声波方程频率域高精度正演的17点格式及数值实现

频率域正演计算是频率域全波形反演的基础.传统的最优9点格式只具有二阶精度,不能满足高精度地震成像的需要.本文考虑两个四阶精度的格式,即经典的四阶9点格式和优化的17点格式.17点格式可将最小波长内所需网格点数减小到2.56.通过在简单模型和Overthrust模型上的数值实验,比较分析了三种格式的正演效果;简单模型数值实验显示了17点格式克服频散误差的能力优于四阶9点格式和最优9点格式;复杂模型数值实验则进一步承认了算法的可行性.

A 17-point scheme and its numerical implementation for high-accuracy modeling of frequency-domain acoustic equation

Frequency-domain modeling is the basis of frequency-domain full waveform inversion. The classical optimal 9-point scheme is only of second-order accuracy, and does not meet the need of high-accuracy seismic imaging. This paper deals with two fourth-order schemes, namely fourth-order 9-point scheme and optimized 17-point scheme. The 17-point scheme reduces the number of grid points required by the shortest wavelength to 2.56. We also perform numerical tests on a simple model and the Overthrust model, and the modeling results with the three schemes are compared. The results demonstrate the superiority of the 17-point scheme over the fourth-order 9-point scheme and optimal 9-point scheme in terms of reducing dispersion errors. Numerical tests on complex model further confirm the feasibility of the 17-point scheme.