Scattering from volume variability

Abstract

Acoustic scattering cross sections for medium fluctuations are derived from the funadmental wave equation. Analysis of the effect of a finite scattering volume is made. Fluid velocity fluctuations are shown to produce no backscatter at scattering angle θ = 180° independent of the statistical form of the velocity field and valid for both atomspheric and oceanic cases. Scattering cross sections for the atmospheric and oceanic cases are compared. Temperature fluctuations for the atmospheric case result in a scattering cross section proportional to a cos 2 θ factor whereas for the oceanic case no such factor arises. Using a cylindrically symmetric form about the vertical direction for temperature fluctuations, explicit expressions for the angular dependence of the scattering cross sections are obtained. These results depend strongly on the parameter α, the ratio of the vertical length scale of the temperature variability to the horizontal length scale. For a typical echo sounder operating at 20 kHz, scattering strengths based on observed one dimensional spectra of temperature microstructure are of order −120 dB if isotropy is assumed (α = 1). For the layered case, where the horizontal scale of the variability is larger than the horizontal dimension of the scattering volume, the same values of variability yield, scattering strengths are of order −70 dB. These results can be applied at other frequencies provided the medium variability spectrum is known.