The Use of Fractal Geometry to Model the Spatial Continuity of Gold Grades

Presently, orebody modelling consists basically of fitting a mathematical model to represent spatially a certain geological variable, generally grade. An orebody model is constructed from a set of sample data obtained from various locations in the orebody, thus it is only one form of representation of the true phenomena. Checking the compatibility of the data with the modelling procedure is the most important factor when assessing confidence in the orebody model. The level of confidence in the model will depend on the adequacy of the data set and the validity of the basic assumption required by the modelling method. Fractal geometry is one way of modelling the spatial distribution of a geological variable in an orebody geometry. Fractals can be used to interpolate the Z(x) geological variable at unsampled sites. The concepts of self similarity and self affinity that form the basic assumption of fractal geometry theory which areinvestigated. The population distribution of the geological variable in question must be examined to determine the appropriateness of both fractal geometry and geostatistical modelling methods. The selection of the most appropriate method depends on the available data. A researcher or a practitioner needs to understand the strengths and limitations of the various modelling methods before choosing the most appropriate method. This study investigates the fractal properties of grade distribution using the variogram and some proposed variations as techniques to measure the fractalness. The aim is to assess applicability of fractal geometry theory to modelling ore grade distribution in a deposit. A comparison of the results demonstrates the methods which better capture the spatial behaviour of the variable under study.