Towards continuous equations behind implicit stratigraphic modeling Implicit stratigraphic modeling problem modeling inputs

Julien Renaudeau and Emmanuel Malvesin and Frantz Maerten and Guillaume Caumon. ( 2017 )
in: 2017 Ring Meeting, pages 1--15, ASGA

Abstract

Structural modeling is the science of interpreting geological structures originated from natural phenomena into numerical models to support estimations and predictions. A widespread way to implement this principle is to approximate the natural geometries by the smoothest possible models. Two existing implicit methods stand as references: the Potential Field Method and the Discrete Smooth Interpolation. This article demonstrates that the assumption of smoothness is common between the two meth- ods and represents the minimization of the bending energy under data constraints. Whether this statement is immediate when using the Potential Field Method defined with Thin Plate Splines as interpolators, it supposes to write the continuous equations for the Discrete Smooth Interpolation. By developping this theoretical background, a general formulation of smoothed implicit modeling is revealed.

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BibTeX Reference

@INPROCEEDINGS{Renaudeau2017a,
    author = { Renaudeau, Julien and Malvesin, Emmanuel and Maerten, Frantz and Caumon, Guillaume },
     title = { Towards continuous equations behind implicit stratigraphic modeling Implicit stratigraphic modeling problem modeling inputs },
 booktitle = { 2017 Ring Meeting },
      year = { 2017 },
     pages = { 1--15 },
 publisher = { ASGA },
  abstract = { Structural modeling is the science of interpreting geological structures originated from natural phenomena into numerical models to support estimations and predictions. A widespread way to implement this principle is to approximate the natural geometries by the smoothest possible models. Two existing implicit methods stand as references: the Potential Field Method and the Discrete Smooth Interpolation. This article demonstrates that the assumption of smoothness is common between the two meth- ods and represents the minimization of the bending energy under data constraints. Whether this statement is immediate when using the Potential Field Method defined with Thin Plate Splines as interpolators, it supposes to write the continuous equations for the Discrete Smooth Interpolation. By developping this theoretical background, a general formulation of smoothed implicit modeling is revealed. }
}