三维偏移分裂算法

A SPLITTING SCHEME OF THREE DIMENSIONAL MIGRATION

长春地质学院

Changchun Geological College

本文提出了近似波动方程的分裂算法。用小数步长延拓及弱近似方法对问题进行了讨论。给出了有限差分分裂算法的延拓公式,并证明了分裂的方程与原方程等价;推导出频率—波数域分裂的外推公式,速度横向变化部分是做为独立一步处理的;利用解算子概念讨论外推算子的可交换性,得到了不交替方向使用方程的方法;对于同层速度相同的各条测线,设计的外推算子可重复使用,这样可节省许多运算时间。

This paper presents a splitting scheme of approximate moditied wave equation. The problem is discussed by means of the weak approximation method and the fractional steps extrapolation, involving a formula of finite difference splitting scheme. The equivalence between the splitting equations and the original eguation has been proved. The paper also gives the extrapolation formula of the splitting scheme in the frequency-wave number domain. The lateral velocity variation is treated as an independent step. By means of the concept of the so-called solution operator, inter-changeability of the extrapolation oprator is discussed, obtaining a scheme for using the epuation without exchange of direction, For the lines within the same layer of constant velocity the extrapolation operator so designed can be used repeatedly, thus saving time of computation.