A nonstationary sparse spike deconvolution with anelastic attenuation

Seismic wavelet estimation and deconvolution are essential for high-resolution seismic processing. Because of the influence of absorption and scattering, the frequency and phase of the seismic wavelet change with time during wave propagation, leading to a time-varying seismic wavelet. To obtain reflectivity coefficients with more accurate relative amplitudes, we should compute a nonstationary deconvolution of this seismogram, which might be difficult to solve. We have extended sparse spike deconvolution via Toeplitz-sparse matrix factorization to a nonstationary sparse spike deconvolution approach with anelastic attenuation. We do this by separating our model into subproblems in each of which the wavelet estimation problem is solved by the classic sparse optimization algorithms. We find numerical examples that illustrate the parameter setting, noisy seismogram, and the estimation error of the Q value to validate the effectiveness of our extended approach. More importantly, taking advantage of the high accuracy of the estimated Q value, we obtain better performance than with the stationary Toeplitz-sparse spike deconvolution approach in real seismic data.