Optimized compact finite difference scheme for frequency-domain acoustic wave equation

Frequency-domain numerical simulation is the most important foundation of frequency-domain full-waveform inversion and reverse time migration. The accuracy of numerical simulation seriously affects the results of the seismic inversion and image. In this article, we develop an optimized compact finite difference scheme for acoustic wave equation in frequency domain to improve numerical simulation accuracy. For the sake of avoiding the extra memory and computational costs caused by solving the inverse of a pentadiagonal band matrix, we calculate the optimized compact finite difference discrete operator for the Laplace operator in the numerical simulation. Although the optimized compact finite difference scheme has only second-order formal accuracy, it has a spectral-like resolution feature. This method can significantly reduce the numerical dispersion and the numerical anisotropy. We find that the results of the optimized compact finite difference scheme agree well with the analytic solution according to accuracy analysis. Two numerical simulations are done to verify the theoretical analysis of the optimized compact finite difference scheme.