Cascade modeling of element concentration values in rocks and mineral deposits

Category Other
Group GSI.IR
Location International Geological Congress,oslo 2008
Author Agterberg, Frederik
Holding Date 08 September 2008

Cascade modeling of geochemical map and mineral deposit data helps to explain the nature of frequency distributions of element concentration values for small samples as well as for large blocks of rocks and ore. Useful frequency distribution models are the lognormal and Pareto distributions which plot as straight lines on logarithmic probability and log-log paper, respectively. Both distributions can be generated by means of a simple multiplicative cascade. The model of de Wijs results in a discrete logbinomial distribution that closely approximates the lognormal. In this model, smaller blocks resulting from dividing larger blocks into parts have concentration values with constant ratios that are scale-independent. The Turcotte model that results in a Pareto distribution is a variant of de model of de Wijs in which only the blocks with largest concentration values participate in the cascade. Often a single straight line on logarithmic probability or log-log paper does not provide a good fit to observed data and two or more distributions should be fitted. For example, geochemical background and anomalies (extremely high values) can have separate frequency distributions for concentration values. Background often is approximately lognormal whereas anomalies and mineral deposit data may be Pareto-type. Such mixtures of distributions can be simulated by adding the results of separate cascade models. Regardless of properties of background, an unbiased estimate can be obtained of the parameter of the Pareto distribution characterizing anomalies in the upper tail of the element concentration frequency distribution. Computer simulation experiments and practical examples are used to illustrate the approach.