Bayesian and fuzzy kriging interpolation techniques for spatial estimation in mining field

Abstract

The focus of this research is in the area of spatial estimation. Such a study is very important in order to improve the spatial prediction performance. Many techniques of prediction that are based on the regionalized variables, and the surface trend change from linear to quadratic or cubic that produces inaccurate results in the prediction process. In this thesis, Bayesian and fuzzy kriging methods are suggested to solve the problem of uncertainty, which requires obtaining a minimum error in the prediction process. This study aims to improve the mixed approaches among methods of spatial prediction that are used for evaluation of prediction. The study also finds the performance of variation interpolation methods of minerals needed to develop the relationship between Bayesian techniques and fuzzy kriging and apply the results for further modeling a spatial relationship. This spatial prediction assumes stationary property. The findings of this study are mathematical models of covariance functions. The variogram and cross variogram functions are computed for all compass directions for the phenomena under the study and its parameters are estimated. Another aspect is to obtain Bayesian predictor, kriging predictor, and Bayesian kriging variance which represent the minimum variance of prediction. In addition, the constraints weights of linear prediction were computed. The practical side of this study includes the applications of the Bayesian and fuzzy kriging techniques on real spatial data with their locations in the mining fields of Australia, Canada, and Colombia. All the computations were carried out by using Matlab software. In conclusion, this study uses two different methods (Bayesian and fuzzy kriging techniques) for incorporating the spatial autocorrelation in order to improve the accuracy of uncertainty and estimation with minimum error. The approach combines more than one prediction methods to determine a model which is based on a cross validation that satisfies the best optimal prediction.