Propagation of an SH‐torque pulse in a sphere

Abstract

An exact solution is obtained for the displacement of the surface of a uniform solid sphere of radius a due to an impulsive SH‐torque pulse from a point source situated at a distance b from the center. The duration of the source was varied from 0.05a/c to 0.5a/c, keeping the time variation of the torque such that the surface displacement stays finite when the time tends to infinity. c is the shear‐wave velocity. Theoretical seismograms have been computed at several distances from a surface source and from buried sources at b = 7a/8, a/2, 0.3a, and 0. Arrival times of reflected pulses coincide with arrival times of reflected rays, where the latter are obtained according to geometrical optics. The solution for buried sources reveals diffracted pulses. They are connected with the two cases in which reflected rays are disallowed by geometrical optics: (1) owing to distance of observer from source and (2) owing to depth of source. In these cases the arrival time as obtained from the ‘steepest descent’ analysis of Jeffreys and Lapwood is complex. The real part of the complex arrival times lies in the time interval during which diffracted pulses occur. There are no diffracted pulses for the surface source.