Modelling the Geometry of Geological Units and its Uncertainty in 3D From Structural Data — The Potential-Field Method

Most 3D geological modelling tools were designed for the needs of the oil industry and are not suited to the variety of situations encountered in other application domains. Moreover, the usual modelling tools are not able to quantify the uncertainty of the geometric models generated. The potential-field method was designed to build 3D geological models from data available in geology and mineral exploration, namely the geological map and a DTM, structural data, borehole data and interpretations of the geologist. This method considers a geological interface as a particular isosurface of a scalar field defined in the 3D space, called a potential field. The interpolation of that field, based on universal cokriging, provides surfaces that honour all the data. Due to the difficulty of inferring the covariance of the potential field, the first implementation of the method used an a priori covariance given by the user. New developments allow this covariance to be identified from the structural data. This makes it possible to associate sensible cokriging standard deviations to the potential-field estimates and to express the uncertainty of the geometric model. Practical implementation issues for producing 3D geological models are presented: how to handle faults, how to honour borehole ends, how to take relationships between several interfaces into account, how to integrate gravimetric and magnetic data. An application to the geological modelling of the Broken Hill district, Australia, is briefly presented.