A stochastic model for scattering from the near-surface oceanic bubble layer.

A stochastic scattering model has been developed that allows the backscatter from a subsurface bubble layer to be written as the product of a geometric factor times the horizontal wave-number (‘‘power’’) spectrum of the bubble layer. By dividing the measured backscatter versus frequency data by the geometric factor, one can ‘‘invert’’ the backscatter data and directly infer the horizontal wave-number spectrum of the bubble layer. Three different data sets give power-law wave-number spectra: P(K)≊A‖K‖−β, where β≊4 for two of the data sets and β≊3 for the third data set. The factor A is a constant that is different for each data set. When the inferred wave-number spectrum is used to predict backscatter versus angle, good agreement is obtained with the data at low frequencies and low grazing angles. The consistency in the inferred wave-number spectrum strongly suggests that a systematic power-law spectrum exists for the near-surface oceanic bubble layer. A time-dependent bubble plume model is discussed that shows how a power-law wave-number spectrum can arise in the bubble layer. [Work supported by ONR.]