基于SVD和PCA方法重构干涉格林函数

Reconstructed interferometric Green's function based on SVD&PCA methods

地震干涉法(SI)是一种用来计算两个信号接收点之间格林函数(GF)的方法,它的基本假设是以其中一个接收点位置为虚拟源,可用来计算两点间震源传播的旅行时间。然而采用直接叠加的方法压制干扰信号,计算得到的干涉格林函数效果不佳,因而计算得到的旅行时间也不够精确。这里基于奇异值分解法(SVD)对叠加前的互相关矩阵进行分解及重构,可以有效压制两点间来自干扰源的信号,再利用主成分分析法(PCA)对固有几何拓扑结构降维特性提取主信号,计算得到新的干涉格林函数。数值模拟及实测数据处理结果表明:使用SVD和PCA综合处理方法,能有效提高干涉格林函数的准确性。

Seismic interferometry (SI) is a method used to calculate the Green's function (GF) between two signal receiver locations.Its basic assumption is that one of the receiver location is a virtual source.However,in many scholars practical cases,they used the direct superposition method to reduce ineffective signal.The interferometric GF is not ideal,and the calculated travel time is not enough precise.Therefore,We apply a singular value decomposition (SVD) method to decompose and reconstruct the cross correlation matrix before superposition in this study.This can effectively suppress signals from invalid source.Then we can extract the main signal for principal component analysis (PCA) on the inherent geometric topology structure dimension reduction features,which will calculate a new interferomertic GF.Finally,the results of numerical simulation and field data processing indicate that combined using SVD and PCA processing method can effectively improve interferometric Greens function.