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P. Borejko:
"A New Benchmark Solution for the Problem of Water-Covered Geophysical Bottom";
Talk: International Symposium on Mechanical Waves in Solids, Zhejiang University, Hangzhou, China (invited); 2006-05-15 - 2006-05-18.

A New Benchmark Solution for the Problem of Water-Covered Geophysical Bottom
Piotr Borejko1*
1 Department of Civil Engineering, Vienna University of Technology, Wiedner Hauptstr. 8/E206/3, Vienna, A-1040, Austria
Abstract
A highly idealized physical model offering an extensive insight into the interaction of acoustic waves with the water-covered geophysical bottom is the Sommerfeld model (liquid half-space over solid elastic half-space), where both a point source and a point receiver are placed in the fluid and the two media (fluid and solid) of contrasting densities and wave speeds are homogeneous. The Sommerfeld model was studied experimentally by Roever and Vining [1] and theoretically by Strick [2], who demonstrated close pressure-response-form agreement between experiment and theory for the particular parameters (such as the characteristic wave speeds in the adjacent media and the source-receiver distance) assumed in the model experiments and the theoretical investigation.
Opposite to Strick´s approximate point source solution (Ref. [2]), obtained by means of the asymptotic expansion method and thus applicable to "large" source-receiver separations, the present point source solution (derived by applying the generalized-ray formalism [3]) is accurate for any separation. In particular, it is also accurate for "small" separations where the asymptotic solution is apparently invalid and the normal mode solution (for the case of a point source in a liquid layer with a solid bottom) becomes impracticable due to poor convergence.
The ray-integral 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 acoustically 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 solve the inverse problem of in situ determination of the bottom rigidity in water-covered areas.
References

[1] Roever W. L. and Vining T. F. (1959) Propagation of elastic wave motion from an impulsive source along a fluid/solid interface. I. Experimental pressure response. Phil. Trans. Roy. Soc. A251: 455-465.
[2] Strick E. (1959) Propagation of elastic wave motion from an impulsive source along a fluid/solid interface. II. Theoretical pressure response. III. The pseudo-Rayleigh wave. Phil. Trans. Roy. Soc. A251: 465-523.
[3] Pao Y.-H. and Gajewski R. R. (1977) The generalized ray-theory and transient responses of layered elastic solids. In Physical Acoustics 13: 184-265, ed. by Mason W. P. and Thurston R. N., New York: Academic Press.