A GENERALIZED 17-POINT SCHEME BASED ON THE　DIRECTIONAL DERIVATIVE METHOD FOR HIGHLY　ACCURATE FINITE-DIFFERENCE SIMULATION OF THE　FREQUENCY-DOMAIN 2D SCALAR WAVE EQUATION

摘要

Forward modeling of the frequency-domain wave equation represents an essential foundation for full waveform inversion in the frequency domain, the accuracy and efficiency of which rely heavily on the forward modeling method employed. To reduce the numerical dispersion, anisotropy, and number of grids per the shortest wavelength in forward modeling methods, rotating coordinate systems have been successfully applied to establish finite-difference (FD) schemes for the forward modeling of the frequency-domain wave equation. However, rotated optimal FD schemes are incapable of handling rectangular sampling grids, which are ubiquitous in practice. Fortunately, optimal FD schemes based on the average-derivative method (ADM) overcome this restriction on different directional sampling intervals. However, the ADM itself is merely an algebraic approach and therefore does not inherit the geometrical properties of the rotating coordinate system. Based on the principle of a rotating coordinate system, a novel optimal directional derivative method (DDM)-based 4th-order, 17-point FD scheme is developed in this paper for the forward modeling of the frequency-domain, two-dimension scalar wave equation to approximate the spatial derivatives. The conventional 4th-order, 9-point scheme and rotated optimal 17-point FD scheme can be derived as special cases of the proposed scheme. Compared with the rotated optimal 17-point FD scheme, the proposed scheme is capable of addressing arbitrary rectangular sampling grids, including equal and unequal directional sampling intervals; moreover, the optimized weighted coefficients can reduce the number of grids per the shortest wavelength from 2.56 to less than 2.4 with maximum phase velocity errors of 1%. Furthermore, the proposed scheme is superior to the ADM-based optimal 17-point FD scheme in suppressing numerical dispersion due to the inherited geometrical properties of the rotating coordinate system. A perfectly matched layer boundary condition is applied to the final FD equation to attenuate boundary reflections. Numerical examples demonstrate the validity and adaptability of our 17-point FD scheme.