Open AccessThe Motion of the Surface of a Uniform Elastic Half‐Space Produced by a Buried Torque‐Pulse *
Author(s) -
Pekeris C. L.,
Longman I. M.
Publication year - 1958
Publication title -
geophysical journal of the royal astronomical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.302
H-Index - 168
eISSN - 1365-246X
pISSN - 0016-8009
DOI - 10.1111/j.1365-246x.1958.tb00045.x
Subject(s) - heaviside step function , dirac delta function , pulse (music) , surface (topology) , amplitude , displacement (psychology) , surface wave , physics , torque , mathematical analysis , optics , motion (physics) , diffraction , half space , mathematics , classical mechanics , geometry , detector , thermodynamics , psychology , psychotherapist
Summary In this investigation we determine the motion of the surface of a uniform elastic half‐space produced by the application of a torque‐pulse at a point below the surface. The axis of the torque is taken to be parallel to the surface and its time variation is assumed to be represented by the Heaviside unit function H(t). Our results are compared with those of Pinney (1954), who treated the same problem by a different method. The principal feature of physical interest which we found is that, for ranges where the direct S wave is preceded by a diffracted SP wave, the displacement at the surface starts with an infinite amplitude at the time of arrival of the SP wave, and that this is followed by an even stronger infinity at the time of arrival of the S wave. Also, for small ranges, for which there is no SP wave, the displacement starts with a sharp pulse in the form of a Dirac delta function. None of these features was brought out by Pinney's curves. The results are shown in Figures 2, 3 and 4.