Implicit {3D} {Subsurface} {Structural} {Modeling} by {Finite} {Elements}

Modeste Irakarama and Morgan Thierry-Coudon and Mustapha Zakari and Pierre Anquez and Guillaume Caumon. ( 2021 )
in: 82nd {EAGE} {Annual} {Conference} \& {Exhibition}, pages 1--5, European Association of Geoscientists \& Engineers

Abstract

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.

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BibTeX Reference

@INPROCEEDINGS{Irakarama20218EACE,
    author = { Irakarama, Modeste and Thierry-Coudon, Morgan and Zakari, Mustapha and Anquez, Pierre and Caumon, Guillaume },
     title = { Implicit {3D} {Subsurface} {Structural} {Modeling} by {Finite} {Elements} },
 booktitle = { 82nd {EAGE} {Annual} {Conference} \& {Exhibition} },
      year = { 2021 },
     pages = { 1--5 },
 publisher = { European Association of Geoscientists \& Engineers },
   address = { Amsterdam, The Netherlands, },
       url = { https://www.earthdoc.org/content/papers/10.3997/2214-4609.202113091 },
       doi = { 10.3997/2214-4609.202113091 },
  abstract = { 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. }
}