Source Description of the 1999 Hector Mine, California, Earthquake, Part I: Wavelet Domain Inversion Theory and Resolution Analysis
We present a new procedure for the determination of rupture complexity from a joint inversion of static and seismic data. Our fault parameterization involves multiple fault segments, variable local slip, rake angle, rise time, and rupture velocity. To separate the spatial and temporal slip history, we introduce a wavelet transform that proves effective at studying the time and frequency characteristics of the seismic waveforms. Both data and synthetic seismograms are transformed into wavelets, which are then separated into several groups based on their frequency content. For each group, we use error functions to compare the wavelet amplitude variation with time between data and synthetic seismograms. The function can be an L1 + L2 norm or a correlative function based on the amplitude and scale of wavelet functions. The objective function is defined as the weighted sum of these functions. Subsequently, we developed a finite-fault inversion routine in the wavelet domain. A simulated annealing algorithm is used to determine the finite-fault model that minimizes the objective function described in terms of wavelet coefficients. With this approach, we can simultaneously invert for the slip amplitude, slip direction, rise time, and rupture velocity efficiently. Extensive experiments conducted on synthetic data are used to assess the ability to recover rupture slip details. We, also explore slip-model stability for different choices of layered Earth models assuming the geometry encountered in the 1999 Hector Mine, California, earthquake.
Additional Information© 2002 by the Seismological Society of America. Manuscript received 6 November 2000. The project was supported by USGS and SCEC. Ji benefited from the discussion with Professor Zhenxing Yao (Institute of Geophysics, Chinese Academy of Sciences). The figures are made using GMT (Generic Mapping Tools) software (Wessel and Smith, 1991). This manuscript was prepared with AGU's LATEX macros v5, with the extension package AGU by P. W. Daly, version 1.6b, from 19 August 1999. This project was supported by SCEC contract No. NSF EAR-8920136 and by the U.S. Geological Survey under Contract No. 1HQGR0098. Contribution 8749, Division of Geological and Planetary Sciences, California Institute of Technology.
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