Fast seismic data recovery by combined minimum norm algorithm in DTCW domain

Abstract

With the development of high-density sampling technology and high-precision seismology, the computational cost that dramatically increases with the sampling rate and resolution requirement becomes very challenging in seismic data recovery. A dual tree complex wavelet (DTCW)-based sparsity-preserving minimization model for seismic data recovery is studied in this paper. Different to other orthogonal transforms, the multi-dimensional DTCW transform (DTCWT) is shift invariant and direction sensitive, which ensures the sparse representation and stable recovery of seismic reflections. Compared with other over-complete transforms, DTCWT is superior in less redundancy and computation complexity. Based on these advantages, a modified split Bregman iterative algorithm in DTCW domain for solving the combined norm minimization model is proposed and its convergence is then established. As a crucial step of the algorithm, how to choose model parameters optimally for over-complete transforms is specifically discussed in this paper. We apply this method to recovery seismic data from severe noisy background. Numerical results show that the proposed DTCWT-based algorithm appears to give significant improvements over the fully decimated orthogonal wavelet transform (DWT) or non-decimated wavelet transform (DyDWT) based-ones both in SNR and visual quality of the results. Its memory and computation cost is much lower than DyDWT and discrete curvelet transform (DCurT)-based methods. Meanwhile, the artificial reflections in the results of the proposed method are much less than some other redundant transform-based ones. So, the DTCWT-based iteration algorithm is applicable in real seismic applications.