Finite Difference Implicit Structural Modeling of Geological Structures
in: Mathematical Geosciences, 53 (785--808)
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.
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BibTeX Reference
@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}
}