Seismic data reconstruction based on CS and Fourier theory

Traditional seismic data sampling follows the Nyquist sampling theorem. In this paper, we introduce the theory of compressive sensing (CS), breaking through the limitations of the traditional Nyquist sampling theorem, rendering the coherent aliases of regular undersampling into harmless incoherent random noise using random undersampling, and effectively turning the reconstruction problem into a much simpler denoising problem. We introduce the projections onto convex sets (POCS) algorithm in the data reconstruction process, apply the exponential decay threshold parameter in the iterations, and modify the traditional reconstruction process that performs forward and reverse transforms in the time and space domain. We propose a new method that uses forward and reverse transforms in the space domain. The proposed method uses less computer memory and improves computational speed. We also analyze the antinoise and anti-aliasing ability of the proposed method, and compare the 2D and 3D data reconstruction. Theoretical models and real data show that the proposed method is effective and of practical importance, as it can reconstruct missing traces and reduce the exploration cost of complex data acquisition.