Transient Acoustic Radiation in a Continuously Layered Fluid — An Analysis Based on the Cagniard Method
In the present paper, the problem of the transient wave propagation in a continuously layered fluid is addressed directly with the aid of the Cagniard method. The standard integral transformations that are characteristic for this method (Cagniard, 1939, 1962; De Hoop, 1960, 1961, 1988; Aki and Richards, 1980) are applied to the first-order acoustic wave equations of a fluid. The resulting system of differential equations in the depth coordinate is next transformed into a system of integral equations. These integral equations admit a solution by a Neumann iteration. Each higher-order iterate can be physically interpreted as to be generated, through continuous reflection, by the previous one. To show the generality of the method, anisotropy of the fluid in its volume density of mass is included. This type of anisotropy is encountered in the equivalent medium theory of finely discretely layered media (Schoenberg, 1984). The compressibility is a scalar. Next, the transformation back to the space-time domain is performed using the Cagniard method, in which a number of steps can be carried out analytically even for the anisotropic case.
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