Calculation of the Wave Fields for Multiple Waves near the Points of Origin

Part of the Seminars in Mathematics book series (SM, volume 9)


In the present paper we obtain computational formulas for the principal parts of displacement fields of multiple reflected and head waves propagating in elastic media near the point of origin of the head wave. Similar formulas for simpler cases have been considered in [1, 2].


Saddle Point Branch Point Displacement Field Wave Field Phase Function 
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Literature Cited

  1. 1.
    Petrashen’, G. I., The general quantitative theory of reflected and head waves in layered media with plane-parallel separating boundaries, in: Problems in the Dynamical Theory of Propagation of Seismic Waves [in Russian], No. 1, Gostoptekhizdat (1957).Google Scholar
  2. 2.
    Smirnova, N. S., Calculation of the wave fields in a neighborhood of singular points, in: Problems in the Dynamical Theory of Propagation of Seismic Waves [inRussian], No. 6, Gostoptekhizdat (1962).Google Scholar
  3. 3.
    Petrashen’, G. I., Propagation of elastic waves in isotropic layered media, Uch. Zap. Len. Gos. Univ., No. 162 (1952).Google Scholar
  4. 4.
    Smirnov, V. I., A Course in Higher Mathematics [in Russian], Vol. 3, Ch., 2, Leningrad (1949).Google Scholar
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    Smirnova, N. S., Abstract of Candidates Dissertion [in Russian], Izd. Len. Gos. Univ. (1963).Google Scholar

Copyright information

© Consultants Bureau, New York 1970

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