Finite difference implicit structural modeling of geological structures

in: 2018 Ring Meeting, ASGA

Abstract

We introduce a new method for implicit structural modeling. The main development in this paper are the new regularization operators we propose by extending inherent properties of the classic 1D discrete second derivative operator to higher dimensions. The proposed regularization operators discretize very naturally on the Cartesian grid using finite differences, owing to the highly sym- metric nature of the Cartesian grid. Furthermore, the proposed regularization operators do not require any spacial 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

@INPROCEEDINGS{,
    author = { Irakarama, Modeste and Laurent, Gautier and Renaudeau, Julien and Caumon, Guillaume },
     title = { Finite difference implicit structural modeling of geological structures },
 booktitle = { 2018 Ring Meeting },
      year = { 2018 },
 publisher = { ASGA },
  abstract = { We introduce a new method for implicit structural modeling. The main development in this paper
are the new regularization operators we propose by extending inherent properties of the classic 1D
discrete second derivative operator to higher dimensions. The proposed regularization operators
discretize very naturally on the Cartesian grid using finite differences, owing to the highly sym-
metric nature of the Cartesian grid. Furthermore, the proposed regularization operators do not
require any spacial 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. }
}