Are Fractal Dimensions of the Spatial Distribution of Mineral Deposits Meaningful? |
| |
| Authors: | Gary L Raines |
| |
| Institution: | (1) U.S. Geological Survey (retired), c/o Mackay School of Earth Sciences, UNR, MS 176, Reno, NV 89557, USA |
| |
| Abstract: | It has been proposed that the spatial distribution of mineral deposits is bifractal. An implication of this property is that
the number of deposits in a permissive area is a function of the shape of the area. This is because the fractal density functions
of deposits are dependent on the distance from known deposits. A long thin permissive area with most of the deposits in one
end, such as the Alaskan porphyry permissive area, has a major portion of the area far from known deposits and consequently
a low density of deposits associated with most of the permissive area. On the other hand, a more equi-dimensioned permissive
area, such as the Arizona porphyry permissive area, has a more uniform density of deposits. Another implication of the fractal
distribution is that the Poisson assumption typically used for estimating deposit numbers is invalid. Based on datasets of
mineral deposits classified by type as inputs, the distributions of many different deposit types are found to have characteristically
two fractal dimensions over separate non-overlapping spatial scales in the range of 5–1000 km. In particular, one typically
observes a local dimension at spatial scales less than 30–60 km, and a regional dimension at larger spatial scales. The deposit
type, geologic setting, and sample size influence the fractal dimensions. The consequence of the geologic setting can be diminished
by using deposits classified by type. The crossover point between the two fractal domains is proportional to the median size
of the deposit type. A plot of the crossover points for porphyry copper deposits from different geologic domains against median
deposit sizes defines linear relationships and identifies regions that are significantly underexplored. Plots of the fractal
dimension can also be used to define density functions from which the number of undiscovered deposits can be estimated. This
density function is only dependent on the distribution of deposits and is independent of the definition of the permissive
area. Density functions for porphyry copper deposits appear to be significantly different for regions in the Andes, Mexico,
United States, and western Canada. Consequently, depending on which regional density function is used, quite different estimates
of numbers of undiscovered deposits can be obtained. These fractal properties suggest that geologic studies based on mapping
at scales of 1:24,000 to 1:100,000 may not recognize processes that are important in the formation of mineral deposits at
scales larger than the crossover points at 30–60 km. |
| |
| Keywords: | Fractal dimensions mineral deposits deposit density |
| 本文献已被 SpringerLink 等数据库收录！ |
|
