A k-space operator-based least-squares staggered-grid finite-difference method for modeling scalar wave propagation

Two staggered-grid finite-difference (SGFD) schemes with fourth- and sixth-order accuracies in time have been developed recently based on new SGFD stencils. The SGFD coefficients of the two schemes are determined by a Taylor-series expansion (TE) approach, which is accurate only near a zero wavenumber. We have adopted the same SGFD stencils and determined the SGFD coefficients by minimizing the errors between the wavenumber responses of the SGFD operators and the first-order k (wavenumber)-space operator in a least-squares (LS) sense. We solved the LS problems by performing a weighted pseudoinverse of nonsquare matrices to obtain the SGFD coefficients and to yield LS-based SGFD methods. We have developed an efficient LS implementation by using a small number of representative wavenumbers, which makes the computational time for estimating the coefficients negligible. Dispersion analysis and numerical examples demonstrate that our LS-based SGFD methods can preserve the original temporal accuracy and achieve better spatial accuracy than the existing TE-based SGFD methods. Extensive numerical tests proved that our LS-based methods do not damage the stability of the corresponding TE-based methods significantly.