Microseismic source deconvolution: Wiener filter versus minimax, Fourier versus wavelets, and linear versus nonlinear

Deconvolution is commonly performed on microseismic signals to determine the time history of a dislocation source, usually modeled as combinations of forces or couples. This paper presents a new deconvolution method that uses a nonlinear thresholding estimator, which is based on the minimax framework and operates in the wavelet domain. Experiments were performed on a steel plate using artificially generated microseismic signals, which were recorded by high-fidelity displacement sensors at various locations. The source functions were deconvolved from the recorded signals by Wiener filters and the new method. Results were compared and show that the new method outperforms the other methods in terms of reducing noise while keeping the sharp features of the source functions. Other advantages of the nonlinear thresholding estimator include (1) its performance is close to that of a minimax estimator, (2) it is nonlinear and takes advantage of sparse representations under wavelet bases, and (3) its computation is faster than the fast Fourier transforms. (C) 2004 Acoustical Society of America