Journal of Applied Mathematics and Decision Sciences
Volume 5 (2001), Issue 2, Pages 105-118

Heat output from spreading and rifting models of the Taupo Volcanic Zone, New Zealand

Graham J. Weir

Applied Mathematics, Industrial Research, New Zealand

Copyright © 2001 Graham J. Weir. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A conceptual model of the Taupo Volcanic Zone (TVZ) is developed, to a depth of 25 km, formed from three constant density layers. The upper layer is formed from eruption products. A constant rate of eruption is assumed, which eventually implies a constant rate of extension, and a constant rate of volumetric creation in the middle and bottom layers. Tectonic extension creates volume which can accomodate magmatic intrusions. Spreading models assume this volume is distributed throughout the whole region, perhaps in vertical dykes, whereas rifting models assume the upper crust is thinned and the volume created lies under this upper crust. Bounds on the heat flow from such magmatic intrusions are calculated. Heat flow calculations are performed and some examples are provided which match the present total heat output from the TVZ of about 4200 MW, but these either have extension rates greater than the low values of about 8 ± 4 mm/a being reported from GPS measurements, or else consider extension rates in the TVZ to have varied over time.