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地球化学面的形态是依赖于采样网格(采样密度)大小变化而不确定的。对于一维情况,元素含量分布曲线长度L与采样间距r之间的关系服从L(r)=Cr~(1-1/H),D=1/H。对于地壳上任一给定区域,沿某一测线进行地球化学测量的任一元素含量数据,由上式确定的D值和H值,对于沿测线方向该元素的含量分布在统计的意义上将是确定的。对浙江省水系沉积物测量数据的统计结果表明,Au、Ag、Cu、Pb、Zn、Mo、Co、Ni 8种元素的含量变化在1～150km尺度范围内遵循分形分布,D=1.03～1.62,H=0.62～0.97。这表明地壳中元素含量在空间上随采样间距的变化可能是一个完全等价于分形布朗运动的随机函数,在1～150km这个尺度范围内,元素含量分布模式具有自相似性和长程相关性。这个结果为“国际地球化学填图”项目(IGCP259)提出的160km×160km采样网格尺度提供了一种理论的支持。
Geochemical surface morphology is dependent on the sampling grid (sampling density) changes in the size of the uncertainty. For the one-dimensional case, the relationship between the elemental content distribution curve length L and the sampling interval r obeys L (r) = Cr ~ (1-1 / H) and D = 1 / H. For any given element in a given area of the earth’s crust, the geochemical measurements along a given line contain data on the D and H values determined by the above formula for statistical distribution of the elemental content along the survey line Will be ok. The statistical results of sediment measurements in Zhejiang Province show that the content of 8 elements of Au, Ag, Cu, Pb, Zn, Mo, Co and Ni follows the fractal distribution in the range of 1 ~ 150km, with D = 1.03-1.62 , H = 0.62 ~ 0.97. This indicates that the spatial variation of the elemental content in the crust may be a stochastic function completely equivalent to the fractal Brownian motion. Within the scale of 1 ~ 150km, the elemental content distribution pattern has self-similarity and long-range correlation. This result provides a theoretical support for the 160km × 160km sampling grid scale proposed by IGCP259.