Two novel Fourier finite-difference schemes for acoustic wave propagation

We have designed two new Fourier finite-difference (FFD) schemes for acoustic wave propagation by cascading the Fourier transform operators and rhombus-shaped finitedifference operator. The Fourier operator of FFD scheme 1 adopts conventional pseudospectral operations while the Fourier operator of FFD scheme 2 incorporates sinc function and reference velocity v0. Using frequency-wavenumber domain Taylor-series expansion method, we deduce the FFD coefficients which can reach 2N-th order temporal accuracy for these two FFD schemes. Besides, we compare and contrast dispersion characteristic of two FFD schemes and analyze the relation between FFD operator length requirement with different velocity. Based upon the analysis, we establish a variable FFD operator length mechanism to minimize the computational cost of two FFD schemes. The operator length variation curves demonstrate that our FFD scheme 2 can be more efficient than FFD scheme 1. And the numerical examples validate the accuracy of two new FFD schemes.