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Clennett EJ, Holt AF, Tetley MG, Becker TW, Faccenna C. Assessing plate reconstruction models using plate driving force consistency tests. Sci Rep 2023; 13:10191. [PMID: 37353512 PMCID: PMC10290141 DOI: 10.1038/s41598-023-37117-w] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/02/2023] [Accepted: 06/15/2023] [Indexed: 06/25/2023] Open
Abstract
Plate reconstruction models are constructed to fit constraints such as magnetic anomalies, fracture zones, paleomagnetic poles, geological observations and seismic tomography. However, these models do not consider the physical equations of plate driving forces when reconstructing plate motion. This can potentially result in geodynamically-implausible plate motions, which has implications for a range of work based on plate reconstruction models. We present a new algorithm that calculates time-dependent slab pull, ridge push (GPE force) and mantle drag resistance for any topologically closed reconstruction, and evaluates the residuals-or missing components-required for torques to balance given our assumed plate driving force relationships. In all analyzed models, residual torques for the present-day are three orders of magnitude smaller than the typical driving torques for oceanic plates, but can be of the same order of magnitude back in time-particularly from 90 to 50 Ma. Using the Pacific plate as an example, we show how our algorithm can be used to identify areas and times with high residual torques, where either plate reconstructions have a high degree of geodynamic implausibility or our understanding of the underlying geodynamic forces is incomplete. We suggest strategies for plate model improvements and also identify times when other forces such as active mantle flow were likely important contributors. Our algorithm is intended as a tool to help assess and improve plate reconstruction models based on a transparent and expandable set of a priori dynamic constraints.
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Affiliation(s)
- Edward J Clennett
- Institute for Geophysics, Jackson School of Geosciences, The University of Texas at Austin, Austin, USA.
- Department of Geological Sciences, Jackson School of Geosciences, The University of Texas at Austin, Austin, USA.
| | - Adam F Holt
- Rosenstiel School of Marine, Atmospheric, and Earth Science, University of Miami, Miami, USA
| | - Michael G Tetley
- Institute for Geophysics, Jackson School of Geosciences, The University of Texas at Austin, Austin, USA
| | - Thorsten W Becker
- Institute for Geophysics, Jackson School of Geosciences, The University of Texas at Austin, Austin, USA
- Department of Geological Sciences, Jackson School of Geosciences, The University of Texas at Austin, Austin, USA
- Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, USA
| | - Claudio Faccenna
- Dipartimento Scienze, Università Roma Tre, Rome, Italy
- GFZ Helmholtz Centre Potsdam, German Research Centre for Geosciences, Potsdam, Germany
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Sobolev SV, Brown M. Surface erosion events controlled the evolution of plate tectonics on Earth. Nature 2019; 570:52-57. [PMID: 31168102 DOI: 10.1038/s41586-019-1258-4] [Citation(s) in RCA: 78] [Impact Index Per Article: 13.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/17/2018] [Accepted: 04/24/2019] [Indexed: 11/09/2022]
Abstract
Plate tectonics is among the most important geological processes on Earth, but its emergence and evolution remain unclear. Here we extrapolate models of present-day plate tectonics to the past and propose that since about three billion years ago the rise of continents and the accumulation of sediments at continental edges and in trenches has provided lubrication for the stabilization of subduction and has been crucial in the development of plate tectonics on Earth. We conclude that the two largest surface erosion and subduction lubrication events occurred after the Palaeoproterozoic Huronian global glaciations (2.45 to 2.2 billion years ago), leading to the formation of the Columbia supercontinent, and after the Neoproterozoic 'snowball' Earth glaciations (0.75 to 0.63 billion years ago). The snowball Earth event followed the 'boring billion'-a period of reduced plate tectonic activity about 1.75 to 0.75 billion years ago that was probably caused by a shortfall of sediments in trenches-and it kick-started the modern episode of active plate tectonics.
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Affiliation(s)
- Stephan V Sobolev
- GFZ German Research Centre for Geosciences, Section of Geodynamic Modeling, Potsdam, Germany. .,Institute of Geosciences, University of Potsdam, Potsdam, Germany.
| | - Michael Brown
- Laboratory for Crustal Petrology, Department of Geology, University of Maryland, College Park, MD, USA
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Dziewonski AM, Forte AM, Su W, Woodward RL. Seismic Tomography and Geodynamics. RELATING GEOPHYSICAL STRUCTURES AND PROCESSES: THE JEFFREYS VOLUME 2013. [DOI: 10.1029/gm076p0067] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/07/2023]
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Aspherical Structure of the Mantle, Tectonic Plate Motions, Nonhydrostatic Geoid, and Topography of the Core-Mantle Boundary. ACTA ACUST UNITED AC 2013. [DOI: 10.1029/gm072p0135] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register]
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Woodward RL, Forte AM, Su WJ, Dziewonski AM. Constraints on the Large-Scale Structure of the Earth's Mantle. EVOLUTION OF THE EARTH AND PLANETS 2013. [DOI: 10.1029/gm074p0089] [Citation(s) in RCA: 34] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/25/2023]
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Ricard Y, Richards M, Lithgow-Bertelloni C, Le Stunff Y. A geodynamic model of mantle density heterogeneity. ACTA ACUST UNITED AC 2012. [DOI: 10.1029/93jb02216] [Citation(s) in RCA: 382] [Impact Index Per Article: 29.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
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Zhong S, Gurnis M. Dynamic feedback between a continentlike raft and thermal convection. ACTA ACUST UNITED AC 2012. [DOI: 10.1029/93jb00193] [Citation(s) in RCA: 115] [Impact Index Per Article: 8.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/10/2022]
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Forte AM, Peltier R. Viscous flow models of global geophysical observables: 1. Forward problems. ACTA ACUST UNITED AC 2012. [DOI: 10.1029/91jb01709] [Citation(s) in RCA: 150] [Impact Index Per Article: 11.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
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Mitrovica JX, Peltier WR. Present-day secular variations in the zonal harmonics of Earth's geopotential. ACTA ACUST UNITED AC 2012. [DOI: 10.1029/92jb02700] [Citation(s) in RCA: 87] [Impact Index Per Article: 6.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
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Pari G, Peltier WR. The heat flow constraint on mantle tomography-based convection models: Towards a geodynamically self-consistent inference of mantle viscosity. ACTA ACUST UNITED AC 2012. [DOI: 10.1029/95jb01078] [Citation(s) in RCA: 44] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
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van Hinsbergen DJJ, Steinberger B, Doubrovine PV, Gassmöller R. Acceleration and deceleration of India-Asia convergence since the Cretaceous: Roles of mantle plumes and continental collision. ACTA ACUST UNITED AC 2011. [DOI: 10.1029/2010jb008051] [Citation(s) in RCA: 235] [Impact Index Per Article: 16.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
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Agard P, Monié P, Gerber W, Omrani J, Molinaro M, Meyer B, Labrousse L, Vrielynck B, Jolivet L, Yamato P. Transient, synobduction exhumation of Zagros blueschists inferred from P-T, deformation, time, and kinematic constraints: Implications for Neotethyan wedge dynamics. ACTA ACUST UNITED AC 2006. [DOI: 10.1029/2005jb004103] [Citation(s) in RCA: 124] [Impact Index Per Article: 6.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Affiliation(s)
- P. Agard
- Laboratoire de Tectonique, UMR CNRS 7072; Université Paris 6; Paris France
| | - P. Monié
- Laboratoire Dynamique de la Lithosphère, UMR CNRS 5573; Université Montpellier 2; Montpellier France
| | - W. Gerber
- Laboratoire de Tectonique, UMR CNRS 7072; Université Paris 6; Paris France
| | - J. Omrani
- Laboratoire de Tectonique, UMR CNRS 7072; Université Paris 6; Paris France
| | - M. Molinaro
- Laboratoire de Tectonique; Université de Cergy Pontoise; Cergy France
| | - B. Meyer
- Laboratoire de Tectonique, UMR CNRS 7072; Université Paris 6; Paris France
| | - L. Labrousse
- Laboratoire de Tectonique, UMR CNRS 7072; Université Paris 6; Paris France
| | - B. Vrielynck
- Laboratoire de Tectonique, UMR CNRS 7072; Université Paris 6; Paris France
| | - L. Jolivet
- Laboratoire de Tectonique, UMR CNRS 7072; Université Paris 6; Paris France
| | - P. Yamato
- Laboratoire de Tectonique, UMR CNRS 7072; Université Paris 6; Paris France
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Bercovici D. Tectonic plate generation and two-phase damage: Void growth versus grain size reduction. ACTA ACUST UNITED AC 2005. [DOI: 10.1029/2004jb003181] [Citation(s) in RCA: 67] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
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Conrad CP, Lithgow-Bertelloni C. The temporal evolution of plate driving forces: Importance of “slab suction” versus “slab pull” during the Cenozoic. ACTA ACUST UNITED AC 2004. [DOI: 10.1029/2004jb002991] [Citation(s) in RCA: 100] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Affiliation(s)
- Clinton P. Conrad
- Department of Geological Sciences; University of Michigan; Ann Arbor Michigan USA
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Forte AM, Mitrovica JX, Espesset A. Geodynamic and seismic constraints on the thermochemical structure and dynamics of convection in the deep mantle. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2002; 360:2521-2543. [PMID: 12460479 DOI: 10.1098/rsta.2002.1079] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/24/2023]
Abstract
We revisit a recent study by Forte & Mitrovica in which global geophysical observables associated with mantle convection were inverted and the existence of a strong increase in viscosity near a depth of 2000 km was inferred. Employing mineral-physics data and theory we also showed that, although there are chemical anomalies in the lowermost mantle, they are unable to inhibit the dominant thermal buoyancy of the deep-mantle mega-plumes below Africa and the Pacific Ocean. New Monte Carlo simulations are employed to explore the impact of uncertainties in current mineral-physics constraints on inferences of deep-mantle thermochemical structure. To explore the impact of the high-viscosity peak at a depth of 2000 km on the evolution of lower-mantle structure, we carried out time-dependent convection simulations. The latter show that the stability and longevity of the dominant long-wavelength heterogeneity in the lowermost mantle are controlled by this viscosity peak.
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Affiliation(s)
- Alessandro M Forte
- Department of Earth Sciences, University of Western Ontario, London, Canada
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Abstract
The gravitational pull of subducted slabs is thought to drive the motions of Earth's tectonic plates, but the coupling between slabs and plates is not well established. If a slab is mechanically attached to a subducting plate, it can exert a direct pull on the plate. Alternatively, a detached slab may drive a plate by exciting flow in the mantle that exerts a shear traction on the base of the plate. From the geologic history of subduction, we estimated the relative importance of "pull" versus "suction" for the present-day plates. Observed plate motions are best predicted if slabs in the upper mantle are attached to plates and generate slab pull forces that account for about half of the total driving force on plates. Slabs in the lower mantle are supported by viscous mantle forces and drive plates through slab suction.
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Affiliation(s)
- Clinton P Conrad
- Department of Geological Sciences, University of Michigan, Ann Arbor, MI 48109, USA.
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Forte AM, Mitrovica JX. Deep-mantle high-viscosity flow and thermochemical structure inferred from seismic and geodynamic data. Nature 2001; 410:1049-56. [PMID: 11323661 DOI: 10.1038/35074000] [Citation(s) in RCA: 287] [Impact Index Per Article: 12.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Abstract
Surface geophysical data that are related to the process of thermal convection in the Earth's mantle provide constraints on the rheological properties and density structure of the mantle. We show that these convection-related data imply the existence of a region of very high effective viscosity near 2,000 km depth. This inference is obtained using a viscous-flow model based on recent high-resolution seismic models of three-dimensional structure in the mantle. The high-viscosity layer near 2,000 km depth results in a re-organization of flow from short to long horizontal length scales, which agrees with seismic tomographic observations of very long wavelength structures in the deep mantle. The high-viscosity region also strongly suppresses flow-induced deformation and convective mixing in the deep mantle. Here we predict compositional and thermal heterogeneity in this region, using viscous-flow calculations based on the new viscosity profile, together with independent mineral physics data. These maps are consistent with the anti-correlation of anomalies in seismic shear and bulk sound velocity in the deep mantle. The maps also show that mega-plumes in the lower mantle below the central Pacific and Africa are, despite the presence of compositional heterogeneity, buoyant and actively upwelling structures.
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Affiliation(s)
- A M Forte
- Department of Earth Sciences, University of Western Ontario, Biology & Geology Building, London, Ontario, N6A 5B7 Canada.
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Bercovici D, Ricard Y, Richards MA. The Relation between mantle dynamics and plate tectonics: A Primer. GEOPHYSICAL MONOGRAPH SERIES 2000. [DOI: 10.1029/gm121p0005] [Citation(s) in RCA: 75] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/07/2023]
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The Quest for self-consistent generation of plate tectonics in mantle convection models. ACTA ACUST UNITED AC 2000. [DOI: 10.1029/gm121p0047] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Forte AM. Seismic-geodynamic constraints on mantle flow: Implications for layered convection, mantle viscosity, and seismic anisotropy in the deep mantle. EARTH'S DEEP INTERIOR: MINERAL PHYSICS AND TOMOGRAPHY FROM THE ATOMIC TO THE GLOBAL SCALE 2000. [DOI: 10.1029/gm117p0003] [Citation(s) in RCA: 16] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/11/2023]
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22
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Čadek O, Fleitout L. A global geoid model with imposed plate velocities and partial layering. ACTA ACUST UNITED AC 1999. [DOI: 10.1029/1999jb900150] [Citation(s) in RCA: 47] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
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Dumoulin C, Doin MP, Fleitout L. Heat transport in stagnant lid convection with temperature- and pressure-dependent Newtonian or non-Newtonian rheology. ACTA ACUST UNITED AC 1999. [DOI: 10.1029/1999jb900110] [Citation(s) in RCA: 117] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
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Blichert-Toft J, Albarède F, Kornprobst J. Lu-Hf Isotope Systematics of Garnet Pyroxenites from Beni Bousera, Morocco: Implications for Basalt Origin. Science 1999; 283:1303-1306. [PMID: 10037596 DOI: 10.1126/science.283.5406.1303] [Citation(s) in RCA: 122] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2022]
Abstract
Six garnet pyroxenites from Beni Bousera, Morocco, yield a mean lutetium-hafnium age of 25 +/- 1 million years ago and show a wide range in hafnium isotope compositions (varepsilonHf = -9 to +42 25 million years ago), which exceeds that of known basalts (0 to +25). Therefore, primary melts of garnet pyroxenites cannot be the source of basalts. The upper mantle may be an aggregate of pyroxenites that were left by the melting of oceanic crust at subduction zones and peridotites that were contaminated by the percolation of melts from these pyroxenites. As a consequence, the concept of geochemical heterogeneities as passive tracers is inadequate. Measured lutetium-hafnium partitioning of natural minerals requires a reassessment of some experimental work relevant to mantle melting in the presence of garnet.
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Affiliation(s)
- J Blichert-Toft
- Ecole Normale Supérieure de Lyon and CNRS, 46 Allée d'Italie, 69364 Lyon Cedex 7, France. L'Unité Mixte de Recherche CNRS "Magmas et Volcans," Observatoire de Physique du Globe de Clermont-Ferrand, 5 rue Kessler, 63038 Clermont-Ferrand, France
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Pari G, Peltier WR. Global surface heat flux anomalies from seismic tomography-based models of mantle flow: Implications for mantle convection. ACTA ACUST UNITED AC 1998. [DOI: 10.1029/98jb01668] [Citation(s) in RCA: 24] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
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Zhong S, Gurnis M, Moresi L. Role of faults, nonlinear rheology, and viscosity structure in generating plates from instantaneous mantle flow models. ACTA ACUST UNITED AC 1998. [DOI: 10.1029/98jb00605] [Citation(s) in RCA: 132] [Impact Index Per Article: 4.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
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Bird P. Testing hypotheses on plate-driving mechanisms with global lithosphere models including topography, thermal structure, and faults. ACTA ACUST UNITED AC 1998. [DOI: 10.1029/98jb00198] [Citation(s) in RCA: 109] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
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Brunei D, Machetel P. Large-scale tectonic features induced by mantle avalanches with phase, temperature, and pressure lateral variations of viscosity. ACTA ACUST UNITED AC 1998. [DOI: 10.1029/97jb01357] [Citation(s) in RCA: 37] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/10/2022]
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Simons M, Hager BH. Localization of the gravity field and the signature of glacial rebound. Nature 1997. [DOI: 10.1038/37339] [Citation(s) in RCA: 105] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
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Wen L, Anderson DL. Present-day plate motion constraint on mantle rheology and convection. ACTA ACUST UNITED AC 1997. [DOI: 10.1029/97jb02159] [Citation(s) in RCA: 34] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
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Mitrovica JX, Forte AM. Radial profile of mantle viscosity: Results from the joint inversion of convection and postglacial rebound observables. ACTA ACUST UNITED AC 1997. [DOI: 10.1029/96jb03175] [Citation(s) in RCA: 284] [Impact Index Per Article: 10.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
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Li XD, Romanowicz B. Global mantle shear velocity model developed using nonlinear asymptotic coupling theory. ACTA ACUST UNITED AC 1996. [DOI: 10.1029/96jb01306] [Citation(s) in RCA: 335] [Impact Index Per Article: 11.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
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Crumpler LS, Head JW, Aubele JC. Relation of Major Volcanic Center Concentration on Venus to Global Tectonic Patterns. Science 1993; 261:591-5. [PMID: 17758169 DOI: 10.1126/science.261.5121.591] [Citation(s) in RCA: 52] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2022]
Abstract
Global analysis of NASA Magellan image data indicates that a major concentration of volcanic centers covering approximately 40 percent of the surface of Venus occurs between the Beta, Atla, and Themis regiones. Associated with this enhanced concentration are geological characteristics commonly interpreted as rifting and mantle upwelling. Interconnected low plains in an annulus around this concentration are characterized by crustal shortening and infrequent volcanic centers that may represent sites of mantle return flow and net down-welling. Together, these observations suggest the existence of relatively simple, largescale patterns of mantle circulation similar to those associated with concentrations of intraplate volcanism on Earth.
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Bai W, Vigny C, Ricard Y, Froidevaux C. On the origin of deviatoric stresses in the lithosphere. ACTA ACUST UNITED AC 1992. [DOI: 10.1029/91jb00292] [Citation(s) in RCA: 52] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
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Ricard Y, Sabadini R, Spada G. Isostatic deformations and polar wander induced by redistribution of mass within the Earth. ACTA ACUST UNITED AC 1992. [DOI: 10.1029/92jb00740] [Citation(s) in RCA: 35] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
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Ricard Y, Doglioni C, Sabadini R. Differential rotation between lithosphere and mantle: A consequence of lateral mantle viscosity variations. ACTA ACUST UNITED AC 1991. [DOI: 10.1029/91jb00204] [Citation(s) in RCA: 184] [Impact Index Per Article: 5.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/10/2022]
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Gable CW, O'Connell RJ, Travis BJ. Convection in three dimensions with surface plates: Generation of toroidal flow. ACTA ACUST UNITED AC 1991. [DOI: 10.1029/90jb02743] [Citation(s) in RCA: 156] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
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Hong H, Yuen DA. Dynamical effects from equation of state on topographies and geoid anomalies due to internal loading. ACTA ACUST UNITED AC 1990. [DOI: 10.1029/jb095ib12p19933] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
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