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Buoyant melting instabilities beneath extending lithosphere: 2. Linear analysis

Hernlund, John W. and Stevenson, David J. and Tackley, Paul J. (2008) Buoyant melting instabilities beneath extending lithosphere: 2. Linear analysis. Journal of Geophysical Research. Solid Earth, 113 (B4). Art. No. B04406. ISSN 2169-9313. doi:10.1029/2006JB004863.

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In a companion paper, numerical models reveal that buoyant melting instabilities can occur beneath extending lithosphere for a sufficiently small mantle viscosity, extension rate, and rate of melt percolation. However, in some cases, instabilities do not develop during extension but only occur after extension slows or stops. These results are suggestive of a critical behavior in the onset of these kinds of instabilities and motivate a linear analysis to study the onset of instability in a partially melting, passively upwelling plane layer of mantle beneath extending lithosphere. The model we employ includes the effects of buoyancy arising from thermal expansion, the presence of a retained fraction of partial melt, and depletion of the solid by melt extraction. We find a critical behavior in the onset of instability controlled by melt retention buoyancy that is characterized by a “Rayleigh” number M, such that M must exceed some critical value M_(crit) which depends on the efficiency of Stokes rise of a partially molten body relative to the rate of background percolation. Comparison of this theory to the numerical results in the companion paper yields a close quantitative agreement. We also find that solid depletion buoyancy can either stabilize or destabilize a partially melting layer, depending upon both the distribution of preexisting depletion and the magnitude of density changes with depth. This theory is compared with previous studies of buoyant melting instabilities beneath mid‐ocean ridges where similar behavior was reported, and it suggests that the stability of passively upwelling, partially melting mantle underlying both narrow and wide rift settings is controlled by similar processes.

Item Type:Article
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Stevenson, David J.0000-0001-9432-7159
Additional Information:© 2008 American Geophysical Union. Received 18 November 2006; revised 18 October 2007; accepted 12 December 2007; published 8 April 2008. Reviews of preliminary versions of this material by Abby Kavner and Gerald Schubert greatly improved this manuscript. We are grateful to Paul H. Roberts for thorough reviews and contributions to the mathematical presentation of the linear stability analysis. Reviews by Todd Bianco and Justin Revenaugh were also helpful in improving the clarity and substance of this manuscript. Discussions with William B. Moore, Lee Bargatze, and Don Anderson were also helpful. This work was supported in part by the NSF CDYEL project and a grant from IGPP Los Alamos.
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Institute of Geophysics and Planetary PhysicsUNSPECIFIED
Subject Keywords:extension; melting instabilities; mantle convection
Issue or Number:B4
Record Number:CaltechAUTHORS:20181127-091034543
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Official Citation:Hernlund, J. W., D. J. Stevenson, and P. J. Tackley (2008), Buoyant melting instabilities beneath extending lithosphere: 2. Linear analysis, J. Geophys. Res., 113, B04406, doi: 10.1029/2006JB004863
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:91212
Deposited By: Tony Diaz
Deposited On:27 Nov 2018 18:12
Last Modified:16 Nov 2021 03:39

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