3-D data interpolation and denoising by adaptive weighting rank-reduction method using singular spectrum analysis algorithm
Farzaneh Bayati, Daniel O. Trad
A difficult challenge in seismic processing and imaging is to address insufficient and irregular sampling. Most processing algorithms require well-sampled data, which involves small sampling intervals with a regular distribution. Recently, rank reduction methods are used in seismic processing algorithms. These methods are based on rank reduction of the trajectory matrices using truncated SVD. Estimation of the rank of the Hankel matrix depends on the number of the plane waves; however, when it comes to more complicated data, the rank reduction method may fail or give poor results as a consequence of curved events not having a small rank (sparse) representation. To satisfy the plane wave assumption for the rank reduction method, one can utilize local windows to assume that events are plane waves. The rank reduction method requires the number of events as the rank parameter. This number defines the minimum rank selected in each step. In this paper, we first propose a method, which selects the rank automatically in each window by finding the maximum ratio of the energy between two singular values. The method may select a large rank to get the best result for very high curved events, which leads to remain residual errors. To overcome the residual errors, then we apply a weighting operator on the selected singular values to minimize the effect of noise projection on the signal projection. We test the efficiency of the proposed method by applying it to both synthetic and real seismic data.