Coseismic Slip Distribution of the 22 December 2003 San Simeon Earthquake

Frédérique Rolandone, Roland Bürgmann, Doug Dreger, and Mark Murray


The $M_{w}$ 6.5 San Simeon earthquake struck the central California coast on December 22 2003, 50 km west of the San Andreas fault. The San Simeon earthquake is one of several destructive blind-thrust earthquakes to have hit the central California Coast Range during the past two decades. This thrust earthquake accommodates a compressional component of the Pacific-North America plate motion. The mainshock nucleated at a depth of 8 km and was followed by a vigorous aftershock sequence primarily southeast of the hypocenter, consistent with the mainshock directivity (Hardebeck et al., 2004). The strong directivity of the rupture resulted in a concentration of damage to the southeast, with high levels of damage in Paso Robles.

We combine geodetic and seismic data sets to constrain the coseismic slip distribution of the San Simeon earthquake. We use continuous and survey-mode GPS observations along with seismic waveform data from the Berkeley Digital Seismic Network (BDSN/CISN). We invert both data sets for fault slip model. Seismic and geodetic data sample ground deformation at different time scales and combining them provide more stable results than the inversion from individual data sets. The inversion results for this event indicate that the slip extend to the southeast of the epicenter approximately 25 km and in a depth range between 1.3 and 8 km.

Figure 14.1: GPS sites and coseismic displacements from the $M_{w}$ 6.5 San Simeon earthquake with 95$\%$ confidence ellipses. The black star shows the epicenter, the pink dots show relocated aftershocks (Hardebeck et al., 2004). Surface fault traces are shown as red and grey lines.
\epsfig{file=rolandone04_1_1.eps, width=8cm}\end{center}\end{figure}

GPS Data and Analysis

We use data from 36 GPS sites in this study. The San Simeon earthquake produced static displacements at 14 continuously operating GPS stations located within 70 km of the epicentral region. These stations are located northeast of the rupture near the Parkfield segment. The cluster of stations near Parkfield were displaced southwest by about 15 mm. One station 35 km northwest of the rupture moved about 60 mm southwest. In addition, one continuous station south of the rupture and 4 continuous stations north of it (operated by the University of Wisconsin since January 2003) recorded small (less than 12 mm) displacements.

Many of the 17 survey-mode GPS sites are located within 40 km of the rupture and provide useful coseismic deformation signals. Following the San Simeon earthquake, we resurveyed 6 GPS stations northeast of the mainshock. The USGS began continuously occupying 3 stations west of the epicenter one day after the event and another site southeast of the mainshock one week later. Three sites east of the rupture were occupied by JPL within 3 days of the event. A survey of 4 additional sites south of the rupture was done 2 months after San Simeon.

For the campaign GPS sites, we have pre-existing GPS observations collected since the mid-1980's. Some of the sites have multiple years of measurements prior to the earthquake and have precise velocities. For the sites with less than 3 campaigns of data, we use interseismic velocities from the SCEC Crustal Motion Map (CMM). The CMM velocities indicate that the epicentral region had a well-constrained secular deformation field, which allows coseismic displacements to be reliably estimated from pre- and post-event measurements. We use the GAMIT/GLOBK GPS processing software to analyze the GPS data and combine our daily solutions and an appropriate set of global and regional solutions from SOPAC. We estimated the coseismic offsets at each site from these time series assuming that the interseismic velocity is the same before and after the earthquake. The southwest sites, closest to the rupture, recorded larger coseismic offsets than the northeast sites (Figure 14.1). The largest measured horizontal displacement was 179 $\pm$ 14 mm.

Geodetic and Seismic Data Inversion for Fault Slip Model

We use the geodetic data to constrain the rupture geometry. We model the observed coseismic displacements using rectangular dislocations in an elastic, homogeneous and isotropic half-space (Okada, 1985). We use a constrained, nonlinear optimization algorithm (Bürgmann et al., 1997), which allows us to estimate the geometry (parameterized by length, depth, width, dip, strike, and location) and the strike-slip and dip-slip offstets of one fault that best fit the GPS data. The optimal fault model has a strike of 303$^{\circ}$and dips 56$^{\circ}$ to the northeast.

We use the results of our geometry inversion to construct the north-dipping fault plane to determine the distribution of fault slip. Our best-fitting single-fault model is enlarged at the down-dip and lateral edges and discretized into 2 by 2 km elements for the distributed slip inversions. We find that the optimal uniform-slip dislocation is consistent with seismological evidence. The San Simeon focal mechanism and the aftershock distribution suggest the Oceanic fault as the main rupture zone (Hardebeck et al., 2004). The oceanic fault has a strike of about 292$^{\circ}$near the epicenter and changes direction to the south with a more northern strike similar to the one given by our geometry inversion. Our measure of misfit, the reduced $\chi ^2$ value, is not improved if we allow for a second dislocation in the geometry inversion.

We combined displacement and velocity waveform data from 9, three-component BDSN/CISN strong motion stations with 36 observations of GPS deformation to simultaneously invert for the distribution of fault slip. The waveform data was processed by deconvolving the instrument response, double integrating the recorded acceleration to displacement (PKD was integrated only to velocity), and high pass filtering above 0.01 Hz to remove long-period noise.

The seismic waveform data may be generally characterized as low-frequency (Figure 14.2) and in order to model this characteristic a multiple time window approach (e.g. Hartzell and Heaton, 1983; Dreger and Kaverina, 2000; Kaverina et al., 2001) was used to resolve the slip rise time distribution of the rupture. The results of the inversions indicate that the rise time was relatively long for a $M_{w}$ 6.5 event with an average of about 3 seconds. The rupture velocity, though not well resolved, was found to be 2.6 km/s. Consistent with the non-linear GPS inversions for fault orientation the combined inversion favors a more northerly striking fault plane (strike=303, dip=56). The resulting slip model is shown in Figure 14.3. The slip is found to be shallow in depth (1.3 to 8 km) and extends approximately 25 km to the southeast of the epicenter. This unusual aspect ratio for reverse fault rupture is consistent with the results of separate GPS and seismic waveform inversions, and leads to a moderate horizontal directivity effect as compared to a more typical updip directivity as was observed in the 1994 Northridge, California earthquake. The spatially concentrated peak slip was found to be 5.5 m, which is unusually high for a $M_w$6.5 event, and it does depend on the applied smoothing. Over much of the fault, however the slip is between 1 to 3 m. The level of fit to the GPS and seismic waveform data is excellent as shown in Figure 14.2 and 14.3.

The extension of slip to the southeast of the epicenter indicates that this event ruptured unilaterally to the southeast producing a pronounced directivity effect in that direction. Elevated ground motions in the Paso Robles region, about 35 km to the southeast, resulted in two deaths from collapsed unreinforced masonry (URM) buildings, and numerous damaged red-tagged URM buildings in Paso Robles.

Figure 14.2: Comparison of observed (black) and simulated (red) displacement waveforms (velocity for PKD) for the combined seismic waveform and GPS model. Quantitatively the fit to the data was found to be excellent with a 72$\%$ variance reduction.
\epsfig{file=rolandone04_1_2.eps, width=8cm}\end{center}\end{figure}

Figure: Map showing the surface projection of slip from the combined inversion. The epicenter is located at the northwestern edge of the slip distribution. Observed (black) and predicted (green) gps vectors are also shown. For reference major highways are also plotted. Quantitatively the fit to the GPS data was found to be excellent with a 94$\%$ variance reduction. A color version of this figure may be found on page [*].
\epsfig{file=rolandone04_1_3.eps, width=10cm}\end{center}\end{figure*}


Bürgmann, R., P. Segall, M.Lisowski, and J. Svarc, Postseismic starin following the 1989 Loma Prieta earthquake from GPS and leveling measurements, J. Geophys. Res., 102, 4933-4955, 1997.

Dreger, D., and A. Kaverina , Seismic remote sensing for the earthquake source process and near-source strong shaking: A case study of the October 16, 1999 hector mine earthquake, Geophys. Res. Lett., 27, 1941-1944, 2000.

Hardebeck, J.L., J. Boatwright, D. Dreger, R. Goel, V. Graizer, K. Hudnut, C. Ji, L. Jones, J. Langbein, J. Lin, E. Roeloffs, R. Simpson, K. Stark, R. Stein, J.C. Tinsley, Preliminary report on the 22 December 2003, M 6.5 San Simeon, California earthquake Seism. Res. Lett., 75, 155-172, 2004.

Hartzell, S. H., and T. H. Heaton, Inversion of strong ground motion and teleseismic waveform data for the fault rupture history of the 1979 Imperial Valley, California, earthquake, Bull. Seism. Soc. Am., 73, 1553-1583, 1983.

Ji, C., K.M. Larson, Y. Tan, K.W. Hudnut, and K. Choi, Slip history of the 2003 San Simeon Earthquake constrained by combining 1-Hz GPS, strong motion, and teleseismic data, submitted, 2004.

Kaverina, A., D. Dreger and E. Price. The combined inversion of seismic and geodetic data for the source process of the 16 October 1999 $M_w$7.1 Hector Mine, California, earthquake, Bull. Seism. Soc. Am., 92, 1266-1280, 2002.

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

Berkeley Seismological Laboratory
215 McCone Hall, UC Berkeley, Berkeley, CA 94720-4760
Questions or comments? Send e-mail:
© 2004, The Regents of the University of California