A heuristic approach to structural consistency of a horizon surface with tectonic faults based on Mallet's discrete model

Oleg Konovalov 

The paper addresses the problem of automating the consistency process between reflecting horizon surfaces and the network of tectonic faults in the construction of three-dimensional digital geological models within the explicit (surface-based) approach. The problem is formalized on the basis of Mallet's discrete model (Discrete Smooth Interpolation, DSI). It is shown that the classical formulation with dynamic weak constraints leads to instability of the gradient descent iteration process. A heuristic approach is proposed, based on restricting the class of sought surfaces to vertically co-oriented triangulated surfaces, which allows reducing the three-dimensional problem to a two-dimensional one. A parametric model of topological consistency is developed with fault amplitude as a control parameter, and an algorithm for sequential incorporation of weak control points is proposed, replacing the gradient descent with stable two-dimensional finite element interpolation. Results of testing on real geological models are presented. The work served as the basis for subsequent development of the approach within a variational free-boundary formulation.