Spatial Variation of Fractal Parameters and Its Geological Implications

Abstract

The spatial variation of the fractal dimension and its geologic implications are studied using an empirical approach. The fractal parameters, including the surface¡¦s fractal dimension, D surf, the angular fractal dimension, D ang, the gamma (£^) value and the break-distance (R), are derived by the variogram method. Synthetic surfaces are generated by the successive random addition (SRA) method by assigning different values to the Hurst exponent. Two test sites were selected to study the link between the fractal parameters and the geologic features. The following conclusions can be drawn from this research: (1) The fractal parameters of a landscape surface are region-dependent and scale-dependent. The spatial distribution of fractal parameters should be studied in a suitable size of spatial unit. (2) The angled variogram method can readily disclose the anisotropic nature of a landscape surface. (3) The surface¡¦s fractal dimension reflects the litho-logic variations underlying a landscape surface, and the gamma value reflects the topographic relief of the surface. (4) The mean direction and the vector resultant of angular fractal dimensions have a close relation with the major geological structures of the landscape.

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