Articles | Volume 11, issue 5
https://doi.org/10.5194/se-11-1909-2020
© Author(s) 2020. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/se-11-1909-2020
© Author(s) 2020. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Research article
| 
22 Oct 2020
Research article |
| 22 Oct 2020
| 22 Oct 2020
Towards the application of Stokes flow equations to structural restoration simulations
Melchior Schuh-Senlis
CORRESPONDING AUTHOR
Université de Lorraine, CNRS, GeoRessources, 54000 Nancy, France
Cedric Thieulot
Department of Earth Sciences, Faculty of Geosciences, Utrecht University, Utrecht, the Netherlands
Paul Cupillard
Université de Lorraine, CNRS, GeoRessources, 54000 Nancy, France
Guillaume Caumon
Université de Lorraine, CNRS, GeoRessources, 54000 Nancy, France
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Subject area: The evolving Earth surface | Editorial team: Rock deformation, geomorphology, morphotectonics, and paleoseismology | Discipline: Structural geology
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Cited articles
Al-Fahmi, M. M., Plesch, A., Shaw, J. H., and Cole, J. C.: Restorations of
faulted domes, AAPG Bull., 100, 151–163, https://doi.org/10.1306/08171514211,
2016. a
Anquez, P., Pellerin, J., Irakarama, M., Cupillard, P., Lévy, B., and
Caumon, G.: Automatic correction and simplification of geological maps and
cross-sections for numerical simulations, C. R. Geosci., 351,
48–58, https://doi.org/10.1016/j.crte.2018.12.001, 2019. a
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.: The
deal.II Library, Version 9.1, J. Numer. Math., 27, 203–213,
https://doi.org/10.1515/jnma-2019-0064, 2019. a
Arndt, D., Bangerth, W., Davydov, D., Heister, T., Heltai, L., Kronbichler, M.,
Maier, M., Pelteret, J.-P., Turcksin, B., and Wells, D.: The deal. II finite
element library: Design, features, and insights, Comput. Math.
Appl., https://doi.org/10.1016/j.camwa.2020.02.022, in press, 2020. a
Asgari, A. and Moresi, L.: Multiscale Particle-In-Cell Method: From Fluid to
Solid Mechanics, in: Advanced Methods for Practical Applications in Fluid
Mechanics, edited by Jones, S. A., chap. 9, IntechOpen, Rijeka,
https://doi.org/10.5772/26419, 2012. a
Athy, L. F.: Density, porosity, and compaction of sedimentary rocks, AAPG
Bull., 14, 1–24, https://doi.org/10.1306/3D93289E-16B1-11D7-8645000102C1865D, 1930. a
Bangerth, W., Hartmann, R., and Kanschat, G.: deal.II – a General Purpose
Object Oriented Finite Element Library, ACM Trans. Math. Softw., 33,
24/1–24/27, https://doi.org/10.1145/1268776.1268779, 2007. a
Bouziat, A., Guy, N., Frey, J., Colombo, D., Colin, P., Cacas-Stentz, M.-C.,
and Cornu, T.: An Assessment of Stress States in Passive Margin Sediments:
Iterative Hydro-Mechanical Simulations on Basin Models and Implications for
Rock Failure Predictions, Geosciences, 9, 469, https://doi.org/10.3390/geosciences9110469, 2019. a
Braun, J.: Pecube: A new finite-element code to solve the 3D heat transport
equation including the effects of a time-varying, finite amplitude surface
topography, Comput. Geosci., 29, 787–794, https://doi.org/10.1016/S0098-3004(03)00052-9, 2003. a
Chamberlin, R. T.: The Appalachian folds of central Pennsylvania, J.
Geol., 18, 228–251, https://doi.org/10.1086/621722, 1910. a, b, c
Chauvin, B. P., Lovely, P. J., Stockmeyer, J. M., Plesch, A., Caumon, G., and
Shaw, J. H.: Validating novel boundary conditions for three-dimensional
mechanics-based restoration: An extensional sandbox model example, AAPG
Bull., 102, 245–266, https://doi.org/10.1306/0504171620817154, 2018. a, b, c, d, e
Clausolles, N., Collon, P., and Caumon, G.: Generating variable shapes of salt
geobodies from seismic images and prior geological knowledge, Interpretation,
7, T829–T841, https://doi.org/10.1190/INT-2019-0032.1, 2019. a, b
Cobbold, P. R. and Percevault, M.-N.: Spatial integration of strains using
finite elements, in: Strain Patterns in Rocks, 299–305, Elsevier, Rennes, France, 1983. a
Colletta, B., Letouzey, J., Pinedo, R., Ballard, J. F., and Balé, P.:
Computerized X-ray tomography analysis of sandbox models: Examples of
thin-skinned thrust systems, Geology, 19, 1063–1067, https://doi.org/10.1130/0091-7613(1991)019<1063:CXRTAO>2.3.CO;2, 1991. a
Cornet, F. H.: Elements of crustal geomechanics, Cambridge University Press, Cambridge, UK, 2015. a
Courant, R., Friedrichs, K., and Lewy, H.: Über die partiellen
Differenzengleichungen der mathematischen Physik, Math. Ann., 100,
32–74, https://doi.org/10.1007/BF01448839, 1928. a
Crameri, F., Schmeling, H., Golabek, G., Duretz, T., Orendt, R., Buiter, S.,
May, D., Kaus, B., Gerya, T., and Tackley, P.: A comparison of numerical
surface topography calculations in geodynamic modelling: an evaluation of the
'sticky air' method, Geophys. J. Int., 189, 38–54, https://doi.org/10.1111/j.1365-246X.2012.05388.x, 2012. a, b, c
Dahlstrom, C.: Balanced cross sections, Can. J. Earth Sci.,
6, 743–757, https://doi.org/10.1139/e69-069, 1969. a, b, c
De Santi, M. R., Campos, J. L. E., and Martha, L. F.: A Finite Element
approach for geological section reconstruction, in: Proceedings of the 22th
Gocad Meeting, Nancy, France, 1–13, Citeseer, 2002. a
Deubelbeiss, Y. and Kaus, B.: Comparison of Eulerian and Lagrangian numerical
techniques for the Stokes equations in the presence of strongly varying
viscosity, Phys. Earth Planet. In., 171, 92–111, https://doi.org/10.1016/j.pepi.2008.06.023, 2008. a, b
Dimakis, P., Braathen, B. I., Faleide, J. I., Elverhøi, A., and Gudlaugsson,
S. T.: Cenozoic erosion and the preglacial uplift of the Svalbard–Barents
Sea region, Tectonophysics, 300, 311–327, https://doi.org/10.1016/S0040-1951(98)00245-5, 1998. a
Donea, J., Huerta, A., Ponthot, J.-P., and Rodriguez-Ferran, A.: Arbitrary
Lagrangian-Eulerian Methods, volume 1 of Encyclopedia of Computational
Mechanics, chap. 14, John Wiley & Sons Ltd, 3, 1–25, https://doi.org/10.1002/9781119176817.ecm2009, 2004. a, b
Dooley, T., McClay, K., Hempton, M., and Smit, D.: Salt tectonics above complex
basement extensional fault systems: results from analogue modelling, in:
Geological Society, London, Petroleum Geology Conference series, 6,
1631–1648, https://doi.org/10.1144/0061631, 2005. a
Durand-Riard, P., Caumon, G., and Muron, P.: Balanced restoration of geological
volumes with relaxed meshing constraints, Comput. Geosci., 36,
441–452, https://doi.org/10.1016/j.cageo.2009.07.007, 2010. a, b, c
Durand-Riard, P., Salles, L., Ford, M., Caumon, G., and Pellerin, J.:
Understanding the evolution of syn-depositional folds: Coupling decompaction
and 3D sequential restoration, Mar. Petrol. Geol., 28, 1530–1539, https://doi.org/10.1016/j.marpetgeo.2011.04.001,
2011. a
Durand-Riard, P., Guzofski, C., Caumon, G., and Titeux, M.-O.: 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 Bull., 97, 87–102, https://doi.org/10.1306/06121211136, 2013a. a, b, c
Durand-Riard, P., Shaw, J. H., Plesch, A., and Lufadeju, G.: Enabling 3D
geomechanical restoration of strike-and oblique-slip faults using geological
constraints, with applications to the deep-water Niger Delta, J. Struct. Geol., 48, 33–44, https://doi.org/10.1016/j.jsg.2012.12.009, 2013b. a
Fillon, C., Huismans, R. S., and van der Beek, P.: Syntectonic sedimentation
effects on the growth of fold-and-thrust belts, Geology, 41, 83–86,
https://doi.org/10.1130/G33531.1, 2013. a
Fletcher, R. C. and Pollard, D. D.: Can we understand structural and tectonic
processes and their products without appeal to a complete mechanics?,
J. Struct. Geol., 21, 1071–1088, https://doi.org/10.1016/S0191-8141(99)00056-5, 1999. a
Fossen, H.: Structural geology, Cambridge University Press, 2016. a
Fullsack, P.: An arbitrary Lagrangian-Eulerian formulation for creeping flows
and its application in tectonic models, Geophys. J. Int.,
120, 1–23, https://doi.org/10.1111/j.1365-246X.1995.tb05908.x, 1995. a
Gassmöller, R., Lokavarapu, H., Heien, E., Puckett, E. G., and Bangerth,
W.: Flexible and Scalable Particle-in-Cell Methods With Adaptive Mesh
Refinement for Geodynamic Computations, Geochem. Geophy. Geosy.,
19, 3596–3604, https://doi.org/10.1029/2018GC007508, 2018. a
Gassmöller, R., Lokavarapu, H., Bangerth, W., and Puckett, E. G.:
Evaluating the accuracy of hybrid finite element/particle-in-cell methods for
modelling incompressible Stokes flow, Geophys. J. Int., 219,
1915–1938, https://doi.org/10.1093/gji/ggz405, 2019. a
Gerbault, M., Poliakov, A. N., and Daignieres, M.: Prediction of faulting from
the theories of elasticity and plasticity: what are the limits?, J. Struct. Geol., 20, 301–320, https://doi.org/10.1016/S0191-8141(97)00089-8, 1998. a
Gerya, T.: Introduction to numerical geodynamic modelling, Cambridge University Press, Cambridge, UK, 2019. a
Giles, K. A. and Lawton, T. F.: Attributes and evolution of an exhumed salt
weld, La Popa basin, northeastern Mexico, Geology, 27, 323–326, https://doi.org/10.1130/0091-7613(1999)027<0323:AAEOAE>2.3.CO;2, 1999. a
Gratier, J.-P.: L'équilibrage des coupes géologiques, Buts,
méthodes et applications, Géosciences-Rennes, 1988. a
Guzofski, C. A., Mueller, J. P., Shaw, J. H., Muron, P., Medwedeff, D. A.,
Bilotti, F., and Rivero, C.: Insights into the mechanisms of fault-related
folding provided by volumetric structural restorations using spatially
varying mechanical constraints, AAPG Bull., 93, 479–502, https://doi.org/10.1306/11250807130, 2009. a, b, c, d
Heister, T., Dannberg, J., Gassmöller, R., and Bangerth, W.: High accuracy
mantle convection simulation through modern numerical methods–II: realistic
models and problems, Geophys. J. Int., 210, 833–851,
https://doi.org/10.1093/gji/ggx195, 2017. a
Hudec, M. R. and Jackson, M. P.: Terra infirma: Understanding salt tectonics,
Earth-Sci. Rev., 82, 1–28, 2007. a
Hughes, T. J.: The finite element method: linear static and dynamic finite
element analysis, Courier Corporation, Dover Publications, Inc., Mineola, New York, 2012. a
Ismail-Zadeh, A., Tsepelev, I., Talbot, C., and Korotkii, A.:
Three-dimensional forward and backward modelling of diapirism: numerical
approach and its applicability to the evolution of salt structures in the
Pricaspian basin, Tectonophysics, 387, 81–103, https://doi.org/10.1016/j.tecto.2004.06.006, 2004. a, b, c
Kaus, B. J. and Podladchikov, Y. Y.: Forward and reverse modeling of the
three-dimensional viscous Rayleigh-Taylor instability, Geophys. Res.
Lett., 28, 1095–1098, https://doi.org/10.1029/2000GL011789, 2001. a, b, c, d
Kaus, B. J., Mühlhaus, H., and May, D. A.: A stabilization algorithm for
geodynamic numerical simulations with a free surface, Phys. Earth Planet. In., 181, 12–20, https://doi.org/10.1016/j.pepi.2010.04.007, 2010. a, b, c, d
Kocher, T. and Mancktelow, N. S.: Dynamic reverse modelling of flanking
structures: a source of quantitative kinematic information, J. Struct. Geol., 27, 1346–1354, https://doi.org/10.1016/j.jsg.2005.05.007, 2005. a
Koyi, H.: Salt flow by aggrading and prograding overburdens, Geol. Soc. Spec. Publ., 100, 243–258, https://doi.org/10.1144/GSL.SP.1996.100.01.15, 1996. a
Kronbichler, M., Heister, T., and Bangerth, W.: High accuracy mantle convection
simulation through modern numerical methods, Geophys. J. Int., 191, 12–29, https://doi.org/10.1111/j.1365-246X.2012.05609.x, 2012. a, b
Lechmann, S. M., Schmalholz, S. M., Burg, J.-P., and Marques, F.: Dynamic
unfolding of multilayers: 2D numerical approach and application to turbidites
in SW Portugal, Tectonophysics, 494, 64–74, https://doi.org/10.1016/j.tecto.2010.08.009, 2010. a, b, c, d
Lovely, P., Flodin, E., Guzofski, C., Maerten, F., and Pollard, D. D.:
Pitfalls among the promises of mechanics-based restoration: Addressing
implications of unphysical boundary conditions, J. Struct. Geol., 41, 47–63, https://doi.org/10.1016/j.jsg.2012.02.020, 2012. a, b, c
Lovely, P. J., Jayr, S. N., and Medwedeff, D. A.: Practical and efficient
three-dimensional structural restoration using an adaptation of the GeoChron
model, AAPG Bull., 102, 1985–2016, https://doi.org/10.1306/03291817191, 2018. a, b
Maerten, F. and Maerten, L.: Unfolding and Restoring Complex Geological
Structures Using Linear Elasticity Theory, in: AGU Fall Meeting Abstracts, San Francisco, USA, December 2001, T22C–0940,
2001. a
Maerten, L. and Maerten, F.: Chronologic modeling of faulted and fractured
reservoirs using geomechanically based restoration: Technique and industry
applications, AAPG Bull., 90, 1201–1226, https://doi.org/10.1306/02240605116, 2006. a, b, c
Massimi, P., Quarteroni, A., and Scrofani, G.: An adaptive finite element
method for modeling salt diapirism, Math. Mod. Meth. Appl. S., 16, 587–614, https://doi.org/10.1142/S0218202506001273, 2006. a, b, c
Massimi, P., Quarteroni, A., Saleri, F., and Scrofani, G.: Modeling of salt
tectonics, Comput. Method. Appl. M., 197,
281–293, https://doi.org/10.1016/j.cma.2007.08.004, 2007. a
Massot, J.: Implémentation de méthodes de restauration
équilibrée 3D, PhD thesis, Institut National Polytechnique de
Lorraine, 2002. a
Moresi, L., Dufour, F., and Mühlhaus, H.-B.: A Lagrangian integration
point finite element method for large deformation modeling of viscoelastic
geomaterials, J. Comput. Phys., 184, 476–497, https://doi.org/10.1016/S0021-9991(02)00031-1, 2003. a
Moretti, I.: Working in complex areas: New restoration workflow based on
quality control, 2D and 3D restorations, Mar. Petrol. Geol., 25,
205–218, https://doi.org/10.1016/j.marpetgeo.2007.07.001, 2008. a
Moretti, I., Lepage, F., and Guiton, M.: KINE3D: a new 3D restoration method
based on a mixed approach linking geometry and geomechanics, Oil Gas Sci. Technol., 61, 277–289, https://doi.org/10.2516/ogst:2006021, 2006. a
Parquer, M. N., Collon, P., and Caumon, G.: Reconstruction of Channelized
Systems Through a Conditioned Reverse Migration Method, Math.
Geosci., 49, 965–994, https://doi.org/10.1007/s11004-017-9700-3, 2017. a
Pellerin, J., Lévy, B., Caumon, G., and Botella, A.: Automatic surface
remeshing of 3D structural models at specified resolution: A method based on
Voronoi diagrams, Comput. Geosci., 62, 103–116, https://doi.org/10.1016/j.cageo.2013.09.008, 2014. a
Poliakov, A. N., Podladchikov, Y. Y., Dawson, E. C., and Talbot, C. J.: Salt
diapirism with simultaneous brittle faulting and viscous flow, Geol. Soc. Spec. Publ., 100, 291–302, https://doi.org/10.1144/GSL.SP.1996.100.01.19, 1996. a
Quinquis, M. E., Buiter, S. J., and Ellis, S.: The role of boundary conditions
in numerical models of subduction zone dynamics, Tectonophysics, 497,
57–70, https://doi.org/10.1016/j.tecto.2010.11.001, 2011. a
Ramberg, H.: Instability of layered systems in the field of gravity, Phys. Earth Planet. In., 1, 427–447, https://doi.org/10.1016/0031-9201(68)90014-9, 1968. a, b
Ramberg, H.: Gravity, deformation and the earth's crust: in theory, experiments
and geological application, Academic Press, London, UK, 1981. a
Ramón, M. J., Pueyo, E. L., Caumon, G., and Briz, J. L.: Parametric
unfolding of flexural folds using palaeomagnetic vectors, Geol. Soc. Spec. Publ., 425, 247–258, https://doi.org/10.1144/SP425.6, 2016. a
Rose, I., Buffett, B., and Heister, T.: Stability and accuracy of free surface
time integration in viscous flows, Phys. Earth Planet. In., 262, 90–100, https://doi.org/https://doi.org/10.1016/j.pepi.2016.11.007, 2017. a
Rowan, M. G., Lawton, T. F., and Giles, K. A.: Anatomy of an exposed vertical
salt weld and flanking strata, La Popa Basin, Mexico, Geol. Soc. Spec. Publ., 363, 33–57, https://doi.org/10.1144/SP363.3, 2012. a
Royden, L. and Keen, C.: Rifting process and thermal evolution of the
continental margin of eastern Canada determined from subsidence curves,
Earth Planet. Sc. Lett., 51, 343–361, https://doi.org/10.1016/0012-821X(80)90216-2, 1980. a
Schmalholz, S. M.: 3D numerical modeling of forward folding and reverse
unfolding of a viscous single-layer: Implications for the formation of folds
and fold patterns, Tectonophysics, 446, 31–41, https://doi.org/10.1016/j.tecto.2007.09.005, 2008. a
Tang, P., Wang, C., and Dai, X.: A majorized Newton-CG augmented
Lagrangian-based finite element method for 3D restoration of geological
models, Comput. Geosci., 89, 200–206, https://doi.org/j.cageo.2016.01.013, 2016. a
Thielmann, M., May, D., and Kaus, B.: Discretization errors in the hybrid
finite element particle-in-cell method, Pure Appl. Geophys., 171,
2165–2184, https://doi.org/10.1007/s00024-014-0808-9, 2014. a, b
Thieulot, C.: FANTOM: Two-and three-dimensional numerical modelling of
creeping flows for the solution of geological problems, Phys. Earth Planet. In., 188, 47–68, https://doi.org/j.pepi.2011.06.011, 2011. a, b, c
Thieulot, C., Steer, P., and Huismans, R.: Three-dimensional numerical
simulations of crustal systems undergoing orogeny and subjected to surface
processes, Geochem. Geophy. Geosy., 15, 4936–4957, https://doi.org/10.1002/2014GC005490, 2014. a
Thieulot, C. C.: Fieldstone: The Finite Element Method in Computational
Geodynamics, https://doi.org/10.23644/uu.9209393.v1, 2019. a
Trim, S., Lowman, J., and Butler, S.: Improving mass conservation with the
tracer ratio method: application to thermochemical mantle flows,
Geochem. Geophy. Geosy., 21, e2019GC008799, https://doi.org/10.1029/2019GC008799, 2019. a
van Keken, P., King, S., Schmeling, H., Christensen, U., Neumeister, D., and
Doin, M.-P.: A comparison of methods for the modeling of thermochemical
convection, J. Geophys. Res.-Sol. Ea., 102,
22 477–22 495, https://doi.org/10.1029/97JB01353, 1997.
a, b, c, d
Weijermars, R., Jackson, M. T., and Vendeville, B.: Rheological and tectonic
modeling of salt provinces, Tectonophysics, 217, 143–174, https://doi.org/10.1016/0040-1951(93)90208-2, 1993. a
Willett, S., Beaumont, C., and Fullsack, P.: Mechanical model for the tectonics
of doubly vergent compressional orogens, Geology, 21, 371–374, https://doi.org/10.1130/0091-7613(1993)021<0371:MMFTTO>2.3.CO;2, 1993. a
Zehner, B., Hellwig, O., Linke, M., Görz, I., and Buske, S.: Rasterizing
geological models for parallel finite difference simulation using seismic
simulation as an example, Comput. Geosci., 86, 83–91, https://doi.org/j.cageo.2015.10.008, 2016. a
Short summary
This paper presents a numerical method for restoring models of the subsurface to a previous state in their deformation history, acting as a numerical time machine for geological structures. The method relies on the assumption that rock layers can be modeled as highly viscous fluids. It shows promising results on simple setups, including models with faults and non-flat topography. While issues still remain, this could open a way to add more physics to reverse time structural modeling.
This paper presents a numerical method for restoring models of the subsurface to a previous...
