求解一维波动方程反问题的消除多次波方法

1．引言一位早期的地球物理学家Noah曾经设想将船和电缆沉入海底采集数据，以避免由海面反射所形成的多次波混响，从而得到更为理想的地震勘探剖面，但是这一方法在实践中是很难实现的．1974年，Ril6y博士［6］从地震波的物理机制出发，提出了一种消除多次波的反卷积方法，可以通过资料处理来实现这个思想．在一继波动方程反问题的研究中，我们重新发现了这一方法［7］；称之为消除多次波方法．方法的基本思想是根据自由表面反射波响应与激发波响应之间的相似关系，通过变换来消除多次波混响，从而近似地得到所需的反射系数信息．与Riley…

THE MUCLI-REFLECTION ELIMINATION METHOD TO SOLE THE INVERSE PROBLEM OF 1-D WAVE EQUATION

In this papert we discuss the inverse problem of 1-dimensional acoustic wave equation and propose an approximate inversion method, called multi-reflection elimination method, with which the approximate reflectivity function can be directly obtained by applying a certain transform to the response. The computation efforts for such method is only of the order N log N, much less than that of solving the direct problem, which is O(N2). On the basis of the proposed method, we also construct an iterative algorithm, and prove that the convergent order of iteration is two.