THE RANGE OF EXISTENCE OF STONELEY WAVES IN AN INTERNAL STRATUM. I. SYMMETRIC VIBRATIONS

Abstract

Summary. We derive the frequency equation and the condition of existence of Stoneley type waves with antisymmetric vibrations which can be propagated along the interfaces between an internal stratum and two adjacent halfspaces of identical elastic properties, all perfectly elastic, homogeneous and isotropic. The ranges of existence of such waves are next obtained by numerical computation and the results are presented both in tabular form and graphically. For large values of the frequency, the frequency equation for these waves, like the one for waves with symmetric vibrations discussed in an earlier paper*, reduces to the velocity equation of Stoneley waves propagated along the interface between two halfspaces. For a low-velocity stratum, the results are similar to those for waves with symmetric vibrations. It is found that, for a pair of media for which waves of some frequency can exist, as the frequency of the waves or the thickness of the stratum is decreased, there is a cut-off value of either below which such waves cannot be propagated. For a high-velocity stratum, the results are in sharp contrast with those for waves with symmetric vibrations. Stoneley waves of all frequencies can exist for some pairs of materials. As the frequency of the waves or the thickness of the stratum is decreased, that is, as the ratio of the wave-length to the thickness of the stratum is increased, the regions of existence expand until a certain limiting region of existence is obtained when this ratio tends to infinity. Another difference between waves with symmetric and antisymmetric vibrations is that whereas for the former the phase velocity could not be less than the smaller of the two Rayleigh wave velocities, for the latter there is no theoretical lower limit.