Implicit modelling of geological structures: a Cartesian grid method handling discontinuities with ghost points

Julien Renaudeau and Modeste Irakarama and Gautier Laurent and Frantz Maerten and Guillaume Caumon. ( 2018 )
in: 2018 Ring Meeting, ASGA

Abstract

In geology, implicit structural modelling constructs the geometry of geological structures (e.g. layers) by interpolating between sparse field data. A model is represented by a volumetric scalar field which is discontinuous on structural discontinuities such as faults or stratigraphic unconformities. The management of such discontinuities may involve boolean operations on several scalar fields or the creation of conformal meshes. Instead, we propose a ghost cell technique for the cartesian grid together with a set of relations between the ghost points, the regular nodes, and the discontinuities. Consequently, poor quality meshes are avoided and only the resolution of the grid has an impact on the solution. The modelling problem is posed as a least squares minimization of a bending energy penalization on data mismatch functions and approximated by finite difference. As all relationships in the grid are implicitly defined, except close to the discontinuities, this algorithm is computationally efficient. We provide some benchmarks of the method on two-dimensional examples with folds, faults, and erosions.

Download / Links

BibTeX Reference

@INPROCEEDINGS{,
    author = { Renaudeau, Julien and Irakarama, Modeste and Laurent, Gautier and Maerten, Frantz and Caumon, Guillaume },
     title = { Implicit modelling of geological structures: a Cartesian grid method handling discontinuities with ghost points },
 booktitle = { 2018 Ring Meeting },
      year = { 2018 },
 publisher = { ASGA },
  abstract = { In geology, implicit structural modelling constructs the geometry of geological structures (e.g. layers) by interpolating between sparse field data. A model is represented by a volumetric scalar field which is discontinuous on structural discontinuities such as faults or stratigraphic unconformities. The management of such discontinuities may involve boolean operations on several scalar fields or the creation of conformal meshes. Instead, we propose a ghost cell technique for the cartesian grid together with a set of relations between the ghost points, the regular nodes, and the discontinuities. Consequently, poor quality meshes are avoided and only the resolution of the grid has an impact on the solution. The modelling problem is posed as a least squares minimization of a bending energy penalization on data mismatch functions and approximated by finite difference. As all relationships in the grid are implicitly defined, except close to the discontinuities, this algorithm is computationally efficient. We provide some benchmarks of the method on two-dimensional examples with folds, faults, and erosions. }
}