Finite Element Implicit 3D Subsurface Structural Modeling

We introduce a method for 3D implicit geological structural modeling from sparse sample points, where several conformable surfaces are represented by one single scalar field. Laplacian and Hessian regularization energies discretized on tetrahedral mesh using finite elements. This scheme is believed to offer some geometrical flexibility as it readily implemented both structured unstructured grids. While grids not new, methods based elements have received little attention. The element routinely used solve boundary value problems. However, because conditions typically unknown in subsurface modeling, the traditional requires adjustments. To this end, we present free discretizations of that do assume vanishing Neumann conditions, thereby eliminating artifacts usually associated with assumption. Furthermore, argue while an appropriate discretization can be minimize curvature function triangulated meshes, may fail so meshes.