用特征线法进行一维波动方程反演的直接算法

1-D wave equation direct inversion algorithms by the method of characteristic

1. 中国新星石油公司石油物探研究所,南京 210014;2. 大庆石油学院勘探系,安达 151400

Research Institute of Geophysical Prospecting for Petroleum, CNSPC, Nanjing 210014

用特征线法直接反演一维波动方程中的速度或波阻抗, 是80年代以来不少学者关心的课题。本文对沿特征线方向的微分和积分算法进行了较详细的研究, 提出了两个三阶精度反演公式, 并对4个模型和4种子波进行了数值计算。结果表明, 对平直的地层或者反射层位不多的地区, 该算法能完全恢复原始模型中的波阻抗信息, 且计算速度非常快, 因而是一种行之有效的方法。但对复杂地层或反演时窗较长的情况, 反演计算会出现振荡现象。最后, 对这类直接反演算法进行了简单的评价, 并对反演的稳定性问题进行了较详细地分析与阐述。

Direct inversion of velocity and impedance in 1-D wave equation by the method of charac-teristic is a task of interest to many scholars since 1980s. In this paper we study in detail the differential and integral algorithms along the characteristic direction, put forward two third-order inversion formu-lae, and make numerical computations on four models and four kinds of wavelets. The results demon-strate that the algorithms can completely recover impedance information of original models in areas with flat strata or with few reflection layers, but for complicated strata or large inversion time window circum-stances the inversion computation may incur oscillation phenomenon. Finally we simply comment upon these direct inversion algorithms and expound the stability problem of inversion in detail.