### ASA 127th Meeting M.I.T. 1994 June 6-10

## 5pUW19. Theoretical study of echo energy scattered by a random
distribution of air-filled fluid spherical shells: Application to fish stock
assessment by the echo integration method.

**Zhigang Sun
**

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Gerard Gimenez
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**
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*Lab. ``Traitement du Signal et Ultrasons,'' URA CNRS 1216, INSA, 69621
Villeurbanne Cedex, France
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This work is intended to give a preliminary examination of the influence
that the swimbladder may have on the linearity principle of the echo
integration method. In doing this, the fish school is modeled as a random
distribution of air-filled fluid spherical shells immersed in water. The wall
of the shell represents the fish body whereas the inside of the shell
represents the swimbladder. The mean echo energy scattered by such a
distribution has been calculated as a function of the ratio b/a of inner to
outer radius of the shell, with the interference of direct echoes, the
shadowing effect, and the second-order scattering being taken into account. The
numerical simulations show that at a given fractional volume number of targets,
the mean echo energy scattered by the distribution is a bit larger than that
predicted by the linearity assumption when b/a is less than a certain value
(kappa), and it may be much smaller than the predicted value when b/a is
greater than (kappa). Consequently, the swimbladder may be the major cause of
the energy attenuation, due to the shadowing effect, and its influence on the
linearity principle depends on its relative size.