Particle relabelling transformations in elastodynamics

Al-Attar, David and Crawford, Ophelia (2016) Particle relabelling transformations in elastodynamics. Geophysical Journal International, 205 (1). pp. 575-593. ISSN 0956-540X DOI https://doi.org/10.1093/gji/ggw032

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Abstract

The motion of a self-gravitating hyperelastic body is described through a time-dependent mapping from a reference body into physical space, and its material properties are determined by a referential density and strain-energy function defined relative to the reference body. Points within the reference body do not have a direct physical meaning, but instead act as particle labels that could be assigned in different ways. We use Hamilton's principle to determine how the referential density and strain-energy functions transform when the particle labels are changed, and describe an associated ‘particle relabelling symmetry’. We apply these results to linearized elastic wave propagation and discuss their implications for seismological inverse problems. In particular, we show that the effects of boundary topography on elastic wave propagation can be mapped exactly into volumetric heterogeneity while preserving the form of the equations of motion. Several numerical calculations are presented to illustrate our results.

Item Type:	Article
Uncontrolled Keywords:	2016AREP; IA71;
Subjects:	02 - Geodynamics, Geophysics and Tectonics
Divisions:	02 - Geodynamics, Geophysics and Tectonics 08 - Green Open Access
Journal or Publication Title:	Geophysical Journal International
Volume:	205
Page Range:	pp. 575-593
Identification Number:	https://doi.org/10.1093/gji/ggw032
Depositing User:	Sarah Humbert
Date Deposited:	01 Sep 2016 17:23
Last Modified:	01 Sep 2016 17:23
URI:	http://eprints.esc.cam.ac.uk/id/eprint/3750

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