Vertical spatial coherence of backscatter from bubbles

A basic formalism is developed to treat the vertical spatial coherence of backscatter from wind-generated microbubbles beneath the ocean surface. This formalism treats signals multiply scattered by the sea surface and the subsurface scatterers, as well as absorption in the bubble layer. Approximate solutions are obtained for the case of narrow beamwidth sources and are applied to study the influence of measurement system and environmental parameters on coherence. Using bubble densities derived from acoustic backscatter data, the coherence is found to depend strongly on source frequency and beam pattern. The primary environmental effect is due to the increase in both bubble density and penetration depth below the surface that occurs with increasing windspeed. At high wind speeds, the vertical coherence is sufficiently dependent on the scatterer depth distribution to provide a viable means of studying this phenomenon.