A Mathematical Model Coupling Heat and Mass Flow and Extension Rate in the Taupo Volcanic Zone, New Zealand

Abstract

A new mathematical model is presented for heat flow from the Taupo Volcanic Zone (TVZ). The model consists of three layers, each with constant density, down to a depth of about 25 km, where the pressure is assumed constant. A constant rate of eruption of material onto Layer 1 is assumed, which implies a constant rate of spreading (extension), and a constant rate of volumetric creation in Layers 2 and 3. Heat flow calculations are performed, by assuming conductive heat transport below 8 km, where the rocks are assumed to be in a ductile state. The top of Layer 3, which moves upwards with time, is assumed to be at a temperature of about 1150?C. 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.