Optimal construction and visualisation of geological structures

Abstract

The authors propose an optimal solution to the problem of generating three-dimensional (3D) geological structures from sectional contours, which, in turn, are generated from sparse information irregularly located in the 3D space. The problem is to construct a 3D orebody, or a topographical surface, from a few planar feature contours defined on a certain number of cross-sections, or more generally any sectional planes, intersecting the unknown structure. The planar contours on the sections are assumed to be simple, closed, concave or convex, polygons for orebodies or polylines for topographical surfaces. The problem is reduced to constructing a sequence of partial approximations, each of which connects two planar contours on two adjacent planes. In the method described here the authors use triangular tiles to construct orebody and topography surfaces and describe an adaptation of the graph theory approach. The authors extend the original algorithms to the more general cases of multiple open and closed curves on sections and to non-parallel sections and non-planar applications (arbitrary 3D contours). Automatic generation of orebody shapes by volume rendering is also presented and compared to the optimal solution generated by the surface-based rendering technique. In a more general context, the algorithm can be used for optimal surface construction between any two arbitrary contours (either planar or non-planar). The C++ computer code for the implementation of the algorithms is described and is available from the IAMG server.