最小二乘叠前深度偏移成像理论与方法

摘要

地震波成像的目的首先是定位反射界面或散射点的空间位置,描述地下地质体的几何结构;然后是估计地下介质的物性参数,主要是与速度和密度相关的参数;最终是与岩石物理结合描述含油气储层.以地震波传播的散射场表达以及逆散射成像为切入点,首先给出散射波的表达形式,讨论了逆散射成像的本质与逆散射成像所需要的叠前地震观测数据及对应的观测方式;然后给出一般的线性化最小二乘叠前深度偏移(Least-squares Prestack Depth Migration,LS_PSDM)基本理论框架,只要能给出用Green函数计算的波传播算子,就可以实现线性化的LS_ PSDM;接着讨论了当前广受关注的最小二乘逆时深度偏移(Leastsquares Reverse Time Migration,LS_RTM)方法,给出了最小二乘偏移成像的迭代实现方法和保反射界面结构的总变差正则化方法以及数值结果;最后分析了基于反射波估计反射系数的成像方法和基于散射波估计散射强度的成像方法的差异,指出针对勘探地震介质特征和波场特征的成像方法是最具实用性的方法,逆散射成像应该在此基础上进行.基于散射波的成像方法能否满足储层描述的要求,有待进一步研究工作的检验.%The purpose of seismic imaging is firstly to determine the spatial location of the reflectivity or diffraction targets.After the structure of the reflection is settled,the rock parameters,related to velocity and density,can be estimated.Combined with the estimated elastic parameters and rock physics,the oil and gas reservoir can be delineated.We start from the seismic wave propagation representation of the scattered wave field and inverse scattering imaging.the formula of the scattered wave field is firstly given.The essence of the inverse scattering imaging is discussed,including the prestack seismic observed data and the corresponding observation mode required by inverse scattering imaging.Then,the theoretical framework of general linearized least-squares prestack depth migration (LS-PSDM) is given.The linearized LS-PSDM can be realized as bng as the wave propagation operator calculated by Green functions can be reached.The least-squares reverse time migration (LS-RTM) is also discussed and the iterative realization method and the structure preserved total variation regularization method are given with numerical results.Finally,the differences between imaging methods based on reflectivity and scattering intensity estimation are analyzed.The most practical imaging methods aiming at the characteristics of medium and wave fields are stated.The inverse scattering imaging should be based on the methods.Further studies are required to testify whether the imaging methods based on scattered wave can satisfy the requirement of reservoir description.