Time-domain explicit finite-difference method based on the mixed-domain function approximation for acoustic wave equation

Abstract

Explicit finite-difference (FD) methods with high accuracy and efficiency are preferred in full-waveform inversion and reverse time migration. The Taylor-series expansion (TE)-based FD methods can only obtain high accuracy on a small wavenumber zone. We have developed a new explicit FD method with spatial arbitrary even-order accuracy based on the mixed [Formula: see text] (wavenumber)-space domain function approximation for the acoustic wave equation, and we derived the FD coefficients by minimizing the approximation error in a least-squares (LS) sense. The weighted pseudoinverse of mixed [Formula: see text]-space matrix is introduced into the LS optimization problem to improve the accuracy. The new method has an exact temporal derivatives discretization in homogeneous media and also has higher temporal and spatial accuracy in heterogeneous media. Approximation errors and numerical dispersion analysis demonstrate that the new FD method has a higher numerical accuracy than conventional TE-based FD and TE-based time-space domain dispersion-relation FD methods. Stability analysis reveals that our proposed method requires a slightly stricter stability condition than the TE-based FD and TE-based time-space domain dispersion-relation FD methods. Numerical tests in the homogeneous model, horizontally layered model, and 2D modified Sigsbee2 model demonstrate the accuracy, efficiency, and flexibility of the proposed new FD method.