Nonstationary deconvolutive Radon transform

Different versions of the Radon transform (RT) are widely used in seismic data processing to focus the recorded seismic events. Multiple separation, data interpolation, and noise attenuation are some of the RT applications in seismic processing workflows. Unfortunately, conventional RT methods cannot focus events perfectly in the RT domain. This problem arises due to the blurring effects of the source wavelet and the nonstationary nature of the seismic data. Sometimes, the distortion results in a big difference between the original data and its inverse transform. We have developed a nonstationary deconvolutive RT (DecRT) to handle these two issues. Our algorithm takes advantage of a nonstationary convolution technique that builds on the concept of block convolution and the overlap method, in which the convolution operation is defined separately for overlapping blocks. Therefore, it allows the Radon basis function to take arbitrary shapes in the time and space directions. In addition, we introduce a nonstationary wavelet estimation method to determine time-space-varying wavelets. The wavelets and the Radon panel are estimated simultaneously and in an alternating way. Numerical examples demonstrate that our nonstationary DecRT method can significantly improve the sparsity of Radon panels. Hence, inverse RT does not suffer from the distortion caused by unfocused seismic events.