A mathematical model of magma transport in the asthenosphere
نویسندگان
چکیده
This article may be used for research, teaching and private study purposes. Any substantial or systematic reproduction, redistribution , reselling , loan or sub-licensing, systematic supply or distribution in any form to anyone is expressly forbidden. The publisher does not give any warranty express or implied or make any representation that the contents will be complete or accurate or up to date. The accuracy of any instructions, formulae and drug doses should be independently verified with primary sources. The publisher shall not be liable for any loss, actions, claims, proceedings, demand or costs or damages whatsoever or howsoever caused arising directly or indirectly in connection with or arising out of the use of this material. We present a mathematical model for the flow of a partial melt through its solid phase. The model is based on the conservation laws of two-phase flow, which reduce to a generalization of porous flow in a permeable medium, when the solid matrix deforms very slowly. The continuity equation for the melt contains a source term (due to melting), which is determined by the energy equation. In addition, the melt fraction is unknown, and a new equation, representing conservation of pore space, is introduced. This equation may also be thought of as a constitutive law for the melt pressure (which is not lithostatic). The model is non-dimensionalized and simplified. Some simple solutions are considered, and it is suggested that the occurrence of high fluid pressures in the solutions may initiate fractures in the lithosphere, thus providing a starting-up mechanism for magma ascent to the surface.
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