Groupe d’études et de recherche en analyse des décisions


Multi-Point Geostatistical Simulation Based on a Quadratic Optimization Algorithm


The spatial continuity of lithology and ore grade is one of the key factor for proper mine planning. Traditional geostatistical methods are used for spatial modeling of lithology and ore grades. These methods are based on only two-point statistics, which are insufficient to capture geological heterogeneity. The recently developed multi-point methods are performing well in reproducing the spatial continuity; however, most of these algorithms (mostly pattern-based) are not guaranteed the reproduction of the data statistics. In this paper, we propose a support vector machine (SVM)-based multi-point algorithm which ensures the reproduction of data statistics. The SVM-based algorithms are solved after mapping the data at high dimensional space and then by a quadratic optimization technique which provides a global optimum solution for any problem. The proposed method estimates the conditional cumulative density function (ccdf ) using SVM and the quadratic optimization algorithm. The ccdf is generated by thresholding the pattern data base, which is generated from a training image, and calculating the probability of each threshold class by solving regression problem by support vector machine and quadratic optimization algorithm. The method is validated by simulating conditional and unconditional simulation of categorical and continuous training images. We also compare the method with the snesim and filtersim methods. The results show that our method is performing better than both methods in reproducing the shape of the complex channels. The first- and second-order statistics are well reproduced by the proposed method for all examples.

, 21 pages