Direct implementation of discontinuous-grid finite-difference method using multiple point sources method and dynamic wavefield injection

Abstract

Summary The classical finite-difference (FD) method stimulates wave propagation in uniform grids. In models with considerable velocity variations, the computational efficiency is compromised by oversampling in time and space. Although adopting a discontinuous grid in different wave-speed regions can improve computational efficiency, such a technique is typically hindered by low accuracy in transition zones (i.e. in the vicinity of the discontinuous-grid interface) and is typically unstable in the long term. We propose a direct implementation of the discontinuous-grid FD method by performing two simulations simultaneously: one on a coarse grid and the other on a fine grid. The proposed method applies a dynamic injection strategy to manage wavefield communication between coarse and fine submodels. Compared with previous discontinuous-grid FD methods, where the number of layers required for wavefield communication is one-half that the order of the FD scheme, the proposed method only requires one single layer, which significantly reduces the communication overhead and suppresses wavefield errors. Numerical experiments show that the results yielded by our method are consistent with the reference solutions yielded by the uniform-grid FD method via a fine grid. Furthermore, our method does not encounter numerical instability in long-term simulations. Therefore, the proposed discontinuous-grid FD method can accelerate numerical simulations while retaining stable numerical accuracy, even for long-term simulations.