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Approaching bed length/area preservation in 3D restorations

Most section-restoration techniques (geometrically, kinematically and geomechanically based restorations) incorporate algorithms to enable the assumption of bed-length preservation during back-stripping of the section top surface to the restoration datum. This facilitates the flattening of folded structures without introducing layer parallel compression during the restoration procedure for example. While such assumption is relatively trivial to implement in 2D geomechanical restorations by prescribing top surface displacements to the restoration surface according to the top surface bed-length, in 3D restorations it becomes more complex due to the added degrees of freedom and the a-priory unknown main direction of deformation in the horizontal plane. We have recently implemented an approach to achieve bed-length/area preservation in 3D restorations in ParaGeo with a workflow as follows:

  1. We introduce a membrane of 2D surface elements which is tied to the current top surface

  2. Such membrane of elements is assigned mechanical properties which are relatively stiff compared to the formations. This would be equivalent to incorporate stiff springs parallel to the top surface that would resist compression during back stripping

  3. A maximum tensional stress for the membrane of elements is defined so that stretch is not hindered by the imposed high stiffness

  4. At each restoration stage, after removal of the top formation a new membrane of elements is tied to the new top surface

In the figures below the algorithm is validated by restoring a synthetic flexural fold benchmark. The solution is compared to the equivalent 2D plane strain model using prescribed displacement-based bed length preservation approach. As can be observed the displacement contours are very similar in both solutions and the final length after back-stripping is consistent with the initial bed length.

A synthetic flexural fold 3D benchmark is restored assuming bed length / area preservation
Usage of stiff membrane elements to approach bed length preservation in a 3D restoration


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