Multi-point Geostatistical Simulation by Applying Quadratic Optimization Algorithm

Abstract

The spatial continuity of lithology/ore grade is one of the key factor for proper mine planning. The pixel-based geostatistical methods are based on only two-point statistics, which are insufficient to capture geological heterogeneity. The multi-point statistical methods are lack a consistent statistical model specification. We propose a quadratic optimization based methods for lithology and ore grade modeling. The proposed method defines a statistical model by efficient estimation of conditional cumulative density function (ccdf) using quadratic optimization algorithm. The ccdf is generated by thresholding the pattern data base, which is generated from training image, and calculating the probability of each threshold class by solving regression problem of support vector machine using convex optimization. The algorithm is validated by simulating conditional and unconditional simulation of categorical as well as continuous training image. We also compare our proposed method with the snesim and filtersim algorithm. The results show that our proposed method is performing better than both the algorithm to reproduce the shape of the complex channels. The first- and second-order statistics are well reproduced by the proposed method for all examples.