Slip of the 2004 Sumatra-Andaman Earthquake from Joint Inversion of Long Period Global Seismic Waveforms and GPS Static Offsets

Junkee Rhie, Douglas Dreger, Roland Bürgmann, and Barbara Romanowicz


The December 26, 2004 Great Sumatra-Andaman earthquake is an important earthquake in may ways. It is the first great event ($M_{w}$ $>$ 9.0) with sufficient data to allow for a detailed analysis of its complex source rupture process. For the first time, global very broadband seismic and geodetic measurements are available. In this study, we present a slip distribution over the finite fault plane constrained by global long period seismic waves and near-field GPS offsets.

Data and Inversion Method

We considered all three components of displacement waveforms recorded at 10 IRIS and GEOSCOPE stations within the epicentral range between 43.6$^{\circ }$and 65.2$^{\circ }$(Figure 23.1). The GPS offset data used for the inversion represent a 38 near-field subset of the 142 coseismic displacement measurements (Banerjee et al., 2006) (Figure 23.1). To account for several weeks of postseismic deformation prior to reoccupation of the GPS stations, we adjusted the offset estimates for near-field campaign-mode GPS sites in this dataset.

To invert data for the slip distribution, we use a widely used least-squares inversion. Here we used normal-mode computed Green's functions for seismic waveforms at teleseismic distances and FORTRAN programs EDGRN/EDCMB (Wang et al., 2003) for GPS Green's functions for flat layered elastic structures. In both cases, PREM is used for the velocity structure. The seismic data and Green's functions were bandpass filtered between 100 and 500 sec. Since the rise time of each sub-fault is very short compared to the passband, we ignored the detailed variation in slip rise time of each sub-fault. The trigger time of each sub-fault is defined by the passage of circular rupture front with constant rupture velocity. In this study, we choose the rupture velocity of 2.5 km/s as it is consistent with other studies (e.g., Ni et al.. 2005). A Laplacian-smoothing operator and slip positivity constraint are applied in all of the inversions and a weighting factor is applied to the GPS data set and Green's functions for optimal slip model explaining both seismic and GPS data sets.

Figure 23.1: The preferred slip distribution model from joint inversion of seismic and GPS static offsets. Color represents total slip and the arrows show the slip vector. Black triangles indicate the locations of the near-field GPS sites and black squares in the small global map on the upper right show 10 selected global seismic stations used in joint inversion. A white star represents the epicenter both in local and global maps.
\epsfig{file=rhie06_2_1.eps, width=8cm}\end{center}\end{figure}

Results and Discussion

We tested a geometry model, slightly modified from a previous study, constrained by aftershock distribution and the fit to the far-field GPS coseismic offsets (Banerjee et al., 2005). In this study, we removed the steeper and deeper segments of the fault and made a simple fault geometry model because our data sets are not sensitive to a slight geometry change at deeper depth. The slip model inverted from only seismic waveforms shows large slip patches at around 4$^{\circ }$N and a high-slip region with slip larger than 10 m extends only up to 10$^{\circ }$N, and its moment magnitude is 9.12. The joint inversion slip model including near-field GPS static offsets data basically keeps the trend of the slip distribution but increases the level of the slip over nearly the whole fault plane, and its seismic magnitude is determined to be $M_w$ 9.20 (for slip distribution see Figure 23.1).

To constrain key model parameters, we consider sensitivity tests for dip angles and rupture velocity, which are important parameters to understand the source process. Unfortunately our data sets are not very sensitive to these two parameters. While neither of the two parameters are well constrained in this study, distribution of aftershocks and several previous studies support that our dip angles and rupture velocity are reasonable (e.g., Bilham et al., 2005; Ni et al., 2005).

A precise estimate of model error is as important as a detailed slip distribution. An error analysis on our slip model is conducted by a random station selection method. We randomly select 50$\%$ of seismic and GPS stations and invert them for slip distribution and then repeat this process 10 times. By doing this, we estimate mean and standard deviation of moment magnitude and also slip at each sub-fault. The mean slip distribution is very similar to the slip distribution inverted from the whole data set. The estimate of mean seismic moment and 1 standard deviation error is $9.19 -0.02/+0.02$.

To confirm our slip distribution model we compare forward GPS static offsets at far-field sites (Figure 23.2). We do not consider stations at $>$ 1000 km because of the large sphericity effect, which we did not consider in our Green's function computation. A forward prediction of GPS vectors at stations on Malaysian Peninsula shows that the slip model inverted using only seismic data significantly underestimates observed GPS offsets but the slip model from the joint inversion can predict observations nearly perfectly.

This indicates that after-slip correction to get coseismic static offsets for near-field campaign GPS offset data is correct and unaccounted post-seismic excess motion is small.

Our slip model from joint inversion is similar to slip models obtained from different data sets in the location of the largest slip patch and the extent of the large slip region (e.g., Ammon et al., 2005). This largest slip patch is consistent with one of the tsunami source regions found by Fine et al., [2005], and the northward extent of significant slip region is consistent with the tsunamigenic region suggested by Lay et al., [2005].

Figure 23.2: Comparison between observed (grey) and synthetic GPS vectors (black) for seismic only and joint inversion models.
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We thank IRIS and GEOSCOPE for providing seismic data. GPS data used in this study were provided by the Survey of India (SOI), BAKO-SURTANAL, the Tectonic Observatory at Caltech, and the Indonesian Institute of Sciences (LIPI).


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