Cox, GA, Livermore, PW and Mound, JE (2013) Forward models of torsional waves: dispersion and geometric effects. Geophysical Journal International. ISSN 0956-540X
Abstract
Alfvén waves are a set of transverse waves that propagate in an electrically conducting fluid in the presence of an ambient magnetic field. Studies of such waves in the Earth's interior are important because they can be used to make inferences about the structure and physical properties of the core that would otherwise remain inaccessible. We produce 1-D forward models of cylindrical torsional Alfvén waves in the Earth's core, also known as torsional oscillations, and study their evolution in a full sphere and an equatorially symmetric spherical shell. Here, we find that travelling torsional waves undergo significant geometric dispersion that increases with successive reflections from the boundaries such that an initial wave pulse becomes unidentifiable within three transits of the core. Low amplitude wakes trail behind sharply defined pulses during propagation, a phenomenon that we interpret using the failure of Huygens’ principle in even dimensions. We investigate the relationship between geometric dispersion and wavelength, concluding that long-wavelength features are more dispersive than short-wavelength features. This result is particularly important because torsional waves that have been inferred in the Earth's core from secular variation are relatively long wavelength, and are therefore likely to undergo significant dispersion within the core. When stress-free boundary conditions on angular velocity are applied, waves are reflected at the equator of the core–mantle boundary with the same sign as the incident wave. Waves that pass through the rotation axis undergo a pseudo-reflection and display a more complicated behaviour due to a phase shift. In an equatorially symmetric shell, we identify a weak reflection at the tangent cylinder due to geometric effects.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | This article has been accepted for publication in Geophysical Journal International. © The Authors 2013. Published by Oxford University Press on behalf of The Royal Astronomical Society. All rights reserved. |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Environment (Leeds) > School of Earth and Environment (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 12 Dec 2013 09:28 |
Last Modified: | 18 Jan 2018 00:20 |
Published Version: | http://dx.doi.org/10.1093/gji/ggt414 |
Status: | Published |
Publisher: | Oxford University Press |
Identification Number: | 10.1093/gji/ggt414 |
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Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:77141 |