基于压缩感知的加权MCA地震数据重构方法

Reconstruction of seismic data with weighted MCA based on compressed sensing

地震数据规则化重构是地震资料处理十分重要的基础性工作.压缩感知理论打破了香农采样定理的制约,利用信号在某个变换域的稀疏特性重构出完整的信号,在地震数据重构领域得到了很好的应用.深反射地震剖面大都布置在地质构造比较复杂的区段,复杂的地质构造使深反射地震剖面上的波阻特征复杂,采用单一稀疏变换不能最有效地表征数据的内部结构特征.MCA(形态成分分析)方法将信号分解为几种形态特征区别明显的分量来逼近数据的内部复杂结构,但是对各成分简单的叠加仍然无法有效地描述复杂构造数据的各种特征.结合两种方法的优点,本文提出了一种新的基于压缩感知的重构算法框架,在MCA方法的基础上对各稀疏字典进行加权,在迭代中不断更新各个稀疏字典的权值系数,对信号内部的各种特征进行最优描述,从而实现对信号的高质量重构.模型测试和实际资料处理结果表明:基于压缩感知的加权MCA方法不仅可以对地质构造复杂的地震数据进行高效的插值重建,而且可以很好的消除空间假频.

The regularized reconstruction of seismic data is one of the most important and fundamental task in seismic data processing.The compressed sensing(CS)theory has been successfully applied in the reconstruction of seismic data,because it breaks the restriction of Shannon sampling theorem and can obtain a complete reconstructed signal by using the sparsity property in a certain transformation domain.Deep reflection seismic profiles commonly deployed in areas with complicated geological structure,resulted in complicated wave impedance characteristics on deep reflection seismic profiles.Consequently,the internal structure characteristics of data cannot be represented effectively by using a single sparse transformation.The morphological component analysis(MCA)method decomposes a signal into several components with distinguished morphological features to approximate the complex internal structure of data.However,the various characteristics of the complex data still cannot be described effectively through a simple summation of the signal components.To solve these problems,a new iterative algorithm frame was proposed based on the combination of the merits of the CS and MCA methods.The sparse dictionaries were weighted on the basis of the MCA method,and then the weight coefficients of each sparse dictionary was updated continuously in the process of iteration.Finally an optimal description of the various internal features of signals was obtained and a high-quality reconstruction was achieved for those complex signals.Model tests and real data processing results show that the weighted MCA method based on CS can not only reconstruct the seismic data from the complicated geological structure through interpolation efficiently,but also eliminate the space aliasing very well.