3D estimation of variables with complexity in cross-correlation structures

摘要

Linear interpolation of geo-related variables is important to different aspects of mining engineering such as long and short-term mine planning (Verly, 2005; Rossi and Deutsch, 2014). The ore deposit description attained from spatial modeling of blast hole datasets has been widely taken into account, particularly, for short-term mine design and grade control, so as to define the ultimate destination of a mined block (Davis, 1992). It is approved in practice that making the wrong decision leads to losing a huge amount of money for choosing the destination of a mined block. In the case of complex ore deposits, the issue of estimation of variables in the region is questionable and somehow tedious. Due to this fact, modeling those complications in the co-spatial behavior of the grades in multi-element deposits prompts one to employ enhanced geostatistical techniques. Traditional approaches of this purpose such as polygon, inverse distance weighted and even (co)-kriging approaches (Chiles and Delfiner, 2012; Wackernagel, 2003), are incapable of reproducing those complexities such as non-linearity, heteroscedasticity and geological constraint that frequently exist among the variables of interest in those deposits. Another difficulty in employing those linear interpolations in grade estimation is smoothing effect, in which the estimated grades are over and under estimated (Chiles and Delfiner, 2012; Goovaerts, 1997; Journel and Huijbregts, 1978).