A Framework for Automatically Choosing the Optimal Parameters of Finite-Difference Scheme in the Acoustic Wave Modeling

An effective finite-difference (FD) scheme requires suitable FD parameters to ensure stability while having sufficient accuracy in the seismic modeling. The FD parameters such as time step, grid spacing and FD operator also affect the computational costs and storage requirements significantly. Thus, choosing the FD parameters should be the optimal trade-off between the stability, numerical accuracy and computational efficiency. However, the FD parameters usually be chosen through repeated manual tests, which is prone to unnecessary consumption. In this paper, we propose a framework for automatically choosing the FD parameters to achieve the optimal FD scheme in the acoustic wave modeling. Considering the computational efficiency, the proposed framework provides the maximum admissible time step under the stability condition. On the premise of the maximum time step, the proposed framework can find suitable parameters to ensure that the FD scheme has sufficient wavenumber bandwidth to deal with the maximum wavenumber or frequency of the wavefield. Dispersion and stability analyses prove that the FD parameters determined by our framework can effectively avoid dispersion errors while ensuring stability under the given conditions. Numerical experiments also prove the effectiveness of the framework in choosing FD parameters for the inhomogeneous velocity model. The framework can easily obtain the optimal FD parameters and can be recommended as a routine step for the FD methods.