空间频率域内二维波动方程解的算法—“混合法”

MIXED METHOD——AN ALGORITHM OF SOLVING THE 2-D WAVE EQUATION IN FREQUENCY DOMAIN

地质矿产部石油物探研究所

在众多的二维波动方程求解算法中,一般都需要对方程进行一定的简化,最后得到一个适合于不同倾角偏移的方程。本文所介绍的方法,不对二维波动方程进行任何简化处理,试图得到较为精确的波动方程的数值解。由于求解过程是非简化的,原则上适用于任何倾角的偏移和具有横向速度变化的情况。 本文使用付氏变换的方法求得一个亥姆霍兹方程,并用差分法求该方程的近似解。文中给出了两个差分格式,并讨论了它们的稳定性和差分解法。此外还给出了该算法的成像法则。

In many of the algorithms for solving the 2-D wave eguation, it generally needs to simplify the eguation to a certain extant so as to make it suitable for the migration of different dip angles,The method introduced here is attempted to get a rather more accurate numerical solution without doing any simplification. Owing to the procedure of the solution is uns-implified, it is suitable for the migration of any dip angles and the case of laterally varied velocity.In this paper, the author has derived a eguation through Fourier transformation. Its approximate solution can be obtained by difference method. Two difference schemes were presented. Their stabilities and difference solu tions were discussed. The imagine principles of the algorithm were also given.