Numerical Simulation of Elastic Waves in VTI Media Using a 17-Point Finite Difference Scheme

To optimize the stiffness matrix structure for frequency-domain elastic wave forward modeling in 2D VTI (transversely isotropic with a vertical symmetry axis) media—thereby reducing memory consumption and improving computational efficiency—we simplify the conventional 25-point finite-difference scheme to derive a 17-point frequency-domain finite-difference scheme. This approach reformulates the finite-difference operators for the partial derivatives and acceleration terms in the elastic wave equations, reducing the number of grid points involved in the computation by 30% compared to the 25-point scheme. The optimized matrix construction leverages sparse matrix storage techniques, decreasing memory usage by approximately 27%. Numerical validation, conducted using a double-layer VTI medium model and the Marmousi model with three major faults and an anticline containing limestone layers at the base of the faults, demonstrates that the 17-point finite-difference scheme maintains comparable accuracy while requiring 14% less computation time and featuring a 25% reduction in nonzero elements within the impedance matrix. Comparisons of wavefield snapshots and receiver components (horizontal component U and vertical component V) support this conclusion. These improvements enable the use of more efficient iterative solvers.