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)].
A residue series solution based on Fock's work in electromagnetic propagation has been used by several investigators to examine sound propagation into a shadow zone. In this paper it is demonstrated that this solution merges smoothly into the Sommerfeld solution for sound propagation above a flat surface as the sound velocity gradient goes to zero. A principle thrust of this investigation is the behavior of the sound propagation above a complex impedance plane as the gradient becomes finite. Initial work indicates that the surface wave pole may contribute to the residue series solution under certain conditions.
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