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A MATHEMATICAL MODEL FOR THE LARGE-SCALE TRANSPORT OF HEAT AND WATER IN THE TAUPO VOLCANIC ZONE OF NEW ZEALAND

Part of: Plastic materials, materials of stress-rate and internal-variable type Generalities, axiomatics, foundations of continuum mechanics of solids

Published online by Cambridge University Press:  03 November 2009

GRAHAM WEIR
GRAHAM WEIR*
Affiliation:
Applied Mathematics, IRL, Wellington, New Zealand (email: [email protected])
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Abstract

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A three-layer compartmental model of the geological structure in the Taupo Volcanic Zone of New Zealand is developed, based on the assumptions of isostasy (constant geostatic pressure at 25 km depth) and a constant rate of volcanism. The upper layer consists of volcanic infill to a depth of about 2500 m, then a middle layer of greywacke-like material to a depth of about 15 km, and a lower layer of andesitic-like material to a depth of 25 km. Our model assumptions predict that the area of each layer increases at a constant rate; that there is a constant ratio between the rate of energy production from volcanic activity and geothermal convection; and that there is the possibility of an abrupt change from rhyolitic to basaltic volcanism, if the middle layer becomes sufficiently thin. Two models are considered: a rifting and a spreading model. Both models predict the lower layer has an andesitic-like density. The spreading model has difficulty matching heat output with observed extension rates. The rifting model predicts the observed extension rates, but requires very deep circulation of groundwater to be consistent with observed chemical and isotopic properties of geothermal fluids.

Keywords

crustal heat and mass flowgeothermal energyvolcanology

MSC classification

Secondary: 74C99: None of the above, but in this section 74A45: Theories of fracture and damage
Type
Research Article
Information
The ANZIAM Journal , Volume 50 , Issue 3: This Special Issue is dedicated to Dr Stephen White , January 2009 , pp. 343 - 354
Copyright
Copyright © Australian Mathematical Society 2009

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