An improved optimal nearly analytical discretized method for 2D scalar wave equation in heterogeneous media based on the modified nearly analytical discrete operator

Abstract

Conventional finite-difference methods will encounter strong numerical dispersion on coarse grids or when higher frequencies are used. The nearly analytic discrete method (NADM) and its improved version, developed recently, can suppress numerical dispersion efficiently. However, the NADM is imperfect, especially in long-time seismic wave propagation simulation. To overcome this limitation, by minimizing the energy-error function, we have developed a modified optimal nearly analytical discretized (MNAD) method. The stencil of MNAD for the 2D wave equation is a novel diamond stencil. MNAD has two major advantages: The first one is that MNAD can suppress numerical dispersion effectively on coarse grids, which significantly improved computational efficiency and reduced memory demands. The second advantage is that the energy error of MNAD is much smaller after long-time simulation. The numerical dispersion analysis shows that the maximum phase velocity error was 5.92% even if only two sampling points were adopted in each minimum wavelength. To simulate a wavefield without visible numerical dispersion, the computational speed of MNAD, measured by CPU time, was approximately 4.32 times and 1.43 times comparing with the fourth-order Lax-Wendroff correction (LWC) method and the optimal nearly analytical discretized method (ONADM), respectively. MNAD also shows good numerical stability. Its CFL condition increased 24.3% comparing with that of ONADM, from 0.523 to 0.650. The total energy error was less than 1.5% after 300-s simulation whereas the error of other numerical schemes, such as the fourth-order and eighth-order LWC, etc., was up to more than 10% under the same computational parameters. Numerical results showed that our MNAD method performed well in computational efficiency, simulation accuracy, and numerical stability, as well as provided a useful tool for large-scale, long-time seismic wave propagation simulation.