Nonstationary blind deconvolution of seismic records

Seismic deconvolution used for improving the bandwidth of data is inherently nonstationary, mixed phase, and blind. Due to some restricting assumptions imposed by conventional deconvolution methods, they are either stationary or semi-blind. A fully nonstationary blind deconvolution method is proposed that is able to simultaneously take into account different sources of nonstationarity and to improve the bandwidth of highly nonstationary seismic data in a fully blind manner. Based on the concept of block convolution and the overlap method, the convolutional model of seismic data is generalized to consider nonstationary cases and to model nonstationary data. This generalized convolutional model is then used for nonstationary blind deconvolution, in which the statistical characteristics of the wavelets are allowed to arbitrarily change in the vertical and horizontal directions. Given a nonstationary seismic record, several time-space-varying wavelets are simultaneously determined with the reflectivity model in an alternating direction algorithm using a variational approach. Numerical tests are presented showing the high performance of our nonstationary blind deconvolution for improving the temporal resolution of data in comparison with their stationary counterparts. The results indicate that in comparison with patched deconvolution, our nonstationary method is more robust and stable for different window sizes and it produces better results with a higher signal-to-noise ratio.