Implicit 3D Subsurface Structural Modeling by Finite Elements

@inproceedings{irakarama:hal-03980872,
 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.},
 address = {Amsterdam, Netherlands},
 author = {Irakarama, M. and Thierry-Coudon, M. and Zakari, M. and Anquez, P. and Caumon, G.},
 booktitle = {{82nd EAGE Annual Conference \& Exhibition}},
 doi = {10.3997/2214-4609.202113091},
 hal_id = {hal-03980872},
 hal_version = {v1},
 month = {October},
 pages = {1-5},
 publisher = {{European Association of Geoscientists \& Engineers}},
 title = {{Implicit 3D Subsurface Structural Modeling by Finite Elements}},
 url = {https://hal.science/hal-03980872},
 year = {2021}
}