surface elevation (GSE) at the nine monitoring wells displayed in Figure 4.1a, which are located near the cross-section of interest. The peaks in groundwater table levels in the White Water sub-basin wells indicate, predominantly, the response to episodes of artificial groundwater recharge (Figure 4.2b). Although the wells are from different locations with significant differences in the averaged ground surface elevation, the depth to the water table at these wells is approximately the same within a given sub-basin and different across sub-basins (Figure 4.2a). Therefore, I assume that the groundwater level within the sub-basins is a subdued replica of the topography. Consequently, an estimate of the groundwater table elevation along the cross-section is given by combining the well and topography data. The groundwater table serves as the upper boundary condition in the numerical model (Figure 3.1b). Figure 4.2b shows the amount of artificial groundwater recharge, Q [m 3 /year],

35 30 40 MCB 1 MCB 2 MCB 3 MCB 4 22 Groundwater Table Depth below GSE [m] GHB 5 WWB 6 WWB 7 WWB 8 WWB 9 a) Year 2.5 x 10 8 Artificial groundwater recharge [m 3 /year] Average artificial groundwater recharge b) Year? Figure 4.2: a) Groundwater table depths, recorded by the CVWD, below averaged Ground Surface Elevation (GSE) calculated from the DEM, at wells near the crosssection of interest (Figure 4.1a). b) Artificial groundwater recharge introduced into upper Coachella Valley from 1993 to 2000 (CVWD, 2002). Data for the year is not available. The horizontal line represents average annual artificial groundwater recharge value for the years 1986 to 1993 (CVWD, 2002). introduced into the White Water sub-basin as part of the water management plan in the upper Coachella Valley (CVWD, 2002). The data for the year is not available. The net artificial groundwater recharge, Q [m 3 /year], is defined as the difference between the amount of average annual artificial groundwater recharge added during 1994 to 2000 and the average annual artificial groundwater recharge of m 3 /year added previously over the years 1986 to 1993 (CVWD, 2002). This Q is responsible for changes in the pore-fluid pressures in the aquifer over the years 1993 to However, only a portion of Q, hereafter denoted Q c [ m3 /year ] (all m

36 23 parameters in our analysis, their definitions, and units are summarized in Table C.1 in Appendix C), flows into the rectangular region of interest (Figure 4.1c) where it causes poroelastic land surface uplift. However, the exact value of Q c [m 2 /year] is unknown. Therefore, for modeling purposes, I estimate Q c by considering the effects of a few parameters such as the width of the rectangular area of interest and the extent to which artificially recharged groundwater diffuses into valley aquifers. I estimate a plausible range of values for Q c, m 2 /year Q c m 2 /year, entering the two-dimensional cross-section of unit thickness in the rectangular region of interest. Therefore, most simulations are conducted for Q c values of 10000, 22500, and m 2 /year. 4.2 Poroelastic model I develop a two-dimensional, numerical model to constrain the permeability structure of the sub-basins of the upper Coachella Valley and of the embeded sections of the San Andreas Fault. The model simulates pore-fluid pressure diffusion, groundwater flow, artificial groundwater recharge, and the associated poroelastic stress redistribution leading to both horizontal and vertical deformation within the cross-section (Section 2.1). COMSOL multiphysics (COMSOL multiphysics is a registered trademark of Comsol AB), a finite-element code that can model fluid flow and plane-strain by coupling pore-fluid pressure changes with associated poroelastic porous medium deformation and vice-versa, is used for this purpose (Appendix D). The finite-element model grid used for the analyses has triangular mesh elements with quadratic shape functions that interpolate parameter values between element corners. The triangular elements are of varied sizes with coarser element resolutions in the middle of the model sub-domains (sub-basins) and finer element resolutions toward domain edges. The total number of elements used in modeling the twodimensional (2D) cross-section of interest ( km 2 ) is The simulation procedure is defined in the following section.

37 4.2.1 Initial state (time = late 1993) 24 The initial pore-fluid pressure distribution (Figure 4.3a) and the state of vertical stresses (Figure 4.4a) in the aquifer are defined by conducting a steady-state simulation for an initial value for the parameter set. The water table at the cross-section is estimated from observed groundwater levels (Section 4.1.3) and the boundary conditions considered for the 2D fluid flow model are summarized in Table 4.1. Here, h is the hydraulic head potential, h o is the water table elevation in 1993, and x is the distance along the cross-section. The initial flow lines in the aquifer and the initial z-displacement of the porous medium matrix are shown in Figure 4.3c and 4.4c, respectively. Equation Boundary h/ x = 0 h o = h o (x), h/ z = 0 left/right surface with 0 x m base Table 4.1: Boundary conditions used in the 2D fluid flow model for the upper Coachella Valley. For the plane-strain model, the boundary conditions restrict the horizontal and vertical movement of the porous medium matrix as described in Table 4.2. Here, δx refers to displacement in the x-direction and δz refers to the displacement in the z-direction (elevation). Equation Boundary δx = 0 f ree δx = δz = 0 left/right boundary surface base Table 4.2: Boundary conditions used in the 2D plane-strain model for the upper Coachella Valley.

38 25 a) c) b) d) Figure 4.3: The water table (black line) is continuous within sub-basins and discontinuous across faults with higher water levels towards NE: a) Simulated pore-fluid pressure distribution in the aquifer during 1993 (initial state), b) Simulated porefluid pressure distribution in the aquifer during 2000 (final state) modeled after the introduction of artificial groundwater recharge from 1993 to 2000, c) Flow lines in the aquifer during 1993, d) Flow lines in the aquifer during 2000.

39 26 a) c) b) d) Figure 4.4: The water table (black line) is continuous within sub-basins and discontinuous across faults with higher water levels towards NE: a) Vertical stress field in the aquifer during 1993 (initial state), b) Vertical stress field in the aquifer during 2000 (final state) modeled after the introduction of artificial groundwater recharge from 1993 to 2000, c) Modeled z-displacement in aquifer during 1993 (initial state), d) Modeled z-displacement in the aquifer during 2000 (final state).

40 4.2.2 Final state (time = mid 2000) 27 The final state of the aquifer is reached by introducing artificial groundwater recharge, i.e., by adding a new boundary condition. This additional constraint is a constantflux term, Q c [m 2 /year], representing the net artificial groundwater recharge (discussed in Section 4.1.3), introduced in the White Water sub-basin along a line source centered at R(x, z) = (3100, 120) m and with a horizontal extent of L = 2500 m (Section 4.2.3). Subsequently, the resultant pore-fluid pressure distribution in the subsurface is modeled (Figure 4.3b) and the corresponding (coupled) sediment matrix deformation (land surface uplift) simulated (Figure 4.4d). The flow lines and vertical stresses in the aquifer in the year 2000 are shown in Figure 4.3d and 4.4b, respectively. As suggested by both observations and simulations, the magnitude of displacement [mm] in the x-direction is much smaller than that in the z-direction. Therefore, for illustration purposes we only show z-displacements and vertical stresses in the porous medium matrix during both the initial (1993) and final (2000) states of simulation. However, in calculating misfit, M [mm 2 ](Chapter 5), we consider the total displacement of the porous medium matrix. The net change in surface deformation between initial and final states is shown as a function of position, x, along the cross-section of interest (e.g., Figure 5.1b). The misfit, M, between the observed (gray shaded area) and simulated land surface uplift (red) along the cross-section reflects non-ideal choices of parameters and/or the conceptual model. I explore the parameter space, as discussed in Chapter 5, until a reasonable match, minimizing the misfit between observed and modeled land surface uplift, is found.

41 Variable and constant parameters I employ forward modeling to constrain the parameters shown in Table 4.3. To reduce the number of variable parameters to a reasonable maximum that can be modeled, several parameters are considered constants (Table 4.4) and are given typical values as reported in the citations. Furthermore, variations in these (considered) constant parameters are likely much less than natural variations in permeabilities as the latter vary by over 15 orders of magnitude in natural systems (Freeze and Cherry, 1979). Variable parameter Symbol Unit Permeability of the GHF k ghf m 2 Permeability of the BSF k bsf m 2 Permeability of the WWB k wwb m 2 Permeability anisotropy of the WWB a wwb Permeability of the GHB k ghb m 2 Permeability anisotropy of the GHB a ghb Net artificial groundwater recharge Q c m 2 /year Table 4.3: Variable parameters in the numerical model. Here, all permeability estimates are horizontal, i.e., in x-direction in the model, and thus permeability anisotropies of a = k z /k x < 1 indicate higher horizontal permeabilities. Faults are considered isotropic and thus no permeability anisotropy is modeled within faults.

42 29 Constant parameter Symbol Value Reference Dip of the GHF θ ghf 90 Yule and Sieh (2003) Dip of the BSF θ bsf 90 Proctor (1968) Young s modulus Y 1 GPa Lee (2003) (clean sand) Poissons ratio (aquifer) ν 0.2 Wang (2000) Biot-Willis coefficient α 0.75 Wang (2000) (sandstone) Depth of basin D 450 m Reichard and Meadows (1992) Width of faults W 50 m Mayer et al. (2007) Location of Q c (center) R(x, z) (3100, 120) m Section Cross-sectional length L 2500 m Section of recharge, Q c Permeability of the k mcb m 2 Mayer et al. (2007) MCB Permeability anisotropy a mcb a ghb of the MCB Density of sediment ρ s 2500 kg/m 3 Density of water ρ f 1000 kg/m 3 Reichard and Meadows (1992) Table 4.4: Constant parameter values in the numerical model. The permeability anisotropy of the Mission Creek sub-basin, a mcb, is not modeled and considered to be the same as the one modeled for the Garnet Hill sub-basin, a ghb.

43 Chapter 5 Results For the results presented here, the misfit, M [mm 2 ], between simulated and observed land surface uplift is quantified by calculating a mean-squared error along the crosssection of interest. The standard deviation, ū o [mm], of the measured land surface uplift, u o [mm], (Figure 4.1d) is used in calculating the misfit as M = 1 n ( u(x i )) 2, (5.1) n i=1 where, u(x i ) u o (x i ) if u(x i ) u o (x i ) ū o (x i ) u(x i ) = 0 if u(x i ) u o (x i ) < ū o (x i ). (5.2) In Equations (5.1) and (5.2), x i [km] are locations along the horizontal distance of the cross-section, u(x i ) [mm] are the simulated land surface uplifts at x i, u o (x i ) [mm] are the observed land surface uplifts at x i, ū o (x i ) [mm] are the standard deviations of the observed land surface uplift at x i, and n is the number of points along the cross-section at which the uplift is measured by InSAR. 30

44 5.1 Permeability structure of the White Water subbasin (WWB) 31 I explore the permeability structure of the White Water sub-basin (WWB), i.e., its horizontal permeability, k wwb, and its permeability anisotropy, a wwb = (k z /k x ) wwb, by conducting simulations (Figure 5.1) of groundwater flow and associated poroelastic porous medium deformation at different values of k wwb vs. a wwb while keeping all other parameters fixed (Table 5.1). Parameter Value/Range k wwb m 2 a wwb Q c m 2 (Figure 5.1c) (Figure 5.1b) m 2 /year (mean) m 2 /year (max) m 2 /year (min) k ghf m 2 k ghb m 2 a ghb k bsf m 2 Table 5.1: Parameter values considered for conducting simulations represented in Figure 5.1. The misfits, M, calculated for all simulation runs with net artificial groundwater recharge rates of Q c = m 2 /year are shown in the contour plot of Figure 5.1a. Contours with lower misfit numbers represent regions with better matches between observed and simulated land surface uplifts. The solid line in Figure 5.1a indicates the approximated locations with minimum misfit values. The dashed and dash-dot lines indicate approximated locations with minimum misfit values for higher ( Q c = 35000

45 32 m 2 /year) and lower ( Q c = m 2 /year) net artificial groundwater recharge rates, respectively. However, the best match is only obtained after optimizing all variable parameters (Table 4.3) considered, as discussed further in the following sections. As expected, an increase in horizontal basin permeability, k wwb, at constant basin permeability anisotropy, a wwb = , results in a decrease in simulated land surface uplift of the WWB (Figure 5.1b). In contrast, an increase in aquifer permeability anisotropy, i.e., corresponding to values of a wwb = (k z /k x ) wwb decreasing further away from 1, at constant k wwb = m 2, results in an increase in simulated land surface uplift (Figure 5.1c). Therefore, my simulations suggest that, for any given Q c value, there is more than one combination of k wwb and a wwb (solid line in Figure 5.1a) for which the misfit, M, is minimized. In addition, it is important to note that these permeability and permeability anisotropy variations, applied to the WWB, also affect simulated land surface uplift in the adjacent Garnet Hill sub-basin (GHB), as shown in Figure 5.1b-c. However, variations to k wwb and a wwb do not affect simulated land surface uplift in the Mission Creek sub-basin (MCB). Simulation results in Figure 5.1a also show that, at constant a wwb, higher amounts of net artificial groundwater recharge, Q c, correspond to low misfit numbers, M, if k wwb is increased and vice-versa. Analogously, for a given permeability, a range of permissible permeability anisotropies, a wwb, can be found when Q c is varied, with higher values of a wwb (i.e., lower anisotropies) corresponding to higher values of Q c. Therefore, considering a range of reasonable Q c values (Section 4.1.3) expands the resultant range of plausible permeabilities and permeability anisotropies for the WWB. Hence, I constrain the permeability structure of the WWB near the crosssection of interest (Figure 3.1a) to m 2 k wwb m 2 and 0.04 a wwb 0.085, i.e., the aquifer appears to be anisotropic, where higher horizontal permeability values, k wwb, are associated with larger permeability anisotropies, i.e., decreasing values of a wwb further away from 1.

46 2 33 a) a WWB = (k z /k x ) WWB increasing anisotropy < Q c (mean) = m 2 /year Q (max) = m 2 /year c Q (min) = m 2 /year c k x WWB [m 2 ] k =5Χ m WWB k WWB =6Χ m 2 k =7Χ WWB m 2 GHF Observed uplift u [mm] BSF WWB GHB MCB b) x [km] 35 a WWB = a 30 WWB = a WWB = Observed uplift GHF 20 u [mm] BSF WWB GHB MCB c) x [km] Figure 5.1: a) Contour plot of misfit, M [mm 2 ], associated with the parameter space of k wwb vs. a wwb, where values of a wwb decreasing further away from 1 represent larger permeability anisotropies. The dots represent parameter combinations of k wwb and a wwb at which simulations are run, keeping all other parameters fixed (see main text). The solid, dashed, and dot-dashed lines represent contours with M 1 mm 2 and simulation runs at Q c [m 2 /year] equal to 22500, 35000, and 10000, respectively. b) Simulated land surface uplift, u(x), as a function of k wwb at constant a wwb = c) Simulated land surface uplift, u(x), as a function of a wwb = (k z /k x ) wwb at constant k wwb = m 2.

47 5.2 Permeability of the Garnet Hill Fault (GHF) 34 To estimate the permeability of the Garnet Hill Fault, k ghf, I explore the parameter space of k ghf vs. a ghb vs. k wwb for simulated land surface uplift and compare simulation results with observed values. When running these simulations, I keep all other parameters fixed (Table 5.2). The contour plot of the resulting misfits, M, is shown in Figures 5.2 and 5.3 where, as before, contours with lower misfit values represent regions of the parameter space with better matches between simulated and observed land surface uplift. Parameter Value/Range k ghf m 2 a ghb k ghb Q c, k wwb a wwb (Figures 5.2d, 5.3d) m 2 (Figures 5.2a-c) m 2 (Figures 5.2d, 5.3d) m 2 (Figures 5.3a-c) m 2 /year, m 2 (Figures 5.2a, 5.3a) m 2 /year, m 2 (Figures 5.2b, 5.3b) m 2 /year, m 2 (Figures 5.2c, 5.3c) m 2 /year, m 2 (Figure 5.2d) m 2 /year, m 2 (Figure 5.2d) m 2 /year, m 2 (Figure 5.2d) m 2 /year, m 2 (Figures 5.3d) k bsf m 2 Table 5.2: Parameter values considered for conducting simulations represented in Figures 5.2 and 5.3. Simulation results suggest that increasing the permeability anisotropy, a ghb, of the Garnet Hill sub-basin, i.e., reducing the value of a ghb further away from 1, requires

48 35 a decrease in the permeability of the Garnet Hill Fault, k ghf, to maintain minimized misfit values, M. However, this trend is not indefinite in either direction so that a clear elliptical contour region with minimized M exists (Figures 5.2, 5.3). Furthermore, the effect of the horizontal permeability values, k ghb, of the Garnet Hill sub-basin (GHB) in estimating k ghf is evaluated by exploring the parameter space of k ghf vs. a ghb at minimum (Figure 5.2a) and maximum (Figure 5.3a) values of k ghb (Reichard and Meadows, 1992). These simulations indicate that lower k ghb values would require lower k ghf and vice-versa, to get a match between the simulated and observed land surface uplift values. More specifically, an order of magnitude increase in k ghb increases estimates of k ghf by about an order of magnitude as well. In addition, the effect of variability in the amount of net artificial groundwater recharge, Q c, is taken into account by running the above simulations (Figure 5.2a and 5.3a) at different Q c values (Figure 5.2b-c, 5.3b-c). These simulations suggest that the estimates for k ghf in the model are not significantly affected by the exact values used for the amount of net artificial groundwater recharge entering the crosssection of interest. I also study the effect of the horizontal permeability values of the White Water subbasin, k wwb, on estimates of k ghf. Simulations (Figure 5.2d) suggest that estimates of k ghf, at fixed values for other parameters (Table 5.2), are not affected by variations in k wwb. However, Figure 5.2d does suggest that increasing the net artificial groundwater recharge, Q c, requires an increase in k wwb to maintain a minimized misfit and viceversa, as seen before in Figure 5.1a, although this does not affect the estimate of k ghf. As expected, an increase in the permeability of the Garnet Hill Fault, at constant values for the other parameters considered in the model (Table 5.2), results in an increase in simulated land surface uplift in the Garnet Hill sub-basin (Figure 5.3d). However, it is important to note that the variations in k ghf considered do not seem to influence the simulated land surface uplift in the White Water sub-basin as may be expected due to an increase in pore-fluid pressures behind a less permeable fault.

49 a) b) k GHF [m 2 ] k GHF [m 2 ] x a GHB x increasing anisotropy 1 Q c =22500 m 2 /year k GHB = 3 X m a GHB 1 increasing anisotropy Q c =35000 m 2 /year k GHB = 3 x m c) d) k GHF [m 2 ] k GHF [m 2 ] x increasing anisotropy a GHB 7 x Q c =10000 m 2 /year k GHB = 3 x m k WWB [m 2 ] x Q c (mean) = m 2 /year Q c (max) = m 2 /year Q c (min) = m 2 /year Figure 5.2: a-c) Contour plots of misfit, M [mm 2 ], for the parameter space of k ghf vs. a ghb, where values of a ghb decreasing further away from 1 represent larger permeability anisotropies. The dots represent parameter combinations of k ghf and a ghb for which simulations are run, keeping all other parameters fixed (see main text). Contour plot of misfit, M, corresponding to simulations run at a different net artificial groundwater recharge values are represented in b) Q c = m 2 /year and c) Q c = m 2 /year. d) Contour plot of misfit, M, calculated for simulations corresponding to the parameter space of k ghf vs. k wwb, at constant values for the rest of the parameters considered (see main text). The dashed and dot-dashed contours (M 0.5 mm 2 ) indicate regions of minimum misfit for simulation runs corresponding to Q c [m 2 /year] values of and 10000, respectively, keeping all other parameters fixed (Table 5.2).

50 37 a) b) k GHF [m 2 ] k GHF [m 2 ] x a GHB x increasing anisotropy Q c =22500 m 2 /year k GHB = 3 X m a GHB increasing anisotropy 5 5 Q c =35000 m 2 /year k GHB = 3 x m c) k GHF [m 2 ] u [mm] x a GHB 35 k GHF = 2.0 Χ10 15 m Q =10000 m 2 c /year k GHB = 3 x m increasing anisotropy k GHF = 3.5 Χ10 15 m 2 k GHF = 5.0 Χ10 15 m 2 GHF Observed uplift BSF WWB GHB MCB 5 0 d) x [km] Figure 5.3: a-c) Contour plots of misfit, M [mm 2 ], for the parameter space of k ghf vs. a ghb. The dots represent parameter combinations of k ghf and a ghb for which simulations are run, considering a different constant value for k ghb ( m 2 ) when compared to Figure 5.2 and keeping the rest of the parameters fixed (see main text). Contour plot of misfit, M, corresponding to simulations run at different values for net artificial recharge are shown in b) Q c = m 2 /year and c) Q c = m 2 /year. d) Effect of variation in k ghf on land surface uplift, u(x), at a constant value for all other parameters (see main text).

51 38 In summary, my simulations suggest an average permeability range for the Garnet Hill Fault of m 2 k ghf m 2 estimated using the mean net artificial groundwater recharge Q c, to which simulation results for the permeability of the Garnet Hill Fault are not particularly sensitive in any case. 5.3 Permeability structure of the Garnet Hill subbasin (GHB) I explore the permeability structure (Figure 5.4a) of the Garnet Hill sub-basin (GHB), i.e., its horizontal permeability, k ghb, and permeability anisotropy, a ghb = (k z /k x ) ghb, by conducting numerical simulations of poroelastic land surface uplift, varying k ghb vs. a ghb. All other parameters are fixed (Table 5.3). However, the estimates of the permeability structure of the Garnet Hill sub-basin, using my model, depend on the estimates of the permeability of the GHF (Figures 5.2a, 5.3a) and vice-versa. Therefore, I use estimates of k ghb from previous studies (Tyley, 1974; Swain, 1978) at the local borehole scale of m 2 k ghb m 2, in the region of interest to explore the permeability anisotropy, a ghb, of the Garnet Hill sub-basin. Parameter Value/Range k ghb m m 2 (Figure 5.4c) a ghb (Figure 5.4b) k wwb m 2 a wwb 0.05 Q c (mean) m 2 /year k ghf m 2 k bsf m 2 Table 5.3: Values assigned to parameters for simulations in Figure 5.4.

52 a GHB = (k z /k x ) GHB increasing anisotropy a) k GHB [m 2 ] x k =5.0Χ10 13 m 2 GHB k =1.2Χ10 12 m 2 GHB k GHB =1.9Χ10 12 m 2 GHF Observed uplift u [mm] WWB GHB BSF MCB b) x [km] 35 a = GHB a 30 GHB =0.003 a =0.004 GHB 25 Observed uplift GHF 20 u [mm] 15 BSF WWB GHB MCB c) x [km] Figure 5.4: a) Contour plot of misfit, M [mm 2 ], associated with the parameter space k ghb vs. a ghb. The dots represent parameter combinations of k ghb and a ghb at which simulations are run, keeping all other parameters fixed (see main text). b) Effect of variations in k ghb at constant a ghb = , on simulated land surface uplift, u(x), along the cross-section of interest. c) Effect of changes in a ghb at constant k ghb = m 2, on simulated land surface uplift, u(x).

53 40 Misfits, M, in Figures 5.2, 5.3, and 5.4 suggest that a permeability anisotropy, a ghb, of a ghb is present in the Garnet Hill sub-basin indicating that horizontal permeabilities are higher than the vertical permeabilities at a given location. Furthermore, my simulation results, displayed in Figure 5.4, suggest that higher horizontal permeabilities, k ghb, for the Garnet Hill sub-basin require higher permeability anisotropies, a ghb, i.e., values of a ghb decreasing further away from 1, to result in a minimized misfit, M. As expected, an increase in horizontal permeability of the GHB, k ghb, at constant values for all other parameters (Table 5.3), results in a decrease in simulated land surface uplift, u(x), in the GHB (Figure 5.4b). In contrast, an increase in the permeability anisotropy of the GHB, i.e., decreasing a ghb values further away from 1, at constant values for all other parameters (Table 5.3), increases simulated land surface uplift, u(x), in the GHB (Figure 5.4c). In addition, these simulations suggest that land surface uplift in the White Water sub-basin (WWB) and the Mission Creek sub-basin (MCB) are independent of the permeability structure of the GHB (Figure 5.4b-c). 5.4 Permeability of the Banning Strand - San Andreas Fault (BSF) To constrain the permeability of the Banning Strand - San Andreas Fault (BSF), I conduct simulations over the parameter space of k bsf vs. k ghb, considering constant values for all other parameters (Table 5.4). My simulations suggest that the permeability of the BSF is at most m 2. Increasing k bsf beyond this value increases the misfit, M (Figure 5.5). However, considering variations of all the parameters affecting k bsf, constraining the permeability of the BSF requires a 5-dimensional parametric analysis, i.e., Q c vs. k wwb vs. k ghf vs. k ghb vs. k bsf, which is beyond the scope of this study.

54 41 Parameter Value/Range k bsf m 2 k ghb m 2 a ghb k wwb m 2 a wwb Q c m 2 /year (mean) k ghf m 2 Table 5.4: Parameter values considered for conducting simulations represented in Figure 5.5a a) k BSF [m 2 ] x k GHB [m 2 ] b) k BSF [m 2 ] M 1 o = 0.41 mm M o = 0.40 mm 3 M o = 0.57 mm 2 M 4 = 0.18 mm 2 o M 5 o = 0.11 mm 2 6 M o = 0.18 mm Reduced misfit, δm = M M [mm 2 ] o Figure 5.5: a) Contour plot of misfit, M [mm 2 ], for the parameter space of k bsf vs. k ghb. The dots represent parameter combinations of k bsf and k ghb at which simulations are run, keeping all other parameters fixed (see main text) and b) Plot of reduced misfit, δm, as a function of the permeability of BSF and fixed values for other parameters for which six different sets of values, corresponding to the six rows of Table 5.5, were used. The minimum misfit, M o [mm 2, obtained from simulations corresponding to different sets are designated as M o i, where i=1 to 6.

55 Instead, I conduct simulations for some plausible combinations of model parameters (Table 5.5) within their likely range of variability as determined in this study and constrain the permeability of the Banning Strand - San Andreas Fault (BSF) to k bsf m 2 for which the reduced misfit, δm, is a minimum (Figure 5.5b). That only an upper limit can be established for k bsf is not surprising as the fault permeability needs to be just low enough to prevent land surface deformation in the adjacent Mission Creek sub-basin (MCB) by limiting pore-fluid pressure diffusion and groundwater flow across the BSF. k wwb [m 2 ] a wwb k ghf [m 2 ] k ghb [m 2 ] a ghb Q c [ m2 year ] k bsf [m 2 ] Table 5.5: Sets of parameter values considered in conducting simulations used for estimating the permeability of the Banning Strand - San Andreas Fault (BSF). 5.5 Pore-fluid pressures For an optimum choice of the parameter set (Table 5.6), for which the misfit, M, is at a minimum, I calculate the changes in pore-fluid pressure in the Garnet Hill Fault (GHF) and in the Banning Strand - San Andreas Fault (BSF) resulting from artificial groundwater recharge. This change in pore-fluid pressure, p, depends on aquifer depth (Figure 5.6).

56 43 Parameter Value k wwb m 2 a wwb Q c m 2 /year k ghf m 2 k ghb m 2 a ghb k bsf m 2 Table 5.6: List of the near optimal values considered for parameters in the best-fit simulation p GHF p BSF Depth below surface [m] Depth below surface [m] a) p [MPa] b) p [MPa] Figure 5.6: Simulated pore-fluid pressure change, δp, due to artificial groundwater recharge in the WWB, as a function of aquifer depth in the a) Garnet Hill Fault (GHF) and b) Banning Strand - San Andreas Fault (BSF). Parameter values employed are listed in Table 5.6

57 Chapter 6 Discussion and Implications In this chapter, modeling results and implications of this work are presented. 6.1 Discussion Before discussing the model results, it is important to note that this study appears to provide the first large-scale average permeability estimates for the upper Coachella Valley. Since estimates of permeability are scale-dependent (Ingebritsen et al., 2006), my study provides additional insights into the subsurface hydrogeologic characteristics of the upper Coachella Valley when combined with previous estimates (Tyley, 1974; Swain, 1978) determined on local scales using well logs and steady-state groundwater flow model calibrations. Figure 6.1a shows a summary of the parameter estimates from this study in comparison to previous studies in the upper Coachella Valley. Figure 6.1b shows the land surface uplift, u(x), along the cross-section of interest for one plausible combination of parameter values (Table 5.6) giving a close-to optimal fit between simulated and observed land surface uplift. My estimation of the horizontal permeability of the White Water sub-basin, k wwb, and its permeability anisotropy, a wwb = (k z /k x ) wwb, employing numerical models is based on i) net artificial groundwater recharge, Q c, (Figures 5.1a, 5.2d) and ii) land 44

58 45 surface uplift, u(x), (Figures 5.1b-c). These simulations suggest that the estimates of k wwb and a wwb are independent of the uncertainty in modeling i) the permeability of the Garnet Hill Fault, i.e., k ghf, (Figure 5.2d) and ii) the permeability structure of the Garnet Hill sub-basin, i.e., k ghb and a ghb, (Figures 5.4b-c), for the range of parameter values considered (Tables 5.1, 5.2, and 5.3). The range of values estimated for the horizontal permeability of the White Water sub-basin (WWB), m 2 k wwb m 2 (Section 5.1), near the region of interest is well within the range suggested to be representative of clean unconsolidated sand deposits (Freeze and Cherry, 1979), which are likely present in the study region. Furthermore, my large-scale permeability estimates match closely to the local-scale permeability estimates reported by previous studies of m 2 k wwb m 2 (Tyley, 1974; Swain, 1978) for the WWB. The permeability anisotropy, 0.04 a wwb = (k z /k x ) wwb 0.085, estimated in this study for the White Water sub-basin (WWB) (Section 5.1) may be caused by stratification due to alternation of coarse- and fine-grained sediment deposits, resulting from variations in stream power from wet to dry years (CDWR, 1964). This is because (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. In contrast, mean (vertical) permeabilities across (horizontal) layers in series are given by the harmonic mean, which is dominated by the lowest-permeability layer (Saar and Manga, 2004; Ingebritsen et al., 2006). Furthermore, permeability anisotropy in sediments may also result from variations, due to tectonic processes, in the type of sediments deposited (Proctor, 1968). This latter type of permeability anisotropy can result from sedimentation processes that tend to produce overall higher horizontal permeabilities, as sedimentary layers with varying permeabilities form horizontally connected permeable zones (Saar and Manga, 2004). My estimation for the permeability of the Garnet Hill Fault (GHF), k ghf, using numerical modeling is based on i) the permeability structure of the Garnet Hill sub-basin

59 46 (GHB), i.e., k ghb (Figure 5.2a, 5.3a) and a ghb (Figure 5.3a) and ii) land surface uplift, u(x), (Figure 5.3d). However, for the range of parameters considered in the model (Tables 5.2), simulations also suggest that estimates of k ghf are independent of the parameter values used for modeling the net artificial groundwater recharge, Q c (Figure 5.2a-d). However, further analysis indicate that the estimates of the permeability structure of the Garnet Hill sub-basin (GHB) is co-dependent on parameter values used in modeling the permeability of the GHF (Figures 5.2a, 5.3a). Therefore, I conclude that the parameters k ghf, k ghb and a ghb cannot be determined independently and knowledge of estimates for at least one parameter is necessary to determine a plausible range of values for the other two. Consequently, I use estimates for k ghb from previous studies at the local borehole scale of m 2 k ghb m 2 (Tyley, 1974; Swain, 1978) to explore the permeability range of the GHF (Figures 5.2a, 5.3a). permeability, k [m 2 ] k 1 a 1 k 2 k 1 k 2 a 1 k 2 k anisotropy, a Land surface uplift, u [mm] GHF Observed uplift, u o [mm] Stan. Dev Simulated uplift, u [mm] WWB GHB BSF MCB k a) WWB GHF GHB BSF MCB b) x [km] Figure 6.1: a) Summary of results from the present study subscripted with one and comparison with permeability results from previous studies; subscript two: Tyley (1974); Swain (1978); subscript three: Mayer et al. (2007) and b) Best-fit simulation of land surface uplift, u(x), for a set of optimal parameters listed in Table 5.6 The contours of minimum misfit, M, in Figures 5.2a-c, 5.3a-c show regions (elongated ellipses) of the parameter space of k ghf vs. a ghb for which the simulated land surface uplift closely matches the observed values. As expected, my simulations suggest that the permeability of the Garnet Hill Fault (GHF) influences the extent of

60 47 pore-fluid pressure diffusion and the amount of groundwater flowing into the GHB and consequently poroelastic land surface uplift (Figure 5.3d) in the GHB. This suggests that the permeability of the GHF is an important hydrogeologic parameter to consider when managing groundwater in the region, for example, to reverse land surface subsidence in both the WWB and the GHB. My estimates (Figure 6.1a) for the GHF permeability ( m 2 k ghf m 2 ) along with the estimated permeability range for the WWB ( m 2 k wwb m 2 ) and the previously reported permeability range for GHB ( m 2 k ghb m 2 ) (Reichard and Meadows, 1992) results in permeability contrasts of 10 2 < k wwb /k ghf < 10 4 and 10 1 < k ghb /k ghf < These estimated permeability contrasts suggest that, on regional scales, the GHF acts as a semi-permeable barrier to groundwater flow. Faults can act as semi-permeable barriers when they juxtapose hydrogeologic units of contrasting permeability structures or contain finer-grained, and thus low-permeability, fault gouge (Galloway and Hoffmann, 2007). In addition, mineral precipitation from circulating fluids in the faults can reduce originally high fault permeabilities over time (Ingebritsen et al., 2006). The presence of a low-permeability barrier in the upper Coachella Valley is also indicated by the significant vertical offset in water tables across the GHF (Figure 3.1b). Along with the factors mentioned above, diagenesis in the San Andreas Fault Zone and the externally imposed flow regime might also contribute to the degree to which the GHF impedes groundwater flow (Heynekamp et al., 1999). My estimation of k ghb and a ghb, i.e., the permeability structure of the Garnet Hill sub-basin, for the range of parameter values considered in the model (Tables 5.2, 5.3), suggests that the following model parameter values need to be considered: i) land surface uplift, u(x) (Figures 5.4b-c), ii) the permeability structure of the White Water sub-basin, k wwb and a wwb (Figure 5.1b-c), iii) the permeability of the Garnet Hill Fault, k ghf (Figures 5.2a, 5.3a), and iv) the net artificial groundwater recharge, Q c (Figures 5.2a-c, 5.3a-c).

61 48 However, as mentioned earlier, my simulations suggest that parameter estimates of the permeability structure of the GHB and the permeability of the GHF are codependent. Therefore, I use values of k ghb ranging over an order of magnitude as reported in previous studies (Tyley, 1974; Swain, 1978) for my numerical analysis (Figure 6.1a) and estimate the range of values plausible for the remaining model parameters. It is important to note that the parameter values used in representing the average horizontal permeability of the Garnet Hill sub-basin (GHB) ( m 2 k ghb m 2 ) along the region of interest are approximately an order of magnitude smaller than those estimated for the White Water sub-basin, ( m 2 k wwb m 2 ). In addition, permeability anisotropies estimated for the GHB (0.002 a ghb 0.016) are on average significantly smaller than those estimated for the White Water sub-basin (0.04 a wwb 0.085). This contrast in the permeability structure of the WWB and the GHB is expected, because strain accumulation data suggest uneven distribution of deformation across the southern San Andreas Fault possibly due to differences in effective shear modulus of the sediments, indicating different sediment types (Fialko, 2006). The difference in the permeability structure estimated for the two sub-basins could result from the sedimentary processes that acted in Coachella Valley. Basic sedimentological principles suggest that sediments deposited farther away from the mountains, e.g., in the Garnet Hill sub-basin, tend to be relatively finer grained when compared to those deposited closer to the mountains, i.e., in the White Water subbasin (CDWR, 1964). In addition, lateral movement across faults might result in offsets between adjacent terrains and can thus juxtapose rocks with different compositions and hydromechanical properties (Thatcher, 1983). Therefore, sediments on either side of the Garnet Hill Fault likely have contrasting permeabilities both in horizontal and vertical directions, thereby impeding groundwater flow across the fault (Galloway and Hoffmann, 2007).

62 49 My numerical simulations (Figure 5.5) suggest only an upper limit for the permeability of the Banning Strand - San Andreas Fault (BSF) of k bsf < m 2. That only an upper limit can be established for k bsf is expected, as land surface uplift in the adjacent Mission Creek sub-basin (MCB) to the east is (close to) zero (Figure 6.1b) so that modeled values of k bsf have to be just low enough to prevent significant pore-fluid pressure diffusion and groundwater flow across the fault from SW to NE. Any further reductions in k bsf will yield the same result of zero land surface uplift in the MCB. Fortunately, however, it is this maximum value of k bsf that is of particular interest when determining the permeability contrast between the sub-basins and the faults, as the basins have much higher permeabilities (Figure 6.1a). Furthermore, because there is no observed land surface uplift in the Mission Creek sub-basin (MCB), the permeability structure of MCB cannot be estimated in this study. Consequently, my result of k bsf < m 2 and the previously reported permeability range for the GHB and MCB of m 2 k ghb m 2 (Reichard and Meadows, 1992) and m 2 k mcb m 2 (Reichard and Meadows, 1992; Mayer et al., 2007), respectively, results in a permeability contrast of k ghb /k bsf > 10 3 and k mcb /k bsf > 10 2 in the upper Coachella Valley. Analogously to the GHF discussed before, this estimated permeability contrast suggests that, on regional scales, the BSF also acts as a semi-permeable barrier to groundwater flow. Figure 6.1 summarizes all results. 6.2 Implications Lower fault permeabilities can result in elevated pore-fluid pressures in the faults, compared to the pore-fluid pressures in higher permeability surrounding rocks, thus leading to a reduction of normal stresses across the faults. Consequently, existing shear stresses along the fault might be sufficient to cause fault slip and therefore effect fault rupture dynamics (Raleigh et al., 1972, 1976; Talwani and Acree, 1984/85;

63 50 Simpson et al., 1988; Gupta, 1992; Saar and Manga, 2003). In particular, by considering San Andreas Fault as a hydrologic barrier, Fulton and Saffer (2009) suggest that elevated pore-fluid pressures can be localized within these vertical faults when realistic permeability and permeability anisotropies are considered for the surrounding rock. Therefore, fault permeabilities estimated in this study along with the estimates of the permeability and permeability anisotropy in the surrounding sediments can help in understanding the rupture dynamics of the southern San Andreas Fault system. This has implications in the context of the southern San Andreas Fault system, as it is predicted to be nearing the end of the interseismic strain accumulation (Fialko, 2006), with the largest threat for an earthquake in the region (Weldon et al., 2005). However, the presented estimates apply only to shallow depths, and can thus serve only as upper limits of sediment and fault permeabilities likely present at depth, as permeabilities are expected to decrease with depth (Manning and Ingebritsen, 1999; Saar and Manga, 2004) (thereby further increasing the likelihood of increasing pore-fluid pressures). Furthermore, for understanding the fault rupture dynamics at shallow depths it is useful to constrain shallow fault permeabilities, even though fault slip is unlikely to initiate at shallow depths. The shallow depth pore-fluid pressure changes calculated from this study, i.e., 0.04 MPa p ghf 0.06 MPa and MPa p bsf MPa, in the Garnet Hill Fault (GHF) and the Banning Strand - San Andreas Fault (BSF), respectively, fall within the range of critical pore-fluid pressure change capable of enhancing the process of fault-rupture along pre-existing, critically stressed faults (Raleigh et al., 1972; Roeloffs, 1996; Wolf et al., 1997; Harris, 1998; Townend and Zoback, 2000; Saar and Manga, 2003) like the southern San Andreas Fault (Fialko, 2006). In addition to its role in affecting fault rupture dynamics, permeability is an important hydrogeologic parameter for groundwater management. It is typically scale-dependent and its estimates vary by several orders of magnitude depending on the spatial scales

64 51 considered during calculations (Saar and Manga, 2004; Ingebritsen et al., 2006). Moreover, understanding regional-scale groundwater flow, spanning over tens of kilometers, is likely more critical when managing basin aquifers like those in Coachella Valley. However, the scarcity of large-scale numerical models limits our understanding of large-scale hydraulic processes. Therefore, as the techniques used in this study can be used to constrain hydrogeologic parameters over large spatial scales, our methods can help devise effective groundwater management schemes of systems extending far beyond the local well and pumping test scale. The ability of InSAR to collect millions of data points to map aquifer system deformation over large regional scales at a relatively cheap cost compared to Global Positioning Systems (GPS) and other techniques is currently under utilized in hydrogeologic characterizations of basin-fill alluvial aquifer systems (Galloway and Hoffmann, 2007). Consequently, this study helps filling this gap by developing an approach that can be used effectively in characterizing subsurface permeability structures of many regions where InSAR data are available and where land surface deformation is due to changes in groundwater storage. Once a calibrated poroelastic model is developed for a given region, it can be used to estimate future aquifer-system deformation, including land surface uplift and subsidence, resulting from changing groundwater flow and storage conditions.

65 Chapter 7 Conclusions The results of this study are summarized in Figure 6.1a. In particular, I find that: InSAR measurements of land surface uplift, when modeled with traditional hydrogeologic data, e.g., groundwater table depth, can aid in understanding the regional-scale variability in subsurface permeabilities and permeability anisotropies. The subsurface permeability structure in the upper Coachella Valley region is heterogeneous over basin scales, with the White Water (WWB), the Garnet Hill (GHB) and the Mission Creek sub-basins (MCB) having permeabilities typical of groundwater aquifers, and the accompanying faults having relatively lower permeabilities forming semi-permeable groundwater flow barriers. The horizontal permeability (k wwb ) and the permeability anisotropy (a wwb ) of the White Water sub-basin in the region of interest is estimated to be m 2 k wwb m 2, and 0.04 a wwb = (k z /k z ) wwb 0.085, respectively. In addition, higher horizontal permeabilities for the WWB are associated with higher permeability anisotropies, i.e., a reduction in a wwb further away from 1. The permeability of the Garnet Hill Fault (k ghf ) is constrained to m 2 52

66 53 k ghf m 2 and results in a permeability contrast of 10 2 < k wwb /k ghf < 10 4 and 10 1 < k ghb /k ghf < 10 3 with respect to the surrounding WWB and GHB, respectively. The permeability of the GHF is an important hydrogeologic parameter to consider when managing groundwater in the region, for example, to reverse land surface subsidence in both the WWB and the GHB. The permeability anisotropy of the Garnet Hill sub-basin, a ghb = (k z /k x ) ghb, in the region of interest is constrained to a ghb using a previously reported permeability range for GHB (Tyley, 1974; Swain, 1978). The parameter values used in representing the permeability structure of the Garnet Hill sub-basin (GHB) along the region of interest is at least an order of magnitude smaller than that estimated for the White Water sub-basin (WWB), suggesting considerable differences in resulting groundwater flow regimes, which, along with the semi-permeable faults, may explain the relatively large changes in the water table elevations across these sub-basins. The permeability of the Banning Strand - San Andreas Fault (BSF) is restricted to an upper limit of k bsf < m 2, suggesting a permeability contrast in the order of k ghb /k bsf > 10 3 and k mcb /k bsf > 10 2 to the GHB and MCB, respectively. Therefore, the overall conclusions of this study are that the present study provides estimates of shallow depth fault permeabilities of the southern San Andreas Fault system. This can serve as upper limits to fault permeabilities at depth which help in understanding the fault rupture dynamics. In addition, the techniques used in this study provide estimates of permeabilities of aquifer at large scales which are helpful in understanding regional scale hydraulic processes and possibly devising groundwater management plans extending beyond the local well and pumping test scales. For

67 54 example, as mentioned before the permeability of the GHF is an important hydrogeologic parameter to consider when managing land surface subsidence in both the WWB and the GHB regions.

68 Appendix A Glossary and Acronyms Care has been taken in this thesis to minimize the use of jargon and acronyms, but this cannot always be achieved. This appendix defines terms in a glossary, and contains a table of acronyms and their definitions. A.1 Glossary Groundwater overdraft A condition in which extraction of aquifer water is greater than the combined natural and artificial recharge to the system. InSAR Interferometric synthetic aperture radar, also abbreviated InSAR or IfSAR, is a radar technique used in geodesy and remote sensing. This geodetic method uses two or more synthetic aperture radar (SAR) images to generate maps of surface deformation or digital elevation, using differences in the phase of the waves returning to the satellite, or aircraft. The technique can potentially measure centimetre-scale changes in deformation over timespans of days to years. Interferometry It is a technique of diagnosing the properties of two or more waves by studying the pattern of interference created by their superposition. 55

69 56 Line-of-sight range change The distance from the satellite to the ground is referred to as range. InSAR measures the range change along the satellite line-of-sight or the look direction between two images taken at different times from the same satellite location. Synthetic Aperture Radar (SAR) SAR is a form of radar in which multiple radar images are processed to yield higher resolution images than would be possible by conventional means. A.2 Acronyms Acronym Definition BSF CDWR CSF CVWD DEM GHB GHF GSE InSAR MCB SAR SAFZ WWB Banning Strand - San Andreas Fault California District of Water Resources Coachella Strand - San Andreas Fault Coachella Valley Water District Digital Elevation Model Garnet Hill sub-basin Garnet Hill Fault Ground Surface Elevation Interferometric Synthetic Aperture Radar Mission Creek sub-basin Synthetic Aperture Radar San Andreas Fault Zone White Water sub-basin Table A.1: Acronyms used in this thesis.

70 Appendix B Groundwater well locations The following table provides the locations and identification numbers (ID) of the wells used for modeling the groundwater table. The data is obtained from the California Department of Water Resources. Well No. ID Latitude Longitude 1 03S04E12B001S S04E12C001S S04E12F001S S04E12H002S S04E13N001S S04E20F001S S04E20J001S S04E29F001S S04E29R001S Table B.1: Well ID numbers and their locations. 57

71 Appendix C Definition of parameters The parameters used in this study, along with their units and definitions are listed in the Table C.1 below. Symbol Units Definition a permeability anisotropy (k z /k x ) a ghb a mcb a wwb permeability anisotropy of the GHB permeability anisotropy of MCB permeability anisotropy of the WWB D m depth of the basin g m/s 2 acceleration due to gravity h m hydraulic head h c m constant term of the hydraulic head h e m elevation head h o m initial hydraulic head h m varying term of the hydraulic head k m 2 permeability tensor K m/s hydraulic conductivity tensor k bsf m 2 horizontal permeability of the BSF 58 continued on next page

72 59 Table C.1: continued Symbol Units Definition k ghb m 2 horizontal permeability of the GHB k ghf m 2 horizontal permeability of the GHF k mcb m 2 horizontal permeability of the MCB k wwb m 2 horizontal permeability of the WWB L m extent of net artificial groundwater recharge M mm 2 mean-squared error (misfit) M o mm 2 minimum misfit n number of observation points N m/s inward flux p Pa pore-fluid pressure q m/s Darcy velocity vector Q m 3 /year amount of artificial groundwater recharge Q s 1/s fluid source or sink per unit volume R(x, z) m co-ordinates of the center of artificial groundwater recharge in the model s m displacement vector S s 1/m specific storage of a confined aquifer s x m component of s in x-direction S y specific yield of an unconfined aquifer s z m component of s in z-direction t s time u mm simulated land surface uplift u o mm observed land surface uplift continued on next page

73 60 Table C.1: continued Symbol Units Definition ū o mm standard deviation of the measured land surface uplift W m width of the faults x m horizontal distance Y Pa Young s modulus year s no. of seconds in a year z m elevation α Biot-willis coefficient δ ij Kronecker delta δm mm 2 reduced misfit Q m 3 /year net artificial groundwater recharge Q c m 2 /year Q entering the model cross-section δx m displacement in x-direction δz m displacement in z-direction η Pa.s dynamic viscosity of fluid θ bsf degree dip of the BSF θ ghf degree dip of the GHF ν Poisson s ratio ρ f kg/m 3 density of the fluid ρ s kg/m 3 density of sediment σ e Pa effective stress tensor σ t Pa total stress tensor Table C.1: Summary of parameters used in this thesis along with their units and definitions.

74 Appendix D COMSOL model details I present the details of the numerical model in COMSOL in the following sections. The model set up considered simulates fluid flow and poroelastic deformation in the averaged cross-section of interest for a near optimal set of values for the parameters during both the initial state (1993) and the final state (2000). D.1 User defined constants Symbol Value Description k wwb [m 2 ] horizontal permeability of the WWB a wwb permeability anisotropy of the WWB k ghf [m 2 ] permeability of the GHF k ghb [m 2 ] horizontal permeability of the GHB a ghb permeability anisotropy of the GHB k bsf [m 2 ] permeability of the BSF y2s number of seconds in a year 61

75 62 Figure D.1: Geometry of the numerical model showing a) subdomain mode and b) boundary mode. See tables in main text for description of the subdomains and boundaries