Fractal characterization of the spatial distribution of geological point processes

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.