The development of the fast field and parabolic equation solutions to the wave equation has made it possible to solve for the combined effects of refraction in a layered atmosphere and the interaction of sound with a complex impedance ground surface. In many respects the numerical methods have advanced beyond our understanding of the basic phenomena. In an earlier study [J. Acoust. Soc. Am. 89, 107-114 (1991)], the residue series solution for upward refraction was investigated and provided insight into the nature of the interaction of refraction and ground reflection. In this paper results are presented of a similar normal mode solution for downward refraction above a complex impedance ground surface. This model is used to investigate when the surface wave is excited for downward refraction conditions and to develop criteria for the maximum range of cylindrical decay as a function of phase and magnitude of the ground impedance and the magnitude of the sound velocity gradient.
An investigation has been carried out on the relationship between the residue series method for the prediction of sound propagation in an upward refracting atmosphere and the spherical wave analysis of sound propagation in a homogeneous atmosphere. It is shown that, in the limit of small sound velocity gradients, the Airy function solution developed by Pierce for sound propagation over the earth’s surface does approach the Sommerfeld integral for spherical wave reflection in a homogeneous atmosphere for a limited range of values of wave number. For complex impedance with phases greater than π/3, it is found that the surface wave pole identified for sound propagation in a homogeneous atmosphere is present in the upward refracting atmosphere. This pole arises from the residue series. Methods suggested in the literature for searching for the poles will fail for impedances with phase angles greater than π/3.
The development of the fast field and parabolic equation solutions to the wave equation has made it possible to solve for the combined effects of refraction in a layered atmosphere and the interaction of sound with a complex impedance ground surface. In many respects the numerical methods have advanced beyond an understanding of the basic phenomena. In an earlier study [J. Acoust. Soc. Am. 89, 107–114 (1991)], the residue series solution for upward refraction was investigated and provided insight into the nature of the interaction of refraction and ground reflection. In this paper, results of a similar normal mode solution are presented for downward refraction by a bilinear sound velocity profile above a complex impedance ground surface. This model is used to investigate when the surface wave is excited for downward refraction conditions and to develop criteria for the maximum range of cylindrical decay as a function of ground impedance phase and magnitude and the magnitude of the sound velocity gradient. [Work supported by NASA Langley Research Center.]
A surface wave like term arises in the analysis of spherical wave propagation above a complex impedance plane. Whether this wave is a true independently propagating surface wave, or a reaction to the incident air wave, has been the subject of discussion for a number of years. In this article, it is demonstrated that this term is a true surface wave that can exist independent of the body wave in air.
A matrix formalism developed by Thomson and Haskell to study the transmission of plane elastic waves through a system of parallel, homogeneous, isotropic layers is extended to the case of parallel poroelastic layers. In a poroelastic medium, there are two dilatation waves and one rotational wave contrasted with one rotational wave and only a single dilatation wave for ordinary elastic media. Formal matrices are obtained which allow the systematic computation of transmission of these waves through layered poroelastic media.
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