AlAttar, David and Woodhouse, John H. (2010) On the parametrization of equilibrium stress fields in the Earth. Geophysical Journal International, 181 (1). pp. 567576. DOI 10.1111/j.1365246X.2010.04527.x

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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 steadystate 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 divergencefree stress tensor field whose boundary tractions vanish. Given n divergencefree and tractionfree tensor fields, we then obtain a simple ndimensional parametrization of equilibrium stress fields in the earth model. The practical construction of such divergence and tractionfree 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. 567576 
Identification Number:  10.1111/j.1365246X.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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