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As a step in the solution of the problem of propagation of a seismic pulse in a spherical earth, an exact solution is obtained for the motion of a uniform compressible fluid sphere due to a pressure pulse from a point source situated below the surface. The time variation of pressure due to the source is represented by the difference between two step functions with rounded shoulders. The surface velocity due to sources of different duration and situated at various depths has been evaluated on WEIZAC for different angular distances. In this first communication results for a depth of source equal to half the radius of the sphere are given. The solution exhibits step-function-type and “logarithmic” arrivals, which one would anticipate from the “steepest descent” analysis of Jeffreys and Lapwood. In addition, the solution reveals diffracted pulses which have no counterpart in ray theory.
Alterman et al. (Tue,) studied this question.