Astronomy and Astrophysics – Astronomy
Scientific paper
Apr 2010
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2010geoji.181..567a&link_type=abstract
Geophysical Journal International, Volume 181, Issue 1, pp. 567-576.
Astronomy and Astrophysics
Astronomy
Inverse Theory, Seismic Tomography, Theoretical Seismology
Scientific paper
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.
Al-Attar David
Woodhouse John H.
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