On the parametrization of equilibrium stress fields in the Earth

Al-Attar, David and Woodhouse, John H. (2010) On the parametrization of equilibrium stress fields in the Earth. Geophysical Journal International, 181 (1). pp. 567-576. DOI 10.1111/j.1365-246X.2010.04527.x

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Official URL: http://gji.oxfordjournals.org/content/181/1/567

Abstract

A new method for parametrizing the possible equilibrium stress fields of a laterally heterogeneous earth model is described. In this method a solution of the equilibrium equations is first found that satisfies some desirable physical property. For example, we show that the equilibrium stress field with smallest norm relative to a given inner product can be obtained by solving a static linear elastic boundary value problem. We also show that the equilibrium stress field whose deviatoric component has smallest norm with respect to a given inner product can be obtained by solving a steady-state incompressible viscous flow problem. Having found such a solution of the equilibrium equations, all other solutions can be written as the sum of this equilibrium stress field and a divergence-free stress tensor field whose boundary tractions vanish. Given n divergence-free and traction-free tensor fields, we then obtain a simple n-dimensional parametrization of equilibrium stress fields in the earth model. The practical construction of such divergence- and traction-free tensor fields in the mantle of a spherically symmetric reference earth model is described using generalized spherical harmonics.

Item Type: Article
Uncontrolled Keywords: NILAREP
Subjects: 02 - Geodynamics, Geophysics and Tectonics
Divisions: 02 - Geodynamics, Geophysics and Tectonics
Journal or Publication Title: Geophysical Journal International
Volume: 181
Page Range: pp. 567-576
Identification Number: 10.1111/j.1365-246X.2010.04527.x
Depositing User: Sarah Humbert
Date Deposited: 25 May 2013 11:17
Last Modified: 23 Jul 2013 10:06
URI: http://eprints.esc.cam.ac.uk/id/eprint/2775

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