Numerical simulation of seismic waves in transversely isotropic media based on orthogonal body-fitted grids

In conventional finite difference numerical simulation of seismic waves, regular grids in Cartesian coordinates are used to divide the calculated region. When simulating seismic wave fields under an irregular surface, such grids are unsuitable to realize the free boundary condition. They also easily generate false scattered waves at the corners of the grids owing to the approximation of the stepped grids. These issues affect the simulation accuracy. This study introduces an orthogonal body-fitted grid generation technique in computational fluid dynamics for generating grids in transversely isotropic (TI) media under an irregular surface. The first-order velocity-stress equation in curvilinear coordinates is calculated using the optimized nonstaggered grids finite difference method. The point oscillation generated by the nonstaggered grids difference is eliminated by selective filtering. The orthogonal body-fitted grids can accurately describe the irregular surface. Further, the orthogonality of the grids allows the implementation of free boundary conditions without complicated coordinate transformation and interpolation operations. Numerical examples show that the numerical solutions obtained by this method agree well with the analytical solutions. By comparing the simulation results of the proposed method with those of the regular grid difference method, the proposed method can effectively eliminate the false scattered waves caused by the stepped grids under the condition of the same grid spacing. Thus, the accuracy of the numerical simulation is improved. In addition, the simulation results of the three-layer TI media model on an irregular surface show that the proposed method is also suitable for complex models.