The Research Of Time-space Domain Finite Difference Based On New Stencil For Reverse Time Migration

One of the key steps of reverse time migration is solving the two-way wave equation.Forward modeling is the foundation of reverse time migration.Thus,it is of great importance to focus on studying fast and high accuracy forward modeling numerical algorithm.Finite difference method(FD)is widely used in seismic wave field calculation as a result of its relatively low requirements of computer memory,high computational efficiency and easily implement.The basic principle of finite difference method is using difference operator instead of the corresponding differential operator,how to suppress numerical dispersion errors caused by difference discretization is crucial for researchers.Traditional finite-difference coefficients is calculated based on space domain dispersion relation,time-space domain staggered-grid or regular-grid finite difference method with fourth-order accuracy in time and arbitrary-even order accuracy in space have been developed based on new stencils recently,but the finite difference coefficients are determined by Taylor-series expansion(TE),which is accurate only nearby zero wavenumber.To further improve modeling accuracy,we adopt convolutional differentiator to calculate finite difference coefficients through relationship between time-space finite difference based on new stencil scheme and a LAX-WENDROFF scheme.Dispersion analysis and numerical examples demonstrate that convolutional differentiator based on time-space domain finite difference method can preserve the original fourth-order temporal accuracy and achieve higher spatial accuracy than the existing TE based time-space domain finite difference method.Due to the restrictions on both computational cost and memory requirement,the model has to be limited in size and focused on the area of interest by introducing artificial boundaries.Therefore,an artificial boundary condition is needed to absorb the energy of the reflections from these artificial boundaries.Two kinds of solutions have been explained for this purpose and compared theirs absorption effect by a homogeneous model.The RTM imaging condition is a zero time-lag cross-correlation between a forward-propagated source wavefield and a backward-propagated receiver wavefield,which requires large saving amount for prestack RTM.We implement backward wavefield reconstruction for regular and staggered grid finite difference based on new stencil.In this paper,we use a simple model to analyze the influences of the initial velocity model building,the numerical dispersion and first-arrival wave.Low-frequency noise in RTM is removed after imaging by employing a Laplace filter or the normalized wavefiled decomposition cross-correlation imaging condition based on the Poynting vector.The paper presents the results of post-stack migration for the Marmousi model data and the real data respectively,this paper also compares the imaging accuracy of the time-space domain finite difference method based on new stencil and traditional finite difference at the same time,and the comparison demonstrates the former one is superior to the latter.What's more,a prestack reverse time migration used time-space domain finite difference method based on new stencil is tested,the result shows the method developed by this paper is reliable and has stronger practicability.