Recursive stochastic deconvolution in the estimation of earthquake source parameters: Synthetic waveforms

Details Recursive stochastic deconvolution in the estimation of earthquake source parameters: Synthetic waveforms Recursive stochastic deconvolution in the estimation of earthquake source parameters: Synthetic waveforms

Nov 1994

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1994pepi...86..301q&link_type=abstract

Physics of the Earth and Planetary Interiors (ISSN 0031-9201), vol. 86, no. 4, p. 301-327

Mathematics

Earthquakes, Error Analysis, Estimating, Mean Square Values, Recursive Functions, Seismic Waves, Seismology, Stochastic Processes, Waveforms, Algorithms, Covariance, Inversions, Kalman Filters, Matrices (Mathematics)

Scientific paper

In this paper, a method of the linear minimum mean-squares error (LMMSE) solution for source inversion is presented in terms of a recursive algorithm. A covariance matrix of estimation error, as well as a resolution matrix are also computed through recursion. It is shown that this recursive solution corresponds to a stationary Kalman filtering estimation for a linear dynamic system, which makes it possible to perform satisfactorily in an environment where complete knowledge of the relevant signal characteristics is not available. In a stationary environment, our recursive solution converges to the optimum Wiener solution. In a rather straightforward manner, the multichannel deconvolution problem is translated into a set of recursive expressions. The procedures have been tested using a number of synthetic data sets, including a point and a complex source, with satisfactory results. It is found that the solution is improved recursively with each addition of new data. We have found further that it is the error-covariance matrix, not the resolution matrix, that gives a measurement of the recursive performance. Since the recursive scheme of LMMSE runs in a manner based on either block-by-block or sample-by-sample operation, the memory requirement can be quite small. For problems involving sparse matrices, the recursive algorithm leads to fast and efficient computation. This method is tested by examining the Sierra Madre earthquake M(sub s) of 28 June 1991, California. This event is well-recorded by the broad-band TERRAscope array. The moment tensor inversion through the presented method indicates that the solution is improved recursively when new data become available. It was found that the later arrivals on the observed seismograms have very little influence on the solution while the inclusion of new data from different stations yields substantial improvement on the mechanism to a certain point where further addition of data will not make much difference to the resulting best double-couple decomposition. However, the content of double-couple components shows a striking increase from approximately 50 to 90% with the inclusion of more data from other stations. This result demonstrates clearly the robustness of our approach since the inadequacy of the source representation and the earth model in the moment-tensor inversion may be remedied by the inclusion of more data.

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