Physical Oceanography, Vol. 17, No. 5, 2007
MODELING OF VOLUME REVERBERATION IN THE RAY APPROXIMATION
A. Kh. Degterev
We propose a numerical model for the evaluation of the three-dimensional scattering of sound in
the sea. The model is based on the construction of ray patterns both for the primary and second-
ary (scattered) radiation. The intensity of secondary radiation is expressed via the coefficient of
backward volume scattering interpreted as the fraction of backward-scattered acoustic energy per
unit length of the primary ray. It is shown that, in the first approximation, it suffices to consider
the secondary rays repeating the paths of the primary rays in the opposite direction. The attenua-
tion of the intensity of sound along the paths of the primary and secondary rays is taken into ac-
count. The results of numerical analysis of the reverberation signal as a function of time are pre-
sented for various conditions (different depths of immersion of the antenna and widths of the di-
rectional diagram and the presence of sound-scattering layers). The proposed approach can be
used for the purposes of modeling of the surface and bottom reverberation and for the solution of
the inverse problems of underwater acoustics.
At present, the analysis of the underwater situation with the help of hydroacoustic methods is one of the
main tools used for the investigation of deep-sea waters. Thus, the method of hydrolocation is used for this pur-
pose fairly extensively. In this case, we encounter the problem of selection of the valid reflected acoustic signal
against the background of reverberation interference caused by the scattering of the emitted acoustic pulses on
the inhomogeneities of the marine medium and irregularities of the water surface and the bottom. Hence, hydro-
acoustics studies the volume, surface, and bottom reverberation. Note that the surface reverberation is caused by
the waves responsible for a similar phenomenon also in the case of radiolocation over the sea surface. For the
evaluation of the acoustic pressure caused by the volume reverberation, it is customary to use simple formulas of
the following form :
where β is the attenuation coefficient of sound in water, t is time, and the constant includes the coefficient of
backward volume scattering m
. In this case, the phenomenon of indirect propagation of sound in water caused
by the dependence of its velocity on depth is completely neglected. On the other hand, the analogy between the
reverberation in the sea and the process of scattering of light is frequently stressed in the hydroacoustic literature
, and the propagation of electromagnetic and other waves in marine media is well described by the models
based on the imitation version of the Monte-Carlo method . In addition, from the mathematical point of view,
reverberation is usually regarded as a random process, which also serves as a basis for the application of the
Monte-Carlo method in this case. In the present work, we use a model of this sort for the numerical analysis of
the volume reverberation.
Marine Hydrophysical Institute, Ukrainian Academy of Sciences, Sevastopol.
Translated from Morskoi Gidrofizicheskii Zhurnal, No.
50–58, September–October, 2007. Original article submitted January 16,
2006; revision submitted April 17, 2006.
296 0928-5105/07/1705–0296 © 2007 Springer Science+Business Media, Inc.