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Geophysical & Astrophysical Fluid Dynamics Volume 33, 1985 - Issue 1-4
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Original Articles

A mathematical model of magma transport in the asthenosphere

A. C. Fowler Mathematical Institute, Oxford University, 24-29 St. Giles, Oxford, England
Pages 63-96 | Received 30 Oct 1983, Accepted 03 Mar 1985, Published online: 01 Dec 2006

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A. C. Fowler. (2018) The philosopher in the kitchen: the role of mathematical modelling in explaining drumlin formation. GFF 140:2, pages 93-105.
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Changyeol Lee, Nestor G. Cerpa, Dongwoo Han & Ikuko Wada. (2024) Modeling liquid transport in the Earth's mantle as two-phase flow: effect of an enforced positive porosity on liquid flow and mass conservation. Solid Earth 15:1, pages 23-38.
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Taras Gerya. 2019. Introduction to Numerical Geodynamic Modelling. Introduction to Numerical Geodynamic Modelling.
Nestor G. Cerpa, Ikuko Wada & Cian R. Wilson. (2018) Effects of fluid influx, fluid viscosity, and fluid density on fluid migration in the mantle wedge and their implications for hydrous melting. Geosphere 15:1, pages 1-23.
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Diogo L. Lourenço, Antoine B. Rozel, Taras Gerya & Paul J. Tackley. (2018) Efficient cooling of rocky planets by intrusive magmatism. Nature Geoscience 11:5, pages 322-327.
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Brandon C. Johnson, Rachel Y. Sheppard, Alyssa C. Pascuzzo, Elizabeth A. Fisher & Sean E. Wiggins. (2017) Porosity and Salt Content Determine if Subduction Can Occur in Europa's Ice Shell. Journal of Geophysical Research: Planets 122:12, pages 2765-2778.
Crossref
Matthew B. Weller, Adrian Lenardic & William B. Moore. (2016) Scaling relationships and physics for mixed heating convection in planetary interiors: Isoviscous spherical shells. Journal of Geophysical Research: Solid Earth 121:10, pages 7598-7617.
Crossref
Tobias Keller & Richard F. Katz. (2016) The Role of Volatiles in Reactive Melt Transport in the Asthenosphere. Journal of Petrology 57:6, pages 1073-1108.
Crossref
Benjamin A. Black & Michael Manga. (2016) The eruptibility of magmas at Tharsis and Syrtis Major on Mars. Journal of Geophysical Research: Planets 121:6, pages 944-964.
Crossref
Christopher W. MacMinn, Eric R. Dufresne & John S. Wettlaufer. (2016) Large Deformations of a Soft Porous Material. Physical Review Applied 5:4.
Crossref
Samuel M. Weatherley & Richard F. Katz. (2016) Melt transport rates in heterogeneous mantle beneath mid-ocean ridges. Geochimica et Cosmochimica Acta 172, pages 39-54.
Crossref
Robert J. Lillis, Josef Dufek, Walter S. Kiefer, Benjamin A. Black, Michael Manga, Jacob A. Richardson & Jacob E. Bleacher. (2015) The Syrtis Major volcano, Mars: A multidisciplinary approach to interpreting its magmatic evolution and structural development. Journal of Geophysical Research: Planets 120:9, pages 1476-1496.
Crossref
Y. Ricard. 2015. Treatise on Geophysics. Treatise on Geophysics 23 71 .
Wladimir Neumann, Doris Breuer & Tilman Spohn. (2014) Modelling of compaction in planetesimals. Astronomy & Astrophysics 567, pages A120.
Crossref
Meng Tian & Jay J. Ague. (2014) The impact of porosity waves on crustal reaction progress and CO2 mass transfer. Earth and Planetary Science Letters 390, pages 80-92.
Crossref
Tobias Keller, Dave A. May & Boris J. P. Kaus. (2013) Numerical modelling of magma dynamics coupled to tectonic deformation of lithosphere and crust. Geophysical Journal International 195:3, pages 1406-1442.
Crossref
C. Havlin, E.M. Parmentier & G. Hirth. (2013) Dike propagation driven by melt accumulation at the lithosphere–asthenosphere boundary. Earth and Planetary Science Letters 376, pages 20-28.
Crossref
J. Besserer, F. Nimmo, J. H. Roberts & R. T. Pappalardo. (2013) Convection‐driven compaction as a possible origin of Enceladus's long wavelength topography. Journal of Geophysical Research: Planets 118:5, pages 908-915.
Crossref
Nicholas K. Lowman & M. A. Hoefer. (2013) Dispersive shock waves in viscously deformable media. Journal of Fluid Mechanics 718, pages 524-557.
Crossref
Mark A. WieczorekGregory A. NeumannFrancis NimmoWalter S. KieferG. Jeffrey TaylorH. Jay MeloshRoger J. PhillipsSean C. SolomonJeffrey C. Andrews-HannaSami W. AsmarAlexander S. KonoplivFrank G. LemoineDavid E. SmithMichael M. WatkinsJames G. WilliamsMaria T. Zuber. (2013) The Crust of the Moon as Seen by GRAIL. Science 339:6120, pages 671-675.
Crossref
Lionel Wilson & Klaus Keil. (2012) Volcanic activity on differentiated asteroids: A review and analysis. Geochemistry 72:4, pages 289-321.
Crossref
S. M. Weatherley & R. F. Katz. (2012) Melting and channelized magmatic flow in chemically heterogeneous, upwelling mantle. Geochemistry, Geophysics, Geosystems 13:5.
Crossref
Guillaume C. Richard, Suranita Kanjilal & Harro Schmeling. (2012) Solitary-waves in geophysical two-phase viscous media: A semi-analytical solution. Physics of the Earth and Planetary Interiors 198-199, pages 61-66.
Crossref
M. A. Hesse, A. R. Schiemenz, Y. Liang & E. M. Parmentier. (2011) Compaction-dissolution waves in an upwelling mantle column. Geophysical Journal International 187:3, pages 1057-1075.
Crossref
Alan Schiemenz, Yan Liang & E. M. Parmentier. (2011) A high-order numerical study of reactive dissolution in an upwelling heterogeneous mantle—I. Channelization, channel lithology and channel geometry. Geophysical Journal International 186:2, pages 641-664.
Crossref
Dan McKenzie. (2011) Compaction and Crystallization in Magma Chambers: Towards a Model of the Skaergaard Intrusion. Journal of Petrology 52:5, pages 905-930.
Crossref
John F. Rudge, David Bercovici & Marc Spiegelman. (2011) Disequilibrium melting of a two phase multicomponent mantle. Geophysical Journal International 184:2, pages 699-718.
Crossref
Andrew FowlerAndrew Fowler. 2011. Mathematical Geoscience. Mathematical Geoscience 539 616 .
Ian J. Hewitt. (2010) Modelling melting rates in upwelling mantle. Earth and Planetary Science Letters 300:3-4, pages 264-274.
Crossref
Richard F. Katz. (2010) Porosity‐driven convection and asymmetry beneath mid‐ocean ridges. Geochemistry, Geophysics, Geosystems 11:11.
Crossref
G. Simpson, M. Spiegelman & M. I. Weinstein. (2010) A multiscale model of partial melts: 1. Effective equations. Journal of Geophysical Research: Solid Earth 115:B4.
Crossref
David L. KohlstedtBenjamin K. Holtzman. (2009) Shearing Melt Out of the Earth: An Experimentalist's Perspective on the Influence of Deformation on Melt Extraction. Annual Review of Earth and Planetary Sciences 37:1, pages 561-593.
Crossref
Lionel Wilson, Cyrena Anne Goodrich & James A. Van Orman. (2008) Thermal evolution and physics of melt extraction on the ureilite parent body. Geochimica et Cosmochimica Acta 72:24, pages 6154-6176.
Crossref
I.J Hewitt & A.C Fowler. (2008) Partial melting in an upwelling mantle column. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 464:2097, pages 2467-2491.
Crossref
Ondřej Šrámek, Yanick Ricard & David Bercovici. (2007) Simultaneous melting and compaction in deformable two-phase media. Geophysical Journal International 168:3, pages 964-982.
Crossref
Y. Ricard. 2007. Treatise on Geophysics. Treatise on Geophysics 31 87 .
Richard F. Katz, Marc Spiegelman & Benjamin Holtzman. (2006) The dynamics of melt and shear localization in partially molten aggregates. Nature 442:7103, pages 676-679.
Crossref
F Nimmo, R.T Pappalardo & B Giese. (2003) On the origins of band topography, Europa. Icarus 166:1, pages 21-32.
Crossref
Marc Spiegelman. (2003) Linear analysis of melt band formation by simple shear. Geochemistry, Geophysics, Geosystems 4:9.
Crossref
John T. Wasson & Byeon-Gak Choi. (2003) Main-group pallasites. Geochimica et Cosmochimica Acta 67:16, pages 3079-3096.
Crossref
M. S. Appold & J. A. Nunn. (2002) Numerical models of petroleum migration via buoyancy‐driven porosity waves in viscously deformable sediments. Geofluids 2:3, pages 233-247.
Crossref
A. C. Fowler. 2002. Resource Recovery, Confinement, and Remediation of Environmental Hazards. Resource Recovery, Confinement, and Remediation of Environmental Hazards 247 262 .
Dan McKenzie & R.Keith O'Nions. (1998) Melt production beneath oceanic islands. Physics of the Earth and Planetary Interiors 107:1-3, pages 143-182.
Crossref
Andrew C. Fowler & Xin-she Yang. (1998) Fast and Slow Compaction in Sedimentary Basins. SIAM Journal on Applied Mathematics 59:1, pages 365-385.
Crossref
N. S. Bagdassarov, A. M. Dorfman & D. B. Dingwell. (1996) Modelling of melt segregation processes by high-temperature centrifuging of partially molten granites-I. Melt extraction by compaction and deformation. Geophysical Journal International 127:3, pages 616-626.
Crossref
A. C. Fowler & D. R. Scott. (1996) Hydraulic crack propagation in a porous medium. Geophysical Journal International 127:3, pages 595-604.
Crossref
L. Preziosi, D.D. Joseph & G.S. Beavers. (1996) Infiltration of initially dry, deformable porous media. International Journal of Multiphase Flow 22:6, pages 1205-1222.
Crossref
C. N. Richardson, J. R. Lister & D. McKenzie. (1996) Melt conduits in a viscous porous matrix. Journal of Geophysical Research: Solid Earth 101:B9, pages 20423-20432.
Crossref
M Nakayama & D P Mason. (1995) On the effect of background voidage on compressive solitary waves in compacting media. Journal of Physics A: Mathematical and General 28:24, pages 7243-7261.
Crossref
R. A. Birchwood & D. L. Turcotte. (2012) A unified approach to geopressuring, low‐permeability zone formation, and secondary porosity generation in sedimentary basins. Journal of Geophysical Research: Solid Earth 99:B10, pages 20051-20058.
Crossref
J.A. Whitehead & Peter Kelemen. 1994. Magmatic Systems. Magmatic Systems 355 379 .
George W. Bergantz & Ralph Dawes. 1994. Magmatic Systems. Magmatic Systems 291 317 .
David W. Sparks & E.M. Parmentier. 1994. Magmatic Systems. Magmatic Systems 55 76 .
Elena Suetnova, Ramon Carbonell & Scott B. Smithson. (2012) Magma in layering at the Moho of the Basin and Range of Nevada. Geophysical Research Letters 20:24, pages 2945-2948.
Crossref
. (1997) Creep closure of channels in deforming subglacial till. Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences 441:1911, pages 17-31.
Crossref
. (1997) Physics of melt extraction: theory, implications and applications. Philosophical Transactions of the Royal Society of London. Series A: Physical and Engineering Sciences 342:1663, pages 23-41.
Crossref
Frank J. Spera. (1992) Lunar magma transport phenomena. Geochimica et Cosmochimica Acta 56:6, pages 2253-2265.
Crossref
M. Nakayama & D.P. Mason. (1992) Rarefactive solitary waves in two-phase fluid flow of compacting media. Wave Motion 15:4, pages 357-392.
Crossref
A. C. Fowler. (1989) Generation and Creep of Magma in the Earth. SIAM Journal on Applied Mathematics 49:1, pages 231-245.
Crossref
Norman H. Sleep. (2012) Tapping of melt by veins and dikes. Journal of Geophysical Research: Solid Earth 93:B9, pages 10255-10272.
Crossref
David R. Scott. (2012) The competition between percolation and circulation in a deformable porous medium. Journal of Geophysical Research: Solid Earth 93:B6, pages 6451-6462.
Crossref
Neil M. Ribe. (1987) Theory of melt segregation — A review. Journal of Volcanology and Geothermal Research 33:4, pages 241-253.
Crossref
Bradford H. Hager & Michael Gurnis. (2010) Mantle convection and the state of the Earth's interior. Reviews of Geophysics 25:6, pages 1277-1285.
Crossref
Bruce Marsh. (2010) Magmatic processes. Reviews of Geophysics 25:5, pages 1043-1053.
Crossref
David Loper. 1987. Structure and Dynamics of Partially Solidified Systems. Structure and Dynamics of Partially Solidified Systems 467 500 .
David J. Stevenson & David R. Scott. 1987. Structure and Dynamics of Partially Solidified Systems. Structure and Dynamics of Partially Solidified Systems 401 415 .
R. P. Lowell & G. Bergantz. 1987. Structure and Dynamics of Partially Solidified Systems. Structure and Dynamics of Partially Solidified Systems 383 400 .
A. C. Fowler. 1987. Structure and Dynamics of Partially Solidified Systems. Structure and Dynamics of Partially Solidified Systems 159 199 .
Sven Maal�e & A. Dana Johnston. (1986) Geochemical aspects of some accumulation models for primary magmas. Contributions to Mineralogy and Petrology 93:4, pages 449-458.
Crossref

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