Unfolding and Restoring Complex Geological Structures Using Linear Elasticity Theory
Abstract
We present a new method to unfold and restore geological structures in 2D and 3D using elasticity theory. A primary motivation for such restoration is to check the consistency of the geological interpretations. Also, measures of the deformation between the restored state and the deformed state give quantitative estimates of strain that can be compared with observed strain markers. Different geometrical and kinematic methods have been proposed in the past 30 years to restore geological structures. Most restorations have been performed in 2D, either in cross section or in map view, based primarily on area conservation. The methods include (1) unfolding in cross section by flexural slip or by vertical or inclined shear; and (2) unfaulting in map view by rigid block translation and rotation of fault blocks. Geometrical and analytical unfolding methods for 3D surfaces have been proposed, based on flexural slip and homogeneous inclined shear. In this new method, structures are unfolded onto a datum defined by the user. The datum can assume any shape. One advantage of using elasticity for the unfolding process is that the solution is unique. The second advantage is that the surface is treated as continuous and deformable, as opposed to other methods where the surface needs to be subdivided into rigid elements. The last and most important advantage is that the method does not use the commonly assumed geometrical assumptions that are (i) conservation of area, (ii) minimization of the changes in segment length (or minimization of the shearing) and (iii) minimization of the deformation energy. Instead, this method honors the fundamental physical laws that govern deformation, that are (i) conservation of mass, (ii) conservation of momentum and (iii) conservation of energy. Therefore, physical laws and linear elastic theory replace geometrical assumptions used by the existing methods for the restoration of geological structures. Examples illustrate how unfolding can be accomplished for 2D cross-sections, 3D surfaces and 3D volumes. Heterogeneous material properties as well as varying boundary conditions yield different but unique solutions even if the model is otherwise identical. One can compute stresses and strains within the deformed surface and these can be related to smaller scale fractures and faults, which might have a large economic impact.
- Publication:
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AGU Fall Meeting Abstracts
- Pub Date:
- December 2001
- Bibcode:
- 2001AGUFM.T22C0940M
- Keywords:
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- 8005 Folds and folding;
- 8010 Fractures and faults;
- 8020 Mechanics;
- 8168 Stresses: general