An Explicit Finite Difference Method Based on the Mixed Domain Function Approximation and Adaptive Spatial Operator Length Scheme
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Summary: Explicit finite-difference (FD) methods with high accuracy and efficiency are preferred in full-waveform inversion and re- verse time migration. The Taylor-series expansion (TE)-based FD methods can only obtain high accuracy on a small wave- number zone. We have developed a new explicit FD method with spatial arbitrary even-order accuracy based on the mixed k (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 k-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 tem- poral and spatial accuracy in heterogeneous media. Approxima- tion 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 condi- tion than the TE-based FD and TE-based time-space domain dispersion-relation FD methods. Numerical tests in the homo- geneous model, horizontally layered model, and 2D modified Sigsbee2 model demonstrate the accuracy, efficiency, and flex- ibility of the proposed new FD method.