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This paper studies sound propagation in a layered atmosphere bounded by a ground, whose impedance is described by the Delany–Bazley–Chessell’s empirical model. The problem is formulated in terms of a Green’s function integral in the spectral domain, and is numerically evaluated by a Fast Field Program (FFP). Numerical results are included to show that (i) in simple test cases, the FFP solution is in excellent agreement with existing asymptotic solutions; (ii) numerical overflow arises when the number of layers is large and/or the frequency is high, and a method to circumvent this difficulty is described; and (iii) the FFP is a most powerful tool in solving propagation problems in layered media bounded by complex impedances.

In an earlier paper, the present authors’ work in adapting the fast field program (FFP) formulation to atmospheric propagation above a complex impedance boundary was described. It was found that numerical overflow problems for high frequencies and multiple layers limited the utility of the FFP in solving atmospheric problems. In this paper is a description of a new formulation which eliminates the overflow problems inherent in the earlier formulation. The results of these two formulations are compared for a test case and the superiority of the new formulation is demonstrated. Results of the FFP2 for a simple atmospheric profile are compared with field measurements and the applicability discussed.

The accurate prediction of sound levels propagating through a layered atmosphere is important in many diverse applications. A powerful prediction method is the Fast Field Program (FFP), in which the Green's function integral in the spectral domain is numerically evaluated by the Fast Fourier Transform. However, existing FFP's require the lowest layer to be semi-infinite liquid or solid, which does not accurately model the effect of the earth's surface on sound propagation. Chessel's [J. Acoust. Soc. Am. 62, 825–834 (1977)] empirical model of the ground surface as a complex impedance plane has produced good agreement between experiment and prediction for homogeneous atmospheres. In this paper, we generalize the FFP by incorporating Chessell's boundary conditions. Thus, our program is capable of calculating the sound attenuation of a point source in a layered medium bounded by a complex impedance surface. In a simple test case (both the source and microphone are above a complex impedance surface in a homogeneous atmosphere), our FFP solution is in excellent agreement with Donato's asymptotic solution [J. Acoust. Soc. Am. 60, 34–39 (1976)].

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