科研之友
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摘要
We transform the seismic wave equations in 2D inhomogeneous anisotropic media into a system of first-order partial differential equations with respect to time t. Based on the transformed equations, a new Runge-Kutta (RK) method using a high-order interpolation approximation is developed in this article. Our method enables wave propagation to be simulated in two dimensions through generally anisotropic and heterogeneous models. The high-order space derivatives are determined by using the wave displacement and its gradients simultaneously, while the time derivatives are approximated by the fourth-order RK method. On the basis of such a structure, the so-called RK-type method can suppress effectively numerical dispersions and source-noise caused by discretizing the wave equations when too-coarse grids are used, and is fourth-order accuracy in both space and time. Numerical calculations of the relative errors show that the numerical error of the RK-type method is less than those of the conventional finite-difference method (FDM) and fourth-order Lax-Wendroff correction (LWC) scheme. The three-component seismic wave-fields in an isotropic model are simulated and compared with the second-order FDM and fourth-order LWC. Meanwhile, we also present the wave-field snapshots computed by the RK-type method in a two-layered model with transversely isotropic symmetry. Promising numerical results further illustrate that the RK-type method has less numerical dispersions and can suppress effectively the source-noise.
