Implicit 3D Subsurface Structural Modeling by Finite Elements

Summary We introduce a method for implicit 3D geological structural modeling based on finite elements. Implicit modeling on tetrahedral meshes has relied on the constant-gradient regularization operator, since this operator was introduced to the geoscience community over a decade ago. We show that this operator is a finite element discretization of the Laplacian operator in disguise. We then propose a finite element discretization of the Hessian energy, leading to a more appropriate regularization operator for minimizing the curvature of the implicit function on tetrahedral meshes. Special attention is needed at model boundary as boundary conditions are unknown.