Journal of Physics of the Earth
Online ISSN : 1884-2305
Print ISSN : 0022-3743
ISSN-L : 0022-3743
Volume 10, Issue 1
Displaying 1-3 of 3 articles from this issue
  • Iya BUBAKAR
    1962 Volume 10 Issue 1 Pages 1-14
    Published: 1962
    Released on J-STAGE: April 30, 2009
    JOURNAL FREE ACCESS
    An approximate solution of the problem of reflection and refraction of plane harmonic SH waves at irregular interfaces is obtained using a perturbation method of approximation on the assumption that the magnitude of the irregularities is small compared with the incident wavelength and that the slope of the interface is everywhere small. In the case of a periodic interface it is found that the reflected and refracted waves are composed of specularly reflected waves and scattered waves travelling in various directions. If the wavelength of the shear waves in the media are long compared with that of the interface, the amplitudes of some of the scattered waves decrease exponentially with distance from the interface. In general the phase angles of the scattered waves are functions of the wavelength of the interface and the angle of incidence of the primary wave. It is verified, in the case of zero angle of incidence, that the energy going into the scattered radiation is obtained at the expense of the energy in the specularly reflected and refracted waves.
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  • Iya ABUBAKAR
    1962 Volume 10 Issue 1 Pages 15-20
    Published: 1962
    Released on J-STAGE: April 30, 2009
    JOURNAL FREE ACCESS
    The effect of an irregular interface with an isolated irregularity like a trough or a depression on the reflection and refraction of plane harmonic SH waves is investigated on the assumption that the maximum depth of the depression is small compared with the wave-lenghth of the incident wave and that the slope of the surface is everywhere small. It is found that besides the specularly reflected and refracted SH waves there exists various scattered SH waves. In particular the scattered field contains the following secondary wave types whose amplitudes are proportional to the depth of the depression: (i) Direct reflected and refracted SH waves which appear to come from the point of intersection of the axis of symmetry of the depression and the horizontal plane asymptotic to the interface. They have cylindrical divergence. (ii) A diffracted wave which travelled along the interface with the higher of the two shear wave velocities for the media and is finally refracted into the medium with the slower velocity at the critical angle. (iii) An interface wave travelling with the slower of the two velocities in the media. Its energy is confined to the neighbourhood of the interface in the higher velocity halfspace.
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  • Iya ABUBAKAR
    1962 Volume 10 Issue 1 Pages 21-38
    Published: 1962
    Released on J-STAGE: April 30, 2009
    JOURNAL FREE ACCESS
    By an application of the method of small perturbations an approximate solution of the problem of a compressional line source in a halfspace whose free surface is irregular is obtained in an integral form, on the assumption that the surface slope and the magnitude of the irregularities are small. The resulting integrals for the secondary waves whose amplitudes are proportional to the depth of the surface corrugation are evaluated approximately by the method of multiple steepest descent. Two particular surfaces are considered: a sinusoidal surface and a symmetrical curvilinear surface in the form of a basin. It is found that if the ratio of the wavelength of the incident wave to the halfwidth of the basin is small the secondary waves are reflected in the directions of specular reflection and if the ratio is large, the waves appear to come from the basin. With the sinusoidal surface, if the ratio of surface wavelength to the length of the incident waves is large the secondary waves are reflected in the specular directions and if the ratio is small then the surface acts as a grating, the secondary waves being reflected from the troughs of the surface. The amplitudes of the secondary waves are inversely proportional to the square root of range and the deeper the source the smaller the amplitudes.
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