Elastic Reverse Time Migration Based On Lowrank Finite Difference Method

Elastic reverse time migration is an important method,oriented to deal with multicomponent data and it makes full use of properties of elastic wavefield.In addition to the PP image results,it can provide PS image results.These properties of elastic reverse time migration are beneficial to reduce the ambiguity in seismic exploration.Elastic wave extrapolation is an essential part of elastic reverse time migration and,to some extends,the quality of image results depends upon accuracy of the elastic wave extrapolation.In this paper,we will exert our efforts to elastic wave extrapolation based on Lowrank finite difference method.Also,we implement elastic reverse time migration based on this extrapolation method.We begin our research from common extrapolation methods,including the standard staggered-grid finite difference method and the rotated staggered-grid finite difference method.And we are to illustrate the details of deduction and numerical procedure of these two methods.Meanwhile,we compare these two methods from the aspects of accuracy,efficiency and the effects on the wavefield separation.Due to inefficiency and massive time-consuming of massive data processing in elastic simulation based on rotated staggered-grid,we choose staggered-grid finite difference simulation method to provide the vector wavefield for wavefield separation in isotropic media.So as to improve the accuracy of wave simulation,the first-order and second-order decoupled elastic recursive time integration methods are deduced based on wavefield decomposition theory and plane wave theory.Due to high calculation complexity of elastic recursive integration operators,we introduce Lowrank approximation method to approximate these operators.The elastic recursive time integration operators are approximated to the products of three small matrices.In accordance to the properties of these matrices,the exact operators are further decomposed and the corresponding finite difference scheme can also be deduced,which can be used for the discretization for the first-order and second-order decoupled elastic equations.Considering the accuracy and applicability,we do some dispersion analysis and use some additional numerical examples to testify the effectiveness of these operators.Eventually,elastic Lowrank finite difference method for the first order decoupled equation is also applied to forward and inverse extrapolation of elastic wavefield and we implement the elastic wave migration based on this method.The effectiveness and the adaptability of this method are also validated by numerical experiments.