Implicit structural modeling by minimization of the bending energy with moving least squares functions

Julien Renaudeau and Emmanuel Malvesin and Frantz Maerten and Guillaume Caumon. ( 2018 )
in: , ASGA

Abstract

Structural modeling algorithms construct geological structures from field data and interpreta- tions. The aimed models should represent natural objects while fitting available data points. We propose a meshless implicit modeling method using locally defined shape functions. The continuous bending energy is minimized to interpolate between data points and approximate natural structures. This method solves a sparse problem without relying on a complex mesh. By using meshless optic techniques, only a very few modifications are performed to handle discontinuities such as faults and unconformities. The method is illustrated on a two-dimensional model with folds, faults and an unconformity. This model is then modified to show the ability of the method to handle sparsity, noise and different reliabilities in the data. Key parameters of the meshless shape functions and the pertinence of the bending energy for structural modeling applications are discussed. From these studies, predefined values are deduced for each parameter to generate automatically good quality models in efficient computing times.

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BibTeX Reference

@INPROCEEDINGS{,
    author = { Renaudeau, Julien and Malvesin, Emmanuel and Maerten, Frantz and Caumon, Guillaume },
     title = { Implicit structural modeling by minimization of the bending energy with moving least squares functions },
      year = { 2018 },
 publisher = { ASGA },
  abstract = { Structural modeling algorithms construct geological structures from field data and interpreta-
tions. The aimed models should represent natural objects while fitting available data points.
We propose a meshless implicit modeling method using locally defined shape functions. The
continuous bending energy is minimized to interpolate between data points and approximate natural
structures. This method solves a sparse problem without relying on a complex mesh. By using
meshless optic techniques, only a very few modifications are performed to handle discontinuities
such as faults and unconformities.
The method is illustrated on a two-dimensional model with folds, faults and an unconformity.
This model is then modified to show the ability of the method to handle sparsity, noise and different
reliabilities in the data. Key parameters of the meshless shape functions and the pertinence of the
bending energy for structural modeling applications are discussed. From these studies, predefined
values are deduced for each parameter to generate automatically good quality models in efficient
computing times. }
}