Back, S., Strozyk, F., Kukla, P. A., and Lambiase, J. J.: Three-dimensional restoration of original sedimentary geometries in deformed basin fill, onshore Brunei Darussalam, NW Borneo, Basin Res., 20, 99–117,
https://doi.org/10.1111/j.1365-2117.2007.00343.x, 2008.
a
Bangerth, W., Hartmann, R., and Kanschat, G.: deal.II – a General Purpose Object Oriented Finite Element Library, ACM T. Math. Software, 33, 24/1–24/27,
https://doi.org/10.1145/1268776.1268779, 2007.
a
Buiter, S. J., Schreurs, G., Albertz, M., Gerya, T. V., Kaus, B., Landry, W., le Pourhiet, L., Mishin, Y., Egholm, D. L., Cooke, M., Maillot, B., Thieulot, C., Crook, T., May, D., Souloumiac, P., and Beaumont, C.: Benchmarking numerical models of brittle thrust wedges, J. Struct. Geol., 92, 140–177,
https://doi.org/10.1016/j.jsg.2016.03.003, 2016.
a
Chauvin, B.: Applicability of the mechanics-based restoration: boundary conditions, fault network and comparison with a geometrical method, PhD thesis, Université de Lorraine,
https://theses.hal.science/tel-01774241v2/file/DDOC_T_2017_0160_CHAUVIN.pdf (last access: 1 August 2024), 2017. a
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,
f,
g
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
Crook, A. J., Obradors-Prats, J., Somer, D., Peric, D., Lovely, P., and Kacewicz, M.: Towards an integrated restoration/forward geomechanical modelling workflow for basin evolution prediction, Oil Gas Sci. Technol., 73, 18,
https://doi.org/10.2516/ogst/2018018, 2018.
a
de Melo Garcia, S. F., Letouzey, J., Rudkiewicz, J.-L., Danderfer Filho, A., and Frizon de Lamotte, D.: Structural modeling based on sequential restoration of gravitational salt deformation in the Santos Basin (Brazil), Mar. Petrol. Geol., 35, 337–353,
https://doi.org/10.1016/j.marpetgeo.2012.02.009, 2012.
a
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, Citeseer, 1–13, 2002. a
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, in: Encyclopedia of Computational Mechanics, vol. 1, Chap. 14, John Wiley & Sons Ltd, 3, 1–25,
https://doi.org/10.1002/9781119176817.ecm2009, 2004.
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
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
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
Espurt, N., Angrand, P., Teixell, A., Labaume, P., Ford, M., de Saint Blanquat, M., and Chevrot, S.: Crustal-scale balanced cross-section and restorations of the Central Pyrenean belt (Nestes-Cinca transect): Highlighting the structural control of Variscan belt and Permian-Mesozoic rift systems on mountain building, Tectonophysics, 764, 25–45,
https://doi.org/10.1016/j.tecto.2019.04.026, 2019.
a
Faulkner, D., Mitchell, T., Healy, D., and Heap, M.: Slip on'weak'faults by the rotation of regional stress in the fracture damage zone, Nature, 444, 922–925, 2006. 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, in: 2nd Edn., Cambridge University Press, ISBN 978-1-107-05764-7, 2016. 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
Gratier, J.-P.: L'équilibrage des coupes géologiques. Buts, méthodes et applications, Géosciences, Rennes,
https://insu.hal.science/insu-00648843/file/Grattier.pdf (last access: 1 August 2024), 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
Hall, J.: II. On the Vertical Position and Convolutions of certain Strata, and their relation with Granite, Transactions of the Royal Society of Edinburgh, 7, 79–108,
https://doi.org/10.1017/S0080456800019268, 1815.
a
IFP and C&C Reservoirs: Principles of Digital Structural Analog Modeling, Tech. rep., 2006.
a,
b
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
Ismail-Zadeh, A. T., Talbot, C. J., and Volozh, Y. A.: Dynamic restoration of profiles across diapiric salt structures: numerical approach and its applications, Tectonophysics, 337, 23–38,
https://doi.org/10.1016/S0040-1951(01)00111-1, 2001.
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
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
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
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
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
Maerten, F. and Maerten, L.: Unfolding and Restoring Complex Geological Structures Using Linear Elasticity Theory, in: vol. 2001, AGU Fall Meeting Abstracts, T22C–0940,
https://ui.adsabs.harvard.edu/abs/2001AGUFM.T22C0940M/abstract (last access: 2 August 2024), 2001.
a,
b
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
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
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,
b
Muron, P.: Méthodes numériques 3-D de restauration des structures géologiques faillées, PhD thesis, INPL,
https://hal.univ-lorraine.fr/tel-01752493/file/2005_MURON_P.pdf (last access: 2 August 2024), 2005.
a,
b,
c,
d
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
Ramberg, H.: Gravity, deformation and the earth's crust: in theory, experiments and geological application, in: 2nd Edn., Academic Press, London, New York, ISBN 10.0125768605, 1981. a
Rouby, D.: Restauration en carte des domaines faillés en extension. Méthode et applications, PhD thesis, Université Rennes 1,
https://theses.hal.science/tel-00675437/file/Rouby.pdf (last access: 2 August 2024), 1994. 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
Schönborn, G.: Balancing cross sections with kinematic constraints: The Dolomites (northern Italy), Tectonics, 18, 527–545, 1999. a
Schreurs, G., Buiter, S. J., Boutelier, J., Burberry, C., Callot, J.-P., Cavozzi, C., Cerca, M., Chen, J.-H., Cristallini, E., Cruden, A. R., Cruz, L., Daniel, J.-M., Da Poian, G., Garcia, V. H., Gomes, C. J., Grall, C., Guillot, Y., Guzmán, C., Hidayah, T. N., Hilley, G., Klinkmüller, M., Koyi, H. A., Lu, C.-Y., Maillot, B., Meriaux, C., Nilfouroushan, F., Pan, C.-C., Pillot, D., Portillo, R., Rosenau, M., Schellart, W. P., Schlische, R. W., Take, A., Vendeville, B., Vergnaud, M., Vettori, M., Wang, S.-H., Withjack, M. O., Yagupsky, D., and Yamada, Y.: Benchmarking analogue models of brittle thrust wedges, J. Struct. Geol., 92, 116–139,
https://doi.org/10.1016/j.jsg.2016.03.005, 2016.
a
Schuh-Senlis, M., Thieulot, C., Cupillard, P., and Caumon, G.: Towards the application of Stokes flow equations to structural restoration simulations, Solid Earth, 11, 1909–1930,
https://doi.org/10.5194/se-11-1909-2020, 2020.
a,
b,
c,
d,
e,
f,
g
Stockmeyer, J. M. and Guzofski, C.: Interplay between extension, salt and pre-existing structure, offshore Angola, in: AAPG Annual Convention and Exhibition, 6–9 April 2014, Houston, Texas, USA, 2014. 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/10.1016/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
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, 2020.
a
Willis, B.: The mechanics of Appalachian structure, vol. 13, US Government Printing Office, ISBN 13:9780332003221, 1894. a
