1887

Abstract

Summary

Restoration of geological structures is commonly used to assess past basin geometry from present-day structures. In geomechanical restoration, numerical methods to date consider the rock properties as fully elastic and the faults as frictionless contact surfaces. However, salt bodies have been proven to behave as Stokes viscous fluids in geomechanics, and faults appear in rocks reaching a plastic limit inside a shear zone.

In order to take these behaviours into account, we introduce a new geomechanical restoration scheme based on Stokes equations. Such a strategy seems reasonable for three main reasons. First, rocks have been found to be mainly ductile in large deformations under long time periods (1e5 to 1e9 years). Second, these equations allow the modelling of other rheologies and boundary conditions closer to natural ones. Third, the reversibility of the Stokes equations can be used to compute the reverse motion of a geological domain.

Our restoration scheme is implemented in a software called FAIStokes. The classic forward modelling part of this software is validated through relevant benchmarks. First tests, including van &s benchmark, on the more innovative backward modelling part, show the great potential of the proposed scheme for restoration using only mechanical (i.e. no geometrical) conditions.

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/content/papers/10.3997/2214-4609.202010733
2021-10-18
2021-12-09
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References

  1. Anquez, P., Pellerin, J., Irakarama, M., Cupillard, P., Lévy, B. and Caumon, G.
    [2019] Automatic correction and simplification of geological maps and cross-sections for numerical simulations.Comptes Rendus Geoscience, 351(1), 48–58.
    [Google Scholar]
  2. Arndt, D., Bangerth, W., Clevenger, T.C., Davydov, D., Fehling, M., Garcia-Sanchez, D., Harper, G., Heister, T., Heltai, L., Kronbichler, M., Kynch, R.M., Maier, M., Pelteret, J.P., Turcksin, B. and Wells, D.
    [2019] The deal.II Library, Version 9.1.Journal of Numerical Mathematics. Accepted.
    [Google Scholar]
  3. Bangerth, W., Dannberg, J., Gassmoeller, R., Heister, T. et al.
    [2019] ASPECT v2.1.0 [software].
    [Google Scholar]
  4. Bangerth, W., Hartmann, R. and Kanschat, G.
    [2007] deal.II — a General Purpose Object Oriented Finite Element Library.ACM Trans. Math. Softw., 33(4), 24/1–24/27.
    [Google Scholar]
  5. Chamberlin, R.T.
    [1910] The Appalachian folds of central Pennsylvania.The Journal of Geology, 18(3), 228–251.
    [Google Scholar]
  6. Chauvin, B.P., Lovely, P.J., Stockmeyer, J.M., Plesch, A., Caumon, G. and Shaw, J.H.
    [2018] Validating novel boundary conditions for three-dimensional mechanics-based restoration: An extensional sandbox model example.AAPG Bulletin, 102(2), 245–266.
    [Google Scholar]
  7. Cornet, F.H.
    [2015] Elements of crustal geomechanics. Cambridge University Press.
    [Google Scholar]
  8. Dahlstrom, C.
    [1969] Balanced cross sections.Canadian Journal of Earth Sciences, 6(4), 743–757.
    [Google Scholar]
  9. Durand-Riard, P., Caumon, G. and Muron, P.
    [2010] Balanced restoration of geological volumes with relaxed meshing constraints.Computers & Geosciences, 36(4), 441–452.
    [Google Scholar]
  10. Durand-Riard, P., Guzofski, C., Caumon, G. and Titeux, M.O.
    [2013] Handling natural complexity in three-dimensional geomechanical restoration, with application to the recent evolution of the outer fold and thrust belt, deep-water Niger Delta.AAPG bulletin, 97(1), 87–102.
    [Google Scholar]
  11. Fossen, H.
    [2016] Structural geology. Cambridge University Press.
    [Google Scholar]
  12. Gerbault, M., Poliakov, A.N. and Daignieres, M.
    [1998] Prediction of faulting from the theories of elasticity and plasticity: what are the limits?Journal of Structural Geology, 20(2–3), 301–320.
    [Google Scholar]
  13. Gerya, T.
    [2019] Introduction to numerical geodynamic modelling. Cambridge University Press.
    [Google Scholar]
  14. Gratier, J.P.
    [1988] L’équilibrage des coupes géologiques. Buts, méthodes et applications. Géosciences-Rennes.
    [Google Scholar]
  15. Hassani, R., Jongmans, D. and Chéry, J.
    [1997] Study of plate deformation and stress in subduction processes using two-dimensional numerical models.Journal of Geophysical Research: Solid Earth, 102(B8), 17951–17965.
    [Google Scholar]
  16. van Keken, P., King, S., Schmeling, H., Christensen, U., Neumeister, D. and Doin, M.P.
    [1997] A comparison of methods for the modeling of thermochemical convection.Journal of Geophysical Research: Solid Earth, 102(B10), 22477–22495.
    [Google Scholar]
  17. Lovely, P., Flodin, E., Guzofski, C., Maerten, F. and Pollard, D.D.
    [2012] Pitfalls among the promises of mechanics-based restoration: Addressing implications of unphysical boundary conditions.Journal of Structural Geology, 41, 47–63.
    [Google Scholar]
  18. Maerten, F. and Maerten, L.
    [2001] Unfolding and Restoring Complex Geological Structures Using Linear Elasticity Theory. In: AGU Fall Meeting Abstracts.
    [Google Scholar]
  19. Massimi, P., Quarteroni, A. and Scrofani, G.
    [2006] An adaptive finite element method for modeling salt diapirism.Mathematical Models and Methods in Applied Sciences, 16(04), 587–614.
    [Google Scholar]
  20. Moresi, L., Dufour, F. and Mühlhaus, H.B.
    [2003] A Lagrangian integration point finite element method for large deformation modeling of viscoelastic geomaterials.Journal of Computational Physics, 184(2), 476–497.
    [Google Scholar]
  21. Muron, P.
    [2005] Méthodes numériques 3-D de restauration des structures géologiques faillées. Ph.D. thesis, INPL.
    [Google Scholar]
  22. Nalpas, T. and Brun, J.P.
    [1993] Salt flow and diapirism related to extension at crustal scale.Tectono-physics, 228(3–4), 349–362.
    [Google Scholar]
  23. Pellerin, J., Lévy, B., Caumon, G. and Botella, A.
    [2014] Automatic surface remeshing of 3D structural models at specified resolution: A method based on Voronoi diagrams.Computers & Geosciences, 62, 103–116.
    [Google Scholar]
  24. Thieulot, C.
    [2011] FANTOM: Two-and three-dimensional numerical modelling of creeping flows for the solution of geological problems.Physics of the Earth and Planetary Interiors, 188(1–2), 47–68.
    [Google Scholar]
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