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Free-surface formulation of mantle convection—I. Basic theory and application to plumes

Zhong, Shijie and Gurnis, Michael and Moresi, Louis (1996) Free-surface formulation of mantle convection—I. Basic theory and application to plumes. Geophysical Journal International, 127 (3). pp. 708-718. ISSN 0956-540X. doi:10.1111/j.1365-246X.1996.tb04049.x.

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In mantle convection models, the top surface is traditionally approximated as a free-slip boundary, and the dynamic topography is obtained by assuming that the normal stress on the free-slip boundary is compensated instantaneously through surface deformation. It has already been shown that this approximation is-'valid for long-wavelength topography. Based on both viscous and viscoelastic models with a free surface, we have found that the characteristic time for topographic growth is comparable to the timescales of mantle convection (∼10^6 year) for short and intermediate wavelengths (10^3 km or less) and/or a high effective lithospheric viscosity (> 10^(24) Pa s). This suggests that the topography is history-dependent under these conditions and that a free-surface formulation is required to study the topography at these wavelengths. We have developed a new Eulerian finite-element technique to model a free surface. Since the technique is based upon an undeformable Eulerian grid, this enables us to study long-term, free-surface dynamics in the presence of evolving buoyancy. We have compared numerical with analytic solutions of viscous relaxation for fixed buoyancy problems. As long as the magnitude of topography is much smaller than the wavelength, we find that the finite-element method is very accurate, with relative errors of less than 1 per cent. This numerical technique can be applied to a variety of geophysical problems with free surfaces. In applying this technique to dynamic models of mantle plumes, we find that surface relaxation retards the topography at intermediate and short wavelengths and produces a smoother topography, compared with topography from free-slip calculations. This reduced topography has a significant influence on the geoid at the corresponding wavelengths. Moreover, free-surface models, by allowing vertical motion on the free surface, yield a hotter lithosphere over ascending plumes than models with free-slip boundaries.

Item Type:Article
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URLURL TypeDescription
Gurnis, Michael0000-0003-1704-597X
Moresi, Louis0000-0003-3685-174X
Additional Information:© 1996 RAS. Accepted 1996 August 9. Received 1996 August 5; in original form 1995 November 22. We wish to thank D. Kemp and C. Eloy for helpful discussions, and H. J. Melosh of the University of Arizona for providing the TECTON code. This work was supported by the David and Lucile Packard Foundation and NSF grants EAR-9496185 and EAR-9417645. SZ was partly supported by a Texaco Fellowship at Caltech. This is contribution 5616 of the Division of Geological and Planetary Sciences, California Institute of Technology.
Group:Seismological Laboratory
Funding AgencyGrant Number
David and Lucile Packard FoundationUNSPECIFIED
Caltech Texaco Postdoctoral FellowshipUNSPECIFIED
Subject Keywords:geoid, mantle convection, plume, rheology, topography
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Caltech Division of Geological and Planetary Sciences5616
Issue or Number:3
Record Number:CaltechAUTHORS:20130116-145941322
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Official Citation:Zhong, S., Gurnis, M. and Moresi, L. (1996), Free-surface formulation of mantle convection—I. Basic theory and application to plumes. Geophysical Journal International, 127: 708–718. doi: 10.1111/j.1365-246X.1996.tb04049.x
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:36434
Deposited By: Tony Diaz
Deposited On:17 Jan 2013 22:53
Last Modified:09 Nov 2021 23:22

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