多维自仿射分布及其在地球化学中的应用

提出了多维自仿射分布的概念，指出多维自仿射分布是自仿射分形的数学基础，论证了多维自仿射分布在截尾条件下具有尺度不变的分形性质，交菜理论研究推广到多维情况。通过实例，说明多维自仿射分布在实际问题中的方法和步骤。并解释了分维数的实际意义。分维数是反映区域化变量在某方向变化程度的定量指标。该方法不仅适用于地球化学金元素和银元素数据，而且还适用于其它元素和地质数据，具有普遍的意义。

APPLICATION OF MULTIDIMENSIONAL SELF AFFINE DISTRIBUTION IN GEOCHEMISTRY

The fractal was founded by Mathematician B.B.Mandelbrot. A fractal is an object made of parts similar to the whole in some way, either exactly the same except for scale or statistically the same. The fractal geometry deals with irregular phenomena or objects in nature, such as topographie relief, fracture strength of rocks, earthquake magnitude etc. It is difficult to describe them by classic mathematical methods. But there is a common characteristic among these phenomena or objects-self-similar. Fractal dimension measures the degree of irregularity based on self-similarity, and is also a numerical index that quantifies the self-similarity of complex phenomena. The character of self-affine fractal is the anisotropic of fractal body n alteration, that is, the different directions have the dissimilarity of scale factor, while self-similar fractal is the special case of self-affine fracta1, that is, the different directions have the homology of scale factors. This paper advances the conception of the multidimensional self-affine distribution points out that the multidimensional self-affine distribution is the mathematical base of the multidimensional self-affine fractal, proofs that the multidimensional self-affine distribution possesses the fractal property of scale-free under truncation and expands the theoretical study of fractal on multidimensional case. Then the paper explains the method and procedure of the multidimensional self-affine distribution in application and real meaning of fractal dimension by examples. The fractal dimension can be regarded as the parameter to reflect the variety degree of region variable on certain direction. The method not only is applied to Au data and Ag data but also suits other geochemical element data or geological data and has general meaning. We expand the theory of fractal to multidimensional case and can study the change courses of the fractal system, i.e., establishing the theoretical system of fractal dynamic mechanism.