Finite Element Implicit Subsurface Structural Modeling

Modeste Irakarama and Morgan Thierry-Coudon and Mustapha Zakari and Pierre Anquez and Guillaume Caumon. ( 2021 )
in: 2021 RING Meeting, ASGA

Abstract

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

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BibTeX Reference

@INPROCEEDINGS{IRAKARAMA_RM2021,
    author = { Irakarama, Modeste and Thierry-Coudon, Morgan and Zakari, Mustapha and Anquez, Pierre and Caumon, Guillaume },
     title = { Finite Element Implicit Subsurface Structural Modeling },
 booktitle = { 2021 RING Meeting },
      year = { 2021 },
 publisher = { ASGA },
  abstract = { We introduce a method for 3D implicit geological structural modeling based on a finite element discretization of two regularization operators: the Laplacian and the Hessian energies. This scheme is believed to offer some geometrical flexibility as it is readily implemented on both structured and unstructured grids. While implicit modeling on unstructured grids is not new, methods based on finite elements have received little attention. The finite element method is routinely used to solve boundary value problems. However, because boundary conditions are typically unknown in implicit subsurface structural modeling, the traditional finite element method requires some adjustments. To this end, we present boundary free discretizations of the Laplacian and Hessian energies that do not assume vanishing Neumann boundary conditions, thereby eliminating the boundary artifacts usually associated with that assumption. We argue that while an appropriate discretization of the Laplacian can be used to minimize the Hessian on triangulated meshes, it may fail to do so on tetrahedral meshes. }
}