Int. Assoc. for Mathematical Geology XI th International Congress Université de Liège - Belgium Liège – September, 3 rd - 8 th 2006 S14-15 Use of Tetrahedral Modelling for Variography and Grade Estimation of a Structurally Deformed Phosphate Deposit I.K. Kapageridis Department of Geotechnology and Environment, Technological Education Institute of Western Macedonia, Greece Corresponding author: ikapa@airlab.teikoz.gr ABSTRACT : The application of geological controls in orebody evaluation and modelling is critical. Stratigraphic orebodies require more accurate location in space and better seam boundary definition. This is achieved by either modelling boundary surfaces of the orebodies or their thickness at specific points in 3D space. Structurally deformed stratigraphic deposits pose a very special problem in variography and grade estimation – it is necessary to bring the locations of samples from the deformed space to the standard XYZ co-ordinate system. This is necessary in order to reconstruct the spatial distribution of grades at the time the deposit was formed and restore the relative positions of samples to their pre-deformed state. Earlier methods of unfolding deposits were based on various geometrical, mathematical or even manual techniques, while more recent methods were based on the use of an unfolded coordinate system for the transformation of every sample and estimation point. The alternative method presented in this paper, Tetrahedral Modelling, can be applied to deposits where mineralization is controlled by a pair of structural surfaces that can be modelled. In tetrahedral modelling the search ellipse is distorted to follow nominated structural surfaces leading to improved estimation accuracy. A case study is presented showing the benefits of this technique. KEYWORDS: grade estimation, variography, unfolding, stratigraphic deposits, tetrahedral modelling. 1. Introduction The dynamics of folding in mineral deposits have been extensively studied in several analyses and simulations. A number of methods for modelling deformations produced by various folding mechanisms have been developed. Earlier methods of unfolding deposits were based on various geometrical, mathematical or even manual techniques such as least squares, cylindrical unfolding or the fitting of splines (Royle 1979, Dagbert et al. 1983, Dowd 1986). Other more recent methods were based on the use of an unfolded coordinate system for the transformation of every sample and every estimation point for variography and grade estimation (Newton 1995). Tetrahedral modelling for variography and grade estimation was developed by Trevor Coulsen in 1995 (Maptek Pty Ltd) and implemented in Maptek’s VULCAN 3D software package. Further improvements to the original algorithm were made by Peter Borovina (Maptek Pty Ltd) in 2002. Tetrahedral modelling is a method of adjusting the search ellipse used in variography and grade estimation to follow the geometrical structure of the deposit by forming a 3D tetrahedral model of the deposit volume. For this model to be generated, the structural surfaces of the deposit need to be modelled as surface triangulations. 2. Modelling of Structural Surfaces Orebody outlines are usually interpreted by geologists from drillhole and development intersections on or near the plane of a cross section. Automated methods for geometrical