A method for the joint inversion of geodetic and seismic waveform data using ABIC: application to the 1997 Manyi, Tibet, earthquake

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Abstract
Geodetic imaging data and seismic waveform data have complementary strengths when considering the modelling of earthquakes. The former, particularly modern space geodetic techniques such as Interferometric Synthetic Aperture Radar (InSAR), permit high spatial density of observation and thus fine resolution of the spatial pattern of fault slip; the latter provide precise and accurate timing information, and thus the ability to resolve how that fault slip varies over time. In order to harness these complementary strengths, we propose a method through which the two data types can be combined in a joint inverse model for the evolution of slip on a specified fault geometry. We present here a derivation of Akaike's Bayesian Information Criterion (ABIC) for the joint inversion of multiple data sets that explicitly deals with the problem of objectively estimating the relative weighting between data sets, as well as the optimal influence of model smoothness constraints in space and time. We demonstrate our ABIC inversion scheme by inverting InSAR displacements and teleseismic waveform data for the 1997 Manyi, Tibet, earthquake. We test, using a simplified fault geometry, three cases—InSAR data inverted alone, vertical component teleseismic broad-band waveform data inverted alone and a joint inversion of both data sets. The InSAR-only model and seismic-only model differ significantly in the distribution of slip on the fault plane that they predict. The joint-inversion model, however, has not only a similar distribution of slip and fit to the InSAR data in the InSAR-only model, suggesting that those data provide the stronger control on the pattern of slip, but is also able to fit the seismic data at a minimal degradation of fit when compared with the seismic-only model. The rupture history of the preferred, joint-inversion model, indicates bilateral rupture for the first 20 s of the earthquake, followed by a further 25 s of westward unilateral rupture afterwards, with slip peaking at 7 m in the upper 6 km of the fault. This joint-inversion approach is thus shown to be a viable method for the study of large shallow continental earthquakes, and may be of particular benefit in cases where near-field seismic observations are not available.

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