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Iterative Thickness Regularization of Stratigraphic Layers in Discrete Implicit Modeling

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Abstract

Discrete implicit modeling consists in representing structural surfaces as isovalues of three-dimensional piecewise linear scalar fields, which are interpolated from available data points. Data are expressed as local constraints that can enforce the value of the scalar fields as well as their gradients. This paper illustrates some limitations of published discrete implicit methods, related to the difficulty of controlling the norm of scalar field gradient and its evolution over the interpolated domain. It is shown that important artifacts may arise due to the intrinsic dependence between variations in the norm and the direction of the scalar field gradient, from one element to its neighbors. Evidence that these artifacts are related to mesh facet direction with respect to gradient direction are given. The artifacts lead to rapid and uncontrolled variations of thickness that may induce erroneous interpolations. This paper proposes two original approaches to overcome these problems. The first one consists in iteratively adjusting the norm of scalar field gradients in the direction obtained after previous iterations. The second solution consists in optimizing the mesh used by the interpolation. This requires finding appropriate mesh facet orientation with respect to scalar field gradient. These methods demonstrate that the results of discrete implicit surface interpolation can be improved and call for further development of available interpolation schemes.

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Acknowledgments

The author would like to gratefully thank anonymous reviewers, as well as Professor Guillaume Caumon and Lachlan Grose, for their very constructive comments and corrections, which helped improve this paper. This work was initiated at Monash University with the Australian Research Council Discovery Grant DP110102531 and further developed at GeoRessources (http://ring.georessources.univ-lorraine.fr/) in the framework of the “Investissements d’avenir” Labex RESSOURCES21 (ANR-10-LABX-21).

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  1. Gautier Laurent

    Present address: GeoRessources (UMR 7359), Université de Lorraine-ENSG, CNRS, CREGU, Campus Brabois, TSA 70605, 54518, Vandoeuvre-lès-Nancy Cedex, France

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  1. School of Earth, Atmosphere and Environment, Monash University, PO Box 28E, Melbourne, VIC, Australia

    Gautier Laurent

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Laurent, G. Iterative Thickness Regularization of Stratigraphic Layers in Discrete Implicit Modeling. Math Geosci 48, 811–833 (2016). https://doi.org/10.1007/s11004-016-9637-y

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