Open Access Te Herenga Waka-Victoria University of Wellington
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Calculation of the Deviatoric Stress Field in New Zealand

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posted on 2021-11-23, 13:57 authored by Hamish Hirschberg

I model the vertically averaged deviatoric stress field for New Zealand using velocity and crustal density data. I use a thin sheet model of a viscously deforming lithosphere, averaging over a depth of 100 km and solve the stress balance equation. Two methods of solving the stress balance equation are compared: one method solves first for deviatoric stresses due to gravitational potential energy per unit volume before accounting for deviatoric stresses due to boundary conditions; the other method assumes an isotropic viscosity to relate deviatoric stress to strain rate, solving for the viscosity field. Under synthetic testing, the two step method is able to cope with high levels of noise but contains edge effects. The method solving for viscosity is accurate at low noise levels, however, it is unreliable at high noise levels. I apply the two step method to New Zealand using a Quaternary and a GPS-derived velocity model. Vertically averaged deviatoric stress magnitudes are found to be 10-30 MPa, similar to magnitudes found for other plate-boundary zones. Gravitational and boundary stresses each account for approximately half of the full deviatoric stress. Effective viscosities are found to be 1-10×10²¹ Pa s in the regions of most active deformation, which can be interpreted in terms of the long term strength of the lithosphere controlled by temperature and/or lithology.


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Te Herenga Waka—Victoria University of Wellington

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Te Herenga Waka—Victoria University of Wellington

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Degree Name

Master of Science

Victoria University of Wellington Unit

Institute of Geophysics

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Victoria University of Wellington Item Type

Awarded Research Masters Thesis



Victoria University of Wellington School

School of Geography, Environment and Earth Sciences


Savage, Martha; Lamb, Simon