Seismic data reconstruction based on CS and Fourier theory  

基于压缩感知理论与傅立叶变换的地震数据重建(英文)

作　　者：张华[1,2] 陈小宏 吴信民 

机构地区：[1]东华理工大学放射性地质与勘探技术国防重点学科实验室,江西抚州344000 [2]海洋石油勘探国家工程实验室,中国石油大学(北京),北京昌平102240

出　　处：《Applied Geophysics》2013年第2期170-180,236,共12页应用地球物理（英文版）

基　　金：sponsored by the National Natural Science Foundation of China (No.41174107);the National Science and Technology projects of oil and gas (No.2011ZX05023-005)

摘　　要：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.传统的地震勘探数据采样必须遵循奈奎斯特采样定理,而本文基于新发展的压缩感知理论,在突破传统采样定理限制的基础上,利用随机欠采样方法将传统规则欠采样所带来的互相干假频转化成较低幅度的不相干噪声,从而将数据重建问题转为更简单的去噪问题。在数据重建过程中引入凸集投影算法(POCS),采用指数规律衰减的阈值参数,在每次迭代过程中,改变以往从时间到空间都需要进行正反变换的做法,提出只对地震数据空间方向进行正反变换,从而可以减少内存空间,提高运算速度,并且也分析了本文POCS算法的抗噪声与反假频能力,同时我们也对二维和三维地震数据重建进行了比较。理论模型和实际数据表明本文方法效果明显,这对于指导复杂地区数据采集、缺失地震道重建及降低勘探成本方面具有重要的实用价值。

关 键 词：Fourier transform compressive sensing （CS） projection onto convex sets （POCS） data reconstruction 

分 类 号：P631.44[天文地球—地质矿产勘探]