Absorbing Boundary Conditions In Staggered-Grid And Mesh-Free Finite-Difference Numerical Modeling For Wave Equations

Reverse-time migration and full waveform inversion are research hotspots and difficulties of seismic exploration in recent years,for which the numerical simulation of seismic wave equation is the key technology.Among the numerical simulation methods,finite difference method attracts extensive attention because of its high precision,easy implementation and high computational efficiency.In this paper,the absorption boundary conditions for the staggered-grid finite difference method of three-dimensional elastic wave and the mesh-free frequency-domain finite difference method of two-dimensional acoustic wave equation are studied respectively.With respect to the absorbing boundary condition for three-dimensional elastic wave staggered-gird finite difference numerical simulation,the first-order Higdon one-way wave equation-based Hybrid absorbing boundary condition is developed from two-dimensional to three-dimensional,synthetic results show that the proposed method has higher efficiency and better absorption effect than the traditional split perfectly matched layer absorbing boundary condition.At the same time,by using the least squares-based optimal implicit finite difference method,which has higher accuracy than the Taylor series expansion-based finite difference method,to solve the spatial derivative,high accuracy could be achieved with short operator length.In the study of two-dimensional acoustic wave mesh-free frequencydomain finite difference numerical simulation,the conventional perfectly matched layer absorbing boundary condition and the complex frequency-shift of perfectly matched layer absorbing boundary condition,which is suitable for attenuating large angle incident waves,are developed respectively from regular-grid to mesh-free discretization.Experimental results indicate the correctness and validity of the two methods.