Achieving Robust Compressive Sensing Seismic Acquisition with a Two-Step Sampling Approach

The compressive sensing (CS) framework offers a cost-effective alternative to dense alias-free sampling. Designing seismic layouts based on the CS technique imposes the use of specific sampling patterns in addition to the logistical and geophysical requirements. We propose a two-step design process for generating CS-based schemes suitable for seismic applications. During the first step, uniform random sampling is used to generate a random scheme, which is supported theoretically by the restricted isometry property. Following that, designated samples are added to the random scheme to control the maximum distance between adjacent sources (or receivers). The null space property theoretically justifies the additional samples of the second step. Our sampling method generates sampling patterns with a CS theoretical background, controlled distance between adjacent samples, and a flexible number of active and omitted samples. The robustness of two-step sampling schemes for reallocated samples is investigated and CS reconstruction tests are performed. In addition, using this approach, a CS-based 3D seismic survey is designed, and the distributions of traces in fold maps and rose diagrams are analyzed. It is shown that the two-step scheme is suitable for CS-based seismic surveys and field applications.