كاربرد احتمالات هندسي در طراحي شبكه هاي اكتشاف كانسارهاي معدني، مطالعه موردي: انديس مس پورفيري واقع در جنوب غرب كرمان

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

در پژوهش حاضر مفاهيم نظري و كاربردي احتمالات هندسي، مورد بررسي قرار گرفته و روابط احتمالات هندسي براي تعيين احتمال تقاطع اشكال هندسي گوناگون با انواع شبكه­ هاي مختلف، ارائه شده است. از آنجايي ­كه پارامترهاي هندسي كانسارهاي معدني داراي ماهيت احتمال ­پذير هستند، اكتشاف كانسارهاي معدني نيز ماهيت احتمال ­پذير داشته و همواره با عدم قطعيت و مقداري ريسك همراه است. در نتيجه از اين نظر مسئله اكتشاف با مسائل احتمالات هندسي شباهت دارد. با توجه به روش ­هاي متداول اكتشاف كانسارهاي معدني توسط شبكه­ هاي اكتشافي مختلف و تشابه كانسارهاي معدني با اشكال هندسي معمول، نحوه طراحي شبكه اكتشاف بهينه براي هر نوع كانسار، براساس روابط موجود در احتمالات هندسي، ارائه شد. در اين راستا به عنوان يك مطالعه ميداني طراحي شبكه اكتشاف بهينه با استفاده از احتمالات هندسي براي دو انديس مس شناسايي شده با عمليات دورسنجي واقع در جنوب غرب كرمان يكي با ساختار تقريباً خطي و ديگري با ساختار تقريباً دايره‌اي، صورت گرفت. براي اين منظور ابعاد شبكه اكتشاف بهينه براي هر انديس با در نظر گرفتن كم‌ترين مقدار احتمال كشف يا 0/5 و احتمال كشف مطلوب يا 0/95 در دو حالت جهت­ يافتگي تصادفي و با جهت ­يافتگي مشخص، محاسبه شد.

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. Introduction 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. That 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, and dimensions of cells and orientation of the grid with 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 is 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.