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. ( 2019 )
in: Mathematical Geosciences

Abstract

In this paper, an implicit structural modeling method using locally defined moving least squares shape functions is proposed. The continuous bending energy is minimized to interpolate between data points and approximate geological structures. This method solves a sparse problem without relying on a complex mesh. Discontinuities such as faults and unconformities are handled with minor modifications of the method using meshless optic principles. 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 shape functions and the pertinence of the bending energy for structural modeling applications are discussed. The predefined values deduced from these studies for each parameter of the method can also be used to construct other models.

Download / Links

BibTeX Reference

@ARTICLE{Renaudeau2019MG,
    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}} },
     month = { "mar" },
   journal = { Mathematical Geosciences },
      year = { 2019 },
      issn = { 1874-8961, 1874-8953 },
       doi = { 10.1007/s11004-019-09789-6 },
  abstract = { In this paper, an implicit structural modeling method using locally defined moving least squares shape functions is proposed. The continuous bending energy is minimized to interpolate between data points and approximate geological structures. This method solves a sparse problem without relying on a complex mesh. Discontinuities such as faults and unconformities are handled with minor modifications of the method using meshless optic principles. 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 shape functions and the pertinence of the bending energy for structural modeling applications are discussed. The predefined values deduced from these studies for each parameter of the method can also be used to construct other models. }
}