Resonance Theory of Elastic Head Waves Propagating in a Solid Layer in Tight Contact With a Thick Solid Base

Abstract

The boundary value problem of elastic wave propagation in the case of a plane solid layer I in tight contact with a thick solid base II with a monopole sonic source placed in layer I is treated analytically by the standing wave method. Solution in the form of contour integrals with the amplitudes in 2 x 2 matrix form are obtained. An inspection of the solution shows that it contains all well-known component waves except the head waves. Particular interest is put on these latter waves. Three kinds of head waves (P, S, and S1) are obtained. The S1 wave is newly predicted, which propagates with the shear wave velocity of the soft layer I. It may be considered as the candidate for the "late S wave" observed in earthquakes. The resonance frequencies of the three head waves are obtained, and the motion of the free surface is also described for the three cases.