Visualization of complex geological structures using 3-D Bézier construction tools

Abstract

Various 3-D visualization methods use structural field data to constrain geological models. One approach is to employ 3-D β-Splines, a class of Bézier curves, to densify point data sets too sparse and clustered for direct spatial interpolation. Bézier curves are implemented to act as construction lines that respect the constraints imposed by structural orientation data. These 3-D construction lines are defined by tangents to local planar features, and the projection of key geologic structures. A method is presented that estimates the local strike and dip of vertices along elevation registered 3-D curvilinear geological features. The local direction cosine estimates derived along the surface traces of geological structures are interpolated, and linearly projected to depth. In regions where subparallel relationships exist between local and regional scale structures it is possible to constrain modeled regional geometry to the field data. The success of any 3-D geological modeling exercise is dependent on the data density, clustering and depth variability of known structural observations, and the geological relationship of local structures to regional bounding surfaces. Ultimately, methodologies to generate geological models from regions of sparse data will need to be able to combine computer aided geometric design (CAGD) tools with constraining software, which respects structural field observations. Several examples are given to emphasize this point.