January 10, 2010 $M_w$6.5 Gorda Plate Earthquake: Automated Finite-Source Modeling

Douglas S. Dreger


Figure 2.37: A) Line-source slip model. B) Plane-source slip model. In both cases the hypocenter is at 16.9 km depth. Both models show unilateral rupture to the SW.
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Figure 2.38: Revised slip model obtained by adjusting hypocenter depth to 21.7 km and adjusting the timing of Green's functions to align with observed S-wave arrival times. Broadband (0.01 to 10 Hz) data (black) and synthetics (red) are compared. The same amplitude scale was used for all stations.
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On January 9, 2010 at 16:27:38 (January 10, 00:27:38 UTC) a $M_w$6.5 Gorda Plate event occurred approximately 43 km offshore of Ferndale, California. Despite its offshore location it was well recorded by broadband, strong motion and GPS stations operated by the BSL, USGS, and CGS (California Geological Survey). Several years ago, we implemented finite-source inversion algorithms to rapidly, and automatically determine the causative fault plane of an earthquake from the automatic seismic moment tensor solution (e.g. Pasyanos et al., 1996), and to solve for both line and planar models of the slip distribution (e.g. Dreger and Kaverina, 2000, and Dreger et al., 2005).

Automatic Finite-Source Solutions

The moment tensor solution (Figure 2.39) is typical for this offshore region with near-vertical nodal planes and a predominant strike-slip motion. Events in the offshore region occur on both the NW and NE striking nodal planes. The November 8, 1980 M7.2 Mendocino earthquake occurred on a NE striking plane approximately 50 km NW of the 2010 event.

The automatic finite-source code tested both nodal plane orientations with both line-source (Figure 2.37A and plane-source (Figure 2.37B) slip inversions of three-component broadband (0.01 to 10 Hz) displacement waveforms. Despite the poor station coverage due to the offshore location of the earthquake, the stations do sample enough of the focal sphere to capture the directivity of the event. These automatic finite-source calculations were completed within 22 minutes of the occurrence of the earthquake, and the results showed that the NE striking nodal plane was the causative structure. Furthermore, as Figure 2.37 shows, the earthquake ruptured unilaterally to the SW, away from the coast, on the NE striking fault plane. The scalar seismic moment of the plane-source model is $6.76 x 10^{25}$ dyne cm, corresponding to $M_w$6.5. A rise time of 1 second was assumed, and the best fitting rupture velocity was 2.2 km/s.

The initial hypocentral depth was 16.4 km, which was used in the finite-source calculations. Figure 2.37 suggests that the actual slip is deeper. The moment tensor solution yielded a centroid depth of 24 km. Revisions of the hypocenter location resulted in updates of the depth to 21.7, and 29.3 km.

Finite-Source Model Revisions

The initial analyst review of the automatic solution updated the hypocenter to the first revised depth of 21.7 km, and a 1 second timing adjustment was applied to all stations to align the Green's functions to the observed S-wave arrivals. A rise time of 2 seconds (increased from 1 second to match the long-period character of the data) and the 2.2 km/s rupture velocity from the automatic processing were assumed. The revised solution (Figure 2.38) shows the rupture was unilateral to the SW with slip occurring in the 17 to 30 km depth range. The peak slip was 2.7m, and the scalar seismic moment increased to $9.33 x 10^{25}$ dyne cm ($M_w$6.6).

As Figure 2.38 shows, the fit to the broadband displacement waveforms is quite good. Stations GASB and HOPS have the largest amplitudes. These stations are approximately the same distance from the source as stations HUMO and YBH, which show much lower amplitudes. In fact, the small amplitudes at HUMO, YBH and WDC, and the notably larger amplitudes at GASB and HOPS illustrate the strong directivity of the source.

Implications for Ground Motion Reporting

Automated finite-source models may be used to improve ShakeMap ground motion reporting by taking the finite rupture extent into account in the computation of ground motions from empirical relations for the purpose of interpolating the observed values (e.g. Dreger et al., 2005). Although the application of the finite-source model in ShakeMap for this event had minimal impact due to the distant offshore location of the event, the 22 minute processing time, and the success of the system in the identification of the causative fault, the slip distribution and the unilateral rupture characteristics, despite the poor station coverage, demonstrates that such information can be made routinely available in a time frame suitable for rapid ground motion reporting.

Ongoing efforts involve improving automated processing times and solutions as well as updating the analyst interface used to examine and revise solutions.

Figure 2.39: Location of event and stations (triangles). The focal mechanism was obtained from moment tensor inversion of long-period (20 to 50 seconds) three-component waveforms.
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Dreger, D. S., and A. Kaverina, Seismic remote sensing for the earthquake source processes and near-source strong shaking: A case study of the October 16, 1999 Hector Mine earthquake, Geophys. Res. Lett., 27, 1941, 2000.

Dreger, D. S., L. Gee, P. Lombard, M. H. Murray, and B. Romanowicz, Rapid finite-source analysis and near-fault strong ground motions: Application to the 2003 Mw6.5 San Simeon and 2004 Mw6.0 Parkfield earthquakes Seism. Soc. Am., 76, 40, 2005.

Pasyanos, M. E., D. S. Dreger, and B. Romanowicz, Towards real-time determination of regional moment tensors, Bull. Seism. Soc. Am., 86, 1255, 1996.

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