1.引言在石油地震勘探中,地震波在各种地层构造中的传播是一个十分复杂的物理现象,因此,人们往往首先研究单层界面的反射波(参见图1),如资料[1]、[2]就从物理地震学的角度研究了这个问题,这些研究对于资料处理方法的改进及时间剖面的解释是有益的。本文从数学方面总结这课题研究的初步成果,在本文中,我们直接从波动方程理论的角度建立了近似公式,即Kirchhoff和式,它大体上与[2]中的公式相类同,但可以直接适用于任意形式的子波。同时,为了大量减少计算时间,以适应较多模型的计算, 1. INTRODUCTION Seismic wave propagation in various stratigraphic structures is a complex physical phenomenon in petroleum seismic exploration. Therefore, it is often the first to study reflected waves at monolayer interfaces (see Figure 1), such as data [1], [2] studied this issue from the point of view of physical seismology, and these studies are helpful for the improvement of data processing methods and the interpretation of time profiles. In this paper, we summarize the preliminary results of this research from the aspects of mathematics. In this paper, we establish the approximate formula directly from the perspective of wave equation theory, that is Kirchhoff sum, which is similar to the formula in [2] Apply directly to any form of wavelet. At the same time, in order to reduce computational time greatly and adapt to the calculation of more models,