Spherical dynamic models of top‐down tectonics

We use the Multipole–Boundary Element Method (MP‐BEM) to simulate regional and global geodynamics in a spherical 3‐D setting. We first simulate an isolated subducting rectangular plate with length (Llitho) and width (Wlitho) varying between 0.5 and 2 times the radius of the Earth (REarth) and with viscosity ηlitho varying between 100 and 500 times the upper mantle (ηUM), sinking in a layered mantle characterized by lower‐upper mantle viscosity ratioλ = ηLM/ηUM varying between 1 and 80. In a mantle with small upper/lower viscosity contrast (λ ≅ 1), trench and plate motions are weakly dependent on Wlitho; plate motion is controlled by slab pull if Llitho ≤ REarth, while for longer plates plate speed strongly decreases because of the plate basal friction and flow reorganization. An increasing viscosity ratio λ gradually breaks this pattern, and for λ ≅ 10 combined with Wlitho ≈ REarth(and greater) trench advance and retreat are simultaneously observed. These results offer a first‐order explanation of the origin of the size (Llitho ≈ Wlitho ≈ REarth) of the largest plates observed over the past 150 Myr. Finally, two global plate tectonic simulations are performed from reconstructed plates and slabs at 25 Ma before present and before 100 Ma, respectively. It is shown that MP‐BEM predicts present plate kinematics if plate‐mantle decoupling is adopted for the longest plates (Llitho > REarth). Models for 100 Ma show that the slab‐slab interaction between India and Izanagi plates at 100 Ma can explain the propagation of the plate reorganization from the Indian to the Pacific plate.

[1]  Mark Turner,et al.  Plate tectonic reconstructions with continuously closing plates , 2012, Comput. Geosci..

[2]  B. Buffett,et al.  Curvature of subducted lithosphere from earthquake locations in the Wadati‐Benioff zone , 2011 .

[3]  D. Giardini,et al.  Signatures of downgoing plate-buoyancy driven subduction in Cenozoic plate motions , 2011 .

[4]  Shin‐Chan Han,et al.  Influence of variable uncertainties in seismic tomography models on constraining mantle viscosity from geoid observations , 2011 .

[5]  Alberto Salvadori,et al.  Analytical integrations in 3D BEM for elliptic problems: Evaluation and implementation , 2010 .

[6]  Georg Stadler,et al.  The Dynamics of Plate Tectonics and Mantle Flow: From Local to Global Scales , 2010, Science.

[7]  P. Koumoutsakos,et al.  The fate of the slabs interacting with a density/viscosity hill in the mid-mantle , 2010 .

[8]  M. Jadamec,et al.  Reconciling surface plate motions with rapid three-dimensional mantle flow around a slab edge , 2010, Nature.

[9]  Maisha Amaru,et al.  Towards absolute plate motions constrained by lower-mantle slab remnants , 2010 .

[10]  C. Faccenna,et al.  Role of the overriding plate in the subduction process: Insights from numerical models , 2010 .

[11]  D. Stegman,et al.  Competing influences of plate width and far-field boundary conditions on trench migration and morphology of subducted slabs in the upper mantle , 2010 .

[12]  Louis Moresi,et al.  Upper plate controls on deep subduction, trench migrations and deformations at convergent margins , 2010 .

[13]  D. Stegman,et al.  A regime diagram for subduction styles from 3-D numerical models of free subduction , 2010 .

[14]  N. Ribe Bending mechanics and mode selection in free subduction: a thin-sheet analysis , 2010 .

[15]  P. Tackley,et al.  Role of iron‐spin transition in ferropericlase on seismic interpretation: A broad thermochemical transition in the mid mantle? , 2010 .

[16]  J. Braun,et al.  From longitudinal slab curvature to slab rheology , 2009 .

[17]  P. Koumoutsakos,et al.  Earth curvature effects on subduction morphology: Modeling subduction in a spherical setting , 2009 .

[18]  R. Mjelde,et al.  Variation of Icelandic and Hawaiian magmatism: evidence for co-pulsation of mantle plumes? , 2009 .

[19]  Hans-Peter Bunge,et al.  The Bent Hawaiian-Emperor Hotspot Track: Inheriting the Mantle Wind , 2009, Science.

[20]  B. Steinberger,et al.  Longitude: Linking Earth's ancient surface to its deep interior , 2008 .

[21]  Gabriele Morra,et al.  A benchmark comparison of spontaneous subduction models – towards a free surface , 2008 .

[22]  C. Conrad,et al.  Reconciling strong slab pull and weak plate bending: The plate motion constraint on the strength of mantle slabs , 2008 .

[23]  D. Stegman,et al.  Global trench migration velocities and slab migration induced upper mantle volume fluxes: Constraints to find an Earth reference frame based on minimizing viscous dissipation , 2008 .

[24]  Ivano Benedetti,et al.  A fast 3D dual boundary element method based on hierarchical matrices , 2008 .

[25]  G. Morra,et al.  Evidence of lower-mantle slab penetration phases in plate motions , 2008, Nature.

[26]  C. Faccenna,et al.  Slab stiffness control of trench motion: Insights from numerical models , 2008 .

[27]  Y. Ben‐Zion,et al.  Mechanics of grain‐size reduction in fault zones , 2008 .

[28]  Leslie Greengard,et al.  A fast multipole method for the three-dimensional Stokes equations , 2008, J. Comput. Phys..

[29]  D. Yuen,et al.  Why is terrestrial subduction one-sided? , 2008 .

[30]  G. Morra,et al.  Dynamics of plate bending at the trench and slab‐plate coupling , 2007 .

[31]  P. Tackley,et al.  Non‐hotspot volcano chains originating from small‐scale sublithospheric convection , 2007 .

[32]  G. Morra,et al.  Dynamic models of downgoing plate-buoyancy driven subduction: subduction motions and energy dissipation , 2007 .

[33]  Ralph Müller,et al.  Major Australian-Antarctic Plate Reorganization at Hawaiian-Emperor Bend Time , 2007, Science.

[34]  Petros Koumoutsakos,et al.  Large Scale Three-Dimensional Boundary Element Simulation of Subduction , 2007, International Conference on Computational Science.

[35]  C. Faccenna,et al.  Plate kinematics, slab shape and back-arc stress: A comparison between laboratory models and current subduction zones , 2007 .

[36]  D. May,et al.  Evolution and diversity of subduction zones controlled by slab width , 2007, Nature.

[37]  J. Platt,et al.  Influence of mantle dynamics on the topographic evolution of the Tibetan Plateau: Results from numerical modeling , 2006 .

[38]  Robert A. Duncan,et al.  Distribution of recent volcanism and the morphology of seamounts and ridges in the GLIMPSE study area: Implications for the lithospheric cracking hypothesis for the origin of intraplate, non–hot spot volcanic chains , 2006 .

[39]  T. Becker On the effect of temperature and strain-rate dependent viscosity on global mantle flow, net rotation, and plate-driving forces , 2006 .

[40]  Henry Power,et al.  A 3-D indirect boundary element method for bounded creeping flow of drops , 2006 .

[41]  T. Dixon,et al.  Feedback between mountain belt growth and plate convergence revealed by forward and inverse tectonic models , 2006 .

[42]  B. Hobbs,et al.  From point defects to plate tectonic faults , 2006 .

[43]  Eh Tan,et al.  GeoFramework: Coupling multiple models of mantle convection within a computational framework , 2006 .

[44]  B. Buffett,et al.  Plate bending at subduction zones: Consequences for the direction of plate motions , 2006 .

[45]  Irina M. Artemieva,et al.  Global 1°×1° thermal model TC1 for the continental lithosphere: Implications for lithosphere secular evolution , 2006 .

[46]  R. Müller,et al.  Controls on back‐arc basin formation , 2006 .

[47]  P. Wessel,et al.  Toward a self‐consistent, high‐resolution absolute plate motion model for the Pacific , 2006 .

[48]  Louis-Noel Moresi,et al.  Influence of trench width on subduction hinge retreat rates in 3‐D models of slab rollback , 2006 .

[49]  W. Schellart Influence of the subducting plate velocity on the geometry of the slab and migration of the subduction hinge , 2005 .

[50]  R. Sutherland,et al.  Prediction of Emperor-Hawaii seamount locations from a revised model of global plate motion and mantle flow , 2004, Nature.

[51]  N. Bellahsen,et al.  Dynamics of Subduction and Plate Motion in Laboratory Experiments. , 2004 .

[52]  C. Lithgow‐Bertelloni,et al.  Origin of the lithospheric stress field , 2004 .

[53]  D. Giardini,et al.  On the Curvature of Oceanic Arcs , 2003 .

[54]  W. Hackbusch,et al.  Introduction to Hierarchical Matrices with Applications , 2003 .

[55]  D. Giardini,et al.  Dynamics of retreating slabs : 2. Insights from three-dimensional laboratory experiments , 2003 .

[56]  Gabriele Morra,et al.  Dynamics of retreating slabs: 1. Insights from two-dimensional numerical experiments , 2003 .

[57]  P. Bird An updated digital model of plate boundaries , 2003 .

[58]  D. Sornette,et al.  Fractal Plate Tectonics , 2002, cond-mat/0202320.

[59]  C. Gable,et al.  Episodic tectonic plate reorganizations driven by mantle convection , 2002 .

[60]  C. Conrad,et al.  How Mantle Slabs Drive Plate Tectonics , 2002, Science.

[61]  D. L. Anderson How many plates , 2002 .

[62]  M. Jessell,et al.  Analogue modeling of arc and backarc deformation in the New Hebrides arc and North Fiji Basin , 2002 .

[63]  T. Becker,et al.  Predicting plate velocities with mantle circulation models , 2001 .

[64]  S. King Subduction zones: observations and geodynamic models , 2001 .

[65]  D. Yuen,et al.  The Initiation of Subduction: Criticality by Addition of Water? , 2001, Science.

[66]  N. Odling,et al.  Scaling of fracture systems in geological media , 2001 .

[67]  Laurent Jolivet,et al.  History of subduction and back‐arc extension in the Central Mediterranean , 2001 .

[68]  N. Ribe,et al.  Bending and stretching of thin viscous sheets , 2001, Journal of Fluid Mechanics.

[69]  B. Hager,et al.  Mantle convection with strong subduction zones , 2001 .

[70]  Paul J. Tackley,et al.  Self‐consistent generation of tectonic plates in time‐dependent, three‐dimensional mantle convection simulations , 2000 .

[71]  P. Tackley Self‐consistent generation of tectonic plates in time‐dependent, three‐dimensional mantle convection simulations 2. Strain weakening and asthenosphere , 2000 .

[72]  Hans-Peter Bunge,et al.  Mesozoic plate-motion history below the northeast Pacific Ocean from seismic images of the subducted Farallon slab , 2000, Nature.

[73]  Louis Moresi,et al.  Role of temperature‐dependent viscosity and surface plates in spherical shell models of mantle convection , 2000 .

[74]  J. Veevers Change of tectono-stratigraphic regime in the Australian plate during the 99 Ma (mid-Cretaceous) and 43 Ma (mid-Eocene) swerves of the Pacific , 2000 .

[75]  B. Hager,et al.  Effects of plate bending and fault strength at subduction zones on plate dynamics , 1999 .

[76]  D. Giardini,et al.  The development of slabs in the upper mantle: Insights from numerical and laboratory experiments , 1999 .

[77]  M. Gurnis,et al.  HOW VALID ARE DYNAMIC MODELS OF SUBDUCTION AND CONVECTION WHEN PLATE MOTIONS ARE PRESCRIBED , 1999 .

[78]  R. Trompert,et al.  Mantle convection simulations with rheologies that generate plate-like behaviour , 1998, Nature.

[79]  M. Richards,et al.  The dynamics of Cenozoic and Mesozoic plate motions , 1998 .

[80]  D. Bercovici Generation of plate tectonics from lithosphere–mantle flow and void–volatile self-lubrication , 1998 .

[81]  D. Giardini,et al.  The dynamics of back‐arc extension: an experimental approach to the opening of the Tyrrhenian Sea , 1996 .

[82]  M. Gurnis,et al.  Constraints on the lateral strength of slabs from three-dimensional dynamic flow models , 1996 .

[83]  J. Mitrovica,et al.  Haskell [1935] revisited , 1996 .

[84]  H. Stone,et al.  Collective hydrodynamics of deformable drops and bubbles in dilute low Reynolds number suspensions , 1995, Journal of Fluid Mechanics.

[85]  D. Sandwell,et al.  Evidence for diffuse extension of the Pacific Plate from Pukapuka ridges and cross‐grain gravity lineations , 1995 .

[86]  Shijie Zhong,et al.  Towards a realistic simulation of plate margins in mantle convection , 1995 .

[87]  M. Gurnis,et al.  Mantle Convection with Plates and Mobile, Faulted Plate Margins , 1995, Science.

[88]  C. Gable,et al.  Linear stability of a layered fluid with mobile surface plates , 1994 .

[89]  Frank Rizzo,et al.  Boundary Integral and Singularity Methods for Linearized Viscous Flow (C. Pozrikidis) , 1994, SIAM Rev..

[90]  W. S. Hall,et al.  Boundary Element Method , 2006 .

[91]  M. Richards,et al.  A geodynamic model of mantle density heterogeneity , 1993 .

[92]  A. Goodwillie,et al.  PLACING BOUNDS ON LITHOSPHERIC DEFORMATION IN THE CENTRAL PACIFIC-OCEAN , 1992 .

[93]  C. Vigny,et al.  Mantle dynamics with induced plate tectonics , 1989 .

[94]  Y. Saad,et al.  GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems , 1986 .

[95]  Piet Hut,et al.  A hierarchical O(N log N) force-calculation algorithm , 1986, Nature.

[96]  D. Yuen,et al.  The interaction of a subducting lithospheric slab with a chemical or phase boundary , 1984 .

[97]  B. Hager Subducted slabs and the geoid: Constraints on mantle rheology and flow , 1983 .

[98]  Bradford H. Hager,et al.  A simple global model of plate dynamics and mantle convection , 1981 .

[99]  A. Acrivos,et al.  A numerical study of the deformation and burst of a viscous drop in an extensional flow , 1978, Journal of Fluid Mechanics.

[100]  Donald W. Forsyth,et al.  On the Relative Importance of the Driving Forces of Plate Motion , 1975 .

[101]  川口 光年,et al.  O. A. Ladyzhenskaya: The Mathematical Theory of Viscous Incompressible Flow, Gordon and Breach Sci. Pub. New York-London, 1963, 184頁, 15×23cm, 3,400円. , 1964 .