Nonstationary sparsity-constrained seismic deconvolution

The Robinson convolution model is mainly restricted by three inappropriate assumptions, i.e., statistically white reflectivity, minimum-phase wavelet, and stationarity. Modern reflectivity inversion methods (e.g., sparsity-constrained deconvolution) generally attempt to suppress the problems associated with the first two assumptions but often ignore that seismic traces are nonstationary signals, which undermines the basic assumption of unchanging wavelet in reflectivity inversion. Through tests on reflectivity series, we confirm the effects of nonstationarity on reflectivity estimation and the loss of significant information, especially in deep layers. To overcome the problems caused by nonstationarity, we propose a nonstationary convolutional model, and then use the attenuation curve in log spectra to detect and correct the influences of nonstationarity. We use Gabor deconvolution to handle nonstationarity and sparsity-constrained deconvolution to separating reflectivity and wavelet. The combination of the two deconvolution methods effectively handles nonstationarity and greatly reduces the problems associated with the unreasonable assumptions regarding reflectivity and wavelet. Using marine seismic data, we show that correcting nonstationarity helps recover subtle reflectivity information and enhances the characterization of details with respect to the geological record.