Explicit Structural Modeling of Geological Horizons Near Fault Networks

Oleg Konovalov 

This article extends the approach of constructing a geological horizon surface near a single tectonic fault to the case of a system of arbitrary, including intersecting, faults. The generalization requires solving four subtasks: formalization of the fault system as a simplicial complex, construction of the modeling domain as a gamma-neighborhood of the cut graph on the triangulation, replacement of retriangulation by mesh deformation, and generalization of the free boundary movement formula to three cases of sub-edge endpoint type combinations. Thanks to the edge-based discretization of the area functional, the problem reduces to independent systems of linear algebraic equations at each iteration — one for each subdomain. Results of testing on real geological objects are presented.