HIGHLY RESOLVED DECONVOLUTION VIA A SPARSITY NORM

摘要

Wavelet deconvolution is, in general, implemented by means of the Wiener-Levinson (WL) approach. This procedure assumes that the polynomial describing the wavelet is minimum phase and that the reflectivity function is a white noise process. If either of these two assumptions is not valici, the WL approach does not perform well. Many studies attempting to improve the wavelet deconvolution problem have been presented in the literature. In this paper we present an iterative least squares approach for wavelet deconvolution based on the l_p norm which corresponds to an adaptation of the method of Porsani et al. (2001). The prediction errors associated with the deconvolved seismic trace are raised to an exponent related to the applied norm, thus defining a nonlinear relationship between the filter coefficients and the output of the inverse filter. By using a first-order Taylor approximation, a weighted system of linear equations may be formed and solved in the least squares sense. The predictive filter is adapted and the iteration continues. The new iterative wavelet deconvolution approach is initialized with the minimum phase WL filter. This causal inverse filter works to compress the minimum-delay component of the wavelet. Following a few iterations, the process is restarted by using the reverse of the WL filter to compress the non minimum-delay component of the wavelet. This forward and backward deconvolution is able to spike the wavelet independent of its phase properties. The new method was tested on synthetic and real marine seismic data. The results obtained are superior to those obtained using the conventional WL approach which is based on the l_2 norm and assumes a minimum phase wavelet. The synthetic examples illustrate that the proposed method recovers a full band sparse impulse response, in spite of the presence of additive random noise.