Computational Geodynamics of the South American Plate: Contributions and Perspectives

Victor Sacek, Naomi Ussami, Agustina Pesce, Claudio Salazar Mora, Edgar Bueno dos Santos, Felipe Baiadori, Jamison Assunção, João Pedro Macedo Silva, Rafael Monteiro da Silva, Tacio Cordeiro Bicudo


Computational geodynamics is a key tool in Earth Sciences, enabling the simulation of different geodynamic processes at any time scale in Nature or those which cannot be adequately reproduced by analogue modelling in laboratorial conditions. Specifically, the coupling of surface processes of erosion and sedimentation with the internal dynamics of the lithosphere is a complex problem that involves the solution of a set of differential equations that are only adequately solved by numerical models. During the last three decades, different numerical models were developed to explain the importance of the coupling between the surface and internal dynamics of the Earth, both in active margins and in stable tectonic domains, showing how the coupling leads to counter-intuitive results not observed when each process is analyzed separately. One example of this complex coupling is the feedback mechanism between erosion of the landscape and the regional isostatic response of the lithosphere. In this work, we present simple isostatic and flexural elements that highlight the importance of surface processes on the stress and strain pattern in lithospheric plates. Initially, we present a review on the development of computational geodynamics at University of São Paulo. This review is followed by an analysis of the density structure of the Earth and how the high-density contrast at the Earth’s surface creates a major impact on the isostatic equilibrium of the lithosphere when variations on topographic loads are taken into account. Additionally, we show that the wavelength of the denudation of the Earth’s surface due to fluvial dynamics corresponds to the characteristic length scale for flexural bending of the lithosphere, maximizing the flexural stresses in the lithosphere. Finally, we present recent works on the coupling between surface and lithospheric processes and future challenges for the development of computational geodynamics, with possible strategies to solve them. 


numerical models; lithospheric geodynamics; surface processes.

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Andrés-Martínez, M., M. Pérez-Gussinyé, J. Armitage, and J. Morgan, 2019, Thermomechanical implications of sediment transport for the architecture and evolution of continental rifts and margins: Tectonics, 38, 641–665, doi: 10.1029/2018TC005346.

Assumpção, M., and V. Sacek, 2013, Intra-plate seismicity and flexural stresses in central Brazil: Geophysical Research Letters, 40, 487–491, doi: 10.1002/grl.50142.

Balay, S., S. Abhyankar, M. Adams, J. Brown, P. Brune, K. Buschelman, L. Dalcin, A. Dener, V. Eijkhout, W. Gropp, D. Karpeyev, D. Kaushik, M. Knepley, D. May, L. McInnes, R. Mills, T. Munson, K. Rupp, P. Sanan, B. Smith, S. Zampini, and H. Zhang, 2021a, PETSc Users Manual: Technical Report ANL-95/11 - Revision 3.15, Argonne National Laboratory.

Balay, S., S. Abhyankar, M. Adams, J. Brown, P. Brune, K. Buschelman, L. Dalcin, A. Dener, V. Eijkhout, W. Gropp, D. Karpeyev, D. Kaushik, M. Knepley, D. May, L. McInnes, R. Mills, T. Munson, K. Rupp, P. Sanan, B. Smith, S. Zampini, and H. Zhang, 2021b, PETSc Web page.

Balay, S., W. Gropp, L. McInnes, and B. Smith, 1997, Efficient management of parallelism in object oriented numerical software libraries, in Modern Software Tools in Scientific Computing: Birkhäuser Press, 163–202. doi: 10.1007/978-1-4612-1986-6_8.

Beaumont, C., R. Jamieson, M. Nguyen, and S. Medvedev, 2004, Crustal channel flows: 1. numerical models with applications to the tectonics of the Himalayan-Tibetan orogen: Journal of Geophysical Research: Solid Earth, 109, doi: 10.1029/2003JB002809.

Beucher, R., and R. Huismans, 2020, Morphotectonic Evolution of Passive Margins Undergoing Active Surface Processes: Large-Scale Experiments Using Numerical Models: Geochemistry, Geophysics, Geosystems, 21, e2019GC008884, doi: 10.1029/2019GC008884.

Bicudo, T., V. Sacek, and R. Almeida, 2020, Reappraisal of the relative importance of dynamic topography and Andean orogeny on Amazon landscape evolution: Earth and Planetary Science Letters, 546, 116423, doi: 10.1016/j.epsl.2020.116423.

Bicudo, T., V. Sacek, R. Almeida, J. Bates, and C. Ribas, 2019, Andean tectonics and mantle dynamics as a pervasive influence on Amazonian ecosystem: Scientific Reports, 9, 1–11, doi: 10.1038/s41598-019-53465-y.

Braun, J., 2010, The many surface expressions of mantle dynamics: Nature Geoscience, 3, 825–833, doi: 10.1038/ngeo1020.

Braun, J., and M. Sambridge, 1997, Modelling landscape evolution on geological time scales: a new method based on irregular spatial discretization: Basin Research, 9, 27–52, doi: 10.1046/j.1365-2117.1997.00030.x.

Braun, J., and S. D. Willett, 2013, A very efficient O(n), implicit and parallel method to solve the stream power equation governing fluvial incision and landscape evolution: Geomorphology, 180, 170–179, doi: 10.1016/j.geomorph.2012.10.008.

Chen, L., T. Gerya, Z. Zhang, G. Zhu, T. Duretz, and W. R. Jacoby, 2013, Numerical modeling of eastern Tibetan-type margin: Influences of surface processes, lithospheric structure and crustal rheology: Gondwana Research, 24, 1091–1107, doi: 10.1016/

Dziewonski, A., and D. Anderson, 1981, Preliminary reference Earth model: Physics of the Earth and Planetary Interiors, 25, 297–356, doi: 10.1016/0031-9201(81)90046-7.

Gallagher, K., and R. Brown, 1999a, Denudation and uplift at passive margins: the record on the Atlantic Margin of southern Africa: Philosophical Transactions of the Royal Society of London. Series A: Mathematical,

Physical and Engineering Sciences, 357, 835–859, doi: 10.1098/rsta.1999.0354.

Gallagher, K., and R. Brown, 1999b, The Mesozoic denudation history of the Atlantic margins of southern Africa and southeast Brazil and the relationship to offshore sedimentation: Geological Society, London, Special Publications, 153, 41–53, doi: 10.1144/GSL.SP.1999.153.01.03.

Gallagher, K., C. Hawkesworth, and M. Mantovani, 1994, The denudation history of the onshore continental margin of SE Brazil inferred from apatite fission track data: Journal of Geophysical Research: Solid Earth, 99, 18117–18145, doi: 10.1029/94JB00661.

Gerya, T., 2014, Precambrian geodynamics: concepts and models: Gondwana Research, 25, 442–463, doi: 10.1016/

Gordon, R., 1965, Diffusion creep in the Earth’s mantle: Journal of Geophysical Research, 70, 2413–2418, doi: 10.1029/JZ070i010p02413.

Hartley, R., A. Watts, and J. Fairhead, 1996, Isostasy of Africa: Earth and Planetary Science Letters, 137, 1–18, doi: 10.1016/0012-821X(95)00185-F.

Ismail-Zadeh, A., and P. Tackley, 2010, Computational methods for geodynamics: Cambridge University Press.

Kaus, B. J., H. Mühlhaus, and D. A. May, 2010, A stabilization algorithm for geodynamic numerical simulations with a free surface: Physics of the Earth and Planetary Interiors, 181, 12–20, doi: 10.1016/j.pepi.2010.04.007.

Koptev, A., M. Nettesheim, S. Falkowski, and T. A. Ehlers, 2022, 3D geodynamic-geomorphologic modelling of deformation and exhumation at curved plate boundaries: Implications for the southern Alaskan plate corner: Scientific Reports, 12, 1–14, doi: 10.1038/s41598-022-17644-8.

Korenaga, J., 2013, Initiation and evolution of plate tectonics on Earth: theories and observations: Annual Review of Earth and Planetary Sciences, 41, 117–151, doi: 10.1146/annurev-earth-050212-124208.

Lenardic, A., A. Jellinek, and L. Moresi, 2008, A climate induced transition in the tectonic style of a terrestrial planet: Earth and Planetary Science Letters, 271, 34–42, doi: 10.1016/j.epsl.2008.03.031.

McKenzie, D., 1967, The viscosity of the mantle: Geophysical Journal International, 14, 297–305, doi: 10.1111/j.1365-246X.1967.tb06246.x.

Minear, J., and M. Toksöz, 1970, Thermal regime of a downgoing slab and new global tectonics: Journal of Geophysical Research, 75, 1397–1419, doi: 10.1029/JB075i008p01397.

Moore, W., and A. Webb, 2013, Heat-pipe Earth: Nature, 501, 501–505, doi: 10.1038/nature12473.

Moresi, L., and M. Gurnis, 1996, Constraints on the lateral strength of slabs from three-dimensional dynamic flow models: Earth and Planetary Science Letters, 138, 15–28, doi: 10.1016/0012-821X(95)00221-W.

Moresi, L., and V. Solomatov, 1998, Mantle convection with a brittle lithosphere: thoughts on the global tectonic styles of the Earth and Venus: Geophysical Journal International, 133, 669–682, doi: 10.1046/j.1365- 246X.1998.00521.x.

Pérez-Gussinyé, M., M. Andrés-Martínez, M. Araújo, Y. Xin, J. Armitage, and J. Morgan, 2020, Lithospheric strength and rift migration controls on synrift stratigraphy and breakup unconformities at rifted margins: Examples from numerical models, the Atlantic and South China Sea Margins: Tectonics, 39, e2020TC006255, doi: 10.1029/2020TC006255.

Petersen, K., S. Nielsen, O. Clausen, R. Stephenson, and T. Gerya, 2010, Small-scale mantle convection produces stratigraphic sequences in sedimentary basins: Science, 329, 827–830, doi: 10.1126/science.1190115.

Riccomini, C., 1989, O rift continental do sudeste do Brasil: PhD thesis, Universidade de São Paulo. Sacek, V., 2014, Drainage reversal of the Amazon River due to the coupling of surface and lithospheric processes: Earth and Planetary Science Letters, 401, 301–312, doi: 10.1016/j.epsl.2014.06.022.

Sacek, V., 2017, Post-rift influence of small-scale convection on the landscape evolution at divergent continental margins: Earth and Planetary Science Letters, 459, 48–57, doi: 10.1016/j.epsl.2016.11.026.

Sacek, V., J. Assunção, A. Pesce, and R. da Silva, 2022, Mandyoc: A finite element code to simulate thermochemical convection in parallel: Journal of Open Source Software, 7, 4070, doi: 10.21105/joss.04070. Sacek, V., J. Braun, and P. Van Der Beek, 2012, The influence of rifting on escarpment migration on high elevation passive continental margins: Journal of Geophysical Research: Solid Earth, 117.

Sacek, V., J. Morais Neto, P. Vasconcelos, and I. de Oliveira Carmo, 2019, Numerical modeling of weathering, erosion, sedimentation, and uplift in a triple junction divergent margin: Geochemistry, Geophysics, Geosystems, 20, 2334–2354, doi: 10.1029/2018GC008124.

Sacek, V., and N. Ussami, 2009, Reappraisal of the effective elastic thickness for the sub-Andes using 3-D finite element flexural modelling, gravity and geological constraints: Geophysical Journal International, 179, 778–786, doi: 10.1111/j.1365-246X.2009.04334.x.

Sacek, V., and N. Ussami, 2013, Upper mantle viscosity and dynamic subsidence of curved continental margins: Nature Communications, 4, 1–6, doi: 10.1038/ncomms3036.

Silva, R. M., and V. Sacek, 2019, Shallow necking depth and differential denudation linked to post-rift continental reactivation: The origin of the Cenozoic basins in southeastern Brazil: Terra Nova, 31, 527–533, doi: 10.1111/ter.12423.

Silva, R. M., and V. Sacek, 2022, Influence of surface processes on postrift faulting during divergent margins evolution: Tectonics, 41, e2021TC006808, doi: 10.1029/2021TC006808.

Torrance, K., and D. Turcotte, 1971, Thermal convection with large viscosity variations: Journal of Fluid Mechanics, 47, 113–125, doi: 10.1017/S002211207100096X.

Turcotte, D., and G. Schubert, 2002, Geodynamics, 2nd ed.: Cambridge University Press.

Ussami, N., and E. Molina, 1999, Flexural modeling of the neoproterozoic Araguaia belt, central Brazil: Journal of South American Earth Sciences, 12, 87–98, doi: 10.1016/S0895-9811(99)00007-3.

Ussami, N., S. Shiraiwa, and J. Dominguez, 1999, Basement reactivation in a sub-Andean foreland flexural bulge: The Pantanal wetland, SW Brazil: Tectonics, 18, 25–39, doi: 10.1029/1998TC900004.

Watts, A., 2001, Isostasy and Flexure of the Lithosphere: Cambridge University Press.

Watts, A., and E. Burov, 2003, Lithospheric strength and its relationship to the elastic and seismogenic layer thickness: Earth and Planetary Science Letters, 213, 113–131, doi: 10.1016/S0012-821X(03)00289-9.

Willett, S., 1999, Orogeny and orography: The effects of erosion on the structure of mountain belts: Journal of Geophysical Research: Solid Earth, 104, 28957–28981, doi: 0.1029/1999JB900248.

Wolf, S., R. Huismans, J. Braun, and X. Yuan, 2022, Topography of mountain belts controlled by rheology and surface processes: Nature, 606, 516–521, doi: 10.1038/s41586-022-04700-6.

Yuan, X., J. Braun, L. Guerit, D. Rouby, and G. Cordonnier, 2019, A new efficient method to solve the stream power law model taking into account sediment deposition: Journal of Geophysical Research: Earth Surface, 124, 1346–1365, doi: 10.1029/2018JF004867.

Zhong, S., 2006, Constraints on thermochemical convection of the mantle from plume heat flux, plume excess temperature, and upper mantle temperature: Journal of Geophysical Research: Solid Earth, 111, doi: 10.1029/2005JB003972.


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