Skip to Main content Skip to Navigation

Formulation continue du problème de modélisation implicite de structures géologiques discrétisée avec des méthodes de réduction de maillage

Abstract : Implicit structural modeling consists in approximating geological structures into a numerical model for visualization, estimations, and predictions. It uses numerical data interpreted from the field to construct a volumetric function on the domain of study that represents the geology. The function must fit the observations, interpolate in between, and extrapolate where data are missing while honoring the geological concepts. Current methods support this interpolation either with the data themselves or using a mesh. Then, the modeling problem is posed depending on these discretizations: performing a dual kriging between data points or defining a roughness criterion on the mesh elements. In this thesis, we propose a continuous formulation of implicit structural modeling as a minimization of a sum of generic functionals. The data constraints are enforced by discrete functionals, and the interpolation is controlled by continuous functionals. This approach enables to (i) develop links between the existing methods, (ii) suggest new discretizations of the same modeling problem, and (iii) modify the minimization problem to fit specific geological issues without any dependency on the discretization. Another focus of this thesis is the efficient handling of discontinuities, such as faults and unconformities. Existing methods require either to define volumetric zones with complex geometries, or to mesh volumes with conformal elements to the discontinuity surfaces. We show, by investigating local meshless functions and mesh reduction concepts, that it is possible to reduce the constraints related to the discontinuities while performing the interpolation. Two discretizations of the minimization problem are then suggested: one using the moving least squares functions with optic criteria to handle discontinuities, and the other using the finite element method functions with the concept of ghost nodes for the discontinuities. A sensitivity analysis and a comparison study of both methods are performed in 2D, with some examples in 3D. The developed methods in this thesis prove to have a great impact on computational efficiency and on handling complex geological settings. For instance, it is shown that the minimization problem provides the means to manage under-sampled fold structures and thickness variations in the layers. Other applications are also presented such as salt envelope surface modeling and mechanical restoration.
Complete list of metadata

Cited literature [301 references]  Display  Hide  Download
Contributor : Thèses Ul <>
Submitted on : Thursday, October 24, 2019 - 12:21:09 PM
Last modification on : Wednesday, April 28, 2021 - 3:34:16 AM
Long-term archiving on: : Saturday, January 25, 2020 - 2:54:43 PM


Files produced by the author(s)


  • HAL Id : tel-02331238, version 1


Julien Renaudeau. Formulation continue du problème de modélisation implicite de structures géologiques discrétisée avec des méthodes de réduction de maillage. Géologie appliquée. Université de Lorraine, 2019. Français. ⟨NNT : 2019LORR0075⟩. ⟨tel-02331238⟩



Record views


Files downloads