Surface Motions of a Thick Plate

Abstract

The motion of a thick elastic plate, infinite in two dimensions and bounded by air on the two parallel faces, has been studied. The plate is excited at a point on one face, as in Lamb's problem, by a force impulsive in time, and directed normal to the surface. The early motions of this surface have been described by Lamb. An exact solution, in closed form, for the motion of the opposite face is available only at the epicenter. The motions at all other points are evaluated by a seismic model. At the epicenter, the measurements and the calculations are in agreement; at this point a strong P pulse and a weaker S pulse are observed. This S phase has a wave form, for short pulses, which is the time integral of the wave form of the P phase. Off the axis of symmetry, the form of the S pulse is the same as that of the P pulse. The S pulse becomes quite strong away from the epicenter, attaining an amplitude of nearly four times that of the P pulse at about 45° in the Solenhofen limestone plate. A bodily S‐surface P phase, whose existence is in agreement with predictions based upon geometrical arguments is discerned at angles exceeding the critical angle. A simplified description of the early motion of the reverse face may be constructed. This simplified response is a useful tool which may be used to reduce the complexity of the calculations encountered in other boundary value problems.