Free oscillations and surface waves of an aspherical Earth

Mochizuki, Etsuko

doi:10.1029/gl013i013p01478

Cited by 30 publications

(25 citation statements)

References 13 publications

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“…The correspondence between free oscillations and surface waves for an isotropic and aspherical earth has been established by Jordan (1978), Woodhouse & Girnius (1982), Woodhouse & Dziewonski (1984) and Mochizuki (1986). In Section 3, these results are extended to the anisotropic case following the procedure of Mochizuki (1986), and the immediate application of our theory is discussed.…”

Section: Introductionmentioning

confidence: 91%

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The Free Oscillations of an Anisotropic and Heterogeneous Earth

Mochizuki

1986

Geophysical Journal International

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Generalized spherical harmonics are used to simplify the calculation of the perturbation matrix elements (coupling coefficients) for the free oscillations of an anisotropic and laterally heterogeneous earth. In the asymptotic limit of large angular order, the local frequency pertubration which depends on the azimuth and on the location of Earth's surface is defined, and the correspondence to surface waves is established.

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Section: Introductionmentioning

confidence: 91%

“…In Section 3, these results are extended to the anisotropic case following the procedure of Mochizuki (1986), and the immediate application of our theory is discussed.…”

Section: Introductionmentioning

confidence: 95%

The Free Oscillations of an Anisotropic and Heterogeneous Earth

Mochizuki

1986

Geophysical Journal International

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“…The first study on a global scale was that of Woodhouse and Dziewonski (1984) whose global upper-mantle shear velocity models, M84A and M84C, were regarded as reference 3-D model upper-mantle models for the following decade. This was later justified theoretically by Mochizuki (1986aMochizuki ( , 1986b and Romanowicz (1987). Though Woodhouse and Dziewonski used normal mode summation to calculate synthetic seismograms, they used a clever trick to account for sensitivity to odd-degree structure by introducing a fictitious epicentral distance shift in the minor and major arc great circle integrals.…”

Section: Higher Mode Dispersion and Waveform Modelingmentioning

confidence: 99%

Theory and Observations – Normal Modes and Surface Wave Measurements

Laske¹,

Widmer‐Schnidrig²

2007

Treatise on Geophysics

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“…Thus, the problem lies with the determination of the odd-degree structure. Mochizuki (1986), Romanowicz (1987), and Park (1987) have shown that normal mode amplitudes depend on both the odd-and even-degree structure, and we shall find that amplitudes are more sensitive to odd-degree structure than even-degree structure. Although the frequency range of this study is more limited than that of previous studies, the principal advantages of using normal mode amplitudes as the primary data source are that the determinations of the odd-and even-degree components are essentially decoupled, and the problems facing the recovery of odd-degree earth structure may be better addressed.…”

Section: Introductionmentioning

confidence: 95%

Recovery of aspherical earth structure from observations of normal mode amplitudes

Pollitz

1990

Geophysical Journal International

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On an aspherical earth, the normal mode amplitude pattern is perturbed by along-branch coupling. In the geometrical optics approximation, the effect of aspherical earth structure on normal mode amplitudes through along-branch coupling is equivalent to a perturbation Q, in the spatial phase of the amplitude pattern. This observable quantity is related to earth structure through a WKBJ phase integral along the source-receiver minor arc. The amplitude pattern is strongly sensitive to odd-degree earth structure and complements the information contained in the frequency shift pattern, which is sensitive to only even-degree structure. We have developed a method to estimate the amplitudes of unresolvably split multiplets from long-period spectra and have applied it to a large number of IDA and GEOSCOPE recordings to obtain a global data set of normal mode amplitudes for spheroidal modes oS26-oS4,. Normal mode amplitude estimation requires that the first surface wave arrival R 1 be available in the seismogram, and coherent amplitude patterns have been obtained for 172 data records.The analysis of normal mode amplitudes affords several advantages not shared by surface wave phase velocity analysis or time-domain waveform fitting. Our method allows the estimation of errors in the model and the ability to cull away modes in the frequency domain, and it makes use of the information contained in the entire seismogram. In addition, our method makes no assumptions concerning the spectral shape of isolated multiplets in the frequency domain. The small data set employed here is only a fraction of the size of previous global data sets, but has the advantage that fewer assumptions are built in to the theory on which the structure inversion is based. Several factors, including uncertainty in the moment tensor scaling and focusing and defocusing effects, prohibit recovery of Q, for individual multiplets and limit us to the recovery of the average Q, over the mode band 1 = 26-43, for each source-receiver pair. Through a preferential weighting of subsets of this mode band, we may obtain estimates of Q, within narrower mode bands centred, respectively, on 1 =31, 1 =34, and 1 =37. Least squares inversion of Q, within the various mode bands, utilizing approximately 100 source-receiver pairs, yields the geographic distribution of local eigenfrequency perturbation S W ,~~, ( 8, 9 ) in a truncated spherical harmonic expansion. Inversion is first performed for the best fitting degree-6 earth model using all available modes within the band 1 = 26-43 with equal weight. The degree-6 earth model is obtained by inverting for degrees 1, 3, and 5 with degrees 2, 4 and 6 fixed according to published results from the frequency studies. Narrower band inversions are performed within 1 = 26-36, I = 29-39, and 1=31-43. Comparison with model M84A shows that the odd degree-1 and 3 components of aspherical earth structure may be reproduced from the amplitude data set. The degree-5 structure differs significantly from that of model M84A.

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Free oscillations and surface waves of an aspherical Earth

Cited by 30 publications

References 13 publications

The Free Oscillations of an Anisotropic and Heterogeneous Earth

The Free Oscillations of an Anisotropic and Heterogeneous Earth

Theory and Observations – Normal Modes and Surface Wave Measurements

Recovery of aspherical earth structure from observations of normal mode amplitudes

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