三维地质模型的分形学研究

Establishing 3-D Geological Model with Fractal Geometry

在概要介绍分形及分形维数的基本概念之后，着重分析了三维地质模型的分形建模法，在此基础上，对实测地质构造数据进行内插和重构，并将所获结果与常用的Ｋｒｉｇｌｎｇ方法进行对比分析。理论分析和用实例得到的结果表明，分形建模法在精细描述三维地质模型的纹理方面具有明显的优势。

Oil prospecting depends heavily on understanding complex geological structure, which is formed mostly in a non-linear and dynamic process. We deem that fractal geometry, beginning to be used in geological studies, is effective in dealing with such a process.Eq. (1) is well known in fractal geometry. From eq. (1) we derive eq. (4), which is the equation of a straight line associated with fractal dimension D. D is computable from eq.(2), where H is the slope of the straight line defined by eq. (4). H is determined from geological data by least squares method.With D known, eq. (5), which is an interpolation formula, can be used to compute a detailed geological model that includes points other than those for which geological data are available.We use this method to establiSh the model of an oil field in western China' We obtain its detailed seologital model as shown in Fis. 1. As compared with Kringing method (Fig. 2),our detailed model shows finer texture while requiring less primitive data.