Prediction of the surface impedance of depth‐varying ground surfaces

Abstract

Many ground surfaces have acoustical characteristics (density, porosity, flow resistivity) which vary with depth. Prediction of the surface impedance can be done by solving the wave equation in the nonhomogeneous medium. An exponential variation with depth of the parameters is usually assumed [R. J. Donato, “Impedance models for grass covered grounds,” J. Acoust. Soc. Am. 61, 1449–1452 (1977); K. Attenborough, “Acoustical impedance models for outdoor ground surfaces,” J. Sound Vib. 99, 521–544 (1984)]. In this paper a new approach is presented. The surface impedance is calculated by discretizing the ground into a suitably large but finite number of homogeneous layers of known characteristics (multilayer approach). This method allows prediction for any depth variation of the ground parameters, and includes the simple hard‐backing effect. The analytical results in terms of the impedance gradient, obtained by this multilayer approach are confirmed by theoretical manipulation of the fundamental equations describing the acoustic field in nonhomogeneous media. The numerical results show the typical tendancies caused by the ground inhomogeneity.Many ground surfaces have acoustical characteristics (density, porosity, flow resistivity) which vary with depth. Prediction of the surface impedance can be done by solving the wave equation in the nonhomogeneous medium. An exponential variation with depth of the parameters is usually assumed [R. J. Donato, “Impedance models for grass covered grounds,” J. Acoust. Soc. Am. 61, 1449–1452 (1977); K. Attenborough, “Acoustical impedance models for outdoor ground surfaces,” J. Sound Vib. 99, 521–544 (1984)]. In this paper a new approach is presented. The surface impedance is calculated by discretizing the ground into a suitably large but finite number of homogeneous layers of known characteristics (multilayer approach). This method allows prediction for any depth variation of the ground parameters, and includes the simple hard‐backing effect. The analytical results in terms of the impedance gradient, obtained by this multilayer approach are confirmed by theoretical manipulation of the fundamental equations desc...