Numerical Simulation Of Two-dimensional Seismic Wave Propagation In Isotropic And Anisotropic Media By Curvilinear Grid Finite-difference Method

The wave equation describing the propagation of seismic waves is a hyperbolic partial differential equation, and the finite difference method is one of the most popular numerical methods for solving the partial differential equations. As a flexible, efficient and adaptable method, the finite difference method for numerically simulating seismic wave field is an important tool to study the law of seismic wave propagation in seismology. But when the geological model has irregular undulating surface or underneath interface, the conventional methods use rectangular grid to divide the model, and apply ladder mesh to approximate the irregular interface, which leads to corner scattering and diffraction interference during the numerical simulation, therefore it's difficult to describe the influence of irregular terrain on seismic wave propagation.In order to study the problem of seismic wave propagation under undulated topography model, in this paper we introduce a new method of seismic wave propagation, which has wide application and great potential in real problems. This method adopts a curve-grid to divide the model, and uses a DRP/opt MacCormack collocated-grid finite difference scheme to discrete first-order velocity-stress wave equation, and the free surface boundary conditions are derived by using a compact MacCormack scheme combined with the traction image method. The curvilinear grid finite difference method using body-conforming grid to describe the free surface, thus avoids of numerical approximation caused by scattering. The wavefield component and the medium parameters are defined at the collocated-grid nodes, which avoids of internal interpolation for wavefield components and ensures the accuracy of calculation.