Regularized phase retrieval for seismic wavelet estimation and blind deconvolution

Abstract

Seismic data can provide more detailed information from subsurface in comparison with data gathered via other geophysical methods. This made the oil and gas exploration industry to pay considerable attention to the seismic methods. The accuracy of the information extracted from seismic data largely depends on the accuracy of the information about the seismic wavelet. Thus, wavelet estimation has become an important step in seismic data processing but the quality of the estimate depends on the complexity of the wavelet phase. In this paper, the phase of the wavelet is estimated by using a regularization method taking into account the sparse characteristics of the subsurface reflectivity model. Unlike the conventional deconvolution methods, here only the amplitude spectrum of the data are inverted as a phase retrieval problem, whereby the sparsest solution to deconvolution problem is found by matching the predicted amplitude spectrum to that of the observations. Then the accuracy of the wavelet is improved by deconvolving the recovered impulse response from the data. The results of the numerical examples from synthetic and field data demonstrate that the proposed method is able to extract complex-phase wavelets with an acceptable accuracy. Furthermore, the reflectivity series is also retrieved as the output of the algorithm. A significant advantage is that the presented algorithm is able to retrieve reflectivity series and the wavelet in only two iterations, compared with the traditional blind deconvolution algorithms.