Theoretical and Experimental Investigation of a Pseudo-Rayleigh Wave

Abstract

If a fluid-solid interface be excited by a transient point or line source in the fluid, then, as was previously discussed [W. L. Roever and T. F. Vining, Bull. Am. Phys. Soc. Ser. II, 1, 98 (1956); E. Strick, ibid.], there will be a buildup in the pressure response that begins well before the time of arrival for critically refracted transverse waves. As the ratio of transverse wave velocity in the solid to longitudinal wave velocity in the fluid is increased, this buildup before the direct wave is followed by a decrease in pressure and for still higher ratios passes through zero. When this zero occurs, the point of zero pressure amplitude travels along the interface with the Rayleigh velocity of the free boundary elastic solid. Even larger contrast allows for a separation of the refracted transverse and pseudo-Rayleigh [L. Cagniard, Réflexion et Réfraction des Ondes Séismiques Progressives (Gauthlers-Villars, Paris, France, 1939), pp. 233–237; J. G. Scholte, Koninkl. Ned. Akad. Wetenschap., Proc. 52, 2, 652–653 (1949)] waves from the Stoneley waves. The pressure amplitude of the pseudo-Rayleigh wave is then roughly fifty times that of the critically refracted arrivals. However, this pressure wave cannot be a true Rayleigh wave because it is radiating into the fluid. Particle velocities have been calculated and show wave forms and retrograde motion almost identical with those obtained by Lamb [H. Lamb, Phil. Trans. Roy. Soc. A203, 1–42 (1904)] for a vertical impulse on a free boundary semi-infinite elastic solid.