Time Reverse Migration Based On Curvilinear Stagger-grid Finite Difference Method For An Undulated Layered Model

Finite difference method is an efficient and concise numerical simulation method,which has been successfully used in seismic exploration,full waveform inversion and so on.When the geologic model contains undulating interface,the conventional step-grid can not meet the requirements of computational accuracy,and even worse is that it produces false scattering waves at the undulating interface,which interferes with the normal numerical simulation.When the curved-grid finite difference method is used to describe the complex undulating terrain(or irregular wave impedance interface),the false scattering caused by ladder approximation can be avoided in the forward modeling of wave field,thus it is grantees the required computational accuracy.Migration imaging method is one of the three important techniques in seismic exploration and is an important way to restore the underground geological structure.With the increasing demand in seismic exploration for fine structure,it is required higher accurate migration technology.The traditional depth-based migration imaging method based on one-way wave equation no longer meets the needs of seismic exploration.While,the time inverse migration imaging method based on two-way wave equations turns out to be a promise migration imaging method,which includes both dynamics and kinematics information for seismic wavefields.Basically,the imaging method of the time inverse migration includes three steps: forward modeling of wavefield,inverse time extrapolation and denoising imaging.In this paper,a curvilinear staggered-grid finite difference method is applied to the time inverse migration of elastic wave,and the first order stress-velocity equation is discretized.The velocity structures(especially for velocity interfaces)inside several two-dimensional complex velocity models with undulating interface are accurately imaged.In the simulation process,the staggered-grid difference scheme for the first-order stress-velocity equation in the curvilinear coordinate system is derived.In the calculation,the artificial boundary reflection is suppressed by the perfectly matched absorbing boundary(PML).The normalized cross-correlation condition is used to realize the time reverse migration.The synthetic data migration for two-layer,three-layer and interface merging model show that the time reversemigration with the curvilinear staggered-grid finite difference method is an efficient and accurate migration imaging method.