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  • Blackwell Publishing Ltd  (3)
  • 1
    Electronic Resource
    Electronic Resource
    Oxford, UK : Blackwell Publishing Ltd
    Geophysical journal international 4 (1937), S. 0 
    ISSN: 1365-246X
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geosciences
    Notes: Lamb, in his classical paper of 1904, found the form of the Rayleigh pulse that travels over the surface of an elastic half-space, which has been struck along a line. Let such a pulse travel on one face of an elastic quarter-space, the crest-line being parallel to and travelling towards the edge. We enquire what form the Rayleigh pulse will have after passing round the corner.The problem is taken as two-dimensional; the elastic solid fills the positive quadrant xOy and the incident Rayleigh pulse arises from a pressure p(x, t)= - Qδ(x -a)φ(t) applied on the face y= o.The differential equations and boundary conditions are reduced to operational form by the use of a Fourier transform with respect to time and Laplace transforms with respect to x and y. Difficulties arise from our lack of knowledge of the displacements at the surfaces x= o and y= o, but solution of the problem is reduced to that of two simultaneous integral equations.An iterative solution can be found, and from this we isolate the parts which describe the incident Rayleigh pulse (identical with Lamb's solution) and the pulse transmitted round the corner.It is found that the form of the pulse is greatly changed, in ways depending on the values of the velocities of P, S and Rayleigh waves. Whereas the dispacements u and v on y= o have the shape of φ(t) and its allied function (Hilbert transform) φ(t) respectively, each of u and v on x= o is given by a linear combination of φ and φ. Since φ may differ greatly from φ in form, the change in shape of each component of displacement when it turns the corner may be very marked.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Oxford, UK : Blackwell Publishing Ltd
    Geophysical journal international 7 (1955), S. 0 
    ISSN: 1365-246X
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geosciences
    Notes: The I.S.S. for 1935 records a series of seven earthquakes with the same epicentre off the east coast of Japan. This series, in which the I.S.S. identifies many arrivals as P* or S*, was examined in the hope of estimating velocities of P* and S*. Straight lines fitted to first arrivals at stations of azimuth 180° to 270° gave the local velocity of P as 7.77 ± 0.04 km/sec. Epicentre and origin-time were then redetermined for each shock, and revised times of arrival plotted against revised epicentral distances. The following conclusions were reached:〈list xml:id="l1" style="custom"〉No series of arrivals could be identified as P* or S*.The redetermined epicentres show an approximately linear arrangement. The uncertainty in position of each epicentre is comparable with the distance between successive epicentres, and may be due to the spatial extent of the focus.There is a clustering of points between Δ=4° and Δ=9° about a line which would represent a pulse travelling with the velocity of S but 15.8 sec later than S. The delay may be used to obtain an estimate of the depth of the Mohorovičié discontinuity.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Oxford, UK : Blackwell Publishing Ltd
    Geophysical journal international 6 (1952), S. 0 
    ISSN: 1365-246X
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geosciences
    Notes: When a hot gravitating sphere cools, gravitational potential energy is lost in contraction. We consider a sphere that can be taken as in continual hydrostatic equilibrium for slow changes of state, and, assuming radial symmetry, set up the modified Fourier equation for heat conduction. This contains two extra terms, one contributed by the heating effect of contraction, and another from the change of temperature gradients with shrinkage. This equation is checked by integration through time and through the sphere to give a comprehensive energy equation.For an initial parabolic temperature distribution in the Earth, the heating effect of contraction is small, and more than counteracted by the extra cooling provided by increased temperature gradients. Moreover, it is probable that the modifications to the first (uniform rigid sphere) approximation which are needed to allow for departures from uniformity in density, specific heat, and thermal conductivity in the Earth are greater than those which allow for contraction.
    Type of Medium: Electronic Resource
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