Hamilton’s principle and normal mode coupling in an aspherical planet with a fluid core

Al-Attar, David and Crawford, Ophelia and Valentine, Andrew P and Trampert, Jeannot (2018) Hamilton’s principle and normal mode coupling in an aspherical planet with a fluid core. Geophysical Journal International. ISSN 0956-540X DOI https://doi.org/10.1093/gji/ggy141

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Official URL: https://doi.org/10.1093/gji/ggy141


Seismic free oscillations, or normal modes, provide a convenient tool to calculate low-frequency seismograms in heterogeneous Earth models. A procedure called ‘full mode coupling’ allows the seismic response of the Earth to be computed. However, in order to be theoretically exact, such calculations must involve an infinite set of modes. In practice, only a finite subset of modes can be used, introducing an error into the seismograms. By systematically increasing the number of modes beyond the highest frequency of interest in the seismograms, we investigate the convergence of full-coupling calculations. As a rule-of-thumb, it is necessary to couple modes 1–2 mHz above the highest frequency of interest, although results depend upon the details of the Earth model. This is significantly higher than has previously been assumed. Observations of free oscillations also provide important constraints on the heterogeneous structure of the Earth. Historically, this inference problem has been addressed by the measurement and interpretation of splitting functions. These can be seen as secondary data extracted from low frequency seismograms. The measurement step necessitates the calculation of synthetic seismograms, but current implementations rely on approximations referred to as self- or group-coupling and do not use fully accurate seismograms. We therefore also investigate whether a systematic error might be present in currently published splitting functions. We find no evidence for any systematic bias, but published uncertainties must be doubled to properly account for the errors due to theoretical omissions and regularization in the measurement process. Correspondingly, uncertainties in results derived from splitting functions must also be increased. As is well known, density has only a weak signal in low-frequency seismograms. Our results suggest this signal is of similar scale to the true uncertainties associated with currently published splitting functions. Thus, it seems that great care must be taken in any attempt to robustly infer details of Earth's density structure using current splitting functions.

Item Type: Article
Uncontrolled Keywords: 2018AREP; IA74
Subjects: 02 - Geodynamics, Geophysics and Tectonics
Divisions: 02 - Geodynamics, Geophysics and Tectonics
12 - PhD
Journal or Publication Title: Geophysical Journal International
Identification Number: https://doi.org/10.1093/gji/ggy141
Depositing User: Sarah Humbert
Date Deposited: 10 Apr 2019 12:43
Last Modified: 10 Apr 2019 12:43
URI: http://eprints.esc.cam.ac.uk/id/eprint/4453

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