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Earth curvature effects on subduction morphology: Modeling subduction in a spherical setting

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Abstract

We present the first application in geodynamics of a (Fast Multipole) Accelerated Boundary Element Method (Accelerated-BEM) for Stokes flow. The approach offers the advantages of a reduced number of computational elements and linear scaling with the problem size. We show that this numerical method can be fruitfully applied for the simulation of several geodynamic systems at the planetary scale in spherical coordinates, and we suggest a general approach for modeling combined mantle convection and plate tectonics. The first part of the paper is devoted to the technical exposition of the new approach, while the second part focuses on the effect played by Earth curvature on the subduction of a very wide oceanic lithosphere (W = 6,000 km and W = 9,000 km), comparing the effects of two different planetary radii (ER = 6,371 km, 2ER = 2 × 6,371 km), corresponding to an "Earth-like" model (ER) and to a "flat Earth" one (2ER). The results show a distinct difference between the two models: while the slab on a "flat Earth" shows a slight undulation, the same subducting plate on the "Earth-like" setting presents a dual behavior characterized by concave curvature at the edges and by a folding with wavelength of the order of magnitude of 1,000 km at the center of the slab.

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References

  1. Barnes J, Hut P (1986) A hierarchical O(N log N) force-calculation algorithm. Nature 324

  2. Bird P (2003) An updated digital model of plate boundaries. Geochem Geophys Geosyst 4(3):1027. doi:10.1029/2001GC000252

    Article  Google Scholar 

  3. Carlson RL, Hilde TWC, Uyeda S (1983) The driving mechanism of plate tectonics: relation to age of the lithosphere at trenches. Geophys Res Lett 10:297–300

    Article  Google Scholar 

  4. Capitanio FA, Morra G, Goes S (2007) Dynamic models of downgoing plate buoyancy driven subduction: subduction motions and energy dissipation. Earth Planet Sci Lett (in press)

  5. Christensen UR (1996) The influence of trench migration on slab penetration into the lower mantle. Earth Planet Sci Lett 140:27–39

    Article  Google Scholar 

  6. Cizkova H, Cadek O, Van den Berg AP, Vlaar NJ (1999) Can lower mantle slab-like seismic anomalies be explained by thermal coupling between upper and lower mantles? Geophys Res Lett 26:1501–1504

    Article  Google Scholar 

  7. Davies G (1980) Thermal histories of convective Earth models and constraints on radiogenic heat production in the Earth. J Geophys Res 85:2517–2530

    Article  Google Scholar 

  8. Davaille A, Jaupart C (1993) Transient high-Rayleigh-number thermal convection with large viscosity variations. J Fluid Mech 253

  9. Davaille A, Jaupart C (1994) Onset of thermal convection in fluids with temperature-dependent viscosity: application to the oceanic mantle. J Geophys Res 99:19,853–19,866

    Article  Google Scholar 

  10. Faccenna C, Davy P, Brun JP, Funiciello R, Giardini D, Mattei M, Nalpas T (1996) The dynamics of back-arc extension: an experimental approach to the opening of the Tyrrhenian Sea. Geophys J Int 126(3):781–795

    Google Scholar 

  11. Fukao Y, Widiyantoro S, Obayashi M (2001) Stagnant slabs in the upper and lower mantle transition zone. Rev Geophys 39:291–323

    Article  Google Scholar 

  12. Funiciello F, Morra G, Regenauer-Lieb K, Giardini D (2003) Dynamics of retreating slabs (part 1): insights from 2-D numerical experiments. J Geophys Res 108(B4):2206. doi:10.1029/2001JB000898

    Article  Google Scholar 

  13. Goes S, Capitanio FA, Morra G (2008) Evidence of lower mantle slab penetration phases in plate motions. Nature (in press)

  14. Greengard L, Rokhlin V (1987) A fast algorithm for particle simulations. J Comput Phys A 73:325–348

    Article  MATH  MathSciNet  Google Scholar 

  15. Gurnis M, Hager BH (1988) Controls of the structure of subducted slabs. Nature 335:317–321

    Article  Google Scholar 

  16. Guillou-Frottier L, Buttles J, Olson P (1995) Laboratory experiments on the structure of subducted lithosphere. Earth Planet Sci Lett 133:19–35

    Article  Google Scholar 

  17. Isacks B, Molnar P (1971) Distribution of stresses in the descending lithosphere from a global survey of focal mechanism solutions of mantle earthquakes. Rev Geophys 9:103–174

    Article  Google Scholar 

  18. Ita J, King SD (1998) The influence of thermodynamic formulation on simulations of subduction zone geometry and history. Geophys Res Lett 25:1463–1466

    Article  Google Scholar 

  19. Jacoby WR (1973) Model experiment of plate movements. Nat Phys Sci 242(122):130–134

    Google Scholar 

  20. Lallemand S, Heuret A, Boutelier D (2005) On the relationships between slab dip, back-arc stress, upper plate absolute motion, and crustal nature in subduction zones. Geochem Geophys Geosyst 6:917

    Article  Google Scholar 

  21. Manga M, Stone HA (1995) Low Reynolds number motion of bubbles, drops and rigid spheres through fluid-fluid interfaces. J Fluid Mech 287:279–298

    Article  MathSciNet  Google Scholar 

  22. Moresi L, Gurnis M (1996) Constraints on the lateral strength of slabs from three-dimensional dynamic flow models. Earth Planet Sci Lett 138:15–28

    Article  Google Scholar 

  23. Morra G, Regenauer-Lieb K (2006) A coupled solid–fluid method for modeling subduction. Phil Mag 86:3307–3323

    Article  Google Scholar 

  24. Morra G, Regenauer-Lieb K, Giardini D (2006) Curvature of oceanic arcs. Geology 34:877–880

    Article  Google Scholar 

  25. Pozrikidis C (1992) Boundary integral and singularity methods for linearized viscous flow

  26. Phillips BR, Bunge H-P (2005) Heterogeneity and time dependence in 3D spherical mantle convection models with continental drift. Earth Planet Sci Lett 233:121–135

    Article  Google Scholar 

  27. Regenauer-Lieb K, Yuen DA (2003) Modeling shear zones in geological and planetary sciences: solid- and fluid-thermal-mechanical approaches. Earth Sci Rev 63:295–349

    Article  Google Scholar 

  28. Regenauer-Lieb K, Yuen D, Branlund J (2001) The initiation of subduction: criticality by addition of water? Science 294:578–580

    Article  Google Scholar 

  29. Ricard Y, Richards MA, Lithgow-Bertelloni C, Lestunff Y (1993) Geodynamic model of mantle density heterogeneity. J Geophys Res 98:21895–21909

    Article  Google Scholar 

  30. Ribe NM, Stutzmann E, Ren Y, van der Hilst R (2007) Buckling instabilities of subducted lithosphere beneath the transition zone. Earth Planet Sci Lett 254:173–179

    Article  Google Scholar 

  31. Royden LH, Husson L (2006) Trench motion, slab geometry and viscous stresses in subduction systems. Geophys J Int 167:881–905

    Article  Google Scholar 

  32. Schellart WP, Freeman J, Stegman DR, Moresi L, May D (2007) Evolution and diversity of subduction zones controlled by slab width. Nature 446. doi:10.1038/nature05615

  33. Sdrolias M, Mueller RD (2006) Controls on back-arc basin formation. Geochem Geophys Geosyst 7. doi:10.1029/2005GC001090

  34. Sornette D, Pisarenko V (2003) Fractal plate tectonics. Geophys Res Lett 30(3):1105. doi:10.1029/2002GL015043

    Article  Google Scholar 

  35. Stegman DR, Freeman J, Schellart WP, Moresi L, May D (2006) Influence of trench width on subduction hinge retreat rates in 3-D models of slab rollback. Geoc Geophy Geosys 7:1–22

    Google Scholar 

  36. Tackley P (2000) Self-consistent generation of tectonic plates in time- dependent, three-dimensional mantle convection simulations, 1. Pseudoplastic yielding. Geochem Geophys Geosyst 1:23

    Google Scholar 

  37. Tornberg AK, Greengard L (2007) A fast multipole method for the three dimensional stokes equations. J Comput Phys (in press)

  38. Van der Hilst RD, Karason H (1999) Compositional heterogeneity in the bottom 1000 kilometers of Earth’s mantle: toward a hybrid convection model. Science 283(5409):1885–1888

    Article  Google Scholar 

  39. Van der Voo R, Spakman W, Bijwaard H (1999) Mesozoic subducted slabs under Siberia. Nature 397:246–249

    Article  Google Scholar 

  40. Warren MS, Salmon JK (1993) A parallel hashed Oct-Tree N-body algorithm. In: Supercomputing, FMM93, pp 12–21

  41. Youngren GK, Acrivos A (1975) Stokes flow part a particle of arbitrary shape: a numerical method of solution. J Fluid Mech 69(2):377–403

    Article  MATH  MathSciNet  Google Scholar 

  42. Zhong S, Gurnis M (1995) Mantle convection with plates and mobile, faulted plate margins. Science 267:838–843

    Article  Google Scholar 

Download references

Acknowledgments

This work, as part of the Eurohorcs/ESF European Young Investigators Awards Scheme, was supported by funds from the National Research Council of Italy and other National Funding Agencies participating in the 3rd Memorandum of Understanding, as well as from the EC Sixth Framework Programme.

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Correspondence to Gabriele Morra.

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Morra, G., Chatelain, P., Tackley, P. et al. Earth curvature effects on subduction morphology: Modeling subduction in a spherical setting. Acta Geotech. 4, 95–105 (2009). https://doi.org/10.1007/s11440-008-0060-5

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  • DOI: https://doi.org/10.1007/s11440-008-0060-5

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