Abstract
Analytic expressions in the time domain are derived for the mean forward field propagated through a waveguide containing random volume and surface inhomogeneities. The results are expressed in terms of the modal attenuation and dispersion coefficients in a waveguide [P. Ratilal and N. C. Makris, 112, 2403 (2002)]. Simulations in a shallow-water waveguide containing bubbles for a finite-time duration pulse show that the scattering leads to additional time delay and distortion of the signal waveform. Stationary phase approximations are also applied to represent the time-domain field in terms of the modal group velocities that are smaller than those in a waveguide without inhomogeneities. We show that the dispersion and attentuation effects cannot be explained by heuristic results based on an effective medium sound speed computed using bulk moduli and volume fractions since it does not account for scattering from inhomogeneities in the medium. The time-domain expressions for the forward propagated field obey causality and are consistent with Kramer–Kronig relations when used in their range of validity.
Published Version
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