Iterative Thickness Regularization of Stratigraphic Layers in Discrete Implicit Modeling

Gautier Laurent. ( 2016 )
in: Mathematical Geosciences, 48:7 (811--833)

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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BibTeX Reference

@ARTICLE{,
    author = { Laurent, Gautier },
     title = { Iterative Thickness Regularization of Stratigraphic Layers in Discrete Implicit Modeling },
   journal = { Mathematical Geosciences },
    volume = { 48 },
    number = { 7 },
      year = { 2016 },
     pages = { 811--833 },
       url = { http://rdcu.be/nezN },
       doi = { 10.1007/s11004-016-9637-y },
  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. }
}