求解三维程函方程的波前扩展法

SOLUTION OF 3-D EIKONAL EQUATION BY EXPANDED WAVEFRONT METHOD

地矿部石油物探研究所

Research Institude of Geophysical Prospecting for Petrolum, MGMR

Vidale给出了求解三维程函方程的有限差分法,但在介质速度变化较大时会严重不满足因果律。本文采用Qin提出的用波前扩展理论改进的Vidale方法,基本克服了Vidale方法所存在的问题。这种方法算出的地震波旅行时是绝对意义上的初至时间。还给出了如何计算反射波及转换波旅行时的方法。本方法没有对程函方程作任何理论上的近似处理。计算结果表明,方法是可行的,即使在速度变化较大的情况下也能得到较精确的解。

Vidale used the finite difference method in solving 3-D eikonal equation. Such method will however violate the causal law in case of large velocity variations. Qin's 2-D general wavefront expansion theory is capable of tackling the problem in vidalc's method, it is thus used here to get an improved solution for the 3-D eikonal equation. The traveltimes calculated by the improved method arc the first arrival times in the absolute sense. The procedure for calculating traveltimes of reflected and converted waves is also involved in this paper without any approximation on the 3-D eikonal equation. The computational results show that the method is practicable and accurate even in case of large velocity variation.