摘要
本文研究了多层介质中地震分界面的数学解析表示法。其目的是为将多层介质中透射波和反射波的运动学正演理论应用于生产实践作一基础工作,以便在地震勘探的进一步实践中,能够获得较精确的正演地震图象和实现地震资料反演过程的人机联作,从而获得较好近似的反演地震结果。为此,我们具体地研究了双三次Coons曲面逼近地震分界面的问题,并将之应用于HQ地区碳酸盐岩三维地质结构。理论证明,无论地震分界面的埋藏深度如何,双三次Coons曲面可以等精度地逼近它们。而实际计算表明,在50×50m2的采样网格上,由Coons曲面公式计算出的插值与原始采样数据的绝对误差一般小于采样读数误差,在倾角小于50°时,其值一般小于5m。由Coons曲面公式计算出的网格中点插值绘制的构造图和网状透视图,与由对应的原始采样数据绘制的构造图和网状透视图几乎完全相同。于是,我们得到以下结论:双三次Coons曲面可以相当好地逼近三维地质结构所具有的诸地震分界面。
Abstract
In this paper, the analytical expressions of seismic interfaces of layered media are reseached. Its purpose is to finish one of the basic tasks for applying the theory of the forward problems of kinematics of refractions and reflections in production practice, so as to be able to gain more precise seismic pictures of forward problems and to realize the man-mechine interaction in the inverse process of seismic data, and then to obtain more approximate inverse seismic results in further practice of seismic prospecting. For this purpose, the problems of approximation to seismic interfaces by bicubic Coons surfaces are discussed and applied to the three-dimensional geologic structure of carbonatite H. Q. region. It is proved theoretically that no matter what is the depth of burial of seismic interfaces, they can be equi-precisely approximated by bicubic Coons surfaces. It is revealed with the aid of computation that the absolute error between the orginal sampling datum and the interpolating value computed by Coons surface formula at any point of 50 × 50m2 grid involed of sampling net is tsually less than sample reading error. In the case of the dip angle of seismis interface in the grid involved less than 50° it will be less than 5m in the general. The structural maps and mesh perspective views drawn from the interpolating values at the center of each grid of the sampling nets involved are almost the same as the corresponding ones drawn from the original sampling data respectively. Hence we have arrived at the conclusion that the seismic interfaces of three-dimensional geologic structure can be approximated well enough by bicubic Coons surfaces.
论文详情