On Azimuthal Variation of Displacements of Normal Mode Solutions of Sh Type Excited by a Double-Couple Point Source With Special Attention to the Mode-Ray Relation

Odaka, Toshikazu

doi:10.4294/jpe1952.20.71

Cited by 2 publications

(2 citation statements)

References 10 publications

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“…The same relation has been derived by ODAKA (1972) comparing radiation patterns of SH pulses and amplitude spectra of toroidal modes. However, it must be noted that the mode-ray correspondence relation pointed out by Ben-Menahem is primarily valid for normal modes with quite small wave-lengths.…”

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confidence: 55%

“…The formulation for displacements due to impulsive point sources in a radially heterogeneous sphere has been developed in detail in the paper by USAMI et al (1970). For azimuthal displacements of the torsional vibration excited by the shear fault, the formula is given in a more compact form by ODAKA (1972). In the present paper, only the azimuthal component is computed at various points on the surface, azimuth…”

Section: Theoretical Seismograms Of Sh Pulsesmentioning

confidence: 99%

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On the Correspondence Relation Between Normal Modes and Rays

Odaka

Usami

1972

J,Phys,Earth

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This paper deals with the torsional vibration of radial higher modes of a spherical earth consisting of a homogeneous elastic mantle and a liquid core with special reference to the correspondence relation between normal modes and body waves. The normal modes and the rays assigned by the mode-ray correspondence relation originally derived by Ben-Menahem are related very closely in several aspects even for the normal modes of the low radial modes having small colatitudinal order numbers. This relation connects modes and rays through the identity of the phase velocity of normal modes and the apparent velocity of body waves. Group velocities of the normal modes associated with a certain ray show nearly constant values independent of radial mode numbers, constants being a function of ray parameter. The travel time of surface waves specified by this constant group velocity gives almost the same value as that of the corresponding body wave. In addition, there are close correlations between the two radii, one to the lowermost maximum or zero

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mentioning

confidence: 55%

Section: Theoretical Seismograms Of Sh Pulsesmentioning

confidence: 99%

On the Correspondence Relation Between Normal Modes and Rays

Odaka

Usami

1972

J,Phys,Earth

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Derivation of asymptotic frequency equations in terms of ray and normal mode theory and some related problems radial and spheroidal oscillations of an elastic sphere.

Odaka

1978

J,Phys,Earth

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Ray theory is applied successfully to derive asymptotic frequency equations of the radial oscillations of a homogeneous elastic sphere and a sphere with one concentric surface of discontinuity in it , and of the spheroidal oscillation of a homogeneous sphere. The method is similar to the one used for getting frequency equations for plane stratified media , and is based on the idea that for steady vibration of a sphere to be possible some interference condition has to be satisfied by body waves traveling in it . It is shown that these equations are identical to those obtained by the normal mode theory.It is found that the solotone effect has an immediate connection with multiple reflections of body waves at the discontinuity in the medium . Decoupling of P-and S-waves at high frequencies is well illustrated for the spheroidal modes in terms of the distribution of eigenfrequencies and the radial dependence of eigenfunctions.

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On Azimuthal Variation of Displacements of Normal Mode Solutions of Sh Type Excited by a Double-Couple Point Source With Special Attention to the Mode-Ray Relation

Cited by 2 publications

References 10 publications

On the Correspondence Relation Between Normal Modes and Rays

On the Correspondence Relation Between Normal Modes and Rays

Derivation of asymptotic frequency equations in terms of ray and normal mode theory and some related problems radial and spheroidal oscillations of an elastic sphere.

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