Simultaneous Interpolation and Deblending of 3-D Seismic Data by Iterative Thresholding

Abstract

Blended acquisition can improve the efficiency of seismic data acquisition sharply, thus decreasing the acquisition costs. However, there may exist irregularity in blended data, which poses challenges for traditional seismic data processing. Thus, the deblending or interpolation should be done as a prerequisite. Because the deblending and interpolation can affect each other, we propose a unified 3-D joint deblending and interpolation method with a sparsifying transform and a sparsity promotion strategy in the blending fold of 4. To overcome the huge computational cost of 3-D curvelet transform (CT), we implement iterative thresholding in each principal frequency slice efficiently with 2-D CT. With decades of iterations, we can obtain an estimate of the regularized and deblended data. The core idea is that unblended signal can be characterized sparsely, and the blending noise and sampling irregularity have low-amplitude values in the CT domain. If blending was not used during acquisition, the proposed method becomes a pure interpolation algorithm. Similarly, if no sampling irregularity is present in the recorded data, the proposed method turns into a traditional deblending method. Numerical examples on the 3-D synthetic and field artificially blended data demonstrate the validity of the proposed method in simultaneously removing the blending noise and sampling irregularity. The regularized, deblended data can be beneficial for subsequent seismic data inversion and migration procedures.