Statistical self-affinity, fractal dimension, and geologic interpretation |
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Authors: | James R. Carr |
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Affiliation: | Department of Geological Sciences, University of Nevada, Reno, NV 89557, USA |
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Abstract: | Properties of statistical self-affinity are explored and explained. Semi-variogram analysis can be used for identifying statistical self-affine behavior. This is, however, not the only method available for such an analysis. Some error and interpretation is involved; therefore, estimating the Hurst dimension (and from this the fractal dimension) from the semi-variogram can be misleading. Simulations based on statistical self-affine properties are alternatively used to develop an empirical approach to assessing statistical self-affine behavior. Analyzing simulations using semi-variograms, and comparing these semi-variograms to those from actual data, offers an alternate and perhaps superior approach to the understanding of the statistical self-affine properties of a geologic phenomenon. This empirical approach offers a method of reverse modeling for verifying estimates of Hurst dimension from semi-variograms. |
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Keywords: | Fractals Fractal dimension Variograms Geology Hurst dimension |
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