基于压缩感知理论的缺失地震数据重构方法

吉林大学学报(地球科学版)

基于压缩感知理论的缺失地震数据重构方法

徐明华^1,2,3，李瑞¹，路交通⁴，蒙杉²，龚幸林³

1.成都理工大学油气藏地质及开发工程国家重点实验室，成都610059;
2.中国石油川庆钻探工程有限公司地质勘探开发研究院，成都610051;
3.中国石油阿姆河天然气公司，北京100012;
4.中国石化集团国际石油工程有限公司，北京100029

收稿日期:2012-01-17 出版日期:2013-01-26 发布日期:2013-01-26
作者简介:徐明华(1973-)，男，博士研究生，高级工程师，主要从事地震资料处理、解释及储层预测研究，Tel：028-86015646，E-mail:xumingh@sina.com
基金资助:
国家重大科技专项项目（2011ZX-05059-001）；中石油重大科技专项项目（2011E-2505）

Study on the Recovery of Aliasing Seismic Data Based on the Compressive Sensing Theory

Xu Minghua^1,2,3, Li Rui¹, Lu Jiaotong⁴, Meng Shan²,Gong Xinglin³

1.State Key laboratory of Oil & Gas Reservoir Geology and Exploitation, Chengdu University of Technology, Chengdu610059, China;
2.Geologic Exploration & Development Research Institute, Chuanqing Drilling Engineer Co., Ltd., CNPC, Chengdu610051, China;
3.CNPC International（Turkmenistan）, Beijing100012, China;
4.International Petroleum Service Corporation, SINOPEC, Beijing100029, China

Received:2012-01-17 Online:2013-01-26 Published:2013-01-26

摘要/Abstract

摘要：

压缩感知是一种新的理论，它打破常规尼奎斯特-香农采样定理的制约，利用信号的稀疏特性或可压缩特性，用较少的数据即可重构恢复完整的信号。建立了基于压缩感知理论的缺失地震数据重构模型。首先在与稀疏变换不相关的测量矩阵基础上引入一种约束矩阵，使地震数据的缺失满足或接近高斯随机分布；随机缺失的地震数据变换到稀疏域会产生很多与有效信号不相干的随机噪声，接着通过一种新的自适应阈值迭代算法可以很好地消除稀疏系数中的随机噪声干扰，经过逆稀疏变换即得到重构后的地震数据。Marmousi 2模型测试及实际地震资料处理均验证了该方法的可行性和有效性。重构缺失地震数据取得了较好的效果。

关键词: 压缩感知, 稀疏变换, 测量矩阵, 重构算法, 缺失地震数据

Abstract:

Compressive sensing(CS) is a new kind of theory which breaks the limitation of the conventional Nyquist-Shannon sampling theorem and recovers the complete signal from few data by using the sparse or compressed characteristics of the signal. With the theory of CS, a seismic data recovery model is built in this paper. Based on the measure matrix which is incoherent with the sparsifying basis,a kind of restrained matrix is proposed as to achieve the effects of seismic missing data with gaussian random distribution or nearly gaussian random distribution and hence the sparsifying coefficient of the aliasing seismic data will contain many random noises which is uncorrelated with the effective signal. The full data can be reconstructed from a new adaptive iterative threshold solution and an inverse sparse transform. From the test of the synthetic seismic data and Marmousi 2 model, we verified the availability and feasibility of our method.

Key words: compressive sensing, sparse transform, measurement matrix, recovery algorithm, aliasing seismic data

中图分类号:

P631.4

徐明华，李瑞，路交通，蒙杉，龚幸林. 基于压缩感知理论的缺失地震数据重构方法[J]. 吉林大学学报(地球科学版), 2013, 43(1): 282-290.

Xu Minghua, Li Rui, Lu Jiaotong, Meng Shan,Gong Xinglin. Study on the Recovery of Aliasing Seismic Data Based on the Compressive Sensing Theory[J]. Journal of Jilin University(Earth Science Edition), 2013, 43(1): 282-290.

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