# Progress in numerical modeling of subducting plate dynamics

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## Abstract

The core concerns of plate tectonics theory are the dynamics of subducting plates, which can be studied by integrating multidisciplinary fields such as seismology, mineral physics, rock geochemistry, geological formation studies, sedimentology, and numerical simulations. By establishing a theoretical model and solving it with numerical methods, one can replicate the dynamic effects of a subducting plate, quantifying its evolution and the surface response. Simulations can also explain the observations and experimental results of other disciplines. Therefore, numerical models are among the most important tools for studying the dynamics of subducting plates. This paper provides a review on recent advances in the numerical modeling of subducting plate dynamics. It covers various aspects, namely, the origin of plate tectonics, the initiation process and thermal structure of subducting slab, and the main subduction slab dynamics in the upper mantle, mantle transition zone, and lower mantle. The results of numerical models are based on the theoretical equations of mass, momentum, and energy conservation. To better understand the dynamic progress of subducting plates, the simulation results must be verified in comparisons with the results from natural observations by geology, geophysics and geochemistry. With the substantial increase in computing power and continuous improvement of simulation methods, numerical models will become a more accurate and efficient means of studying the frontier issues of Earth sciences, including subducting plate dynamics.

## Keywords

Subducting plate Dynamics Numerical simulation## Notes

### Acknowledgements

Thanks to Yongfei Zheng for his help in writing this article. The opinions of Zhonghai Li and other three anonymous review experts have greatly contributed to the improvement of this article. This work was supported by the National Key Basic Research and Development Program Project (Grant No. 2015CB856106) and the Sichuan-Yunnan National Earthquake Monitoring and Forecasting Experimental Site Project (Grant No. 2017CESE0102).

## References

- Agrusta R, Goes S, van Hunen J. 2017. Subducting-slab transition-zone interaction: Stagnation, penetration and mode switches. Earth Planet Sci Lett, 464: 10–23Google Scholar
- Ammann M W, Brodholt J P, Wookey J, Dobson D P. 2010. First-principles constraints on diffusion in lower-mantle minerals and a weak D? layer. Nature, 465: 462–465Google Scholar
- Andrews E R, Billen M I. 2009. Rheologic controls on the dynamics of slab detachment. Tectonophysics, 464: 60–69Google Scholar
- Bercovici D, Ricard Y. 2014. Plate tectonics, damage and inheritance. Nature, 508: 513–516Google Scholar
- Betts P G, Mason W G, Moresi L. 2012. The influence of a mantle plume head on the dynamics of a retreating subduction zone. Geology, 40: 739–742Google Scholar
- Billen M I. 2008. Modeling the dynamics of subducting slabs. Annu Rev Earth Planet Sci, 36: 325–356Google Scholar
- Billen M I, Hirth G. 2007. Rheologic controls on slab dynamics. Geochem Geophys Geosyst, 8: Q08012Google Scholar
- Bird P. 1988. Formation of the Rocky Mountains, western United States: A continuum computer model. Science, 239: 1501–1507Google Scholar
- Bunge H P, Richards M A, Baumgardner J R. 1996. Effect of depthdependent viscosity on the planform of mantle convection. Nature, 379: 436–438Google Scholar
- Capitanio F A, Faccenna C, Zlotnik S, Stegman D R. 2011. Subduction dynamics and the origin of Andean orogeny and the Bolivian orocline. Nature, 480: 83–86Google Scholar
- Christensen U R. 1996. The influence of trench migration on slab penetration into the lower mantle. Earth Planet Sci Lett, 140: 27–39Google Scholar
- Christensen U R, Yuen D A. 1985. Layered convection induced by phase transitions. J Geophys Res, 90: 10291–10300Google Scholar
- Cížková H, Bina C R. 2013. Effects of mantle and subduction-interface rheologies on slab stagnation and trench rollback. Earth Planet Sci Lett, 379: 95–103Google Scholar
- Condie K C, Pease V. 2008. When did Plate Tectonics Begin on Planet Earth? Boulder: Geological Society of America, 294Google Scholar
- Coney P J, Reynolds S J. 1977. Cordilleran Benioff zones. Nature, 270: 403–406Google Scholar
- Connolly J A D. 2005. Computation of phase equilibria by linear programming: A tool for geodynamic modeling and its application to subduction zone decarbonation. Earth Planet Sci Lett, 236: 524–541Google Scholar
- Conrad C P, Lithgow-Bertelloni C. 2002. How mantle slabs drive plate tectonics. Science, 298: 207–209Google Scholar
- Davies J H. 1999. Simple analytic model for subduction zone thermal structure. Geophys J Int, 139: 823–828Google Scholar
- Deschamps F, Godard M, Guillot S, Hattori K. 2013. Geochemistry of subduction zone serpentinites: A review. Lithos, 178: 96–127Google Scholar
- Duesterhoeft E, Quinteros J, Oberhänsli R, Bousquet R, de Capitani C. 2014. Relative impact of mantle densification and eclogitization of slabs on subduction dynamics: A numerical thermodynamic/thermokinematic investigation of metamorphic density evolution. Tectonophysics, 637: 20–29Google Scholar
- England P, Wilkins C. 2004. A simple analytical approximation to the temperature structure in subduction zones. Geophys J Int, 159: 1138–1154Google Scholar
- English J M, Johnston S T, Wang K. 2003. Thermal modelling of the Laramide orogeny: Testing the flat-slab subduction hypothesis. Earth Planet Sci Lett, 214: 619–632Google Scholar
- Enns A, Becker T W, Schmeling H. 2005. The dynamics of subduction and trench migration for viscosity stratification. Geophys J Int, 160: 761–775Google Scholar
- Flament N, Gurnis M, Müller R D, Bower D J, Husson L. 2015. Influence of subduction history on South American topography. Earth Planet Sci Lett, 430: 9–18Google Scholar
- Flament N, Gurnis M, Muller R D. 2013. A review of observations and models of dynamic topography. Lithosphere, 5: 189–210Google Scholar
- Forsyth D, Uyeda S. 1975. On the relative importance of the driving forces of plate motion. Geophys J Int, 43: 163–200Google Scholar
- Fukao Y, Obayashi M, Inoue H, Nenbai M. 1992. Subducting slabs stagnant in the mantle transition zone. J Geophys Res, 97: 4809–4822Google Scholar
- Fukao Y, Obayashi M, Nakakuki T. 2009. Stagnant slab: A review. Annu Rev Earth Planet Sci, 37: 19–46Google Scholar
- Garel F, Goes S, Davies D R, Davies J H, Kramer S C, Wilson C R. 2014. Interaction of subducted slabs with the mantle transition-zone: A regime diagram from 2-D thermo-mechanical models with a mobile trench and an overriding plate. Geochem Geophys Geosyst, 15: 1739–1765Google Scholar
- Gerya T. 2011. Future directions in subduction modeling. J Geodyn, 52: 344–378Google Scholar
- Gerya T V, Yuen D A. 2003. Rayleigh-Taylor instabilities from hydration and melting propel ‘cold plumes’ at subduction zones. Earth Planet Sci Lett, 212: 47–62Google Scholar
- Gerya T V, Stern R J, Baes M, Sobolev S V, Whattam S A. 2015. Plate tectonics on the Earth triggered by plume-induced subduction initiation. Nature, 527: 221–225Google Scholar
- Goes S, Agrusta R, van Hunen J, Garel F. 2017. Subduction-transition zone interaction: A review. Geosphere, 13: 644–664Google Scholar
- Gorbatov A, Fukao Y. 2005. Tomographic search for missing link between the ancient Farallon subduction and the present Cocos subduction. Geophys J Int, 160: 849–854Google Scholar
- Grand S P, van der Hilst R D, Widiyantoro S. 1997. Global seismic tomography: A snapshot of convection in the Earth. GSA Today, 7: 1–7Google Scholar
- Groome W G, Thorkelson D J. 2009. The three-dimensional thermo-mechanical signature of ridge subduction and slab window migration. Tectonophysics, 464: 70–83Google Scholar
- Gurnis M, Hager B H. 1988. Controls of the structure of subducted slabs. Nature, 335: 317–321Google Scholar
- Gurnis M, Hall C, Lavier L. 2004. Evolving force balance during incipient subduction. Geochem Geophys Geosyst, 5: Q07001Google Scholar
- Gurnis M, Dietmar Meller R, Moresi L. 1998. Cretaceous vertical motion of Australia and the Australian-Antarctic discordance. Science, 279: 1499–1504Google Scholar
- Gutscher M A, Spakman W, Bijwaard H, Engdahl E R. 2000. Geodynamics of flat subduction: Seismicity and tomographic constraints from the Andean margin. Tectonics, 19: 814–833Google Scholar
- Hacker B R, Peacock S M, Abers G A, Holloway S D. 2003. Subduction factory 2. Are intermediate-depth earthquakes in subducting slabs linked to metamorphic dehydration reactions? J Geophys Res, 108: 2030Google Scholar
- Hager B H, Clayton R W, Richards M A, Comer R P, Dziewonski A M. 1985. Lower mantle heterogeneity, dynamic topography and the geoid. Nature, 313: 541–545Google Scholar
- Hall P S. 2012. On the thermal evolution of the mantle wedge at subduction zones. Phys Earth Planet Inter, 198-199: 9–27Google Scholar
- Hall C E, Gurnis M, Sdrolias M, Lavier L L, Müller R D. 2003. Catastrophic initiation of subduction following forced convergence across fracture zones. Earth Planet Sci Lett, 212: 15–30Google Scholar
- Hasenclever J, Morgan J P, Hort M, Rüpke L H. 2011. 2D and 3D numerical models on compositionally buoyant diapirs in the mantle wedge. Earth Planet Sci Lett, 311: 53–68Google Scholar
- Hayes G P, Wald D J, Johnson R L. 2012. Slab1.0: A three-dimensional model of global subduction zone geometries. J Geophys Res, 117: B01302Google Scholar
- He L J. 2017. Wet plume atop of the flattening slab: Insight into intraplate volcanism in East Asia. Phys Earth Planet Inter, 269: 29–39Google Scholar
- Hermann J, Spandler C, Hack A, Korsakov A V. 2006. Aqueous fluids and hydrous melts in high-pressure and ultra-high pressure rocks: Implications for element transfer in subduction zones. Lithos, 92: 399–417Google Scholar
- Hernlund J W, Thomas C, Tackley P J. 2005. A doubling of the postperovskite phase boundary and structure of the Earth’s lowermost mantle. Nature, 434: 882–886Google Scholar
- Hopkins M, Harrison T M, Manning C E. 2008. Low heat flow inferred from >4 Gyr zircons suggests Hadean plate boundary interactions. Nature, 456: 493–496Google Scholar
- Huang J, Zhao D. 2006. High-resolution mantle tomography of China and surrounding regions. J Geophys Res, 111: B09305Google Scholar
- Jarrard R D. 1986. Relations among subduction parameters. Rev Geophys, 24: 217–284Google Scholar
- Kellogg L H, Hager B H, van der Hilst R D. 1999. Compositional stratification in the deep mantle. Science, 283: 1881–1884Google Scholar
- Kincaid C, Sacks I S. 1997. Thermal and dynamical evolution of the upper mantle in subduction zones. J Geophys Res, 102: 12295–12315Google Scholar
- King S D, Frost D J, Rubie D C. 2014. Why cold slabs stagnate in the transition zone. Geology, 43: 231–234Google Scholar
- Kirby S H, Durham W B, Stern L A. 1991. Mantle phase changes and deepearthquake faulting in subducting lithosphere. Science, 252: 216–225Google Scholar
- Kirby S H, Stein S, Okal E A, Rubie D C. 1996. Metastable mantle phase transformations and deep earthquakes in subducting oceanic lithosphere. Rev Geophys, 34: 261–306Google Scholar
- Korenaga J. 2013. Initiation and evolution of plate tectonics on Earth: Theories and observations. Annu Rev Earth Planet Sci, 41: 117–151Google Scholar
- Lee C, King S D. 2011. Dynamic buckling of subducting slabs reconciles geological and geophysical observations. Earth Planet Sci Lett, 312: 360–370Google Scholar
- Leng W, Gurnis M, Asimow P. 2012. From basalts to boninites: The geodynamics of volcanic expression during induced subduction initiation. Lithosphere, 4: 511–523Google Scholar
- Leng W, Gurnis M. 2011. Dynamics of subduction initiation with different evolutionary pathways. Geochem Geophys Geosyst, 12: Q12018Google Scholar
- Leng W, Gurnis M. 2015. Subduction initiation at relic arcs. Geophys Res Lett, 42: 7014–7021Google Scholar
- Leng W, Mao W. 2015. Geodynamic modeling of thermal structure of subduction zones. Sci China Earth Sci, 58: 1070–1083Google Scholar
- Li Z H, Ribe N M. 2012. Dynamics of free subduction from 3-D boundary element modeling. J Geophys Res, 117: B06408Google Scholar
- Li Z X, Li X H. 2007. Formation of the 1300-km-wide intracontinental orogen and postorogenic magmatic province in Mesozoic South China: A flat-slab subduction model. Geology, 35: 179–182Google Scholar
- Liu L. 2015. The ups and downs of North America: Evaluating the role of mantle dynamic topography since the Mesozoic. Rev Geophys, 53: 1022–1049Google Scholar
- Liu L, Spasojevic S, Gurnis M. 2008. Reconstructing Farallon plate subduction beneath North America back to the late Cretaceous. Science, 322: 934–938Google Scholar
- Liu L, Stegman D R. 2012. Origin of Columbia River flood basalt controlled by propagating rupture of the Farallon slab. Nature, 482: 386–389Google Scholar
- Liu M Q, Li Z H, Yang S H. 2017. Diapir versus along-channel ascent of crustal material during plate convergence: Constrained by the thermal structure of subduction zones. J Asian Earth Sci, 145: 16–36Google Scholar
- Liu S, Currie C A. 2016. Farallon plate dynamics prior to the Laramide orogeny: Numerical models of flat subduction. Tectonophysics, 666: 33–47Google Scholar
- Mao Z, Li X Y. 2016. Effect of hydration on the elasticity of mantle minerals and its geophysical implications. Sci China Earth Sci, 59: 873–888Google Scholar
- McKenzie D P. 1969. Speculations on the consequences and causes of plate motions. Geophys J Int, 18: 1–32Google Scholar
- McNamara A K, Zhong S. 2005. Thermochemical structures beneath Africa and the Pacific Ocean. Nature, 437: 1136–1139Google Scholar
- Molnar P, England P. 1990. Temperatures, heat flux, and frictional stress near major thrust faults. J Geophys Res, 95: 4833–4856Google Scholar
- Molnar P, England P. 1995. Temperatures in zones of steady-state underthrusting of young oceanic lithosphere. Earth Planet Sci Lett, 131: 57–70Google Scholar
- Molnar P, Freedman D, Shih J S F. 1979. Lengths of intermediate and deep seismic zones and temperatures in downgoing slabs of lithosphere. Geophys J Int, 56: 41–54Google Scholar
- Monnereau M, Yuen D A. 2007. Topology of the postperovskite phase transition and mantle dynamics. Proc Natl Acad Sci USA, 104: 9156–9161Google Scholar
- Morishige M, van Keken P E. 2014. Along-arc variation in the 3-D thermal structure around the junction between the Japan and Kurile arcs. Geochem Geophys Geosyst, 15: 2225–2240Google Scholar
- Mueller S, Phillips R J. 1991. On the initiation of subduction. J Geophys Res, 96: 651–665Google Scholar
- Mueller B, Zoback M L, Fuchs K, Mastin L, Gregersen S, Pavoni N, Stephansson O, Ljunggren C. 1992. Regional patterns of tectonic stress in Europe. J Geophys Res, 97: 11783–11803Google Scholar
- Murakami M, Hirose K, Kawamura K, Sata N, Ohishi Y. 2004. Postperovskite phase transition in MgSiO3. Science, 304: 855–858Google Scholar
- Nakagawa T, Tackley P J. 2004. Effects of a perovskite-post perovskite phase change near core-mantle boundary in compressible mantle convection. Geophys Res Lett, 31: L16611Google Scholar
- Nakagawa T, Tackley P J. 2005. The interaction between the post-perovskite phase change and a thermo-chemical boundary layer near the core-mantle boundary. Earth Planet Sci Lett, 238: 204–216Google Scholar
- Nakao A, Iwamori H, Nakakuki T. 2016. Effects of water transportation on subduction dynamics: Roles of viscosity and density reduction. Earth Planet Sci Lett, 454: 178–191Google Scholar
- Nikolaeva K, Gerya T V, Marques F O. 2010. Subduction initiation at passive margins: Numerical modeling. J Geophys Res, 115: B03406Google Scholar
- Nikolaeva K, Gerya T V, Marques F O. 2011. Numerical analysis of subduction initiation risk along the Atlantic American passive margins. Geology, 39: 463–466Google Scholar
- Nutman A P, Friend C R L, Bennett V C. 2002. Evidence for 3650–3600 Ma assembly of the northern end of the Itsaq Gneiss Complex, Greenland: Implication for early Archaean tectonics. Tectonics, 21: 5–1–5–28Google Scholar
- Oganov A R, Ono S. 2005. Theoretical and experimental evidence for a post-perovskite phase of MgSiO
_{3}in Earth’s D? layer. Nature, 430: 445–448Google Scholar - Peacock S M, Wang K. 1999. Seismic consequences of warm versus cool subduction metamorphism: Examples from southwest and northeast Japan. Science, 286: 937–939Google Scholar
- Peacock S M. 2003. Thermal structure and metamorphic evolution of subducting slabs. Washington D C: Geophysical Monograph-American Geophysical Union. 7–22Google Scholar
- Penniston-Dorland S C, Kohn M J, Manning C E. 2015. The global range of subduction zone thermal structures from exhumed blueschists and eclogites: Rocks are hotter than models. Earth Planet Sci Lett, 428: 243–254Google Scholar
- Piromallo C, Morelli A. 2003. P wave tomography of the mantle under the Alpine-Mediterranean area. J Geophys Res, 108: 2065Google Scholar
- Rey P F, Coltice N, Flament N. 2014. Spreading continents kick-started plate tectonics. Nature, 513: 405–408Google Scholar
- Schellart W P, Freeman J, Stegman D R, Moresi L, May D. 2007. Evolution and diversity of subduction zones controlled by slab width. Nature, 446: 308–311Google Scholar
- Shi Y, Wei D, Li Z H, Liu M Q, Liu M. 2018. Subduction mode selection during slab and mantle transition zone interaction: Numerical modeling. Pure Appl Geophys, 175: 529–548Google Scholar
- Stadler G, Gurnis M, Burstedde C, Wilcox L C, Alisic L, Ghattas O. 2010. The dynamics of plate tectonics and mantle flow: From local to global scales. Science, 329: 1033–1038Google Scholar
- Stern R J. 2002. Subduction zones. Rev Geophys, 40, doi: 10.1029/2001RG000108Google Scholar
- Stern R. 2004. Subduction initiation: Spontaneous and induced. Earth Planet Sci Lett, 226: 275–292Google Scholar
- Stern R J, Gerya T. 2017. Subduction initiation in nature and models: A review. TectonophysicsGoogle Scholar
- Syracuse E M, van Keken P E, Abers G A, Suetsugu D, Bina C, Inoue T, Wiens D, Jellinek M. 2010. The global range of subduction zone thermal models. Phys Earth Planet Inter, 183: 73–90Google Scholar
- Tackley P J, Stevenson D J, Glatzmaier G A, Schubert G. 1993. Effects of an endothermic phase transition at 670 km depth in a spherical model of convection in the Earth’s mantle. Nature, 361: 699–704Google Scholar
- Tan E, Leng W, Zhong S, Gurnis M. 2011. On the location of plumes and lateral movement of thermochemical structures with high bulk modulus in the 3-D compressible mantle. Geochem Geophys Geosyst, 12: Q07005Google Scholar
- Thielmann M, Kaus B J P. 2012. Shear heating induced lithospheric-scale localization: Does it result in subduction? Earth Planet Sci Lett, 359-360: 1–13Google Scholar
- Thorkelson D J. 1996. Subduction of diverging plates and the principles of slab window formation. Tectonophysics, 255: 47–63Google Scholar
- Torii Y, Yoshioka S. 2007. Physical conditions producing slab stagnation: Constraints of the Clapeyron slope, mantle viscosity, trench retreat, and dip angles. Tectonophysics, 445: 200–209Google Scholar
- Torsvik T H, Burke K, Steinberger B, Webb S J, Ashwal L D. 2010. Diamonds sampled by plumes from the core-mantle boundary. Nature, 466: 352–355Google Scholar
- Tschauner O, Ma C, Beckett J R, Prescher C, Prakapenka V B, Rossman G R. 2014. Discovery of bridgmanite, the most abundant mineral in Earth, in a shocked meteorite. Science, 346: 1100–1102Google Scholar
- Turcotte D L, Schubert G. 2002. Geodynamics. 2nd ed. New York: Cambridge University Press. 456Google Scholar
- Ulmer P, Trommsdorff V. 1995. Serpentine stability to mantle depths and subduction-related magmatism. Science, 268: 858–861Google Scholar
- van der Hilst R D, de Hoop M V, Wang P, Shim S H, Ma P, Tenorio L. 2007. Seismostratigraphy and thermal structure of Earth’s core-mantle boundary region. Science, 315: 1813–1817Google Scholar
- van der Hist R, Engdahl R, Spakman W, Nolet G. 1991. Tomographic imaging of subducted lithosphere below northwest Pacific island arcs. Nature, 353: 37–43Google Scholar
- van der Hilst R D, Widiyantoro S, Engdahl E R. 1997. Evidence for deep mantle circulation from global tomography. Nature, 386: 578–584Google Scholar
- van der Lee S, Nolet G. 1997. Seismic image of the subducted trailing fragments of the Farallon plate. Nature, 386: 266–269Google Scholar
- van Hunen J, Moyen J F. 2012. Archean subduction: Fact or fiction? Annu Rev Earth Planet Sci, 40: 195–219Google Scholar
- van Hunen J, van den Berg A P, Vlaar N J. 2002. On the role of subducting oceanic plateaus in the development of shallow flat subduction. Tectonophysics, 352: 317–333Google Scholar
- van Hunen J, van den Berg A P, Vlaar N J. 2004. Various mechanisms to induce present-day shallow flat subduction and implications for the younger Earth: A numerical parameter study. Phys Earth Planet Inter, 146: 179–194Google Scholar
- van Keken P E, Hacker B R, Syracuse E M, Abers G A. 2011. Subduction factory: 4. Depth-dependent flux of H2O from subducting slabs worldwide. J Geophys Res, 116: B01401Google Scholar
- van Keken P E, Kiefer B, Peacock S M. 2002. High-resolution models of subduction zones: Implications for mineral dehydration reactions and the transport of water into the deep mantle. Geochem-Geophys-Geosyst, 3: 1056Google Scholar
- Wada I W, King S. 2015. Dynamics of subducting slabs: Numerical modeling and constraints from seismology, geoid, topography, geochemistry and petrology. Treatise Geophys, 7: 339–391Google Scholar
- Wada I, Wang K, He J, Hyndman R D. 2008. Weakening of the subduction interface and its effects on surface heat flow, slab dehydration, and mantle wedge serpentinization. J Geophys Res, 113: B04402Google Scholar
- Wada I, Wang K. 2009. Common depth of slab-mantle decoupling: Reconciling diversity and uniformity of subduction zones. Geochem Geophys Geosyst, 10: Q10009Google Scholar
- Wilson C R, Spiegelman M, van Keken P E, Hacker B R. 2014. Fluid flow in subduction zones: The role of solid rheology and compaction pressure. Earth Planet Sci Lett, 401: 261–274Google Scholar
- Yoshioka S, Naganoda A, Suetsugu D, Bina C, Inoue T, Wiens D, Jellinek M. 2010. Effects of trench migration on fall of stagnant slabs into the lower mantle. Phys Earth Planet Inter, 183: 321–329Google Scholar
- Zheng Y F. 2012. Metamorphic chemical geodynamics in continental subduction zones. Chem Geol, 328: 5–48Google Scholar
- Zheng Y F, Chen Y X. 2016. Continental versus oceanic subduction zones. Nat Sci Rev, 40: nww049Google Scholar
- Zheng Y F, Chen R X, Xu Z, Zhang S B. 2016. The transport of water in subduction zones. Sci China Earth Sci, 59: 651–682Google Scholar
- Zhong S J, Zhang N, Li Z X, Roberts J H. 2007. Supercontinent cycles, true polar wander, and very long-wavelength mantle convection. Earth Planet Sci Lett, 261: 551–564Google Scholar