2．5D傅氏变换法声波方程数值模拟及精度分析

Numeric simulation and precision analysis of acoustic equation by 2.5D Fourier transform.

本文在前人研究的基础上,提出了2.5D傅氏变换法的高阶有限差分算法,推导出2.5D高阶差分算子的稳定性条件,重点进行了2.5D傅氏变换法的精度分析,定性分析了影响2.5D傅氏变换法有限差分数值解精度的可能因素,获得了确保2.5D有限差分数值解逼近3D解析解的模拟参数选取的基本原则。数值模拟结果表明:在恰当的波数最大值限制条件的约束下,可变波数步长和高阶差分算子的使用能够确保2.5D数值解满足3D地震波场数值模拟要求。该算法模拟结果正确,精度高,能够节省计算成本,非常适合处理大尺度地震勘探问题。

On the basis of predecessor studies, the paper presented high-order finite-difference algorithm by 2.5D Fourier transform, deduced stability condition of 2.5D high-order difference operator, in which the precision analysis of 2.5D Fourier transform was highlighted, qualitatively analyzed the possible factors affecting the precision of 2.5D Fourier high-order finite-difference numeric solution and acquired the basic principle of modeling parameters selection ensuring the numeric solution of 2.5D finite-difference algorithm to approach the 3D analytic solution. The numeric simulation showed that under the appropriate constraint of limitation of max wavelength value, the usage of variable wavelength step and high-order difference operator are able to ensure the 2.5D numeric solution to meet the requirement of numeric simulation of 3D seismic wavefield. The algorithm is characterized by correct modeling results, high precision and economizing computational cost, which is very suitable to deal with large-scale seismic exploration issue.