Fractal characterization of the spatial distribution of geological point processes |
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| Authors: | Renguang Zuo Frederik P Agterberg Qiuming Cheng Lingqing Yao |
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| Institution: | 1. State Key Laboratory of Geological Processes and Mineral Resources, China University of Geosciences, Wuhan, Hubei 430074, China;2. Geological Survey of Canada, 601 Booth Street, Ottawa, Ontario K1A 0E8, Canada;3. Department of Earth and Space Engineering, Department of Geography, York University, 4700 Keele Street, Toronto, Ontario M3J 1P3, Canada |
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| Abstract: | Geological point processes can be used to model point patterns occurring frequently in a wide variety of geoscience fields, including the study of mineral deposits, oil producing wells, earthquakes, and landslides. Characterization of the spatial distribution of GPP has implications for understanding the properties of the underlying geological processes and events. Three examples of GPP dealing with (1) metallic mineral deposits, (2) oil producing wells, and (3) aftershocks of the Wenchuan earthquake (on 12 May 2008, magnitude 8.0) are presented to illustrate that (1) the spatial distribution of geological point processes generally shows clustering implying rejection of the Poisson model because L(r) > LPois(r); (2) the clustering statistics of the underlying geological processes are fractal; and (3) the size distribution of geological point processes is scale invariant. These results indicate existence of a fundamental law concerning the fractal nature of the point distributions generated by geological point processes. |
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| Keywords: | Geosciences Point process Earthquakes Oil wells Mineral deposits L function Fractal |
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