Model and algorithm for constructing a horizon surface in the vicinity of a single fault

Oleg Konovalov 

The article addresses the problem of constructing 3D structural models of geological horizons under faulting conditions. The most labor-intensive stage of structural reservoir modeling is the construction of horizon surfaces that must simultaneously fit seismic data and satisfy structural consistency conditions near faults. It is proposed to reduce the problem of recovering the "unreliable" portion of the horizon surface to solving a mixed boundary value problem with a free boundary (BVPFB) in a variational formulation. The sought surface is defined as a minimizer of an energy functional representing a weighted combination of the Dirichlet energy and the area functional. The weight parameter theta allows the geologist to tune the balance between smoothness and realism of the surface shape near the fault. An original edge-based discretization is developed, yielding a linear problem for any value of theta. Algorithms for constructing the initial triangulation with topological cutting and for the consistent movement of the free boundary are proposed. A practical approach to handling self-intersection of the cut edges is described, naturally extending the algorithm to the case of reverse faults. Results of model tests and testing on real geological objects are presented.