Mathematical Geosciences

, 43:741 | Cite as

A Hamilton–Jacobi Framework for Modeling Folds in Structural Geology

  • Øyvind HjelleEmail author
  • Steen A. Petersen


A novel mathematical framework for modeling folds in structural geology is presented. All the main fold classes from the classical literature: parallel folds, similar folds, and other fold types with convergent and divergent dip isogons are modeled in 3D space by linear and non-linear first-order partial differential equations. The equations are derived from a static Hamilton–Jacobi equation in the context of isotropic and anisotropic front propagation. The proposed Hamilton–Jacobi framework represents folded geological volumes in an Eulerian context as a time of arrival field relative to a reference layer. Metric properties such as distances, gradients (dip and strike), curvature, and their spatial variations can then be easily derived and represented as three-dimensional continua covering the whole geological volume. The model also serves as a basis for distributing properties in folded geological volumes.


Folding Dip isogons Front propagation Anisotropy Fast marching 


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Copyright information

© International Association for Mathematical Geosciences 2011

Authors and Affiliations

  1. 1.Kalkulo AS (Subsidiary of Simula Research Laboratory)LysakerNorway
  2. 2.Statoil ASABergenNorway

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