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Finite Fault Inversion of the Loma Prieta Earthquake Incorporating Complex Structure

David Schmidt and Douglas Dreger


Source complexity and 3D structure were identified as important avenues of research by early source studies of the 1989 Loma Prieta earthquake, but this work was never completed. We attempt to resolve some of these lingering issues by evaluating how the source model is affected by station geometry, structural complexity, and multiple rupture planes.

Bürgmann et al. (1997) found that afterslip may have occurred on a shallow thrust fault located to the northeast of the main rupture. It was never explored whether this region may have also participated in the coseismic event. The spatial distribution of aftershocks suggest that the rupture geometry was complex and may have occurred on multiple planes with distinctly different orientations. We test the possibility of a complex rupture geometry by performing an inversion with a vertical SAF and an additional low angle thrust.

Several tomography studies in the region have identified a strong lateral velocity discontinuity across the San Andreas Fault. We evaluate how this lateral discontinuity may have biased the finite source inversion by comparing results using a 1D velocity model with those using a composite set for stations west and east of the San Andreas Fault.


We perform the finite source inversion using the non-negative least squares approach described by Kaverina et al. (2001) and Dreger and Kaverina (2000). Moment minimization and smoothing are included in the inversion. Green's functions are calculated using the previously published one-dimensional velocity models. We restrict the seismic data to corrected velocity records collected at stations with absolute time by the USGS, CDMG, and UCSC. The geodetic data used in the combined inversion include GPS, EDM, VLBI, and leveling data described in Arnadottir et al. (1994). All seismic data and Green's functions are filtered using a two pass butterworth filter with corners at 0.1 and 1 Hz, and sampled at 0.1 seconds. We performed a jack-knife test on the seismic data and determined that no individual station dominated the inversion. We also determined which smoothing and moment minimization weights produce the best results for each data set.


We perform inversions using Green's functions calculated from 3 distinct one-dimensional velocity models to evaluate whether the choice in velocity structure significantly impacts the slip distribution. Three published velocity models are tested from early source studies for the Loma Prieta event (Wald et al., 1991; Beroza, 1991; Steidl et al., 1991). All inversions were performed for a single 70 degree west dipping plane. Beroza (1991) presents two distinct velocity models, one for stations to the northeast of the San Andreas fault and one for stations to the southwest. We do not find a significant difference between slip distributions for the three velocity models. Given our choice of inversion parameters, the velocity model from Wald et al. (1991) produces the best fit to the data. However, the slip distribution most resembles the distribution found by Beroza (1991).

A combined seismic waveform and geodetic inversion was also performed (Figure 21.1). We choose to weight the seismic versus geodetic data such that the fit to the seismic data is maximized without degrading the fit to the geodetic data. Slip is allowed to occur in 5 overlapping time windows that are delayed by 0.35 seconds where the dislocation rise time is constrained to 0.7 seconds. We find that the majority of the slip occurs in the first time window, similar to what was found by previous studies.

We test 3 fault geometries: 1) a 70 degree west dipping plane, 2) a 65 degree west dipping plane which meets a vertical plane at a depth of 10 km, and 3) a 65 degree west dipping plane with a vertical plane that intersects a 30 degree west dipping thrust at a depth of 5 km (Figure 21.2). We find a gradual improvement in fit to the data, although it is not clear if this improvement is statistically significant or simply reflects the increase in model parameters. The slip distribution for the single 70 degree dipping plane supports the view that the event nucleated between two segments. The southeastern segment was dominated by strike skip motion where as the northwest segment experienced the highest slip magnitudes.

Future Work

Additional fault geometries will be tested, including a change in dip along strike and a delay in rupture to the northwest patch. We will also determine whether the various geometries produce a statistically significant improvement in fit to the data.


We wish to acknowledge the support of the Hellman Family Faculty Fund.


Arnadottir, T., and P. Segall, The 1989 Loma Prieta earthquake images from the inversion of geodetic data, J, geophys. Res., 99, 21,835-21,855, 1994.

Beroza, G.C, Near-source modeling of the Loma Prieta earthquake: evidence for heterogeneous slip and implications for earthquake hazard, Bull. Seism. Soc. Am., 81, 1603-1621, 1991.

Bürgmann, R., Segall, P., Lisowski, M., and J. Svarc, Postseismic strain following the 1989 Loma Prieta earthquake from GPS and leveling measurements, J, geophys. Res., 102, 4,933-4,955, 1997.

Dietz, D. and W. Ellsworth, Aftershocks of the Loma Prieta Earthquake and their tectonic implications, USGS Professional Paper 1550-D, 5-47, 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.

Horton, S., J.G. Anderson, and S.H. Mendez, Frequency-domain inversion for the rupture characteristics during the earthquake using strong motion data and geodetic observations, USGS Professional Paper 1550-A, 59-74, 1997.

Steidl, J.H., R.J. Archulta, and S.H. Hartzell, Rupture history of the 1989 Loma Prieta California earthquake, Bull. Seism. Soc. Am., 81, 1573-1602, 1991.

Wald, D., D.V. Helmberger, and H.T. Heaton, Rupture model of the 1989 Loma Prieta earthquake from the inversion of strong-motion and broadband teleseismic data, Bull. Seism. Soc. Am., 81, 1540, 1991.

Figure 21.1: Slip distribution for a combined seismic and geodetic inversion on a 70 degree, southwesterly dipping plane.
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Figure 21.2: Three fault geometries were tested in the inversion. See text for a description.
\epsfig{file=schmidt01_1_2.eps, width=8cm}\end{center}\end{figure}

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