Propagation of elastic wave motion from an impulsive source along a fluid/solid interface

Abstract

Parts I and II of this report compare the experimentally observed pressure response for the impulse-excited fluid/solid interface problem with that derived from a corresponding theoretical investigation. In the experiment a pressure wave is generated in the system by a spark and detected with a small barium titanate probe. The output of the probe is displayed on an oscilloscope and photographed. Two cases are investigated: one where the transverse wave velocity is lower than the longitudinal wave velocity of the fluid and the other where the transverse wave velocity is higher. Both of these observed responses are shown to agree even as to details of wave-form, with exact computations made for a delta-excited line source. This comparison is justified by making an approximate calculation for the decaying point source and showing that at these distances it does not differ appreciably from the delta-excited line source. In the case of low transverse wave velocity one finds, besides critically refracted P, direct, and reflected waves, a Stoneley type of interface wave. Although the emphasis in recent years has been towards minimizing the importance of Stoneley waves, the evidence here is that a Stoneley wave can be the largest contributor to a response curve. In the case of high transverse wave velocity the critically refracted P wave is smaller, and the Stoneley wave, though it tends to maintain a rather constant amplitude, becomes compressed in time and arrives very soon after the reflexion. Between the critically refracted P wave and the direct arrivals one finds both experimentally and theoretically a pressure build-up preceding the arrival time that might be expected for a critically refracted transverse wave. In part III this pressure build-up is investigated and found to consist of the superposition of three arrivals. The most prominent of these is a pseudo-Rayleigh wave. The others are the critically refracted transverse wave and the build-up to the later arriving Stoneley wave. Detailed investigation of the pseudo-Rayleigh wave shows it to have the velocity of a true Rayleigh wave which is independent of the existence of the fluid. Furthermore, it has the same retrograde particle motion as the true Raylcigh wave. However, it is radiating into the fluid as it progresses and therefore has many of the properties of a critically refracted arrival when measurements are made in the fluid. Mathematically it differs from the true Rayleigh wave in that its origin is not from a pole on the real axis of the plane of the variable of integration, but rather from a pole which lies on a lower Riemann sheet in the complex plane. In the high transverse wave velocity case this pole is not too far removed from the real axis and the imaginary part of the pole location might be interpreted as a decay factor. The real part, however, yields only approximately the velocity of the pseudo-Rayleigh wave, for the actual velocity as pointed out above is precisely that of the truc Rayleigh wave velocity. The migration of this complex pole explains why such a pseudo-Rayleigh wave was not observed in parts I and II in the low transverse velocity case. The problem under discussion is intimately related to the classic work of Horace Lamb On the propagation of tremors over the surface of an elastic solid. One need make only a minor re-interpretation of the source function in order to compare directly the wave-forms (excluding of course the Stoneley wave contribution). Finally, a method is suggested for obtaining the solid rigidity of bottom sediments in water-covered arcas from in situ measurements of the pseudo-Rayleigh wave and/or Stoneley wave velocities and arrival times.