A High-Order Temporal and Implicit Spatial Staggered-Grid Finite-Difference Scheme for Modelling Scalar Wave Propagation

Abstract

Summary Finite difference (FD) is a commonly used tool for modelling seismic wave propagation. Temporal high-order FD methods can enhance the accuracy and stability compared with the methods with second-order accuracy in time. The implicit calculation of spatial derivatives also contributes to the improvement in accuracy. We propose a new implicit staggered-grid FD (SFD) scheme based on a combined stencil, which is the combination of pyramid and cross stencils in 3D case. Our scheme calculates the temporal and spatial derivatives by using high-order temporal and implicit spatial FD operators, respectively. Based on the dispersion relations, we optimize the temporal and implicit spatial FD coefficients by using Taylor series expansion (TE) and least squares (LS). We formulate four implicit SFD operators: TE-TE, TE-LS, LS-TE and LS-LS operators. 2D and 3D modelling examples determine that our implicit scheme has greater accuracy than other schemes. Additionally, our implicit SFD scheme allows for a larger grid spacing, which can increase the computational efficiency.