Abstract
A preliminary application is made of the general theory and method proposed in the preceding companion paper (Part I [1]) to the calculation of statistical properties of the reverberation and scattered field caused by randomly moving discrete scatterers. Two kinds of random motion of scatterers are considered: (i) the displacements of the scatterers are stochastic vector processes with stationary increments, but they are mutually independent; (ii) the displacements of the scatterers are stationary stochastic vector processes, but they can be statistically dependent. Some general expressions for the space-time correlation function the spectral density and of the reverberation and scattered field are obtained. In the derivation of these expressions, the radiated signal, the directivity of the radiation, the non-homogeneity of the surrounding medium and the character and spatial distribution of the scatterers are not restricted to being certain particular forms. Some more specific and simpler expressions are obtained from these general expressions in certain special cases. Some formulas established by other authors, such as Ol'shevskii [2], Zubakov [3], Faure [4], Gorelik [5], Sukharevskii [6, 7] and Battan [8], can be obtained from these expressions under special conditions. As an example, the statistical properties of back scattering from bubbles beneath the sea surface, the random motions of which are caused by waves, are studied. The relation between the space-time correlation function of the scattered field and the space-time correlation function of the sea surface is obtained. It is shown that the statistical dependence between the motions of the bubbles is an important factor, which cannot be neglected. When the radiated signal is monochromatic, the time correlation function of the envelope of the scattered field is not the “exponential-cosinusoidal” form as obtained by Ol'shevskii, but a form which can give better agreement with experimental results.
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