RECURSIVE STOCHASTIC DECONVOLUTION IN THE ESTIMATION OF EARTHQUAKE SOURCE PARAMETERS - SYNTHETIC WAVE-FORMS

In this paper, a method of the linear minimum mean-squares error (LMMS E) solution for source inversion is presented in terms of a recursive algorithm. A covariance matrix of estimation error, as well as a resol ution matrix are also computed through recursion. It is shown that thi s recursive solution corresponds to a stationary Kalman filtering esti mation for a linear dynamic system, which makes it possible to perform satisfactorily in an environment where complete knowledge of the rele vant signal characteristics is not available. In a stationary environm ent, our recursive solution converges to the optimum Wiener solution. In a rather straightforward manner, the multichannel deconvolution pro blem is translated into a set of recursive expressions. The procedures have been tested using a number of synthetic data sets, including a p oint 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-convariance matrix, not the resolution matrix, that gives a measurement of the recursive performa nce. Since the recursive scheme of LMMSE runs in a manner based on eit her block-by-block or sample-by-sample operation, the memory requireme nt can be quite small. For problems involving sparse matrices, the rec ursive algorithm leads to fast and efficient computation. This method is tested by examining the Sierra Madre earthquake (M(s) = 5.8) of 28 June 1991, California. This event is well-recorded by the broad-band T ERRAscope array. The moment tensor inversion through the presented met hod 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 incl usion of new data from different stations yields substantial improveme nt on the mechanism to a certain point where further addition of data will not make much difference to the resulting best double-couple deco mposition. However, the content of double-couple components shows a st riking increase from approximately 50 to approximately 90% with the in clusion of more data from other stations. This result demonstrates cle arly 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.