Extreme Value Distribution Of Geological Data And Its Application In Gejiu Tin Ore Deposits

Based on the geological anomaly theory and the'three-components'mineral prediction theory, this paper does research work with the data gathered in the Gejiu Tin ore deposits. Focusing on the problems in the mineral resources exploration such as three difficulties: difficult to identify, difficult to find, difficult to exploit, we combine mathematics with geology to develop our research work based on the systemic study of the background of region mineral forming and on the enough data analysises. We have applied extreme value theory (EVT) to analysis the data of Gejiu Tin ore deposits. We use extreme value theory to recognize, extract and delineate anomaly. The investigations and comparisons are completed for parameter estimation in the model with generalized Pareto distribution (GPD), moreover, the theoretical and applied aspects are completed for building GPD model with anomaly data exceeding the threshold.The paper mainly describes a method of finding lower limit by using peak over threshold (POT) in extreme value theory, which is different from the experiential method. We provide a method of finding threshold and compare this method with the statistical method X + 2S. Also, we study the parameter estimation in GDP. The characterizations, advantages and disadvantages of several main methods of parameter estimation are given. As we know, the likelihood equation obtained by parameters maximum likelihood estimation in GDP has no analytic solution, so we provide an approximate maximum likelihood estimation and derive its formulae in detail. The formulae can give its analytic solutions and one should pay attention to some problems when applying the formula which has been emphasized in this paper. The following results are mainly achieved after applying extreme value theory to study the data of Pb,Zn,Ag,Sn,Mn in Gejiu Tin ore deposits in 2003.1. The method in this paper is different from previous the method which is used to recognize, extract and delineate geological anomaly. Extreme value theory not only can fit the distribution which the data exceed the lower limit value of anomaly and characterize the probability of anomaly occurring, but also can delineate geological anomaly objectively and quantitatively,as a result, the indeterminacy in quantitative prediction of minerals is characterized,which is one of assignment in quantitative prediction of minerals.2. Through the computations, it is shown that the threshold calculated by extreme value theory's POT method is smaller than that calculated by the statistical method X + 2S. Therefore, when determining the lower limit of anomaly, it is possible not to eliminate such data that is probably anomalous. This corresponds with the principle that the mine forming prediction should leak ore-body at least and reduce the required area for detail investigation at most.3. The results also show that the parameterσwill increase and the parameterξwill decrease when the threshold increases, whereξandσare the parameters in generalized Pareto distribution of Pb.