Normal Modes of a Rotating, Self-gravitating Inhomogeneous Earth

Luh, Peter C.

doi:10.1111/j.1365-246x.1974.tb04116.x

Cited by 73 publications

(55 citation statements)

References 25 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In the Appendix, however, we give the completely general matrix element, correcting the part pertaining to ellipticity (Dziewonski & Sailor 1976;Dahlen 1976;Woodhouse & Dahlen 1978) and also correcting some minor misprints in Luh's (1974) result. This matrix element, given here for reference, has rather wider applications than those considered in the present paper; it is needed, for example, in determining the first order corrections to the eigenfunctions in degenerate perturbation theory and also in calculating the second and higher order corrections to the eigenfrequencies (Dahlen 1968;Dahlen & Sailor 1979).…”

Section: Introductionmentioning

confidence: 97%

“…For the low frequency multiplets considered by Luh (1974) the dominant coupling influences were shown to be rotation and ellipticity, and in this study of the effect of attenuation on quasi-degenerate multiplets we shall confine our attention to these asphericities alone. In the Appendix, however, we give the completely general matrix element, correcting the part pertaining to ellipticity (Dziewonski & Sailor 1976;Dahlen 1976;Woodhouse & Dahlen 1978) and also correcting some minor misprints in Luh's (1974) result.…”

Section: Introductionmentioning

confidence: 98%

See 1 more Smart Citation

The coupling and attenuation of nearly resonant multiplets in the Earth's free oscillation spectrum

Woodhouse

1980

Geophysical Journal International

211

204

View full text Add to dashboard Cite

The effect of attenuation on the coupling of nearly resonant multiplets in the Earth's free oscillation spectrum is investigated and numerical results are presented for several of the most strongly coupled low frequency multiplet pairs. The coupling influences considered are those of the Coriolis forces due to rotation and of the Earth's hydrostatic ellipticity of figure. It is found that the effects of attenuation (in particular the difference in Q-' for the two multiplets) can significantly change the splitting diagrams and the degree to which coupling takes place. The Q values for the coupled singlets are, in general, all different and lie between the two Q values of the uncoupled multiplet pair. In addition it is shown that the diagonal sum rule may be readily extended to sets of coupled multiplets.

show abstract

Section: Introductionmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 98%

The coupling and attenuation of nearly resonant multiplets in the Earth's free oscillation spectrum

Woodhouse

1980

Geophysical Journal International

211

204

View full text Add to dashboard Cite

show abstract

“…Overall, three of the four models have smallest misfits between the data and synthetics when there is no inner core anisotropy at all; this is because the models used were created using SC. Coupling rules (Luh, 1974) do not allow radial modes to be affected by inner core anisotropy when SC is used. The imposition of an isotropic layer has a much smaller effect on the radial modes when the Tr model is used than when the other three models are used.…”

Section: Radial Modesmentioning

confidence: 99%

Stratified anisotropic structure at the top of Earth's inner core: A normal mode study

Irving

Deuss

2011

Physics of the Earth and Planetary Interiors

View full text Add to dashboard Cite

Please cite this article as: Irving, J.C.E., Deuss, A., Stratified anisotropic structure at the top of Earth's inner core:a normal mode study, Physics of the Earth and Planetary Interiors (2010), doi:10.1016/j.pepi.2011 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. Page 1 of 40A c c e p t e d M a n u s c r i p tWe probe the isotropic layer at the top of Earth's inner core using normal modes. Normal mode data are compatible with an isotropic layer of up to 250km thick. Normal modes can therefore be reconciled with previous body wave studies. We further show seismic data support the presence an S-wave isotropic layer. *HighlightsPage 2 of 40 A c c e p t e d M a n u s c r i p t AbstractBody wave studies support the presence of an isotropic layer at the top of the inner core. Recent normal mode models of inner core anisotropy do not contain such a layer, but instead have anisotropic structure extending to the inner core boundary. Here, we use full-coupling of normal mode oscillations sensitive to inner core structure in order to investigate the discrepancy between models of the inner core developed using these two different types of data. We impose an isotropic layer onto existing normal mode models of inner core anisotropy, and calculate frequencies, quality factors and synthetic seismograms for radial modes, PKIKP modes and PKJKP modes. Using full-coupling allows us to make the first simulations of the effect of an isotropic layer on radial modes.The presence of an uppermost isotropic layer has an effect on the frequencies and attenuation of normal modes. By calculating the misfit between data from four large earthquakes and synthetic seismograms created for models of the inner core with isotropic layers of varying thickness, we find that normal mode data are compatible with the presence of an isotropic layer of up to 250km thickness at the top of the inner core. Thus, normal modes can be reconciled with previous body wave studies. The influence of such a layer on PKJKP modes is the only way that S-wave isotropy at the top of the inner core can currently be studied;we show, for the first time, that seismological data support the presence an S-wave isotropic layer.

show abstract

“…Madariaga & Aki (1972) argue that the range of the continent-induced splitting is rather sensitive to the contrasts between the continental and oceanic models, at least for I > 20. Their calculations indicate that differences in an 0 Luh (1974) .8 t Earth model of 5 per cent in p can change the continent-induced splitting by factors of 2 to 4. Thus, some differences between the results shown in Fig.…”

Section: O M P a R I S O N S T O P R E V I O U S R E S U L T Smentioning

confidence: 96%

Eigenvibrations of laterally inhomogeneous Earth models

Stifler

Bolt

1981

Geophysical Journal International

View full text Add to dashboard Cite

A realistic three-dimensional Earth having both radial and lateral variations in seismic properties has been modelled using finite elements. Numerical algorithms are produced that yield efficient estimations of the non-degenerate eigenfunctions and eigenfsequencies of this laterally inhomogeneous spheroid. These serve as quite independent alternatives t o previous mathematical methods used to study this problem. The algorithms rely upon Rayleigh's Variational Principle to solve the finite element eigenproblem. The Earth model used is perfectly elastic and non-rotating.The finite element formulation is demonstrated numerically in the case of eigenvibrations of low order torsional oscillations, 0T2 to oTlo, but also applies to the spheroidal oscillations. Theoretical splitting of the eigenfrequencies due t o the Earth's ellipticity and to the structural contrasts between continents and oceans is obtained. Eigenfunctions of a realistic laterally inhomogeneous Earth model are computed for this suite of torsional oscillations. It is seen that the relative positions of the continents establish patterns of displacement which may provide explanations for the variations in eigenspectra observed from one seismographic station to another.The deviations in eigenfrequencies due t o the structural contrasts between the continents and the oceans are found to increase from 0.01 per cent of the unperturbed frequency for 0T2 to 0.1 per cent for oTl,. Over the same range of eigenvibrations, the effects on the eigenfrequencies of the Earth's ellipticity are about 0.2 per cent.The amplitudes of the eigenfunctions of these oscillations are seen to have significant global variation. The lower order modes show a latitudinal dependence of the amplitudes that would be expected were the Earth a simple ellipsoid. The higher order modes have more longitudinal amplitude dependence as a result of the increased perturbation effects of the continents. l h s work demonstrates that the finite element method can be used as a practical scheme for calculating theoretical eigenspectra for global seismographic stations. introduction

show abstract

Normal Modes of a Rotating, Self-gravitating Inhomogeneous Earth

Cited by 73 publications

References 25 publications

The coupling and attenuation of nearly resonant multiplets in the Earth's free oscillation spectrum

The coupling and attenuation of nearly resonant multiplets in the Earth's free oscillation spectrum

Stratified anisotropic structure at the top of Earth's inner core: A normal mode study

Eigenvibrations of laterally inhomogeneous Earth models

Contact Info

Product

Resources

About