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Melt production by viscous dissipation: Role of heat advection by magma transport
Author(s) -
Feigenson Mark D.,
Spera Frank J.
Publication year - 1980
Publication title -
geophysical research letters
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.007
H-Index - 273
eISSN - 1944-8007
pISSN - 0094-8276
DOI - 10.1029/gl007i002p00145
Subject(s) - peridotite , geology , mechanics , deformation (meteorology) , advection , thermodynamics , dissipation , materials science , physics , mantle (geology) , geophysics , oceanography
An energy conservation equation is formulated that balances the heat generated by viscous dissipation in a peridotite simultaneously undergoing partial fusion and penetrative constant shear stress deformation with the heat removed by mobilization and ascent of basaltic magma from the region undergoing deformation. The solution of this parameterized energy equation gives the volume fraction of melt (θ) as a function of time (t) after the initiation of deformation. A stability analysis of the conservation equation shows that stable (θ<100%) or unstable (θ→∞) solutions exist depending on the magnitude of two dimensionless parameters K 1 /K 2 and K 3 . For geologically reasonable values of K 1 /K 2 and K 3 , the analysis indicates that peridotitic thermo‐mechanical systems undergoing penetrative deformation at constant shear stress show a two‐stage history. An early stage of growth where θ increases monotonically on a 2 to 3 m.y. time scale eventually is replaced by a steady state regime (constant θ). Typical values of θ lie in the range 3 to 5 volume percent; melting of peridotite to the extent of 20‐30% appears to be precluded by this model.