Economics of the Mineral Industry - A Probability Model of Mineral Wealth

The construction of a model to associate probability of occurrence of some measure of mineral wealth with the geology for each subdivision (cell) of the area is postulated. The questions (1) are the observations made in reconnaissance geology sufficiently related to mineral wealth to distinguish the cells of high value from those of low value, and (2) can this geology be related mathematically to mineral wealth and probability are answered in a case study of 97,000 square miles in Arizona and New Mexico. Measurements on mineral wealth and geologic variables of 243 cells were made. The geologic variables, valued in counts, percentages and lengths, quantified the theoretical concepts of the model. It was found that multiple discriminant analysis and classification analysis by Bayesian statistics and multivariate normal probability function constitute a two-phase probability model that associates probabilities with geologic information and mineral wealth. The cells of explored area must be allotted the value class indicated by their cumulative production and estimate reserves (given well-defined geological relationships in a mineral wealth area), and a discriminant and classification analysis must be performed in which probabilities of the cell belonging to each of the value groups are generated as a function of the geologic variables. This determines whether high value cells can be distinguished from low value cells by their geology as well as indicating those cells misclassified by the model into a higher value group than warranted by their known mineral wealth. The second use of the model is for extrapolation. It is demonstrated how geologic information on an explored area can be utilized in guiding exploration in an unexplored area. Exploration decisions can be predicted on explicitly determined measures of uncertainty (the probabilities). SUMMARY This study postulates the construction of a model to associate probability of occurrence of some measure of mineral wealth with the geology for each subdivision (cell) of the area. Such a model will distinguish those cells deserving further exploration on the basis of their geology: The basic postulates of this study are as follows: v = Q(R,S,F,A) P(V) = G(R,S,F,A,V), where V = a measure of mineral wealth P(V) = the probability of occurrence of V R = age and type of rock F = rock fracturing A =age of igneous activity and contact relationships. There are really two questions to be answered: 1) are the observations made in reconnaissance geology sufficiently related to mineral wealth to distinguish the cells of high value from those of low value, and 2) can this geology be related mathematically to mineral wealth and probability? In order to answer these questions, an area of about 97,000 square miles situated chiefly in Arizona and New Mexico was selected as a case study. This case study area was divided into 243 cells, each 20 miles square, and measurements were made on mineral wealth and geologic variables. Crude geologic variables valued in counts, percentages and lengths are constructed to reflect the above postulated variables. These measurement variables thus provide quantified values defining the theoretical concepts of the model. It was found that multiple discriminant analysis and classification analysis by Bayesian statistics and the multivariate normal probability function constitute a two-phase probability model that associates probabilities with geologic information and mineral wealth. Given the availability of an area that is well explored and upon which the relationships of mineral wealth to geology can be adequately defined, there are two ways in which the analysis outlined in this paper can prove beneficial. First, the cells of the explored area must be allotted the value class indicated by their cumulative production and estimated reserves, and a discriminant and classification analysis must be performed in which probabilities of the cell belonging to each of the value groups are generated as a function of the geologic variables. Such an analysis determines whether cells of high