逐层向下的递推反演方法

A new method for layer-by-layer downward recursion inversion

本文由系统函数模型H（jω）出发，导出了逐层向下的一维反演公式。该方法的基点是给定频率f处的系统函数值只含有一定深度H以上的构造信息．而更深处的构造信息只影响更低频处的系统函数值。于是从已有最高频率的H（jωmax）出发，以二分层结构作初始假设，可反演第二层的参数。然后，逐步针对较低频率的H（jω），在更深处引入新的离散分层，反演出第三层参数，并依此向深层类推。计算机模拟结果表明，反演方法是有效的，对产P1的初值不敏感，抗噪性能良好。

OGP, 1997 - 32 (2)214~220The formula for layer-by-layer downward 1D inversion is derived from the system function model H(jω). The method is based on the assumptions that the system function value for a given frequency involves only the structure informations above a definite depth H,and that the deeper structure Informatlons only influence on the system functlon values corresponding to the lower frequencies. The inversion starts with H(jωmax) at the highest frequency and the initial two-layer structure to determine the parameters of the second layer, then continues with H(jωmax) at lower frequency and the structure added in a deeper discrete layer to produce the parameters of the third layer. The inversion goes on in lower and lower frequencies along with deeper and deeper discrete layers untll we achleve the expected object.Computer's modeling result shows that the inversion method is effective,insensitive to the initial choice of p1,and noise resistant.