A new point-weighting finite-difference modelling for the frequency-domain wave equation

Abstract

In this paper, we propose a new 21 point finite-difference scheme for modelling the frequency-domain wave equation in 2-dimensional domain. To discretize the second derivative term, we develop a modified central difference scheme in which each of the gridpoints is replaced with a linear combination of it and its neighbouring girdpoints along one direction. For the discretization of the zeroth-order term, we use the weighted average of all the 21 points. The combination coefficients and the weight parameters are determined by minimizing the numerical dispersion. In comparison with the scheme of a derivative-weighting one, the new scheme has a much better performance in reducing the numerical dispersion when the step sizes are not equal in different directions. Numerical experiments are presented to illustrate the effectiveness of the new scheme.