A new multiple-point grade estimation method by implicit volterra series

Abstract

Ore grade estimation plays an important role in recoverable resource calculations and mining projects. Classic geostatistical estimation methods are based on two-point statistics and cannot make use of multiple-point and higher-order statistics of the data. Very few studies have been conducted on determination of the possible effects of these features on the results of ore grade estimation. In view of this, the present study introduced a new multiple-point interpolation method based on the implicit Volterra series. In this regard, least square support vector machines (LS-SVM) were used to implicitly estimate the Volterra series coefficients. Regularized risk minimization in the LS-SVM can increase generalization of the Volterra series and reduce sensitivity of these series to data noise. Also, conjugate gradient iterative algorithm was used to solve the linear equations of the implicit Volterra series estimation problem. This sets the stage to solve large-scale problems for Volterra series. With the use of Volterra series, multiple-point multiplicative interactions of spatial data can be used in the ore grade estimation process. In this study, multiple point spatial templates were used to extract multiplicative features of the input data. Therefore, an algorithm was presented to search the 3D space by these templates. The applicability of the regularized implicit Volterra series in capturing the higher-order features of the spatial data is successfully evaluated in a synthetic example. Also, the generalization ability of the introduced method is successfully examined in a synthetic 2D example and one real 3D mining example at the Sarcheshmeh porphyry copper deposit. The results revealed that the introduced multiple-point method could present better results than the ordinary kriging method.