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Wave propagation in a slightly lossy random medium

1976; American Institute of Physics; Volume: 14; Issue: 2 Linguagem: Inglês

10.1103/physreva.14.796

0556-2791

Hisanao Ogura, Yasuo Yoshida,

Ultrasonics and Acoustic Wave Propagation

One-dimensional wave propagation in a slightly dissipative random medium is studied by applying a probabilistic theory developed in a previous work, which showed the presence of the cutoff mode in a random medium and its detailed characteristics, the cutoff mode being an exponentially increasing or decreasing standing wave without energy flow. The medium loss is assumed to be constant and small enough so that the mode is regarded as the cutoff mode perturbed by the dissipation. Including in the analysis an imaginary constant describing either attenuation or amplification of the medium indicates the need of correct choice of the branches in solving the dispersion equation, which was overlooked in the loss-free case. The local power-reflection coefficient of the cutoff mode, which in the loss-free case equals unity, meaning no energy flow, is shown to become a stationary process in the lossy medium. The average increment of the logarithmic amplitude is increased by the loss, but the fluctuations in the phase and amplitude are decreased because of the medium attenuation screening the effect of multiple scattering. The average phase shift is unchanged by the loss in the lowest-order approximation. Computer simulations for the lossy random medium are made to obtain those statistical characteristics, which are compared with the theory in good agreement.