Seismic data reconstruction based on CS and Fourier theory
Zhang Hua1,2, Chen Xiao-Hong2, and Wu Xin-Min1
1. Fundamental Science on Radioactive Geology and Exploration Technology Laboratory, East China Institute of Technology, Fuzhou, Jiangxi 344000, China.
2. National Engineering Laboratory for Offshore Oil Exploration, China University of Petroleum, Beijing 102249, China.
Abstract 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.
This research work was sponsored by the National Natural Science Foundation of China (No. 41174107) and the National Science and Technology projects of oil and gas (No. 2011ZX05023-005).
Cite this article:
ZHANG Hua,CHEN Xiao-Hong,WU Xin-Min. Seismic data reconstruction based on CS and Fourier theory
[J]. APPLIED GEOPHYSICS, 2013, 10(2): 170-180.
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2013, Vol. 10 
