地表的分形测量及其大地构造学意义

以湖北红安地区为例,采用投影覆盖法(projectivecoveringmethod)对地表进行了二维分形测量,结果表明,地表面积具有双分形(bifractal)关系,即具有小尺度的结构分形(texturalfractal)和大尺度的构造分形(structuralfractal),分叉点(breakpoint)的尺度为3610m,分维值都在2～3之间且结构分维值大于其构造分维值。可见,地表形态具有分形性质,分维值可以指示地表形态的复杂程度。构造分维值可作为构造活动强度的一个指标,可为大地构造单元的划分提供定量依据。复杂地表形态主要是由构造活动(内营力作用)和各种复杂表生地质作用(外营力作用)引起的,前者主要控制大尺度的地形起伏,后者则塑造小尺度的地表形态。地表分维值可以指示地表的发育成熟度,该地区小尺度的结构分维值大于大尺度的构造分维值表明其处于地表形态的发育晚期。此外,地表的分形尺度可以来用确定构造活动尺度,从而指导构造地质与找矿勘探研究。

FRACTAL MEASURE OF THE EARTH'S SURFACE AND ITS SIGNIFICANCE TO GEOTECTONICS

Two-dimensional fractal measurement about the earth’s surface in H ong’an district, Hubei Province, China was carried out by using projective cove ring method in this paper. The results indicate that the earth’s surface area s hows a bifractal relationship between area and scale, which involves a textural fractal at small scale and a structural fractal at large scale, with the average breakpoint being at 3610m, the fractal dimension values ranging generally from 2 to 3 and the textural fractal dimension values being larger than their structu ral counterparts. This demonstrates that the earth’s surface morphology is of t he fractal type, and the fractal value can be used to indicate the complexity of the morphology of the earth’s surface and the intensity of tectonic movement. As a result, the fractal value may be a quantitative parameter for the division of tectonic units. The complex pattern of the earth’s surface is resulted from tectonic movement (endogenetic forces) and all kinds of complex hypergeneses (ex ogenic forces). The former controls the topographic inequality on larger scale a nd the latter shapes surface configuration on smaller scale. The fractal dimensi on values can indicate the maturity of the earth’s surface. During the earlier growth stage, the structural fractal dimension value on a larger scale is larger than the textural fractal dimension value on a smaller scale, and contrarily, d uring the later stage the textural fractal dimension value will be larger than t he structural fractal dimension value. At the same time, we can determine the sc ale of the tectonic movement in a district by its fractal scale of the earth’s surface, and what’s more, the scale can help us to study the structural geology and mineral exploration in this district.