Acoustic radiation from an impulsive point source in a continuously layered fluid—An analysis based on the Cagniard method

Abstract

Acoustic radiation from an impulsive point source in a continuously layered fluid with depth-varying parameters is investigated theoretically with the aid of the modified Cagniard method, that starts with a one-sided Laplace transformation with respect to time and a Fourier transformation with respect to the horizontal space coordinates. Using appropriate one-sided Green's functions, the system of transform-domain differential equations in the depth coordinate is rewritten as a system of integral equations that, for not too rapidly varying fluid properties, can be solved by iteration. The modified Cagniard method leads to space-time expressions for the relevant iterates. To show the generality of the method, the fluid is assumed to show anisotropy in its volume density of mass. The continuously refracted waves emitted by the source and the singly, continuously, reflected wave in an isotropic fluid are discussed in detail. With this method, no difficulties arise with “turning rays” as is the case in the frequency-domain analysis of the problem. [Work done as a Visiting Scientist at Schlumberger-Doll Research, Old Quarry Road, Ridgefield, CT 06877-4108.]