Fractal invariable distribution and its application in large-sized mineral deposits

Category Sedimentology
Group GSI.IR
Location International Geological Congress,oslo 2008
Author Shen, Wei۱; Du, Haiyan۲
Holding Date 03 September 2008

Fractal modelling has been applied extensively as a means of characterizing the spatial distribution of geological phenomena that display self-similarity at differing scales of measurement. A fractal distribution exists where the number of objects exhibiting values larger than a specified magnitude displays a power-law dependence on that magnitude, and where this relationship is scale-invariant. This paper shows that the general power-function distribution is scale-invariant under upper truncation and the truncated power-function distribution possesses the fractal property of scaling under upper and lower truncation. The general Pareto distribution is scale-invariant under lower truncation and the truncated Pareto distribution also possesses the fractal property of scaling under upper and lower truncation. The lognormal distribution remains a log-normal distribution with fixed σ and changed μ under a positive multiplicative constant; The Zipf distribution possesses the fractal property of scaling under lower truncation. These fractal invariable distributions are the mathematical base of fractal models. Population limits, derived from fractal modelling using a summation method, are developed with plot modelling of Au geochemical data from Shandong province, China. The anomalous areas containing > 200 ppb Au include some known large-sized and super large-sized gold mineral deposits in the research region.