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在前一篇文章中我们分析了地震反射图象的一般概念和均匀介质条件下反射图象的分析,导出了根据地震观测值求反射图象的计算式。本文是前文所讨论的问题的继续,主要是分析非均匀介质条件下反射图象的计算表达式。我们选择的非均匀介质是指速度沿垂直深度方向的变化率为常数的介质,即所谓垂直连续介质。本文所引用的概念和某些公式都与前文相同,不再重复推导。垂直连续介质条件下反射图象分析在这里我们不再进行正演问题的讨论,因为在前文中已证明了反射图象公式(9)的普遍适用性。同时在非均匀介质条件下解正演问题是很复杂而繁琐的。我们主要关心的还是逆解问题。因此我们在这里着重讨论垂直连续介质条件下根据观测值求任意未知界面的反射图象的计算式。我们设速度参数为已知,它表示为:
In the previous article, we analyzed the general concept of seismic reflection images and the analysis of reflection images under uniform medium conditions, and derived the formulas for calculating reflection images based on the observed values of seismic data. This article is the continuation of the issues discussed earlier, mainly to analyze the expression of reflection images under inhomogeneous media conditions. The non-uniform medium we choose is the medium whose rate of change along the vertical depth is constant, the so-called vertical continuous medium. The concepts and some formulas quoted in this paper are the same as the previous one and will not be deduced again. Reflection image analysis in the case of vertical continuous media We will not discuss the problem of forward problems here because the universal applicability of the reflection image equation (9) has been proved in the previous section. At the same time, it is very complicated and cumbersome to solve the problem of forward modeling under the condition of heterogeneous media. Our main concern is the problem of anti-solution. Therefore, we focus here on the calculation of the reflection image of an arbitrary unknown interface based on the observed values under the condition of a continuous continuous medium. We set the speed parameter to be known, which is expressed as: