An Efficient and high accuracy finite-difference scheme for the acoustic wave equation in 3D heterogeneous media

TL;DR

This paper introduces a new explicit high-order finite difference scheme for 3D acoustic wave equations in heterogeneous media, achieving high accuracy and efficiency for seismic simulations.

Contribution

The paper develops a novel compact finite difference scheme with fourth-order accuracy in space and second-order in time, suitable for heterogeneous media, improving stability and efficiency.

Findings

The scheme achieves $O( au^2) + O(h^4)$ accuracy.

Numerical experiments confirm high accuracy and efficiency.

The method is conditionally stable with a slightly lower CFL number.

Abstract

Efficient and accurate numerical simulation of 3D acoustic wave propagation in heterogeneous media plays an important role in the success of seismic full waveform inversion (FWI) problem. In this work, we employed the combined scheme and developed a new explicit compact high-order finite difference scheme to solve the 3D acoustic wave equation with spatially variable acoustic velocity. The boundary conditions for the second derivatives of spatial variables have been derived by using the equation itself and the boundary condition for $u$. Theoretical analysis shows that the new scheme has an accuracy order of $O(\tau^2) + O(h^4)$, where $\tau$ is the time step and $h$ is the grid size. Combined with Richardson extrapolation or Runge-Kutta method, the new method can be improved to 4th-order in time. Three numerical experiments are conducted to validate the efficiency and accuracy of the new scheme. The stability of the new scheme has been proved by an energy method, which shows that the new scheme is conditionally stable with a Courant - Friedrichs - Lewy (CFL) number which is slightly lower than that of the Pad\'{e} approximation based method.