带边界条件声波方程速度提取的摄动方法

A PERTURBATION APPROACH FOR VELOCITY EXTRACTION FROM ACOUSTIC WAVE EQUATION WITH BOUNDARY CONDITIONS

地质矿产部石油物探研究所

利用摄动方法可以在数学上较严谨地获得地下介质的速度分布。然而在生产上至今尚未有广泛应用,值得继续深入探讨。本文继续了[1]中的工作,从更加符合地震勘探的实际模型出发,采用了带边界条件声波方程的提法,并使用了与[1]完全不同的数学推导,最终得出地下介质的深度剖面与通常使用的叠加偏移技术所得的剖面相仿,结果表明利用摄动方法对地震资料进行解释是可行的。 《石油地球物理勘探》1980年第5期上发表了北京大学陈亚浙老师“地震波速度计算的摄动方法”一文。这种方法从数学上求出速度解,获得深度剖面。在求速度解时,给了两个简化条件:(1)地层中传播的波可以用声波方程描述;(2)速度变化不大时,可将非线性问题化为线性问题。其中为简化声波波场在地面所满足的边界条件,文章考虑了一个近似问题,即假设介质完全充满全空间,且上下两半空间关于地面是对称的,可对波场施行偶延拓,从而略去了边界条件的提法。本文则保留边界条件的提法。为简单起见,仅对层状介质进行讨论。

By means of the perturbation approach, it is possible to get the rigorous velocity distribution mathematcially in underground media. However, for its wide use in practice, some research work is still needed to be done. This article is the continuation of work [1]. In order to better fit the practical model in seismic exploration the author is attempting to adopt the acoustic wave equation with bondary conditions and to use the mathematical deduction entirely different from that used in CO. The ultimate depth profile of underground media obtained is similar to that derived from routine stacking migration technique. The results suggest that the perturbation approach is feasible for interpreting the seismic data.