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Inversions for buried slip along the northern Hayward fault from GPS and InSAR data

Roland Bürgmann, Eric Fielding, Mark Murray, David Schmidt


Introduction

On October 21, 1868, the only major historic earthquake on the Hayward fault produced a 30-40-km-long surface rupture with slip of up to 2 m which may have extended at depth from Fremont to as far north as Berkeley. No large historic earthquake has been unequivocally attributed to the Hayward fault north of this rupture, suggesting a lack of coseismic rupture since before the establishment of the first Spanish mission in the region, in 1776 (Toppozada and Borchardt 1998). A paleoseismic trenching investigation on the northern Hayward fault suggests an earthquake rupture after 1640 AD (Schwartz et al. 1998, pers. comm.). Long-term slip rate estimates of  10 mm/yr indicate that more than 2 m of seismic slip potential has accumulated since the most recent event, making the northern Hayward fault capable of M > 6.5 events.

Earthquake potential estimates are complicated by the occurrence of shallow aseismic creep along the Hayward fault whose depth extent is not known. At the surface, the Hayward fault creeps at 3-9 mm/yr (Lienkaemper et al., 1997). It is not clear over what depths locked and creeping portions of the Hayward fault extend, leading to substantial uncertainty about potential earthquake magnitudes and probabilities.

Measurements of surface displacements surrounding a fault using GPS or terrestrial surveys can be used to compute models of the distribution of slip on a fault system. However, most precisely surveyed points near the Hayward fault are spaced more than 10 km apart and it is therefore difficult to determine a reliable slip estimate. Space based Interferometric Synthetic Aperture Radar (InSAR) can map ground deformation at 10s-of-meter resolution over large areas with sub-cm precision. This technique only provides measurements of one component of the displacement field along the look direction of the radar. The Global Positioning Systems (GPS) can measure the three-dimensional displacements at very high precision, but station spacing currently are limited to several km. We utilize surface creep rates established over several decades (Lienkaemper et al., 1997), GPS measurements spanning about 4 years, and InSAR data spanning a 5-year period from June 1992 to September 1997 (Figure 17.1), to invert for the depth of creep on the northern Hayward fault.


  
Figure 17.1: Unwrapped interferogram of two ERS images spanning 5.25-year period of faulting and strain accumulation near Hayward fault (ERS track 70, frames 2835 and 2853; June 10, 1992, ERS-1 orbit 4724, and September 06, 1997, ERS-2 orbit 12449). Range changes are computed from InSAR interferogram by unwrapping angular phase delays and converting from phase delay to range change. Steep topography and heavy vegetation cause decorrelation leading to loss of range change information (blank areas). Good correlation occurs almost exclusively in urban areas. An abrupt offset follows trace of recently active strands of Hayward fault indicated by thin red line.
\begin{figure*}
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\epsfig{file=burgmann99_1.ps, width=15cm}\end{center}\end{figure*}


  
Figure 17.2: Joint inversion of GPS and InSAR data. We can now formally combine the two data sets in our model inversions. Preliminary results using the existing GPS data set shown in the bottom panel (solid arrows) and 1992-1997 InSAR data shown in the top left panel (subsampled to the number of data points shown) suggest a best fitting model with creep to 7 km. Additional GPS data and additional redundant InSAR data are required to better constrain our models.
\begin{figure*}
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\epsfig{file=burgmann99_2.ps, width=15cm}\end{center}\end{figure*}

Results

Measurements of active deformation along the northern Hayward fault consist of surface creep data at the active fault trace, GPS measurements of benchmark motions, and InSAR measurements of range change differences near the Hayward fault. We assume that the deformation has been steady and integrate creep rates from the last several decades with GPS derived displacements between 1993 and 1998, and InSAR measured range changes between 1992 and 1997.

Along the northern 15 km of the subaerial portion of the Hayward fault, surface creep rate estimates average 5-6 mm/yr (Lienkaemper et al., 1997). GPS station velocities along the northern Hayward fault are from continuously operating receivers of the BARD (Bay Area Regional Deformation) network, as well as from campaign style measurements collected since 1993 by the U.S. Geological Survey and the University of California, Berkeley.

We use synthetic aperture radar (SAR) data collected by the European Space Agency (ESA) ERS-1 space craft on June 10, 1992 and September 06, 1997. Bürgmann et al. (1998) utilized a 1992-1995 image pair to examine anomalous slip patterns along the southern Hayward fault resulting from the effects of the 1989 Loma Prieta earthquake. Discrete offsets due to aseismic creep at the surface are apparent along the trace of the actively creeping Hayward fault. This suggests a component of surface fault displacement in the satellite range direction. InSAR only measures the motion as it projects into the satellite range direction which is 23 degrees off vertical for ERS.

We use elastic dislocation models to estimate the distribution of locked and slipping portions of the Hayward fault. For the purpose of this study, we assume that the northern Hayward fault northwest of Berkeley is characterized by uniform creep from the surface to some depth. Regional interseismic strain accumulation across the San Andreas fault system is represented by slip on deeply buried dislocations below the San Andreas and Hayward fault zones. The regional model is formally derived from the GPS data, which are well fit by the model.

Integration of the range change data with sparse, but precise GPS measurements in the region helps us better constrain the locking depth and rupture potential of the Hayward fault (Figure 17.2). The figure shows results from joint inversions of both the InSAR and GPS data for slip rate on the creeping Hayward fault. We find that the current GPS data set provides little added constraint to the shallow slip on the Hayward fault. However, the GPS data allow us an improved representation and integration of the deeply seated regional strain accumulation. The initial inversions of the two data sets suggests a creep depth of 7 km is favored by the 1992-1997 InSAR data and current GPS data set (Figure 17.3). We are currently in the process of establishing a denser GPS network in this area with sites chosen to optimize our resolution of slip potential on the northern Hayward fault. The L1 system developed at UNAVCO is currently being tested at BSL to aid us in this effort. InSAR geodesy promises to be an extremely valuable tool to resolve highly detailed images of subsurface slip and elastic strain accumulation.


  
Figure 17.3: Misfit (WRSS) and creep rates from joint inversion of GPS and InSAR data as a function of depth of uniformly creeping model fault. Misfits (thin lines) are shown separately for InSAR and GPS data. Note that while the InSAR data favor creep to greater depths, the GPS data do not have a pronounced minimum. The best-fitting creep rates of 8-10 mm/yr for depths > 5 km (bold line) are higher than those observed at the surface.
\begin{figure*}
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\epsfig{file=burgmann99_3.ps, width=15cm}\end{center}
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References

Bürgmann, R., E. Fielding, and J. Sukhatme, Slip along the Hayward fault, California, estimated from space-based synthetic aperture radar interferometry. Geology, 26, 559-562, 1998.

Lienkaemper, J.J., J.S. Galehouse, and R.W. Simpson, Creep response of the Hayward fault to stress changes caused by the Loma Prieta earthquake, Science, 276, 2014-2016, 1997.

Toppozada, T.R., and G. Borchardt, Re-evaluation of the 1836 "Hayward fault" and the the 1838 San Andreas fault earthquakes, Bull. Seismol. Soc. Am., 88, 140-159, 1998.


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