Journal of Physics of the Earth
Online ISSN : 1884-2305
Print ISSN : 0022-3743
ISSN-L : 0022-3743
Volume 25, Issue 4
Displaying 1-5 of 5 articles from this issue
  • Ryosuke SATO, E. R. LAPWOOD
    1977 Volume 25 Issue 4 Pages 345-360
    Published: 1977
    Released on J-STAGE: April 30, 2009
    JOURNAL FREE ACCESS
    The detailed pattern of eigenfrequencies of radial overtones of torsional modes of oscillation of a radially-symmetric layered sphere appears to be intimately related to the set of discontinuities of the parameters μ(γ) (rigidity) and ρ(γ) (density).
    In order to elucidate this relationship, we explored in Part I of this series (SATO and LAPWOOD, 1977) the asymptotic approximations available for the discussion of the frequency equation for radial overtones corresponding to a given Legendre parameter for two simple models-a uniform shell and a shell composed of two uniform layers.
    In this paper we extend the theory to a general shell of l uniform layers, and obtain asymptotic approximations to the frequency equation by means of (a) Stokes-type approximations for spherical Bessel functions, (b) Green-type approximations, and (c) Sturm-Liouville theory. We show how (b) and (c) take both Earth-curvature and internal reflexions into account.
    The theory is applied to an Earth-model with a three-layer shell, which is obtained by averaging from PEM-A of DZIEWONSKI et al. (1975). This model has discontinuities a approximate depths 400km and 600km. The relative accuracy of three approximations is explored, and the existence of a solotone effect is exhibited.
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  • E. R. LAPWOOD, Ryosuke SATO
    1977 Volume 25 Issue 4 Pages 361-376
    Published: 1977
    Released on J-STAGE: April 30, 2009
    JOURNAL FREE ACCESS
    In the two previous papers of this series (SATO and LAPWOOD, 1977a, b) we examined approximate methods for calculating eigenfrequencies of radial overtones of torsional oscillations of spherically symmetrical shells. For shells composed of uniform layers we were able to obtain an exact frequency equation, in terms of spherical Bessel functions, for which roots could be computed with any desired precision. They thus supplied a standard for the measurement of the accuracy of approximate methods.
    In applications to shells of two and three uniform layers, which were simple representations of an Earth with inner surfaces of discontinuity, we noted the presence of the solotone effect, which is the existence of recurring patterns of eigenfrequencies owing to internal reflection.
    In this paper we take up the analysis of the solotone effect, showing how it may be predicted from knowledge of the Shell structure, and how it may be interpreted in terms of ray theory. Applications to the same Earth-models as used before show that for them the theory of the solotone gives an excellent fit to the precisely computed eigenfrequencies. The pattern of eigenfrequencies proves to be very sensitive to changes in layer thickness, and thus offers the possibility of future use in determining the positions of surfaces of discontinuity within the mantle of the Earth.
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  • Yoshio SUMINO, Osamu NISHIZAWA, Takayasu GOTO, Ichiro OHNO, Mituko OZI ...
    1977 Volume 25 Issue 4 Pages 377-392
    Published: 1977
    Released on J-STAGE: April 30, 2009
    JOURNAL FREE ACCESS
    Elastic constants of forsterite Mg2SiO4 were measured by the rectangular parallelepiped resonance (RPR) method at temperatures between -190° and 400°C. Elastic constant Cij(Mbar) and their temperature derivatives ∂Cij/∂T (kbar/deg) are:
    The adiabatic bulk modulus Ks=1.292Mbar (25°C) and its temperature derivatives ∂Ks/∂T=-0.160kbar/deg (20°-400°C) are obtained by the Voigt-Reuss-Hill scheme.
    In the temperature range from 100 to 1000K, the Gruneisen constant calculated from the measured bulk modulus is virtually constant at 1.1±0.1, while the Gruneisen-Anderson parameter δs, defined as -(∂ In Ks/∂T)/α(α: the coefficient of volume thermal expansion), decreases with increase of temperature, but tends to approach a constant value of 4.0±0.1 above 500K.
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  • Kazuro HIRAHARA
    1977 Volume 25 Issue 4 Pages 393-417
    Published: 1977
    Released on J-STAGE: April 30, 2009
    JOURNAL FREE ACCESS
    A large-scale three-dimensional seismic velocity structure down to 650 km under the Japan Islands and the Sea of Japan has been investigated to clarify the subduction of lithospheric plates by applying the inversion method of Aki and others. About 3500 data of P-wave travel time residuals observed at 330 Japanese and foreign stations from 20 intermediate and deep-focus earthquakes around Japan were used to determine the velocity anomalies in a number of blocks and source corrections simultaneously. This analysis has well revealed lateral heterogeneities in the upper mantle above 450km. A high velocity zone corresponding to the descending Pacific plate has been clearly identified, particularly in the north Honshu arc, indicating good correlations with the horizontal and vertical distributions of a number of earthquakes around there. It was found that intermediate and deep-focus earthquakes take place mainly in the upper portions of the descending plate with a thickness of about 100km. The highest velocity anomalies are +5-6%(50-250km), +3%(350km), +2%(450km) within the plate, and about -2% down to 350km over a region on the continental side of the descending plate.
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  • Teruo YAMASHITA
    1977 Volume 25 Issue 4 Pages 419-445
    Published: 1977
    Released on J-STAGE: April 30, 2009
    JOURNAL FREE ACCESS
    Crack models in which nucleation can be treated are physically analysed by considering non-uniform initial stress or strain, and static and sliding frictional stress. The proposed models are, in the strict sence, applicable to physical phenomena near the foci of large earthquakes having bilateral rupture propagation.
    Crack models of two kinds are discussed in detail. In one model, rigidity, static and sliding frictional stress are assumed to be constant everywhere. In this case, the proposed model is applied to the 1961 Kitamino and the 1966 Parkfield earthquakes and the initial tectonic fields and frictional stress of these earthquakes are determined.
    In the other model, rigidity is assumed to be a function of position. This model yields the result that stress drop is directly proportional to effective stress, defined by the static frictional stress minus the sliding frictional stress, and the final stress is lower than the sliding frictional stress.
    In each case, the factors accelerating dislocation motion are a broadly accumulated initial stress and a small ratio of sliding to static frictional stress.
    This result is qualitatively the same as in a paper of YAMASHITA (1977). In Case II, it is shown that stress drop is not influenced by the spatial distribution of rigidity but strain drop is heavily influenced by that distribution. Accordingly a treatment like that of Case II is required when the value of strain drop is discussed.
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