San Joaquin River Delta: Joint P-Wave/Gravity

Seismic Tomography of the Sacramento – San Joaquin River Delta: Joint P-wave/Gravity

and Ambient Noise Methods

By Alexander C. Teel

A dissertation submitted in partial fulfillment

of the requirements for the degree of

Doctor of Philosophy

(Geophysics)

At the

UNIVERSITY OF WISCONSIN-MADISON

2012

Date of final oral examination: 8/1/12

The dissertation is approved by the following members of the Final Oral Committee: Clifford Thurber, Professor, Geoscience Harold Tobin, Professor, Geoscience Kurt Feigl, Professor, Geoscience Herbert Wang, Professor, Geoscience Dante Fratta, Associate Professor, Geological Engineering i

Abstract

The Sacramento – San Joaquin River Delta (SSJRD) is an area that has been identified as having high seismic hazard but has resolution gaps in the seismic velocity models of the area due to a scarcity of local seismic stations and earthquakes. I present new three-dimensional (3D) P- wave velocity (Vp) and S-wave velocity (Vs) models for the SSJRD which fill in the sampling gaps of previous studies.

I have created a new 3D seismic velocity model for the SSJRD, addressing an identified need for higher resolution velocity models in the region, using a new joint gravity/body-wave tomography algorithm. I am able to fit gravity and arrival-time residuals jointly using an empirical density-velocity relationship to take advantage of existing gravity data in the region to help fill in the resolution gaps of previous velocity models in the area. I find that the method enhances the ability to resolve the relief of basin structure relative to seismic-only tomography at this location. I find the depth to the basement to be the greatest in the northwest portion of the

SSJRD and that there is a plateau in the basement structure beneath the southeast portion of the

SSJRD. From my findings I infer that the SSJRD may be prone to focusing effects and basin amplification of ground motion.

A 3D, Vs model for the SSJRD and surrounding area was created using ambient noise tomography. The empirical Green‟s functions are in good agreement with published cross- correlations and match earthquake waveforms sharing similar paths. The group velocity and shear velocity maps are in good agreement with published regional scale models. The new model maps velocity values on a local scale and successfully recovers the basin structure beneath the Delta. From this Vs model I find the maximum depth of the basin to reach approximately 15 ii km with the Great Valley Ophiolite body rising to a depth of 10 km east of the SSJRD. We consider our basement-depth estimates from the Vp model to be more robust than from the Vs model.

iii

Acknowledgements

I am immensely grateful to my advisor Cliff Thurber for the mentorship he has provided me during my time at the University of Wisconsin – Madison. Beyond affording me the opportunity to pursue a PhD (and MS) with one of the true experts in the field of seismology,

Cliff has made me a better writer and helped me develop more linear and more critical thought processes. Cliff has pushed me when I needed pushing, given me space when I needed it, and always tried to make sure I was on-course with my research. I can not begin to thank Cliff enough for investing so much time in me. I can‟t imagine a better PhD advisor.

I would like to acknowledge all of my committee members (Cliff Thurber, Dante Fratta,

Kurt Feigl, Harold Tobin, and Herb Wang) for their role in developing me as a scientist. In classes, seminars, and from discussions in the hallway I have learned a lot from their collective expertise. While not serving on my PhD committee, Chuck DeMets has played the same role as the aforementioned professors in helping me to reach this point.

I have benefited from great technical and moral support thanks to my contemporary

CTSeisers (Guoqing Lin, Jeremy Pesicek, Ninfa Bennington, Ellen Syracuse, Emily

Montgomery-Brown, Summer Ohlendorf, Rachel Murphy, Helena Menendez, and Jessica

Feenstra). They have played an immense role in helping me get this far.

Joe Kington is great and amazing. Enough said.

I have received much help from the Department of Geoscience staff during my time here.

Lee Powell, Neal Lord, Peter Sobol, Ben Abernathy, and Patrick Kuhl have provided me with copious technical assistance. Jane Fox-Anderson, Jansi Prabakran, Judy Gosse, Shirley Baxa, iv

Mary Schumann and Michelle Szabo have also played an important role in getting me through grad school.

I have also received technical support (including codes upon which most of my thesis is based!) from Haijiang Zhang and Matt Haney, mostly on their personal time, for which I am very thankful.

I have made many friends in Madison, in the department and without, and I want to thank them all for helping make my time in Wisconsin enjoyable.

My parents have been always been very supportive of me and have encouraged me along the way throughout my graduate career.

Finally I want to thank my fiancée Julie Keating who has provided me unlimited moral and emotional support during this endeavor. There are times where I would have been lost without her and in the time I spent writing this dissertation I likely would have starved to death without her reminding me to eat. I know it can not have been easy to have dealt with me in my most stressed-out states but she has put up with me anyways. Thank you!

Table of Contents

Abstract ...... i

Acknowledgements ...... iii

List of Figures and Tables ...... vii

CHAPTER 1: Introduction ...... 1 1.1 Introduction ...... 1

1.2 Geologic Setting ...... 2

1.3 Seismic background ...... 4

CHAPTER 2: Joint P-wave/Gravity Tomographic Imaging at the Sacramento – San Joaquin River Delta ...... 12 Abstract ...... 12

2.1 Introduction ...... 12

2.2 Seismic and Gravity Datasets ...... 15

2.3 Methods ...... 17

2.3.1 Joint seismic-gravity tomographic inversion ...... 17

2.3.2 Empirical Relationship Sensitivity ...... 21

2.3.3 Application to the Sacramento – San Joaquin River Delta ...... 22

2.4 Results and Discussion...... 23

2.4.1 Joint Inversion Effectiveness...... 23

2.4.2 Sacramento – San Joaquin River Delta Velocity Structure ...... 25

2.4.3 Implications for Seismic Hazard ...... 28

2.5 Conclusions ...... 29 vi

Acknowledgements ...... 29

References ...... 31

CHAPTER 3: Ambient Noise Tomography at the Sacramento – San Joaquin River Delta 58 Abstract ...... 58

3.1 Introduction ...... 58

3.2 Dataset ...... 60

3.3 Method ...... 60

3.4 Results and Discussion...... 63

3.4.1 Ambient Noise Correlations ...... 63

3.4.2 Dispersion Curves ...... 65

3.4.3 Group Velocity Maps ...... 65

3.4.4 Vs Model ...... 67

3.5 Conclusions ...... 69

Acknowledgements ...... 69

References ...... 71

CHAPTER 4: Conclusions ...... 92 4.1 Importance of work ...... Error! Bookmark not defined.

4.2 Comparison of results ...... 93

4.3 Future work ...... 93

References ...... 95

vii

List of Figures and Tables

Chapter 1 Table 1.1 ...... 8 Properties of six fault segments and systems Figure 1.1 ...... 9 Major geologic provinces of California Figure 1.2 ...... 10 Select faults near the SSJRD Figure 1.3 ...... 11 Satellite image of the SSJRD

Chapter 2

Table 2.1 ...... 35 Polynomial coefficients for the Brocher (2005) density – Vp empirical relationship. Table 2.2 ...... 36 Velocity Perturbations by velocity and density perturbation Figure 2.1 ...... 37 Seismic stations and recent earthquakes near the SSJRD Figure 2.2 ...... 38 Bouguer gravity anomaly data points Figure 2.3 ...... 39 Upward continued gravity Figure 2.4 ...... 40 Comparison of empirical density-velocity relationships Figure 2.5 ...... 41 Tomographic inversion horizontal node spacing Figure 2.6 ...... 42 Relative arrival-time and gravity misfits by iteration Figure 2.7 ...... 43 Maps of gravity residual change and DWS Figure 2.8 ...... 45 Vp contour cross-sections for seismic-only and joint inversions Figure 2.9 ...... 47 Vp model map views Figure 2.10 ...... 49 Velocity model gradient cross-sections Figure 2.11 ...... 50 Example crustal schematics Figure 2.12 ...... 51 Vp model cross-sections viii

Figure 2.13 ...... 53 5.5 km/s surface map

Figure 2.S1 ...... 54 Earthquake travel times at Delta network stations Figure 2.S2 ...... 55 Gravity weighting trade-off curves Figure 2.S3 ...... 57 Seismic smoothing trade-off curves

Chapter 3

Figure 3.1 ...... 74 Maps of seismic stations and correlation path Figure 3.2 ...... 76 Example dispersion curve Figure 3.3 ...... 79 Example frequency filtered cross-correlation Figure 3.4 ...... 81 Example vertical-vertical vs vertical-radial cross-correlation comparison Figure 3.5 ...... 82 Cross-correlation record section for station CMB Figure 3.6 ...... 83 Example station-pair cross-correlation comparison Figure 3.7 ...... 84 Map of earthquake and stations used in waveform – cross-correlation comparison Figure 3.8 ...... 85 Comparison of earthquake waveforms to cross-correlations Figure 3.9 ...... 86 Group velocity checkerboard test Figure 3.10 ...... 87 Comparison of eight second period group velocity maps Figure 3.11 ...... 88 Vs model map views Figure 3.12 ...... 89 Vs model cross-sections Figure 3.S1 ...... 90 Number of useable paths versus frequency Figure 3.S2 ...... 91 Number of useable paths versus frequency

CHAPTER 1: Introduction

1.1 Introduction

The Sacramento-San Joaquin River Delta (SSJRD) occurs at the confluence of the

Sacramento and San Joaquin rivers in the Great Valley of California (Figure 1.1) and is home to a series of levees that control about half of California‟s annual stream flow. More than half of

Californians get their drinking water from the SSJRD area (Lund et al., 2007). Torres et al.

(2000) show that ground motion in the SSJRD from hypothetical magnitude 6.0 earthquakes on nearby faults (Figure 1.2), which have a recurrence interval of about 100 years in the area, is capable of causing levee failure and disrupting the water supply. To prepare for an inevitable damaging earthquake it is necessary to assess the geologic hazard in the region. One important aspect of assessing which areas have high earthquake hazard is imaging the subsurface velocity structure to model seismic effects such as basin amplification. Previous tomography studies which include the SSJRD (e.g. Hole et al., 2000; Thurber et al., 2007; Yang et al., 2008;Thurber et al., 2009; Lin et al., 2010) lack resolution there. We present the results of two new three- dimensional (3D) velocity models for the SSJRD to fill in the gaps of these previous studies.

In Chapter 2 we perform joint gravity/P-wave (Vp) tomography using an empirical relationship to link density and Vp. For the purposes of this study, gravity data primarily complement body-wave data by providing information on shallow density structure and are more effective at delineating lateral density variations. Seismic waves provide better depth resolution but are limited by the spatial distribution of earthquake and receiver locations. We find our method enhances resolution of basin relief beneath the SSJRD. We find the depth to the 2 basement to be the greatest in the northwest portion of the SSJRD and that there is a plateau in the basement structure beneath the southeast portion SSJRD. From our findings we infer the

SSJRD may be prone to focusing effects and basin amplification of ground motion.

In Chapter 3 we perform ambient noise tomography (ANT) to obtain a 3D S-wave velocity (Vs) model of the SSJRD. ANT relies on the principle that the cross-correlation of ambient noise between two seismic stations is representative of the Greens function between the two stations. The waveforms that emerge dominantly correspond to Rayleigh waves which can be inverted for Vs. We recover the basin structure and find the greatest depth to basement to be approximately 15 km. Our results are in good agreement with regional ANT studies encompassing the SSJRD and with S-wave tomography studies, as resolved near the SSJRD.

1.2 Geologic Setting

The Sacramento-San Joaquin River Delta (SSJRD) is an inter-woven network of streams that makes up the eastern portion of the San Francisco Estuary, where the Sacramento and San

Joaquin rivers converge (Figure 1.3). Typically deltas form through the deposition of sediments that have been deposited from up-stream. The SSJRD however was created by the deposition of various marsh plants which formed thick layers of peat over thousands of years which kept pace with a slow rise in sea-level (Mount and Twiss, 2005; Lund et al., 2007). The construction of the levees coupled with drainage and irrigation for agricultural purposes has lead to subsidence, causing much of the SSJRD region to lie below sea level at present (Mount and Twiss, 2005).

The SSJRD is situated on the edge of a sedimentary basin called the Great Valley (Figure

1), composed of the Sacramento Valley to the north and the San Joaquin Valley to the south.

The Great Valley extends roughly 650 km north-northwest–south-southeast and averages around 3

80 km in width. Pleistocene alluvium ranging from tens to over one hundred meters thick covers the Great Valley‟s surface (Harden, 2004). The primary sources of the alluvium are the Sierra

Nevada range to the east and the Coast Ranges to the west. Underneath the relatively recently deposited sediments is the Great Valley Sequence. The Great Valley Sequence is composed of sandstones, shales, and conglomerates which were deposited when the Great Valley was previously submerged as a forearc basin (Harden, 2004). The eastern edge of the Great Valley abuts the Sierra Nevada Range which was formerly the volcanic arc along the western edge of the North American continent. Here the sediments of the Great Valley sequence reflect shallow water depositional environments and the basement beneath the valley slopes gradually westward

(Harden, 2004). The western portion of the Great Valley Sequence was largely deposited as turbidity currents and the basement dips much more steeply than the eastern portion of the valley due to compressional uplift from the accretion of the Coast Ranges (Harden, 2004). Beneath the

Great Valley Sequence lies an ophiolite sequence, reflective of the fact that the Great Valley was formerly a forearc basin (Jachens et al., 1995; Godfrey et al., 1997; Harden, 2004).

Mountain ranges run parallel to the Great Valley on either side. As noted above, east of the Great Valley stands the Sierra Nevada Range. The Sierra Nevada formed in the past 10 million years from uplift of the Sierran Batholith (Figure 1) coupled with volcanism over the past several million years (Schoenherr, 1992). The Sierran Batholith is made of plutonic, granitic rocks which are Mesozoic in age.

West of the Great Valley are the Coast Ranges. The Coast Ranges formed by accretion of terranes to the western edge of the North American plate. Accretion ended when the Farrallon

Plate was completed subducted beneath the North American plate. This created the modern 4 transform boundary (the San Andreas Fault) between the Pacific and North American Plates.

The two main tectonic elements associated with the Coast Ranges are the Salinian Block and

Franciscan assemblage (Figure 1.1). The Salinian block is composed of plutonic granitoids. The

Salinian block is believed to have formed south of the Sierra Nevada and to have been transported to its present location by transform motion along the San Andreas (Schoenherr,

1992). The Franciscan rocks are a subduction complex composed largely of greywackes that have been serpentinized and intruded by igneous rocks.

1.3 Seismic background

Historical seismicity has caused little damage to the SSJRD levee system. The 1906 San

Francisco earthquake was 75 km west of the delta, but the levees were too short at that time to be susceptible to the induced shaking (Torres et al, 2000). Torres et al. (2000) show that ground motion from hypothetical nearby magnitude 6.0 earthquakes is capable of causing levee failure in the modern SSJRD. Lund et al. (2007) conclude that the highest risk of levee failure is in the western SSJRD due to proximity to at least five major faults, however a medium to high risk of catastrophic levee failure also exists for most of the central SSJRD. These assessments incorporate qualitative estimates of parameters such as basin amplification based on individual knowledge and experience, since geotechnical information is limited in the area (Torres et al.,

2000).

Many faults capable of producing Mw > 6.0 earthquakes lie to the west of the SSJRD

(Figure 1.2). These faults include the Calaveras Fault, the Concord-Green Valley Fault, the

Greenville Fault, the Hayward-Rogers Creek Fault, the Mount Diablo Thrust, and the San 5

Andreas Fault (Field et al., 2008). The 2007 Working Group on California Earthquake

Probabilities developed 30 year forecasts of the probability each of the listed faults would have a

Mw > 6.7 earthquake over the 30 year period of 2007-2037 (Field et al., 2008). The fault length, distance from the delta, and probability of producing a Mw > 6.7 earthquake as determined by

Field et al. (2008) are listed in Table 1.1. Beneath the SSJRD is a blind thrust fault, the Southern

Midland Fault, estimated to be capable of producing Mw 6.6 earthquakes (URS, 2008). Wong et al. (2006) found the fault to have been reactivated in the late Cenozoic, however more recent work by Unruh and Hitchcock (2009) identified this thrust as active in the mid to late Holocene. 6

References

Field, E. H., T. E. Dawson, K. R. Felzer, A. D. Frankel, V. Gupta, T. H. Jordan, T. Parsons, M. D. Petersen, R. S. Stein, R. J. Weldon II, and C. J. Wills, (2008), The uniform California earthquake rupture forecast, Version 2 (UCERF 2) by 2007 working group on California earthquake probabilities; USGS Open File Report 2007-1437

Godfrey, N. J., B. C. Beaudoin, S. L. Klemperer and Mendocino Working Group, (1997), Ophiolitic basement to the Great Valley forearc basin, California, from seismic and gravity data: implications for crustal growth at the North American continental margin; Geological Society of America Bulletin 1997; 109, 12, 1536-1562, doi:10.1130/0016-7606

Harden, Deborah R., California Geology Second Edition, (2004), Pearson Education, Inc.

Hole, J. A., T. M. Brocher, S. L. Klemperer, T. Parsons, H. M. Benz, H. P. Furlong, (2000), Three-dimensional seismic velocity structure of the San Francisco Bay area; J. Geophys. Res., 105, B6, 13859-13874

Jachens, R. C., Griscom, A., C. W. Roberts, 1995, Regional extent of Great Valley basement west of the Great Valley, California: Implications for extensive tectonic wedging in the California Coast Ranges; J. Geophys Res, 100, B7, 12769-12790

Lin, G., C. H. Thurber, H. Zhang, E. Hauksson, P. M. Shearer, F. Waldhauser, T. M. Brocher, J. Hardebeck, (2010), A California statewide three-dimensional seismic velocity model from both absolute and differential times; Bull. Seis. Soc. Am., 100, 1, 225-240, doi:10.1785/0120090028

Mount, J., R. Twiss, (2005), Subsidence, sea level rise, and seismicity in the Sacramento-San Joaquin delta; San Francisco Estuary and Watershed Science, Vol. 3, Issue 1, Article 5 National Geophysical Data Center, http://www.ngdc.noaa.gov/

Schoenherr, A. A., (1995), A natural history of California; University of California Press

Thurber, C., H. Zhang, T. Brocher, V. Langenheim, (2009), Regional three-dimensional seismic velocity model of the crust and uppermost mantle of northern California; J. Geophys. Res., 114, B01304, doi: 10.1029/2008JB005766

Torres, R. A., N .A. Abrahamson, F. N. Brovold, G. Cosio, M. W. Driller, L. F. Harder, Jr., N. D. Marachi, C. H. Neudeck, L. M. O‟Leary, M. Ramsbotham, R. B. Seed, (2000), Seismic vulnerability of the Sacramento – San Joaquin delta levees; CALFED Bay-Delta Program, Levees and Channels Technical Team, Seismic Vulnerabiltiy Sub-Team

Unruh, J. R., and C. S. Hitchcock, (2009), Characterization of potential seismic sources in the Sacramento-San Joaquin delta, California; U. S. Geological Survey National Earthquake Hazards Reduction Program, Final Technical Report 08HQGR0055 7

URS Corporation, (2008), Delta Risk Management Strategy, Phase 1, Risk Analysis Report, http://www.water.ca.gov/floodmgmt/dsmo/sab/drmsp/docs/Risk_Report_Section_6_Final.pdf

Wallace, R. E., W. P. Irwin, R. D. Brown, D. P. Hill, J. P. Eaton, L. M. Jones, W. L. Ellsworth, W. Thatcher, G. S. Fuis, W. D. Mooney, A. Griscom, R. C. Jachens, A. Lachenbruch, A. McGarr, (1990), The San Andreas fault system, California; USGS PP 1515, 63pp

Wong, I., K. Coppersmith, B. Youngs, M. McCann, (2006), Probabilistic seismic hazard analysis for ground shaking and estimation of earthquake scenario probabilities; URS corporation technical framework report to the California Department of Water Resources 8

Fault Distance (km) Length (km) P(Mw ≥6.7) Calaveras 39 124 .074 Concord-Green Valley 17 57 .034 Greenville 25 50 .031 Hayward-Rogers Creek 41 150 .311 Mount Diablo Thrust 28 25 .007 North San Andreas 75 137 .206

Table 1.1 – Properties of six fault segments and systems capable of producing damaging

earthquakes near the SSJRD. Approximate distance from the SSJRD is in the second

column. The third column gives the length of the fault as listed in the 2002 National Seismic

Hazard Map Parameters database (http://geohazards.usgs.gov/cfusion/c2002_search/). The

mean probability of each fault yielding a Mw ≥ 6.7 earthquake over the 30 year period

2007-2037 as determined by Fields et al. (2008) is given in the fourth column. 9

Figure 1.1 - Major geologic provinces of California. Prominent faults are marked with heavy lines where a fault trace is visible at the surface and dotted where the fault is inferred. The red box southeast of Sacramento marks the approximate SSJRD area. Numbered regions include 1) Great Valley quaternary alluvium, 4) Great Valley Sequence, 5) Franciscan Assemblage, 6 ) Sierran Batholith, 7) Sierra Nevada Metamorphics, and 9) Salinian Block. Figure modified from Wallace et al. (1990). 10

Figure 1.2 - Select faults near the SSJRD in dashed black lines. CaF-Calaveras Fault, CF- Concord Fault, GF-Greenville Fault, GVF-Green Valley Fault, HF-Hayward Fault, RCF-Rogers Creek Fault, SAF-San Andreas Fault, VKHF-Vaca-Kirby Hills Fault. The approximate area of the SSJRD is shown as the black triangle. Major rivers are shown in blue. 11

Figure 1.3 – Google Earth satellite image of the SSJRD with triangle overlay of the Delta corresponding to Figure 1.2.

CHAPTER 2: Joint P-wave/Gravity Tomographic Imaging at the

Sacramento – San Joaquin River Delta

Abstract

We have created a new 3D seismic velocity model for the Sacramento –San Joaquin

River Delta, addressing an identified need for higher resolution velocity models in the region, using a new joint gravity/body-wave tomography algorithm. We are able to jointly fit gravity and arrival-time residuals using an empirical density-velocity relationship to take advantage of existing gravity data in the region to help fill in the resolution gaps of previous velocity models in the area. The method enhances our ability to resolve the relief of basin structure relative to seismic-only tomography at this location. We find the depth to the basement to be the greatest in the northwest portion of the SSJRD and that there is a plateau in the basement structure beneath the southeast portion of the SSJRD. From our findings we infer that the SSJRD may be prone to focusing effects and basin amplification of ground motion.

2.1 Introduction

To mitigate loss of life and wealth from earthquakes it is important to accurately assess the geologic hazards they pose. In 2001, FEMA estimated the average US annual losses from earthquakes at $4.4 billion (FEMA, 2001). Vranes and Pielke (2009) adjust that value to $8 billion when taking into account inflation to 2005 US dollars along with population and wealth growth. Earthquakes do not generally exhibit detectable early warning signs so these costs are currently best decreased through an improved ability to estimate earthquake strong ground 13 motion and then attempting to make structures in areas which are deemed liable to suffer a devastating earthquake more earthquake resistant.

One important aspect of assessing which areas have high earthquake hazard is imaging the subsurface velocity structure to model seismic effects such as basin amplification, basin- induced surface waves, and focusing effects (Kawase, 2003). One of the best ways to develop a model of the Earth‟s crust is with seismic tomography. Different rock types generally have different seismic velocities, so we are able to obtain an image of rock formations in the crust indirectly by solving for seismic velocity models. Such models are also used to compute estimated ground motions from hypothetical earthquake sources. For body-wave tomography, the resolution of a velocity model at any given point in the Earth is related to the number of seismic ray paths, and their geometry, from earthquakes and possibly explosions that have passed nearby. We only have information from ray paths between where earthquakes and explosions occur and where seismic receivers record these events. Since earthquakes tend to be clustered at faults at plate boundaries, explosions are done at a small number of points, and seismic recording instruments typically sit at a fixed location on Earth‟s surface, there are significant limitations to ray path coverage in many areas, resulting in substantial model resolution gaps.

To circumvent a lack of seismic data, seismic tomography inversions have been performed jointly with complementary data types that do not suffer these same spatial limitations, such as gravity measurements. Gravity data suffer their own limitations however, such as generally having poor depth resolution relative to body-waves. A joint inversion can 14 take advantage of each data type‟s strengths to mitigate the shortcomings of individual separate inversions.

Joint inversions of body-wave arrivals and gravity data have been performed both sequentially and simultaneously. For a sequential inversion of the two data types (e.g. Lines et al., 1988), seismic arrival-time data are first inverted for velocity, which is then transformed to density using empirical relationships (e.g. Birch, 1961; Gardner et al., 1974; Christensen and

Mooney, 1995; Brocher, 2005). Next, gravity data are inverted to perturb the density model, which is then converted back to a velocity model. That velocity model serves as the starting point for the next iteration of the velocity inversion, and so on to convergence. The simultaneous method is a true joint inversion where arrival-time and gravity data are inverted in the same step, with a constraint based on the empirical density-velocity relationships to link the two data sets together (e.g. Lees and VanDecar, 1991; Parsons et al., 2001; Roecker et al., 2004). Due to the rapid fall-off of gravity resolving power with distance, most joint body-wave/density inversions have been limited to local scales (e.g. Savino et al., 1977; Lees and VanDecar, 1991; Nielsen and Jacobsen, 2000; Roecker et al., 2004; Roy et al., 2005), but regional scale (Parsons et al.,

2001) and even global scale (Forte et al., 1994) joint inversions have been attempted.

We have developed a joint body-wave/gravity tomography algorithm and applied it to the

Sacramento-San Joaquin River Delta (SSJRD). The SSJRD occurs at the confluence of the

Sacramento and San Joaquin rivers in the Great Valley of California and is home to a series of levees that control about half of California‟s annual stream flow. More than half of Californians get their drinking water from the SSJRD area (Lund et al., 2007). Torres et al. (2000) show that 15 ground motion from magnitude 6.0 earthquakes, which have a recurrence interval of about 100 years in the area, is capable of causing levee failure and disrupting the water supply.

Previous ground motion modeling of the San Francisco Bay Area (Aagaard et al., 2008;

Aagaard et al., 2010) concludes that basin amplification causes increased shaking from earthquakes on nearby faults at some of the surrounding basins such as the Livermore, Santa

Jose, and Santa Rosa basins. Aagaard et al. (2008) finds that ground motion at the SSJRD is characterized by large-amplitude long-duration surface waves however they note that their modeling of the SSJRD and Great Valley is limited by their poorly constrained 3D velocity model (Aagaard et al. 2008; Aagaard et al., 2010). Previous regional tomography studies lack resolution in the SSJRD (Hole et al, 2000; Thurber et al., 2009; Lin et al., 2011) due to a dearth of earthquakes and seismic stations in the SSJRD and Great Valley. For the purposes of this study, gravity data primarily complement body-wave data by providing information on shallow density structure and are more effective at delineating lateral density variations. Seismic waves provide better depth resolution but are limited by the spatial distribution of earthquake and receiver locations. This study provides a new 3D velocity model of the SSJRD region that allows for revised assessments of the local geologic hazard.

2.2 Seismic and Gravity Datasets

Previous tomography studies that have encompassed the SSJRD (e.g. Hole et al., 2000;

Thurber et al., 2009; Lin et al., 2010) have limited resolution in the area. This lack of resolution is due to limited earthquakes originating beneath the SSJRD coupled with an absence of seismic stations located in the SSJRD. Most of our seismic dataset comes from the Lin et al. (2010) 16 study however we augment that dataset with recently acquired local data to increase ray coverage in the SSJRD.

The USGS has operated a temporary seismic network (network code YU) comprising approximately a dozen sites in the SSJRD region. Figure 2.1 shows the distribution of seismic stations used in this study. The temporary network‟s initial deployment included 7 stations in

2006 and peaked at 11 active stations at one time during 2008 and 2009. Due to the close spacing of some stations, for our purposes the network effectively started with 4 stations and peaked at 9 stations. We incorporated hand-picked P-arrivals from YU network stations into our dataset and included supplemental earthquake arrivals for the picked events from the Northern

California Earthquake Data Center (Northern California Seismic Network, www.ncedc.org).

Figure 2.S1 shows picks we made for YU network stations as P-arrival time picks versus distance. We find a good fit to a mean velocity of approximately 6 km/s. Most events from this study that were recorded on YU network stations occur to the south of the SSJRD (Figure 2.1).

In total, the seismic dataset in this study comprises 4742 events and 230,073 P-arrivals, of which

82 events have arrivals at YU network stations.

Our gravity dataset comes from the NGS99 database (National Geophysical Data

Center), a 1.6 million record compilation of gravity surveys taken by United States governmental organizations and academia. The NGS99 stations have been adjusted to the International Gravity

Standardization Net 1971 (Morelli at al., 1971), gravity anomaly latitude corrections were calculated using the Geodetic Reference System 1967 theoretical gravity formula, and Bouguer anomalies were calculated assuming a density of 2.67 gm/cm3. Figure 2.2 shows the 37,958 sample subset of the database that lies in the bounds of 36° N and 40° N and between 119.5° W 17 and 123.5° W, used in this study. The gravity data have good spatial coverage of the SSJRD and features such as the Great Valley are evident. We determined and removed the regional trend in the gravity data, perpendicular to the Great Valley, using a least squares fit. We then interpolated the gravity data to a regular grid with 32 nodes per side, spaced 8 km apart and centered at the origin of our Cartesian model space. After interpolation we upward continued the data (Figure 2.3) to a height of 5 km (Blakely, 1995).

2.3 Methods

2.3.1 Joint seismic-gravity tomographic inversion

Our seismic-gravity joint tomographic inversion algorithm (tomoDDG) is based on the double-difference tomography algorithm tomoFADD (Zhang and Thurber, 2006), which is regional in scale, performs finite-difference travel time and ray path calculations, and allows flexible node spacing. We updated the tomoFADD algorithm to solve simultaneously for slowness from arrival time residuals and Bouguer gravity anomalies, using an empirical relationship to convert density perturbations to slowness.

The standard version of tomoFADD solves the general equation

∆푥 퐺 퐺 = ∆푡푡 (1) 푒 푟 ∆푢 where Ge is the earthquake location kernel, Gr is the ray-path kernel which keeps track of the ray- path length associated with each model node for each earthquake, ∆푥 are the perturbations to earthquake location and origin time, ∆푢 are the perturbations to slowness, and ∆푡푡 are the arrival 18 time residuals. We modified this system of equations to incorporate Bouguer gravity anomalies similar to the method of Lees and VanDecar (1991),

퐺푒 퐺푟 ∆푥 ∆푡푡 = (2) 0 푤퐺푔 ∆푢 푤∆푔 where 0 is a matrix of zeros, w is a weighting factor applied to the gravity portion of the problem, Gg is the modified gravity kernel, and ∆푔 is the gravity residual. The gravity kernel to quantify each model cell‟s contribution to each gravity anomaly value is constructed using the

Talwani equations for a rectangular parallelepiped volume (Talwani, 1973). The modified gravity kernel is the gravity kernel multiplied by a velocity-dependent factor to transform density perturbations to slowness perturbations.

The general equation relating gravity anomalies and density anomalies is

∆푔푗 = ∆휌푖퐺푗 ,푖 (3) 푖 with 휌 representing density, G the gravity kernel value incorporating geometry and volume, i the ith model parameter, and j the jth gravity residual. We modify this equation to solve for slowness through the application of the Brocher (2005) empirical relationship.

The Brocher relationship models density as a fifth order polynomial in velocity. We re- write this equation in terms of slowness (u) to yield:

−1 −2 −3 −4 −5 휌 = 푐1푢 + 푐2푢 + 푐3푢 + 푐4푢 + 푐5푢 = 푓 푢 (4)

The coefficients to the polynomial equation are represented as cn and are listed in table 2.1. We take the derivative of equation 3 with respect to slowness

푑휌 = −푐 푢−2 − 2푐 푢−3 − 3푐 푢−4 − 4푐 푢−5 − 5푐 푢−6 = 푓′ 푢 (5) 푑푢 1 2 3 4 5 19 and rearrange to obtain

−2 −3 −4 −5 −6 ∆휌 = −푐1푢 − 2푐2푢 − 3푐3푢 − 4푐4푢 − 5푐5푢 ∆푢 (6) = ∆푢 푓′ 푢

Equation 6 is substituted into equation 3 giving

′ ∆푔푗 = ∆푢푖푓 (푢푖)퐺푗 ,푖 (7) 푖

which yields

′ 퐺푔푗 ,푖 = 푓 푢푖 퐺푗 ,푖 (8) in equation 2.

The Lees and VanDecar (1991) implementation of this method used a linear density-

−1 velocity relationship which simplifies 푓′ 푢 to where b is the slope of their linear 푖 푏푢2 relationship. This relationship has the advantage of being mathematically well-behaved, as discussed in the next section, but does not provide as true a relationship between density and velocity across a wide-range of values.

We initially attempted a joint inversion which created both velocity and density models that were linked with a joint constraint to minimize the misfit between the density model and the corresponding velocity model parameters transformed to density using the Brocher (2005) relationship. The resulting matrix equation was

퐺푒 퐺푟 0 ∆푥 ∆푡푡 0 0 푤퐺푔 ∆푢 = 푤∆푔 (9) 0 푄(푣) −1 ∆휌 ∆푗

20 where ∆휌 are the perturbations to density, -1 is an identity matrix multiplied by -1, ∆푗 is the misfit between the density model and the density calculated from the velocity model, and 푄(푣)is the derivative of density with respect to slowness for Brocher‟s equation (푓′ 푢 in equation 6).

The joint constraint is derived in an attempt to minimize the difference between the densities calculated from the velocity model and the density model.

휌 푣 푖 + ∆휌 푣, ∆푢 푖 − 휌푖 + ∆휌푖 = 0 (10)

th th where 휌 푣 푖 is the i velocity model parameter transformed to density, ∆휌 푣, ∆푢 푖 is the i velocity model perturbation transformed to a density perturbation as a function of the ith velocity

th th parameter, 휌푖 is the i density model parameter and ∆휌푖 is the i density model perturbation.

This is rearranged to

∆휌 푣, ∆푢 푖 − ∆휌푖 = 휌푖 − 휌 푣 푖 (11)

′ Equation 6 replaces ∆휌 푣, ∆푢 푖 푎푠 ∆푢푖 푓 푢 푖 and by converting slowness to density yields

∆푢푖 ∗ 푄 푣 푖 + −1 ∗ ∆휌푖 = ∆푗푖 (12)

which is the bottom row of equation 9, where 휌푖 − 휌 푣 푖 = ∆푗푖. We believe this equation was not able to successfully constrain a joint inversion due to the non-linear derivative discussed in the next section coupled with the freedom of the joint constraint to trade off between slowness and density perturbations.

2.3.2 Empirical Relationship Sensitivity

The motivation for using a non-linear density-velocity relationship, instead of a linear relationship, is to model the density-velocity relationship as accurately as possible. A problem that arises when employing a non-linear relationship, though, can be large changes in derivative values that arise from posing the relationship in terms of slowness. Figure 2.4 compares the

Brocher relationship and a linear relationship with the same equations being cast in terms of slowness. The Brocher relationship in terms of velocity (Figure 2.4a) is fairly linear and can be fit with a linear trend with R2=0.9763. By contrast, the relationships (Brocher and linear-with- respect-to-velocity) are clearly non-linear in terms of slowness (Figure 2.4c,d).

The non-linear aspect of these slowness relationships requires care to ensure model perturbations stay within appropriate bounds. For example, Brocher‟s relationship in terms of slowness has a distinct change in behavior near the slowness value corresponding to 5.5 km/s, marked by regimes R1 and R2 in Figure 2.4b. Within a regime, the slowness-density relationship is nearly linear so the derivative is approximately constant. Thus a perturbation to density can be multiplied by the constant derivative to give the slowness perturbation from any slowness value to any other slowness value in the same regime. If the perturbation is so large that it creates a slowness value outside of its original regime then it will not fit the empirical relationship any longer. This concept can be extended to a continuous system rather than considering a piecewise system. Increasingly large perturbations to density (since this joint inversion method transforms density perturbations into slowness perturbations) will create slowness perturbations that increasingly deviate from the density-slowness relationship and thus the density-velocity relationship. Table 2.2 lists example velocity perturbations calculated at a 22 given velocity value with accompanying density perturbations. This table shows that gravity anomalies that require density perturbations as small as 0.05 gm/cm3 can produce velocity perturbations up to 0.4 km/s. At larger density perturbations, impossibly large velocity perturbations can arise. These unreasonable perturbations arise from the misfit between the local derivative of density with respect to slowness and the overall trend of the density-slowness relationship, as described above.

We employed two methods of counteracting the deleterious effects of large density perturbations. The first method we used was to start with an initial velocity model (which is transformed to density) that is close to the final model. Our starting model for the joint inversion was the final velocity model produced from a seismic-only tomographic inversion. The second method to control the perturbation size was to cap the maximum perturbation allowed. In this case, any slowness value that would have created a velocity perturbation greater than 0.2 km/s was capped to only perturb the velocity value by 0.2 km/s.

2.3.3 Application to the Sacramento – San Joaquin River Delta

We performed joint seismic-gravity tomography at the SSJRD with the tomoDDG algorithm. We used a 39 x 39 x 9 regular grid centered at latitude 38.0° and longitude -120.5°.

The left-handed Cartesian coordinate system was oriented with the Y-axis rotated 36° counterclockwise from North and with Z positive in depth. Nodes were spaced symmetrically about zero at X=-700, -500, -400, -300, -240, -200, -160 and then every 10 km from 120 to 0.

The Y spacing was the same as the X spacing and Z nodes were located at -25, -1, 1, 4, 8, 14, 20,

28, and 150 km. The grid spacing used is shown overlaying an outline of California in Figure 23

2.5. Our starting velocity model was the final velocity model produced by tomoFADD for the seismic data used in this study.

The gravity constraint was applied to nodes between -120 and 120 km inclusive in the X and Y directions and between 1 and 20 inclusive in the Z direction. The gravity portion of the inversion was up-weighted 10 times in producing the model discussed in this paper and seismic smoothing was set to 1. Figures 2.S2 and 2.S3 show the trade-off curves supporting the choice of these parameters.

2.4 Results and Discussion

2.4.1 Joint Inversion Effectiveness

Our joint body-wave/gravity inversion is a complex, non-linear problem that involves a trade-off between fitting the two datasets wherever they are inconsistent with one another and where our assumed empirical relationship between density and velocity is not a perfect match for the actual density-velocity relationship of the earth. In Figure 2.6 we present the relative misfits at each iteration of our inversion, relative to the initial misfit. As noted earlier, our starting velocity model was a converged solution of seismic-only tomography. After the first iteration we see a 9% percent increase in misfit to the arrival-time residuals as the velocity model is first perturbed trying to fit gravity residuals. For the later iterations we then see a consistent decrease in arrival-time residuals until the final residual is 2% greater than the initial seismic-only residual. The fit to the gravity data improves after each iteration, ending with a 19% improvement in fit to the gravity data. The arrival-time and gravity residuals both decreased by

1% between the final iteration and the iteration preceding it. 24

Figure 2.7 compares the distribution of gravity residual change to the initial residual and

Derivative Weight Sum (DWS) for nodes at 1 km depth. DWS (Thurber and Eberhart-Phillips,

1999) is the sum of the model partial derivatives for a model node. DWS is reflective of the total sampling for a node and serves as a proxy for model resolution. We observe the largest changes in gravity residual to be in regions with high initial misfit and low DWS. In this study those two conditions are largely overlapping so we investigate points P1 and P2 (Figure 2.7) to examine this relationship more closely. P1 and P2 both are points of high initial misfit but P1 had very little reduction in residual while P2 had a large reduction. We see that point P1 sits in a region of high DWS (≥ 100,000) whereas the DWS at P2 was very low (≤ 10). P1 was approximately

10,000 times more strongly constrained by the arrival-time data than P2 which is why the gravity data there were not fit well, unlike P2. This does also imply that the arrival-time and gravity data are inconsistent or the empirical relationship is a poor fit at P1. The purpose of the joint inversion is to add constraints to velocity in regions lacking sufficient seismic data but not to override regions with adequate arrival-time data, so the general behavior exhibited at P1 and P2 is expected and desired.

To observe the effects of the gravity data on the velocity model for the SSJRD we compare 4 km/s and 6 km/s contours from the seismic-only inversion and the joint inversion

(Figures 2.8) through cross-sections of the SSJRD. Figure 2.9a shows the location of the cross- sections in Figure 2.8 in map view. Figure 2.9a shows southwest-northeast cross-sections with y=30 being the northwestern-most cross-section and y=-20 being the most southeasterly. For y=-20 to y= 0 we see little change between the seismic-only and joint models beneath the SSJRD with the largest change being a slight rise in the 6 km/s contour for the southwestern portion of 25 the SSJRD at y=-10. For the three more northwesterly cross-sections (y=10-30) we observe larger changes between the contours with a tendency towards greater basin relief of the SSJRD.

Figure 2.8b shows northwest-southeast cross-sections through the SSJRD, perpendicular to those in Figure 2.8a. As is visible in the first set of cross-sections we see greater relief in the joint- inversion contours, particularly with the 6 km/s contour deepening at x=10 and the 4 km/s contour deepening in x=0. On the whole, we observe the joint-inversion creates modest changes relative to the seismic-only inversion that mainly serve to enhance the basin features beneath the

SSJRD.

2.4.2 Sacramento – San Joaquin River Delta Velocity Structure

Figure 2.10 shows the velocity model gradient at three cross sections through the SSJRD and Great Valley. We use the gradient to help identify the boundary between Great Valley sediments and the underlying basement. The gradient should be largest in transitions between geologic units and lowest within geologic units. In Figure 2.10 we identify the Great Valley as the low velocity, high gradient area on top of low gradient areas interpreted as the Franciscan

Complex and the Great Valley Ophiolite Body (GVOB). Our assessment of the boundary between the Great Valley and the GVOB generally agrees with the basement depths reported in

Wentworth et al. (1995) which were determined using oil and gas well borehole data along with seismic reflection and refraction profiles. There are no wells in the western Great Valley near the SSJRD where we find the Wentworth et al. (1995) basement to continue deeper than our estimate of the Franciscan basement beneath the Great Valley. Their basement profile closely matches our estimate of the Franciscan/GVOB boundary, however. Comparing velocity 26 contours to the velocity-gradient derived basement boundaries, we see the 5.5 km/s velocity contour seems to most closely match our estimated basement boundaries and generally matches the westward dipping profile from Wentworth et al. (1995) above the GVOB. The major boundaries identified in Figure 2.10 are consistent with interpretations from other geophysical studies which gives confidence in their use to determine basement structure. Figure 2.11 presents schematic interpretations of major geologic units from aeromagnetic data (Jachens et al., 1995) and seismic and gravity data (Godfrey et al., 1997). One difference between these two models is whether Coast Range Ophiolite outcrops seen at the surface of the western edge of the

Great Valley (Bailey et al., 1970; Blake et al., 1984) are continuous at depth to the GVOB.

Using a suite of geophysical data, including from the Bay Area Seismic Imaging eXperiment

(McCarthy and Hart, 1993), Weber-Band et al. (1997) interpret the Great Valley Sequence to directly abut the Franciscan Complex at the SSJRD which is consistent with our interpretation of the velocity gradient. From active source seismic profiles in the northwestern portion of the

Great Valley, Constenius et al. (2000) conclude that the Coast Range Ophiolite floors the Great

Valley above the Franciscan Complex, however using many of the same seismic lines Unruh et al. (2004) interprets the Coast Range Ophiolite to thin out and that the Franciscan Complex directly underlies Great Valley sediments at depth. This could imply greater complexity in the basement geology in the more northerly portions of the Great Valley than in the SSJRD. It is however possible that the velocity gradient is not capable of distinguishing a transition between a hypothetical Coast Range Ophiolite layer and Franciscan rocks. An inability to resolve such a layer could be due to a lack of velocity contrast between the geologic units or if the layer is too thin. 27

At a depth of 1 km we find the lowest velocities in the SSJRD to be near its western edge

(Figure 2.9). At 4 km and 8 km depth we observe the northwest portion of the SSJRD to be the slowest with the highest velocities in the southeast, consistent with the shape of the 3.7 km/s contour. At 8 km and shallower the velocities beneath the SSJRD are lower than the surrounding region, however at 14 km depth the velocity beneath the SSJRD is higher than to the southwest and northeast, indicating the presence of the Great Valley Ophiolite Body (Godfrey et al., 1997;

Harden, 2004; Thurber et al., 2009) and not basin sediments.

In cross-section views through constant Cartesian y-values (Figure 2.12a) we get a sense of the basin shape and how it varies across the SSJRD. In cross-section view it is still evident that the lowest velocities extend deepest in the northwest of the SSJRD as seen in profiles through y = 30 and y = 20. The depth to basement decreases moving southeast (high y-values to low y-values) which is seen clearly in cross-sections through constant Cartesian x-values (Figure

2.12b). Using the 5.5 km/s contour as a proxy for the Great Valley-basement boundary we see a maximum depth of around 10 km beneath the SSJRD. Previous studies estimate a range of values for the maximum depth of the basement beneath the SSJRD. Thurber et al. (2007) conclude low velocity sediments may be up to 10 km thick in the SSJRD which is consistent with our 5.5 km/s contour. Thurber et al. (2009) infer depths greater than 10 km and Hole et al.

(2000) estimate low velocity sediments to extend to a depth greater than 12 km. In the northwest portion of the Delta the velocity gradient suggests the basement could alternatively lie between

10 km and 13 km depth (Figure 2.10a). This would be consistent with the depths estimated by

Thurber et al. (2009) and Hole et al. (2000), although a basement depth in that range would be a large departure from the Wentworth et al. (1995) basement profile and the velocity contours. 28

While velocity contours and the velocity gradient only serve as proxies for basement depth with some amount of uncertainty, there should be a basic agreement between the true shape of the basement surface and seismic velocity. This makes the alternative basement depth of 13 km less plausible in this model.

Figure 2.13 shows a 3D view from the south of the 5.5 km/s contour, representative of the basement surface at depth, for the SSJRD. We see a northwest-southeast trending depression corresponding to the western edge of the Great Valley sedimentary basin. Beneath the southeast portion of the SSJRD a plateau in the basement is evident with a sharp drop off to the southwest.

These deeper basement depths wrap around the plateau to the west and north.

2.4.3 Implications for Seismic Hazard

Our seismic velocity model suggests the SSJRD may be prone to basin amplification of seismic waves, basin-induced surface waves, and focusing effects. Olsen (2000) estimated the site response for the Los Angeles basin using 3D finite-difference, finite-fault simulations which reproduced the particle velocities from the 1994 Northridge earthquake reasonably well. The

Olsen (2000) study found the greatest basin amplifications corresponded to the deepest portions of the basin with amplification factors around 6 for 9 km basin depth. Furthermore, the greatest amplifications seemed to be at locations further from the basin edge. These findings indicate that the northwestern portion of the SSJRD could experience large ground motion amplifications.

The SSJRD may also experience focusing effects due to the irregular basement topography in the southeast portion of the SSJRD. Semblat et al., (2002) performed simulations of wave amplifications for a flat-bottomed and an irregularly shaped basin and found the 29 irregular basin shape led to focusing effects. Hartzell et al. (1996) attribute amplifications at the southern edge of the San Fernando Valley to irregular layer boundaries. This suggests there is a possibility the “plateau” in the basement topography for the SSJRD could potentially focus seismic waves.

2.5 Conclusions

We have created a new 3D velocity model for the Sacramento –San Joaquin River Delta, addressing an identified need for higher resolution velocity models in the region, using a new joint gravity/body-wave tomography algorithm. We are able to jointly fit gravity and travel-time residuals using an empirical density-velocity relationship to take advantage of existing gravity data in the region to help fill in the resolution gaps of previous velocity models in the area. We find that our method enhances our ability to resolve the relief of basin structure relative to seismic-only tomography at this location. We find the depth to the basement to be the greatest in the northwest portion of the SSJRD and that there is a plateau in the basement structure beneath the southeast portion SSJRD. From our findings we infer the SSJRD may be prone to focusing effects and basin amplification of ground motion.

Acknowledgements

We thank Ninfa Bennington and Haijiang Zhang for his assistance with modification of the tomoFADD algorithm. Seismic waveforms for the SSJRD temporary seismic network (YU), deployed by Joe Fletcher of the USGS, were obtained from the IRIS DMC

(http://www.iris.edu/dms/dmc/). Earthquake arrival-time data were obtained from the Northern

California Earthquake Data Center (www.ncedc.org). Many of the figures in this paper were 30 produced using the Generic Mapping Tools software package (Wessel and Smith, 1991). This research was supported by the U.S. Geological Survey (USGS), Department of the Interior, under USGS award numbers G09AP000115 and G11AP20031. The views and conclusions contained in this document are those of the authors and should not be interpreted as necessarily representing the official policies, either expressed or implied, of the U.S. Government.

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Coefficient Value C1 1.6612 C2 -0.4721 C3 0.0671 C4 -0.0043 C5 0.000106

Table 2.1 – Polynomial coefficients for the Brocher (2005) density – Vp empirical relationship. 36

Figure 2.1 – Seismic stations and recent earthquakes near the SSJRD. Northern California Seismic Network stations are shown as purple triangles and the temporary Delta array stations (network code YU) are shown as red triangles. Earthquakes with arrivals at the temporary Delta network are shown as green circles scaled by magnitude.

Figure 2.2 – Bouguer gravity anomaly data points used in this study. Each data point is plotted as a circle colored by value of the gravity anomaly.

Figure 2.3 – Upward continued, de-trended gravity data shown as colored squares. The black triangle outlines the general area of the SSJRD. Major rivers are shown in blue. 40

Figure 2.4 – Comparison of empirical density-velocity relationships plotted with density on the horizontal axis and velocity/slowness on the vertical axis. Each point on the graph marks an increment of 0.5 km/s. a) Brocher‟s relationship in terms of velocity. b) Brocher‟s relationship in terms of slowness. Gray shaded areas mark Regimes 1 and 2 (R1, R2) described in the text. c) Example linear density-velocity relationship (best fit to Brocher‟s relationship). d) The linear (with respect to velocity) relationship in part c, plotted in terms of slowness.

Figure 2.5 – Tomographic inversion horizontal node spacing used in this study. Nodes are shown as orange circles. The Cartesian coordinate system has been rotated 36 degrees counterclockwise and is centered on 38° latitude -120.5° longitude. The finest horizontal node spacing used was 10 km.

Figure 2.6– Misfit to the arrival-time residual (red) and gravity residual (black) relative to the initial misfit of each respective data type. The vertical axis shows the relative misfit and the horizontal axis shows the iteration.

Figure 2.7a 44

Figure 2.7b

Figure 2.7- Maps of (a) gravity residual change and (b) DWS. a) The gravity residual change between the initial and final iterations in mGal with blue shading representing a negative residual change and red representing positive residual change. Contours show initial residual values: 0 mGal – black, 12 mGal – magenta, 20 mGal – pink. b) DWS values are shaded on a logarithmic gray scale.

Figure 2.8a 46

Figure 2.8b

Figure 2.8 – Velocity contours for the listed cross-sections. a) Cross sections in y. Red contours represent the seismic-only model and black contours represent the joint model. The top set of contours are for 4 km/s and the bottom set of contours are 6 km/s. b) Same as (a) but cross- sections are in x.

Figure 2.9a

Figure 2.9b

Figure 2.9 – Map view of the velocity model at a) 1 km depth and b) 4, 8, 14, and 20 km depth . Velocity values are shaded from 3km/s (red) to 7 km/s (blue). Rivers are shown as blue lines. Faults are black lines. Straight gray lines are cross-sections in y and cyan lines are cross-sections in x shown in Figure 2.9. Black triangle outlines general area of the SSJRD. CaF – Calaveras Fault, CoF – Concord Fault, GF – Greenville Fault, GVF – Green Valley Fault, HF – Hayward Fault, SAF –San Andreas Fault, VKHF – Vaca-Kirby Hills Fault.

Figure 2.10a

Figure 2.10b

Figure 2.10c

Figure 2.10 – Cross sections through the SSJRD and Great Valley showing velocity gradient in km/s per kilometer. Black lines show velocity contours at 5, 5.5, 6, and 6.5 km/s. The 5.5 km/s contour is thickened. The black circles show the profile of the crystalline basement from Wentworth et al. (1995). The cyan lines show approximate boundaries of the Great Valley (GV), Great Valley Ophiolite Body (GVOB) and Franciscan Complex. The dashed line in (a) is a possible alternative boundary.

Figure 2.11 – Schematic interpretations of major geologic units in Central California from aeromagnetic data (top, Jachens et al., 1995) and seismic and gravity data (bottom, Godfrey et al., 1997). 51

Figure 2.12a 52

Figure 2.12b

Figure 2.12 – Cross-sections through the velocity model (a) in y and (b) in x. a) Black dots show earthquake hypocenters within ±5 km of each listed cross-section. The black line shows the 5.5 km/s velocity contour representing the depth of the basement. CaF – Calaveras Fault, CoF – Concord Fault, GF – Greenville Fault,, HF – Hayward Fault, SAF –San Andreas Fault, VKHF – Vaca-Kirby Hills Fault 53

Figure 2.13 – Aerial view of the SSJRD region from the south. The green surface shows the 5.5 km/s velocity surface, representing the shape of the basement.

Figure 2.S1 – Earthquake travel times from the temporary Delta network stations. Travel time (arrival time minus estimated origin time) is plotted on the vertical axis and distance from the event to the seismic receiver is plotted on the horizontal axis. The solid black line marks an average seismic velocity of 6 km/s.

Figure 2.S2 – Trades off curves for gravity weighting with weighting values labeled a) Gravity misfit versus Arrival-time misfit. b) Model perturbation norm versus gravity misfit. c) Model perturbation norm versus arrival-time misfit. The selected value was 10. 57

Figure 2.S3 – Trade off curve for the seismic smoothing parameter plotted as model perturbation norm versus arrival-time misfit. Parameter values are labeled on the plot. The selected value was 1.

CHAPTER 3: Ambient Noise Tomography at the Sacramento – San

Joaquin River Delta

Abstract

We present a three-dimensional shear wave velocity model for the Sacramento – San

Joaquin River Delta and surrounding area from ambient noise tomography. Our empirical

Greens functions are in good agreement with published cross-correlations and match earthquake waveforms sharing similar paths. Our group velocity and shear velocity maps are in good agreement with published regional scale models. Our model maps velocity values on a local scale and successfully recovers the basin structure beneath the Delta. We find the maximum depth of the basin to reach approximately 15 km with the Great Valley Ophiolite body rising to a depth of 10 km east of the SSJRD.

3.1 Introduction

The Sacramento-San Joaquin River Delta (SSJRD) occurs at the confluence of the

Sacramento and San Joaquin rivers in the Central Valley of California (Figure 1.1) and is home to a series of levees that control about half of California‟s annual stream flow. More than half of

Californians obtain their drinking water from the SSJRD area (Lund et al., 2007). Torres et al.

Traditional body-wave tomography has lacked resolution in the SSJRD (e.g. Hole et al.,

2000; Thurber et al., 2009; Lin et al., 2011). With S-wave arrivals generally being scarcer than

P-wave arrivals, few studies have even attempted to create shear velocity models encompassing the SSJRD. A technique in seismology that allows for shear velocity modeling in areas without earthquake arrivals is ambient noise tomography (ANT) (Snieder and Wapenaar, 2010). Due to the ubiquitous nature of seismic noise (Kedar and Webb, 2005; Stehly et al., 2006), ambient noise tomography can be performed almost anywhere with an appropriate array of seismic stations. ANT is based on the idea that the cross-correlation of the ambient noise between a pair of seismic stations produces a time series representing wave propagation between the two stations (Campillo and Paul, 2003). The waveforms that emerge predominantly correspond to surface-wave propagation that can be used to determine shear velocity structure.

Regional ANT studies have included the SSJRD (e.g. Lin et al., 2008) however no previous local ANT studies have been performed there. This study presents a new model of the shear velocity structure at the SSJRD determined through ANT. Our results determine the depth to basement and define the shear wave velocity structure of the SSJRD on a finer scale than previous studies and will assist in future seismic hazard analysis of the SSJRD.

3.2 Dataset

Our dataset is composed of three-component, broadband, continuous seismic waveforms from permanent and temporary seismic arrays in central California (Berkeley Digital Seismic

Network, EarthScope Transportable Array, Northern California Seismic Network, Southern

California Seismic Network, Temporary Delta Network). We selected data from two time periods to take advantage of temporally varying station coverage. Figure 3.1a shows the arrangement of seismic stations used in this study. In the first half of 2007 the EarthScope

Transportable Array (network code TA) was covering California, providing data during the early stages of a temporary seismic network deployment in the SSJRD (network code YU; Fletcher and Boatwright, 2007; Fletcher and Sell, 2009). In 2009, the temporary delta network was at its maximal deployment but the Transportable Array had been relocated. Figure 3.1b shows the paths of station-pair correlations determined in this study. Both time periods of data used provide unique coverage of the SSJRD region.

3.3 Method

ANT utilizes cross-correlations of continuous seismic records covering long intervals of time, typically at least one month. The cross-correlation of ambient noise at a pair of seismic stations produces a time series representing wave propagation between the two stations due to an impulse (i.e. the Green‟s function). Before cross-correlating all pairs of stations in a local network, the method includes pre-processing steps intended to damp earthquake signals, thereby accentuating the continuous, mainly ocean-generated noise known as microseisms. ANT proceeds as a form of Rayleigh wave tomography based on group velocities derived from the 61 inversion of dispersion curves (Figure 3.2) of the inter-station correlations. The dispersion curves show how group velocity changes with frequency. Since lower frequency waves have longer wavelengths and probe deeper in the Earth than higher frequency waves they also tend to have higher velocities than higher frequency waves. We create dispersion curves by filtering our cross-correlations in narrow frequency bands (Figure 3.3) to find the time at which the peak amount of energy in the noise-correlation envelope, in that frequency band, travels from one station to another. This example shows clear dispersion over several frequency bands with lower frequencies arriving before 50 seconds and higher frequencies arriving around 60 seconds. This is evident in both the original cross-correlation (Figure 3.3a) and by the timing of the peaks in the noise correlation envelopes (Figure 3.3b). Since we know the distance between the stations used in the cross-correlation we can calculate the average velocity at which the noise envelopes traveled. Doing this for many different frequencies creates a dispersion curve. Using the information contained in the dispersion curves, surface wave group velocity travel times are established between each station pair for each frequency and are inverted with the 2D, ray-based, cross-well tomography algorithm Pronto (Aldridge and Oldenburg,1993) to create horizontal group velocity maps at each frequency. With the group velocity known laterally as a function of frequency, a 1D (depth) inversion for Vs is performed at each cell. An initial 1D Vs profile is updated iteratively to fit forward-modeled Rayleigh wave group velocities to the mapped group velocities at that horizontal position. Rayleigh waves are modeled using the method of Lysmer

(1970) with an assumed Vp/Vs ratio of 1.732 for a Poisson solid and using Gardner‟s relationship (Gardner and Gardner, 1974) to calculate density. The result is a 3D Vs model 62 extending to depths which are dependent on the particular frequency band used and the velocity of the region under study.

We followed the approach described above using codes developed by Matt Haney

(Masterlark et al., 2010). We filtered our data from 0.04 to 0.448 Hz and normalized using a running RMS normalization window of 100 seconds. Our cross-correlations consist of standard vertical-vertical correlations as well as vertical-radial and radial-radial correlations. One benefit of vertical-radial correlations is that Rayleigh wave particle motion is in the vertical-radial plane.

This means off-line arrivals, especially body-waves, will not be coherent in these channels but

Rayleigh waves will be, resulting in less body-wave contamination than vertical-vertical. Figure

3.4 shows an example case for which the vertical-vertical cross-correlation yielded an unusable

Green‟s function but the vertical-radial correlation obtained a good Green‟s function. These cross-correlations highlight one benefit of including vertical-radial correlations in ANT.

Our tomography grid had coordinate origin at latitude 37.7787° and longitude -121.2782° with the Y axis oriented north. The cell size was 10 km in the horizontal direction and 1 km in the vertical direction, with maximal extents of X=-220 and 220, Y = -320 and 280, and Z = 0 and

-50. Group velocity maps were created from our cross-correlations for each frequency from 0.04 to 0.448 at every 0.003 Hz (~ 2 to 25 s periods). We only accepted paths that were at least one wavelength long, had a signal to noise ratio of at least 7 and had group velocities between 0.5 and 5 km/s. The group velocity maps were then inverted on the 3D grid to create the 3D shear velocity model.

3.4 Results and Discussion

3.4.1 Ambient Noise Correlations

In order to obtain meaningful ANT results, the station-pair correlations must represent the Greens function between station pairs. We inspected our correlations to ensure quality and compared them against the IRIS database of Western US Ambient Noise Cross-Correlations

(WUDB, http://www.iris.edu/dms/products/ancc-ciei) as well as earthquake waveforms.

Figure 3.5 shows a record section of two-sided cross-correlations with BDSN station

CMB (Figure 3.1a). Despite being two-sided correlations, these cross-correlations have a very one-sided nature. Correlations at positive and negative lags represent wave propagation in both directions between a given pair of stations. A strongly one-sided correlation is indicative of asymmetric noise sources (Bensen et al., 2007). Positive lags for these cross-correlations represent wave propagation from station CMB to the other stations. Negative lags dominate the cross-correlations indicating the primary noise sources for the frequencies we used originate in the directions of the pair stations, relative to station CMB. CMB is the eastern-most station in this set of correlations which means the main noise source is to the west. This is expected since the Pacific Ocean is the known source of ambient noise for California in our frequency band

(Stehly et al., 2006).

We see three different velocity regimes apparent from the move-out of the cross- correlations in Figure 3.5. To the west of station CMB, temporary Delta network stations HOL,

PLA, SRT and STF have a move-out velocity of approximately 1.3 km/s. Northwest of station

CMB are stations AFD and GDX which have a move-out velocity near 2.4 km/s. Stations BBG,

GDX, and SAO to the southwest of CMB have a move-out velocity of about 3.1 km/s. BDSN 64 station SAO and NCSN station BBG are also a similar distance from station CMB which results in them having similar cross-correlations to one another.

A comparison of our correlation for stations TA.BNLO and TA.R04C to that of the

WUDB shows very similar waveforms. Figure 3.6 shows a 0.12 Hz corner-frequency low-pass filtered version of our correlation for the station pair overlaying the WUDB correlation. Our correlations and those in the WUDB were based on the processing method of Bensen et al.

(2007), however we filtered our data over different frequency bands. The UWDB used a frequency band of approximately 0.02 to 0.0667 Hz whereas we employed a 0.04 to 0.448 Hz band. We investigated using other frequency bands, however we observe a rapid drop off in the amount of useable information at frequencies outside our selected range (Figure 3.S1). Despite the difference in frequency filters our correlations yielded similar results.

We also compared our correlations to earthquake waveforms. Campillo and Paul (2003),

Prieto and Beroza (2008) and Prieto et al. (2011) have shown that ambient noise correlations can produce waveforms similar to those of actual earthquakes. This comparison requires an earthquake to occur near a seismic station so that the path of the earthquake is effectively the same as the station-station correlation. A Mw 3.5 earthquake occurred at approximately 7 km depth and 13 km southeast of BDSN station SAO (San Andreas Geophysical Observatory)

(Figure 3.7). This event occurred on January 21, 2009 at 8:57:23 and was observed at several stations (Figure 3.7) for which we have cross-correlations with station SAO. Figure 3.8 shows our station-pair correlations plotted on top of the waveform at each respective seismic receiver for the earthquake that occurred near station SAO. Time 0 s corresponds to the earthquake origin with the first P-arrivals occurring between 20 and 25 seconds later. All of the stations 65 exhibit a reasonable fit to the earthquake surface waves around time 60 s and later, demonstrating that our correlations reflect empirical Greens functions of the propagation between the station pairs.

3.4.2 Dispersion Curves

Figure 3.2 shows dispersion curves for three station pairs. For the intra-SSJRD pair

(BYR-STF) we see the lowest velocities around 1 km/s at high frequencies (shallow depths).

The inter-SSJRD pair (R04C-BYR) has a velocity around 2 km/s at high frequencies and the non-SSJRD pair (Q04C-R04C) has velocities around 3 km/s. In all cases the velocities tend to be lower at higher frequencies. The SSJRD is known to have low seismic velocities relative to the surrounding area and velocity tends to increase with depth in the Earth so our dispersion curves show expected results. There is a discrepancy with the expected trends at the large velocity inversion evident in the BYR-STF dispersion curve, at the low end of the frequency range. This is not a reflection of true velocity structure since it occurs at low frequencies corresponding to wavelengths greater than the station separation (~25 km) for group velocities around 2 km/s. This station pair would not be used in the lower frequency range where the dispersion curve suggests a velocity inversion because we reject station-pair paths at frequencies where one wavelength is greater than the station separation, as mentioned in the method section.

3.4.3 Group Velocity Maps

We performed a checkerboard test for group velocity resolution at 0.15 Hz. Figure 3.9 shows our true checkerboard model and our recovered model from an initial guess of uniform 2.9 66 km/s velocities. The recovery of the input model at the SSJRD and east into the Great Valley suggests our velocity model has resolution in these areas. This test indicates that we lack resolution west of the SSJRD and east of the Great Valley, in the Sierra Nevada. We are able to resolve the area of the SSJRD and the adjacent portion of the Great Valley.

Previous ambient noise studies encompassing the SSJRD have been regional in scale and produced group velocity maps at periods generally greater than 8 seconds (Moschetti et al.,

2007; Lin et al., 2008; Yang et al., 2008). These works imaged major geologic features but lack finer scale structure. Using many of the same seismic stations as the listed ambient noise studies, along with temporary Delta network stations (Figure 3.1), we were able to create group velocity maps in a frequency band that recover the same major geologic features (i.e. the Great Valley,

Figure 3.10) and show finer scale features on a local scale.

Figure 3.10 compares the SSJRD portion of the 8 second period group velocity map from

Moschetti et al. (2007) to our ~8 second period velocity map. We see many similar features between the two maps - most strikingly a low-velocity area at the SSJRD abutting a high velocity, northwest-southeast trending zone which corresponds to the Great Valley Ophiolite

Body (GVOB). More subtly, we also notice matching local velocity highs to the northeast of

Monterey Bay. One key difference between the two group velocity maps is that the model presented here more sharply defines the strong low-velocity area centered on the SSJRD, showing one benefit of the finer scaled model. Additionally, while the locations of relative velocity highs and lows are largely the same in the two maps, the values of the velocities differ.

Our model has group velocity in the 2.2-2.3 km/s range for the SSJRD which increases to 2.9 km/s at the eastern edge of the Great Valley. In contrast Moschetti et al. (2007) reports values at 67 and/or below 2.0 km/s in the SSJRD with velocities increasing to 2.6 km/s at the edge of the

Great Valley.

3.4.4 Vs Model

Few shear-wave velocity models exist for the SSJRD. Yang et al. (2008) inverted for Vs from phase velocity maps created by ANT and multi-plane-wave tomography (from teleseismic surface wave arrivals). Their regional study was focused on long wavelength (~60 km) features and only had three inversion nodes in the crust. Lin et al. (2010) performed S-wave tomography for the state of California, however the model was generally unresolved in the SSJRD and Great

Valley above 14 km depth. Our results are complementary to these studies as our model primarily focuses on the upper 15 km.

Figure 3.11 shows map view plots of our Vs model at 3, 7, 11, and 15 km depth. Again we recover major geologic features, namely the low velocity sediments of the Great Valley and the high velocities of the Great Valley Ophiolite Body (GVOB). The GVOB is evident as high velocity values (> 3.3 km/s) to the east of the SSJRD at depth. Our velocity values for the

GVOB range from about 3.5 km/s at 11 km depth to 3.7-4.1 km/s at 15 km depth. This is consistent with the results from Lin et al. (2010) for the same location who have velocity values around 3.2-3.4 km/s at 8 km depth and 3.4-4.2 km/s at 14 km depth. The Yang et al. (2008) model has a Vs anomaly of +5% broadly for the area beneath the SSJRD and GVOB at 15 km depth which is higher than our anomaly beneath the SSJRD at 15 km depth (-5%) but lower than our anomaly for the GVOB (+17%). Over longer wavelengths this would average out to a moderate positive anomaly such as what Yang et al. (2008) found. 68

Great Valley sediments are manifest as the low velocity area (< 2.7 km/s at 3 km depth) over the SSJRD and the relative velocity lows oriented northwest-southeast below the SSJRD and north-south above the SSJRD. These absolute and relative velocity lows persist to 15 km depth. Our Great Valley/SSJRD velocity values are consistent with the Vs models of Yang et al.

(2008) and Lin et al. (2010). Yang et al. (2008) report their results in terms of percentage Vs anomaly and find the SSJRD area to have a Vs anomaly below -10% above 10 km depth. At 3 km depth our 2.5 km/s low over the SSJRD is roughly a -21% Vs anomaly relative to the ~3.15 km/s background used by Yang et al. (2008) at 5 km depth. Lin et al. (2010) are able to resolve

Vs on the western edge of the SSJRD and find values around 2.6 km/s which are in our range for the SSJRD (2.5 - 2.7 km/s).

We see the low-velocity Great Valley extend east to longitude -121° at 3 km depth which is consistent with the known boundary between the Great Valley and Sierra Nevada (Figure

3.11). At depth, the base of the Great Valley dips to the west. At 11 km depth we see the Great

Valley basin-basement boundary directly below the eastern edge of the SSJRD (longitude ~-

121.5°). The boundary between the basin and basement is also seen clearly in cross-section

(Figure 3.12). From cross-sections we see the shape of the Great Valley sedimentary basin and the underlying basement. From cross-section views the basin shape reaches a maximum depth of about 15 km beneath the SSJRD. East of the SSJRD we see the GVOB underlying the Great

Valley. Figure 3.S2 shows the depth sensitivity of the Vs model to group velocity frequency.

Below 10 km Vs becomes relatively insensitive to the group velocity maps so even in areas with well-resolved group velocities the model loses resolution at depth. The P-wave tomography results of Thurber et al. (2009) are similar to our findings, with basin shape extending to a depth 69 around 15 km at the SSJRD and the GVOB rising to 10 km to the east, helping to add confidence to our results.

3.5 Conclusions

We present a 3D shear velocity model for the Sacramento – San Joaquin River Delta and surrounding area from ambient noise tomography. Our empirical Greens functions are in good agreement with published cross-correlations and match earthquake waveforms sharing similar paths. Our group velocity and shear velocity maps are in good agreement with published regional scale models. Our model maps velocity values on a local scale and successfully recovers the basin structure beneath the Delta. We find the maximum depth of the basin to reach approximately 15 km with the Great Valley Ophiolite body rising to a depth of 10 km east of the

SSJRD.

Acknowledgements

We thank Matt Haney for providing his ANT routines. Seismic waveforms were from the Berkeley Digital Seismic Network, the Southern California Seismic Network, the EarthScope

Transportable Array and for the SSJRD temporary seismic network (YU), deployed by Joe

Fletcher of the USGS, from the IRIS DMC (http://www.iris.edu/dms/dmc/). Waveforms for the

Northern California Seismic Network were obtained from the Northern California Earthquake

Data Center (www.ncedc.org). Many of the figures in this paper were produced using the

Generic Mapping Tools software package (Wessel and Smith, 1991). This research was supported by the U.S. Geological Survey (USGS), Department of the Interior, under USGS 70 award numbers G09AP000115 and G11AP20031. The views and conclusions contained in this document are those of the authors and should not be interpreted as necessarily representing the official policies, either expressed or implied, of the U.S. Government.

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Figure 3.1a 75

. Figure 3.1b

Figure 3.1 - Maps showing the seismic stations used in this study (a) and the paths of the station- station cross-correlations created between them (b). a) Yellow triangles represent seismic stations from which data was obtained for January 1, 2007 through August 31, 2007. Blue triangles represent stations from which data was obtained for all of 2009. Green triangles show stations in both time periods. The format of station labels is the two digit network identifier code followed by a decimal and then the seismic station abbreviation. b) Colored lines represent the paths of cross-correlations in 2007 (yellow), 2009 (blue), and both time periods (green).

Figure 3.2a

Figure 3.2b

Figure 3.2c

Figure 3.2 - Example dispersion curve for a) intra-SSJRD stations YU. BYR and YU.STF. b) inter-SSJRD stations YU.BYR and TA.R04C. c) non-SSJRD stations TA.R04C and TA.Q04C. These plots can be thought of as the station pair cross-correlation time series plotted vertically, repeatedly. Each instance of the time series is filtered over a narrow frequency band (horizontal axis) with the color scale representing the relative amplitude of each point on the time series in that frequency band. Each point in the time series is converted to group velocity (vertical axis) using the known station separation, producing a plot of velocity versus frequency. The dispersion curve (black line) is picked by the highest amplitude velocity at each frequency value. 79

Figure 3.3a 80

Figure 3.3b

Figure 3.3 – (a) The vertical- radial cross-correlation of TA.R04C and YU.BYR and (b) several time series generated from filtering the cross-correlation in (a) with narrow frequency bands shown on the vertical axis. The peak of the noise correlation envelope in each frequency band is picked with a red „x‟. 81

Figure 3.4 – Comparison of vertical-vertical correlation (top) and vertical-radial correlation (bottom) for EarthScope Transportable Array stations BNLO and R04C. 82

Figure 3.5 – Cross-correlation record section for BDSN station CMB. The vertical axis shows the distance between station CMB and its cross-correlation pair station (listed at right). The red line shows ~3.1 km/s, the green line 2.4 km/s, and the blue line 1.3 km/s.

Figure 3.6 – Example station-pair cross-correlation. Our vertical-vertical correlation of Temporary Array stations BNLO and Q04C is shown in magenta on top of the same correlation from IRIS‟ Western United States Ambient Noise Cross-Correlation Database. Our correlation has been low-pass filtered to more closely match the lower-frequency correlations in the Database.

Figure 3.7 – Map showing the layout of the Delta stations (green triangles), station SAO (blue triangle) and earthquake (red circle) shown in Figure 3.5. 85

Figure 3.8 – Cross-correlations from five temporary Delta network stations with Berkeley Digital Seismic Network station SAO as red lines. The black lines show the waveforms of a Mw 3.5 earthquake that occurred near station SAO recorded at each respective station. Time zero corresponds to the earthquake origin time. 86

Figure 3.9 – Checkerboard test. a) True checkerboard. b) Recovered model. Magenta triangles show seismic station locations. The white outline in part b indicates the approximate area in which the velocity model has resolution. Color scale shows velocity in km/s.

Figure 3.10 – Eight second period group velocity maps of the SSJRD and surrounding region from Moschetti et al. (2007) (left) and this study (right). The dark black line in Moschetti et al. (2007) denotes the approximate boundary between the Great Valley and Sierra Nevada. The black triangle shows the approximate location of the SSJRD. Black lines show faults and blue lines are rivers. CaF-Calaveras Fault, CF-Concord Fault, GF-Greenville Fault, GVF-Green Valley Fault, HF-Hayward Fault, MB – Monterey Bay, SAF-San Andreas Fault, VKHF-Vaca- Kirby Hills Fault

Figure 3.11 – Vs maps for the model presented in this study at depths of 3, 7, 11, and 15 km. The color scale ranges from 2.5 km/s (red) to 3.5 km/s (blue). The black triangle shows the approximate location of the SSJRD.

Figure 3.12 – Cross-section views beneath the SSJRD and surrounding region down to 17 km depth at four different latitudes. Vs is colored from 2.5 km/s (red) to 3.5 km/s (blue). GVOB – Great Valley Ophiolite Body, SSJRD – Sacramento - San Joaquin River Delta.

Figure 3.S1 - Plot showing the number of useable rays (vertical axis) at each frequency used in this study (horizontal axis). 91

Figure 3.S2 – Sensitivity kernel of Vs by depth and group velocity frequency. Red indicates highest sensitivities and blue lowest sensitivities.

CHAPTER 4: Conclusions

The works in this thesis represent an effort to better understand the velocity structure of the Sacramento-San Joaquin River Delta with the express intent of improving the ability to assess seismic hazard in the region. Efforts to model ground motions in the San Francisco Bay area from nearby faults have recognized the need for higher resolution seismic velocity models in the SSJRD and Great Valley which makes the velocity models inherently important. The models also offer insight into potential factors that increase seismic hazards at the SSJRD, such as seismic wave focusing and basin amplification, without performing any ground motion simulations.

The further development of tomography algorithms that do not rely solely on body-wave arrival data, such as joint and ambient noise methods, are also important. Areas which lack arrival-time data but are still prone to having large, damaging earthquakes require methods like those in this thesis. For example, the central United States has generally poor seismic station coverage and lacks numerous earthquakes but has a record of occasional damaging earthquakes

(Wheeler et al., 2003).

These studies have also contributed to collaborative seismic attenuation work at the

SSJRD with Donna Eberhart-Phillips of the University of California – Davis (Eberhart-Phillips et al, 2010).

4.2 Comparison of results

Both the Vp and Vs models produced in these works resolve the basin structure beneath the SSJRD and the high-velocity Great Valley Ophiolite Body to the east. We are capable of resolving finer detail features in our joint body-wave/gravity tomography than in our ambient noise tomography. This is expected since ANT generally has lower horizontal resolution than body-wave tomography. An unexpected 5 km discrepancy arises in the difference in SSJRD basin depths estimated between the two methods. While the literature includes a range of basement depths (e.g. Hole et al., 2000; Thurber et al., 2007; Thurber et al., 2009) it is important to determine the depths within a smaller range.

Likely causes of the basement-depth discrepancy between the two models presented here are the methodology of determining the basement depth and the depth sensitivity of the ANT.

The basement depth for the joint inversion was estimated using the velocity gradient while the interpretation of the ANT was purely based on the shape of velocity structure. Using the velocity gradient to estimate the basin depth in the Vs model is likely to be less successful due to the lack of model sensitivity at depth. Smoothing has potentially vertically smeared the Vs model to appear deeper than it truly is. Taking these factors into consideration we consider the

10 km basement depth estimated in our Vp model to be more robust.

4.3 Future work

There are many steps that can be taken to continue improving the methods and results of this thesis. For joint body-wave gravity tomographic inversion, it would be preferable to employ a constraint that allows for separate velocity and density models. A number of ways exist to 94 attempt this including using separate constraints relating velocity and density rather than combining them in one term as we originally attempted. Using a different empirical relationship for velocity and density could also potentially avoid the problems encountered with our original joint constraint. The issue of non-linear derivatives for empirical relationships can be avoided altogether by using structural constraints. Joint inversions rely upon the idea that the geologic units being imaged have coherent geophysical properties that are unique from the surrounding units and thus using a complementary type of data can provide information about seismic velocity. Structural constraints have been used in previous joint inversion studies for gravity

(Haber and Oldenburg, 1997; Roy et al., 2005) and MT data (Gallardo and Meju, 2007;

Bennington et al., [in revision]). A structurally-controlled joint inversion of seismic and gravity data at the SSJRD could help identify the relative strengths of these different constraints and potentially offer further insight to the velocity structure of the SSJRD and Great Valley.

The biggest shortcoming in the ANT modeling was the frequency range selected. The number of useable rays greatly dropped off at higher and lower frequencies than in the frequency band we used, which limited the model sensitivity at depths less than 3 km and greater than 10 km (Figure 3.S2). Inclusion of short period data and more distant stations could help improve the amount of useable data in a wider frequency band. Some dispersion curves between stations in the temporary Delta network indicated group velocities around 1 km/s at high frequencies however the lowest velocities in the group velocity maps is just under 2 km/s. This indicates a lack of resolution at the shallowest depths. Another potential shortfall with the ANT work may be the smoothing of model parameters. Greater effort may need to be taken to prevent over- smoothing of the Vs model. 95

References

Bennington, N., H. Zhang, C. Thurber, P. Bedrosian, [in revision], Joint Inversion of Seismic and Magnetotelluric Data in the Parkfield Region of California Using the Normalized Cross-Gradient Constraint; Geophys. J. Int.

Eberhart-Phillips, D. M., C. H. Thurber, A. Teel, 2010, Characterizing seismic properties of the Sacramento – San Joaquin River Delta, California; American Geophysical Union, Fall Meeting 2010, abstract #S43B-2059

Gallardo, L., M. Meju, 2007, Joint two-dimensional cross-gradient imaging of magnetotelluric and seismic traveltime data for structural and lithological classification; Geophys. J. Int., 169, 1261-1272

Haber, E., D. Oldenburg, 1997, Joint inversion: a structural approach; Inverse Problems, 13, 63- 77

Roy, L. M. K. Sen, K. McIntosh, P. L. Stoffa, Y. Nakamura, (2005), Joint inversion of first arrival seismic travel-time and gravity data; J. Geophys. Eng., 2, 277-289

Wheeler, R. L., E. M. Omdahl, R. L. Dart, G. D. Wilkerson, R. H. Bradford, 2003, Earthquakes in the central United States – 1699-2002, USGS Geologic Investigation Series I-2812