Modeling Seismic Wave Propagation Based On Perfectly Matched Layer With Rotated Staggered Dual-variable Grid

Seismic wave field forward modeling is not only an important method to study the propagation of seismic wave,but also the research basis of inversion imaging.Improving computational efficiency and simulation effect and reducing storage space are the core research contents of wave field forward modeling.The selection of the nature of medium,forward algorithm and boundary conditions is the key to the simulation effect.In this paper,the simulation of seismic wave field is systematically studied from three directions: forward algorithm,boundary conditions and medium.In the staggered grid finite difference algorithm,the model mesh generation principle is closely related to the forward calculation efficiency.When there are small inhomogeneous bodies or low deceleration layers in the model,in order to ensure the accuracy and meet the stability conditions,it is necessary to adopt small grid step size,resulting in local oversampling and reducing the calculation efficiency.In this paper,the wave field is simulated by the high-order finite difference simulation method combining the variable spatial grid and time step length.However,the spatiotemporal dual-variable grid algorithm has the inherent disadvantages of staggered grid.When simulating the wave field propagation of complex medium with strong heterogeneity,the medium parameters need to be averaged or interpolated.When the elastic modulus changes greatly,it is easy to produce instability.Even in some media simulation,staggered grid finite difference is difficult to realize.At the same time,the variable grid implementation of the algorithm in space and time is very complex.Based on the dual-variable grid algorithm,a rotated staggered dual-variable grid algorithm is proposed in this paper.The algorithm retains the advantages of rotating grid and dual-variable grid.In the process of rotating spatial variable grid,it simplifies the process of wave field transmission and fine point interpolation in the transition region.This method does not need to interpolate each time layer,and the calculation points required for interpolation are in a global time cycle.It does not need to introduce additional storage variables to calculate the wave field component at the next time of the large grid separately for fine time layer interpolation.In order to reduce false reflection of artificial boundary in forward simulation and achieve higher simulation accuracy,absorbing boundary conditions need to be introduced.The absorption effect of boundary conditions affects the simulation accuracy of forward modeling,and different boundary conditions have different effects on the efficiency of forward modeling.The main purpose of this paper is to improve the calculation efficiency and simulation accuracy of the forward algorithm.Therefore,the research and improvement of the absorbing boundary conditions is also very important.The perfectly matched layer is the most widely used absorption boundary with the best absorption attenuation effect at present.In this paper,the perfectly matched layer is systematically studied.At the same time,taking the nearly perfectly matched layer as the starting point,this method has the advantages of not changing the equation form and easy implementation.However,in TTI medium simulations it is found that the NPML is very unstable and cannot absorb near-grazing incident waves.This explains why the CPML is currently used more frequently.In this study,the complex frequency shifted transform is used to enhance the absorption of near-grazing incident waves with NPML and to avoid the generation of low-frequency singular values.At the same time,the double damping profile is used to improve the stability of the boundary we called MCFS-NPML.In order to further improve the absorption capacity of the boundary and weaken the deviation caused by the discrete difference,a new attenuation function is proposed.Based on the introduction of multi axis complex frequency shift technology,this paper puts forward the design scheme of scale factor,frequency shift factor and stability factor under the new attenuation function.While comprehensively studying the perfect matching layer,a new alternative implementation of the PML is presented.We call this method residual perfectly matched layer(RPML)because it is based on residual calculation between the original equations and the PML formulations.This new approach has the same form as the original governing equations and there is only one first order partial derivative with respect to time in the auxiliary differential equation which is simplest compared to the other PMLs.Therefore,the RPML shows great advantages of implementation simplicity and computational efficiency over the standard complex stretched coordinate PML.At the same time,the absorption performance is improved by adopting the complex frequency shifted stretching function;the stability of the boundary is enhanced by applying the double damping profile.In this paper,a variety of perfect matching layers are successfully applied to the rotated staggered dual-variable grid algorithm,including MCFS-NPML and MCFS-RPML.The performance of the above algorithms is further studied and the above technology is extended to the seismic wave simulation of anisotropic medium.