Subdivide and Conquer: Adapting Non-Manifold Subdivision Surfaces Method to Represent and Approximate Complex Geological and Reservoir Structures

Abstract

Computer graphics have gradually developed practical techniques to address models with the complex topology, in particular, by parametric surface-based modeling approach. Also, geologists have used this approach because it provides significant gains over grid-based modeling (e.g., implicit modeling) by using grid-free surfaces. However, since this approach originates from computer graphics, not all the capacities and limitations of this approach have been considered and investigated in geological modeling.With this aim in mind, this paper investigates surface-based geological modeling through both geological and computer graphics approaches. NURBS (Non-Uniform Rational B-Splines) and subdivision surfaces, as two main parametric surface-based modeling methods, are investigated, and the strengths and weaknesses of both are compared. Although NURBS surfaces have been used in geological modeling, subdivision surfaces as a standard method in the animation and gaming industries, have received little attention in geological modeling. Subdivision surfaces support arbitrary topologies and watertight modeling, which are quite useful for complex geological modeling.Investigating subdivision schemes with semi-sharp creases is an important part of this paper. Semi-sharp creases show the resistance of a mesh structure to the subdivision procedure, which provides a unique method for complex geological and reservoir modeling. Moreover, non-manifold topologies, as a challenging concept in complex geological and reservoir modeling, are explored, and the subdivision surfaces compatible with non-manifold topology are declared.Finally, the approximation of complex geological structures by the non-manifold subdivision surface method is investigated with two different case studies. The approximated mesh is a simplified and less complex version of the original mesh while the important details of the original mesh are preserved. It not only significantly reduces the cost of modeling and simulation (by reducing the number of vertices to less Preprint-Moulaeifard et al. (Submitted to Mathematical Geoscince) 3 than 5% of the number of vertices of the original mesh) but also, has features such as being watertight, smooth, topologically identical to the main original mesh and controllable with few control points. Keywords Surface-based modeling. Subdivision surfaces. Non-manifold topology. Approximation of geological structures. Grid free. NURBS.