Optimal staggered-grid finite-difference schemes based on least-squares for wave equation modelling

Abstract

I develop least-squares (LS)-based schemes to derive globally optimal spatial explicit staggered-grid finite-difference (SGFD) coefficients of the first-order derivative over a given wavenumber range for a given operator length, with no iterations involved. Dispersion analyses show that the dispersion error reduces with an increase of the operator length and a decrease of the wavenumber range. Therefore, globally optimal spatial SGFD coefficients with the shortest operator length can be found to satisfy the given error limitation in the given wavenumber range. Examples of optimal explicit SGFD coefficients are given. In addition, a LS-based scheme to derive optimal implicit SGFD coefficients is meanwhile put forward. Examples of optimal implicit SGFD coefficients are given. Numerical experiments for a homogeneous model and a heterogeneous model demonstrate that the LS-based SGFD method has a higher accuracy than the Taylor-series expansion (TE)-based SGFD method for the same operator length. Compared to the TE-based SGFD method, the LS-based SGFD method can adopt a shorter operator to achieve the same accuracy and thus is more efficient.