断层粗糙表面的分形模拟

Fractal Simulation of the Fault Surface

根据二元分形插值理论， 运用断层面上部分信息点数据， 对断层面的粗糙形态进行了分形插值模拟． 由于岩石断裂表面具有统计自相似的特征，提出了局部邻域的划分以及纵向压缩比的确定的改进分形插值曲面的方法． 根据地质统计学中变差函数原理， 以变差函数的变程来划分局部邻域； 运用多元统计分析原理， 以观测数据一次趋势面的偏差值来确定分形插值中的纵向压缩比， 从而使得模拟结果更加符合真实断层面的特征． 研究结果表明， 分形插值曲面的理论与方法比传统的插值方法更加精确地反映断层表面的粗糙特征， 它的应用为研究断层面的粗糙程度对工程的影响提供了一套新的方法．

Based on the theory of the bivariate fractal interpolation, by using the data obtained from the fault surface by physical exploring, the roughness shape of the fault is simulated. As rock fracture surfaces have the feature of statistical self similarity, the improved methods of the fractal interpolation surface, the partition of a local area and determination of the vertical scaling, are posed. The local areas are partitioned according to the range of variogram in geostatistics and the vertical scaling is determined based on the deviation values of one order trend surface which comes from the principles of multivariate statistical analysis. The result indicates that the fractal interpolation surface method is better than the traditional interpolation method in simulating the roughness of the fault surfaces. So the theory and the method of fractal interpolation surface provide a new way for studying the influence of the roughness of the fault on the practical projects.