Application of geometric probability to design exploration grid of mineral deposits, case study: porphyry copper index located in the south-west of Kerman

In present research, theoretical and applied concepts of geometric probability have been studied ‎and the relationships of geometric probability have been presented to determine the probability of ‎intersection of various geometric shapes with diverse types of grids. In this regard mineral deposits ‎based on defining the shape ratio parameter as ratio of breadth to length of the deposit (‎ ‎) ‎were classified to 3 types of linear, circular and elliptical shape. The detection of mineral deposit is ‎possible under condition that the deposit is intersected at least once by the lines of exploration grid. ‎ Arrangement of accurate and optimum location of exploration works entitled designing of ‎exploration grid is one of the essential requirements in all stages of mineral deposits exploration. ‎Designing the optimum exploration grid is the most important as well as critical stage for ‎exploration of mineral deposits which is carried out on the basis of geological conditions and ‎characteristics of deposit and the amount and type of available exploratory information. The type, ‎shape, dimension of cells and orientation of the grid respect to the estimated direction of the ‎deposit, perform the geometry of exploration grid. Since the geometric parameters of mineral ‎deposits are stochastic, exploration of mineral deposits is also stochastic and always associated with ‎uncertainty and some risk. As a result from this view point the exploration problem is similar to the ‎geometric probability problems.‎ Methodology and Approaches: According to conventional exploration methods of mineral deposits by various exploration grids as ‎well as similarity of mineral deposits with the usual geometric shapes, designing the optimum ‎exploration grid for each type of deposit was presented based on existing relationships in geometric ‎probability. In this context as a case study, designing the optimum exploration grid for two copper ‎indices detected by remote sensing operation located in the south-west of Kerman, one with ‎approximately linear structure (with a shape ratio of 0.14) and the other one with approximately ‎circular shape, was carried out using the geometric probability.‎ Results and Conclusions: Due to the similarity of exploration of mineral deposits to geometric probability problems in this ‎research, existing relationships in geometric probabilities were used to determine the probability of ‎detection by the various exploration grids. By employing the mentioned approach, the size of ‎optimum exploration grid was calculated for each index considering minimum exploration ‎probability, 0.5 and favorite exploration probability, 0.95 for both randomly oriented and oriented ‎situations.‎