Abstract

In this investigation we determine the motion of the surface of a layered elastic half-space produced by a torque-pulse from a point-source situated inside the layer. The axis of the torque is vertical (SH) and its time variation is represented by a step-function with rounded shoulders. The displacement due to the source approaches a saw-tooth shape at large distances. The displacement of the surface was evaluated exactly by the ray-theory method for ranges r = 100 H and r = 400 H, H denoting the thickness of the layer. The spectrum of the forerunner ground wave and of the Love wave can be interpreted in terms of the normal mode theory. The form of the displacement-curve is found to be sensitive to the width Δ of the pulse at the source. For small Δ the Love wave starts with a strong high frequency amplitude comparable to that of the Airy phase arriving later. This is due to a peak in the excitation function of the first mode. As Δ grows, this peak disappears and the Love wave builds up in the normal fashion to a maximum amplitude at the time of arrival of the Airy phase. For the pulse shape assumed, the normal mode theory predicts a factor of [sin2 (ωΔ/2)]/Δ in the amplitude, where ω denotes the frequency. This is verified in the displacement curves obtained.

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