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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: G.weir@irl.cri.nz)
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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

References

[1]Bibby, H. M., Caldwell, T. G., Davey, F. J. and Webb, T. H., “Geophysical evidence on the structure of the Taupo Volcanic Zone, and its hydrothermal circulation”, J. Volcanol. Geotherm. Res. 68 (1995) 29–58.Google Scholar
[2]Clauser, C. and Huenges, E., “Thermal conductivity of rocks and minerals”, in: Rock physics and phase relations, A Handbook of Physical Constants, AGU Reference Shelf 3 (ed. T. J. Ahrens), (American Geophysical Union, Washington, DC, 1995) (http://www.agu.org/reference/rock.html).Google Scholar
[3]Cole, J. W., “Structural control and origin of volcanism in the Taupo Volcanic Zone, New Zealand”, Bull. Volcanol. 52 (1990) 445–459.Google Scholar
[4]Davey, F. J., Henrys, S. A. and Lobolo, E., “Asymmetrical rifting in a continental backarc environment, North Island, New Zealand”, J. Volcanol. Geotherm. Res. 68 (1995) 209–238.Google Scholar
[5]Delahaye, E., Townend, J., Reyners, M. and Rogers, G., “Microseismicity but no tremor associated with slow slip in the Hikurangi subduction zone, New Zealand”, Earth Planet. Sci. Lett. 277 (2009) 21–28.Google Scholar
[6]Giggenbach, W. F., “Isotopic shift in waters from geothermal and volcanic systems along convergent plate boundaries and their origin”, Earth Planet. Sci. Lett. 113 (1992) 495–510.Google Scholar
[7]Graham, I. J., Cole, J. W., Briggs, R. M., Gamble, J. A. and Smith, I. E. M., “Petrology and petrogenesis of volcanic rocks from the Taupo Volcanic Zone: a review”, J. Volcanol. Geotherm. Res. 68 (1995) 59–87.Google Scholar
[8]Hall, C. E., “Catastrophic initiation of subduction following forced convergence across fracture zones”, Earth Planet. Sci. Lett. 212 (2003) 15–30.Google Scholar
[9]Hochstein, M. P., “Crustal heat transfer in the Taupo Volcanic Zone (New Zealand): comparison with other volcanic arcs and explanatory heat source models”, J. Volcanol. Geotherm. Res. 68 (1995) 117–151.Google Scholar
[10]Housemann, G. and Molnar, P., “Gravitational (Rayleigh–Taylor) instability of a layer with non-linear viscosity and convective thinning of continental lithosphere”, Geophys. J. Int. 128 (1997) 125–150.Google Scholar
[11]Kissling, W. M. and Weir, G. J., “The spatial distribution of the geothermal fields in the Taupo Volcanic Zone, New Zealand”, J. Geophys. Res. 145 (2005) 136–150.Google Scholar
[12]McNabb, A., “The Taupo-Rotorua Hot-Plate”, Proc. 14th New Zealand Geothermal Workshop (eds S. F. Simmons, J. Newson and K. C. Lee), (Geothermal Institute, University of Auckland, Auckland, 1992) 111–114.Google Scholar
[13]Modrinak, N. and Studt, F. E., “Geological structure and volcanism of the Taupo-Tarawera District”, N.Z. J. Geol. Geophys. 2 (1959) 654–684.Google Scholar
[14]Simmons, S. F. and Weaver, S. D. (eds), “Taupo Volcanic Zone, New Zealand”, J. Volcanol. Geotherm. Res. 68 (1995) 1–238.Google Scholar
[15]Soengkono, S., ‘A magnetic model for deep plutonic bodies beneath the central Taupo Volcanic Zone, North Island, New Zealand’, J. Volcanol. Geotherm. Res. 68 (1995) 193–207.Google Scholar
[16]Stern, T. A., “Asymmetrical back-arc spreading, heat flux and structure associated with the central volcanic region of New Zealand”, Earth Planet. Lett. 85 (1987) 265–276.Google Scholar
[17]Stern, T. A., Stratford, W. R. and Salmon, M. L., “Subduction evolution and mantle dynamics at a continental margin: Central North Island, New Zealand”, Rev. Geophys. 44 (2006) RG4002–RG4038.Google Scholar
[18]Tapponnier, P. and Molnar, P., “Slip line field theory and large-scale continental tectonics”, Nature 264 (1976) 319–324.Google Scholar
[19]Watts, A. B., Isostasy and flexure of the lithosphere (Cambridge University Press, Cambridge, 2001).Google Scholar
[20]Weir, G. J., “Transport processes in the Taupo Volcanic Zone, New Zealand”, J. Volcanol. Geotherm. Res. 84 (1998) 61–72.Google Scholar
[21]Weir, G. J., “Heat output from spreading and rifting models of the Taupo Volcanic Zone, New Zealand”, J. Appl. Math. Decis. Sci. 5(1) (2001) 119–132.Google Scholar
[22]Weir, G. J., “A mathematical model of rainfall-controlled geothermal fields”, Transp. Porous Media 77 (2009) 323–334.Google Scholar
[23]Wilson, C. J. N., Houghton, B. F., McWillaims, M. O., Lanphere, M. A., Weaver, S. D. and Briggs, R. M., “Volcanic and structural evolution of Taupo Volcanic Zone, New Zealand: a review”, J. Volcanol. Geotherm. Res. 68 (1995) 1–28.Google Scholar
[24]Wilson, C. J. N., Rogan, A. M., Smith, I. E. M., Northey, D. J., Nairn, I. A. and Houghton, B. F., “Caldera volcanoes of the Taupo Volcanic Zone, New Zealand”, J. Geophys. Res. 89 (1984) 8463–8484.Google Scholar