A ray-integral solution for the wave-field in the Sommerfeld model

Abstract

A ray-integral solution is presented for the wave-field in the Sommerfeld model (liquid half-space over solid half-space), where a point source is placed in the fluid and the two media (fluid and solid) of contrasting densities and wave speeds are homogeneous. This exact closed form solution is then used to evaluate complete time records of the acoustic pressure (at a point receiver located in the fluid in the vicinity of the penetrable fluid-solid interface) for two Sommerfeld models: one where the shear wave speed in the solid bottom is lower than the sound speed in the fluid and the other where the shear wave speed is higher. These pressure response curves indicate the relative importance of the various wave-forms (the critically refracted longitudinal and shear waves, the pseudo-Rayleigh and Stoneley interface waves, the direct wave, and the totally reflected wave) contributing to the solution and the possibility of utilizing the arrival times of the refracted and interface waves to determine the bottom rigidity. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)