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Finite Difference Implicit Structural Modeling of Geological Structures

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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https://hal.univ-lorraine.fr/hal-02953073
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Submitted on : Tuesday, September 29, 2020 - 6:55:43 PM
Last modification on : Friday, February 19, 2021 - 4:22:04 PM
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Modeste Irakarama, Gautier Laurent, Julien Renaudeau, Guillaume Caumon. Finite Difference Implicit Structural Modeling of Geological Structures. Mathematical Geosciences, Springer Verlag, inPress, ⟨10.1007/s11004-020-09887-w⟩. ⟨hal-02953073⟩

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