Finite Difference Implicit Structural Modeling of Geological Structures

@article{irakarama:hal-02953073,
 abstract = {We introduce a new method for implicit structural modeling. The main developments in this paper are the new regularization operators we propose by extending inherent properties of the classic one-dimensional discrete second derivative operator to higher dimensions. The proposed regularization operators dis-cretize naturally on the Cartesian grid using finite differences, owing to the highly symmetric nature of the Cartesian grid. Furthermore, the proposed regulariza-tion operators do not require any special treatment on boundary nodes, and their generalization to higher dimensions is straightforward. As a result, the proposed method has the advantage of being simple to implement. Numerical examples show that the proposed method is robust and numerically efficient.},
 author = {Irakarama, Modeste and Laurent, Gautier and Renaudeau, Julien and Caumon, Guillaume},
 doi = {10.1007/s11004-020-09887-w},
 hal_id = {hal-02953073},
 hal_version = {v1},
 journal = {{Mathematical Geosciences}},
 keywords = {Implicit modeling ; Structural modeling ; Regularization operators ; Finite differences ; Interpolation},
 pages = {785--808},
 pdf = {https://hal.univ-lorraine.fr/hal-02953073v1/file/IrakaramaMG2020Author.pdf},
 publisher = {{Springer Verlag}},
 title = {{Finite Difference Implicit Structural Modeling of Geological Structures}},
 url = {https://hal.univ-lorraine.fr/hal-02953073},
 volume = {53},
 year = {2021}
}