Surface Deformation and Fault Kinematics of the San Francisco Bay Area from PS-InSAR Analysis

Gareth Funning and Roland Bürgmann

Introduction

The aim of this project is to use high-precision geodetic data to characterize, and subsequently model, the surface deformation field of the San Francisco Bay Area. In so doing we hope to recover information about the fault kinematics of the region, the distribution of creeping and locked areas on the Hayward fault, and also about the sources of nontectonic deformation (such as landsliding, subsidence and acquifer recharge) around the Bay, and thus improve our knowledge of the whereabouts and mechanisms of the principal natural hazards in the region. This study builds upon previous work by members of the Active Tectonics group at the Berkeley Seismological Laboratory (Schmidt and Bürgmann, 2003, 2005; Hilley et al., 2004; Ferretti et al., 2004; d'Alessio et al., 2005; Bürgmann et al., 2006).

Figure 22.1: PS-InSAR velocities for the San Francisco Bay Area. Red colors indicate motion of the ground away from the satellite, blue colors motion towards. Where a feature has the same color in both datasets, surface deformation is vertical; where colors are opposite, deformation is horizontal. Pink arrows indicate track (T) and line-of-sight (L) directions for each satellite. White arrowheads show the location of the surface trace of the Hayward fault. [SF - San Francisco, OK - Oakland, SJ - San Jose]
\begin{figure*}\begin{center}
\epsfig{file=gareth06_1_1.eps, width=10cm}\end{center}\end{figure*}

PS-InSAR

Permanent Scatterer Interferometric Synthetic Aperture Radar (PS-InSAR) is a sophisticated geodetic technique that can be used to construct spatially dense datasets detailing the rates of surface deformation over wide ( $\sim 100\times100$ km) areas (e.g. Ferretti et al., 2004). The technique differs from conventional InSAR in that it uses information from features on the ground - typically buildings or other man-made structures, but also natural features such as rock outcrops - which can act as permanent reflectors of incident radar radiation. These can be identified even when surrounded by vegetation, allowing a substantial improvement in coverage in areas such as the East Bay Hills which are poorly suited to conventional InSAR. A further benefit of the PS-InSAR technique is the ability to mitigate noise sources using spatial and temporal filtering. By making certain assumptions - that surface deformation is correlated in time but not in space, and that atmospheric signals are correlated over small spatial wavelengths ($<20$ km) but not in time - it is possible to decompose the radar signal into deformation and atmospheric components, and thus to eliminate the main source of uncertainty in the measurements.

The PS-InSAR data presented here were processed by our long-standing collaborators at Tele-Rilevamento Europa (TRE), Milan, Italy. One of us (GF) visited Milan in the past year to learn about PS-InSAR methods in detail and to supervise data processing. We are also exploring the possibility of using one of the few freely-available codes (e.g. Hooper et al., 2004) in order to have our own in-house processing capability in future.

Figure 22.2: (a) Distribution of creep on the Hayward fault. Creep at the surface reaches a maximum of $\sim 9$ mm/yr at Fremont ($\sim 66$ km). The white area between 20 and 58 km along-strike is the area we believe to be locked. (b) Modeled (left) and residual (right) PS-InSAR and GPS velocities. Only ERS PS velocities are shown here for an example. Black arrows are BAVU GPS velocities, pink arrows show modeled GPS velocities, gray arrows show residual GPS velocities (note change in scale). Solid black lines are faults modeled in the inversion. Most residuals are of the order 1-2 mm/yr; prominent residual uplift features (blue colors) can be seen where there is unmodeled uplift occurring within stepovers and restraining bends of the fault. Coordinate system is UTM km, zone 10.
\begin{figure*}\begin{center}
\epsfig{file=gareth06_1_2.eps, width=14cm}\end{center}\end{figure*}

Data

We analyse data from two sources - the European Space Agency ERS satellites (49 descending track radar image acquisitions from 1992-2000), and the Canadian Radarsat platform (31 ascending track images from 2001-2004). Both data sets are plotted in Figure 22.1. Each data set provides a dense coverage of surface velocity observations in the line-of-sight direction of the satellite. Given the different viewing geometries of the two data sets, if we assume that the rates of displacement do not vary with time, we can use the two independent measurements to infer the horizontal and vertical deformation rates across the region.

Creep on the Hayward fault

The Hayward fault is currently considered to pose the greatest threat of a $M\sim 7$ earthquake of the major faults of the San Francisco Bay Area (Working Group on California Earthquake Probabilities, 2003). The fault creeps at the surface - this can be seen in both PS-InSAR data sets as an abrupt change in velocity either side of a linear feature (Figure 22.1). Knowledge of the extent and magnitude of creep at depth is important for understanding the future seismic hazard posed by the structure; areas of very low ($<2$ mm/yr) or zero creep can be considered locked, and therefore in potential danger of rupture in future.

We model the distribution of creep on the Hayward fault using elastic dislocation modeling (Okada, 1985), assuming a vertical fault geometry with a surface trace matching that of the mapped fault, subdivided into $2\times2$ km patches, and applying Laplacian smoothing. The regional strain gradient is described by placing further, deep, dislocations beneath each of the major faults in the region. The velocity on each fault is inverted for using least squares methods with a positivity constraint to prevent retrograde motion. In addition to the PS-InSAR data, appropriately sub-sampled, we also invert GPS data from 185 sites across the region (d'Alessio et al., 2005), and surface creep rates measured at 18 alignment arrays along the trace of the Hayward fault (Lienkaemper et al., 2001).

Our model of fault slip is plotted in Figure 22.2a. We find evidence for a patch of very low/zero creep which extends between $\sim20$ and 58 km along-strike (measured southeast from Pt Pinole, where the fault trace goes offshore into San Pablo Bay), corresponding to the portion of the fault between south Oakland and Union City. The overall pattern is similar to that obtained in other studies where characteristic repeating earthquake data are used to constrain creep behavior at depth (e.g. Schmidt et al., 2005). If we assume a long-term slip rate for the Hayward fault of 10 mm/yr, within the uncertainties of geologic estimates (e.g. Lienkamper and Borchardt, 1996), this implies that this `locked' portion of the fault is accumulating a moment deficit equivalent to a $M_w$ 6.74 event per century. If loading rates have been constant since the last event on the Hayward fault in 1868, the total deficit is equivalent to a $M_w$ 6.9 earthquake; this represents an upper bound of the size of any potential earthquake, as we do not know how much of the total moment deficit would be released aseismically as afterslip or accelerated creep following an earthquake.

This model generally fits the data well, with mean residuals of less than 1 mm/yr (Figure 22.2b). The most prominent residual features are uplift features seen in the Mt Diablo stepover and San Andreas fault restraining bend, which are consistent with the strike-slip fault geometries, but presumably occurring upon structures that we have not modeled in this study. We also see evidence in the Loma Prieta region of the San Andreas fault for continuing residual postseismic subsidence and contraction following the 1989 earthquake in this location. These findings are consistent with other attempts to identify vertical tectonic motions in the San Francisco Bay Area (e.g. Bürgmann et al., 2006).

Acknowledgements

We would like to thank our collaborators at TRE, especially Alessandro Ferretti, Fabrizio Novali and Chiara Giannico, for their continuing assistance with the PS-InSAR processing and with data acquisition/ordering issues. ERS data are copyrighted by the European Space Agency and supplied through the WInSAR consortium, and under project AOE 750. Radarsat data are copyrighted by the Canadian Space Agency and supplied under an agreement with the Alaska SAR Facility. This project is funded by grants from the National Science Foundation, and the National Earthquake Hazard Reduction Program.

References

Bürgmann, R., G. Hilley, A. Ferretti, and F. Novali, Resolving vertical tectonics in the San Francisco Bay area from GPS and Permanent Scatterer InSAR analysis, Geology, 34, 221-224, 2006.

d'Alessio, M. A., I. A. Johanson, R. Bürgmann, D. A. Schmidt and M. H. Murray, Slicing up the San Francisco Bay Area: Block kinematics and fault slip rates from GPS-derived surface velocities, J. Geophys. Res., 110, B06403, doi:10.1029/2004JB003496, 2005.

Ferretti, A., C. Prati and F. Rocca, Permanent Scatterers in SAR Interferometry, IEEE Trans. Geosci. Remote Sens., 39, 8-20, 2001.

Ferretti, A., F. Novali, R. Bürgmann, G. Hilley and C. Prati, InSAR Permanent Scatterer Analysis Reveals Ups and Downs in San Francisco Bay Area, EOS Trans. AGU, 85, 317, 2004.

Hilley, G. E., R. Bürgmann, A. Ferretti, F. Novali and F. Rocca, Dynamics of slow-moving landslides from permanent scatter analysis, Science, 304, 1952-1955, 2004.

Lienkaemper, J. J. and G. Borchardt, Holocene slip rate on the Hayward fault at Union City, California, J. Geophys. Res., 101, 6099-6108, 1996.

Lienkaemper, J. J., J. S. Galehouse and R. W. Simpson, Long-term monitoring of creep rate along the Hayward fault and evidence for a lasting creep response to the 1989 Loma Prieta earthquake, Geophys. Res. Lett., 28, 2265-2268, 2001.

Okada, Y., Surface deformation due to shear and tensile faults in a half-space, Bull. Seismol. Soc. Am., 75, 1135-1154, 1985.

Schmidt, D. A. and R. Bürgmann, Time-dependent land uplift and subsidence in the Santa Clara valley, California, from a large interferometric synthetic aperture radar data set, J. Geophys. Res., 108, B9, 2416, doi:10.1029/2002JB002267, 2003.

Schmidt, D. A. and R. Bürgmann, Distribution of aseismic creep rate on the Hayward fault inferred from seismic and geodetic data, J. Geophys. Res., 110, B08406, doi:10.1029/2004JB003397, 2005.

Working Group on California Earthquake Probabilities, Earthquake probabilities in the San Francisco Bay Region: 2002 to 2031, U.S. Geol. Surv. Open File Rep., 03-214, 2003.

Berkeley Seismological Laboratory
215 McCone Hall, UC Berkeley, Berkeley, CA 94720-4760
Questions or comments? Send e-mail: www@seismo.berkeley.edu
© 2006, The Regents of the University of California