Mathematical Geosciences

, Volume 45, Issue 3, pp 255–276 | Cite as

A Numerical Framework for Modeling Folds in Structural Geology

  • Øyvind Hjelle
  • Steen A. Petersen
  • Are Magnus Bruaset


A numerical framework for modeling folds in structural geology is presented. This framework is based on a novel and recently published Hamilton–Jacobi formulation by which a continuum of layer boundaries of a fold is modeled as a propagating front. All the fold classes from the classical literature (parallel folds, similar folds, and other fold types with convergent and divergent dip isogons) are modeled in two and three dimensions as continua defined on a finite difference grid. The propagating front describing the fold geometry is governed by a static Hamilton–Jacobi equation, which is discretized by upwind finite differences and a dynamic stencil construction. This forms the basis of numerical solution by finite difference solvers such as fast marching and fast sweeping methods. A new robust and accurate scheme for initialization of finite difference solvers for the static Hamilton–Jacobi equation is also derived. The framework has been integrated in simulation software, and a numerical example is presented based on seismic data collected from the Karama Block in the North Makassar Strait outside Sulawesi.


Folding Dip isogons Front propagation Hamilton–Jacobi Anisotropy Upwind finite differences Fast marching 



The authors thank TGS for their permission to let us use the seismic profile from Sulawesi in the numerical example section. We thank Hans Petter Langtangen and Tor Gillberg for helpful discussions, and we also thank the reviewers for useful comments and suggestions that have significantly improved the paper. This work was financed by Statoil ASA.


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Copyright information

© International Association for Mathematical Geosciences 2013

Authors and Affiliations

  • Øyvind Hjelle
    • 1
  • Steen A. Petersen
    • 2
  • Are Magnus Bruaset
    • 3
    • 4
  1. 1.Kalkulo ASSimula Research LaboratoryLysakerNorway
  2. 2.Statoil ASABergenNorway
  3. 3.Simula Research LaboratoryLysakerNorway
  4. 4.Department of InformaticsUniversity of OsloOsloNorway

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