PROPAGATION OF A PULSE IN A FLUID SPHERE

Abstract

The exact solution obtained in a previous paper for the motion of a uniform compressible fluid sphere due to a pressure pulse from a point source situated below the surface is applied to a source at a distance of one‐eighth of the radius below the surface. Taking the sphere as a simplified model of the earth, this corresponds to a source at a depth of about 800 km, which is not far from the depth of a deep‐focus earthquake. 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 durations has been evaluated for eight angular distances. The solution exhibits step function type and “logarithmic” reftected pulses, which one would anticipate from the “steepest descents” analysis of Jeffreys and Lapwood. In addition, the solution reveals single diffracted pulses and groups of diffracted pulses which have no counterpart in ray theory. When geometrical optics allows a ray to appear only after a minimum range [Formula: see text] from the epicenter, the complete wave‐theoretical solution shows that these pulses show up earlier in the forbidden zones. Similarly, in the case where the geometrical optics predicts that a certain ray should appear only for ranges [Formula: see text], and should not appear for [Formula: see text], the wave‐theoretic solution shows that such a ray does appear, by diffraction, for some range of [Formula: see text]. Arrival times of the diffracted pulses of the first group increase with increasing θ, while for the second group they decrease with θ.