The effect of saturated transmission scintillation on ocean acoustic intensity measurements

Coherence theory is used to analyze the statistical properties of ocean-acoustic intensity fluctuations measured after saturated multipath propagation. Previous analyses in this area have been implicitly limited to certain special cases for which the time-bandwidth product of the field received from a given source is unity. In this paper, the statistical description is extended and generalized to be a function of measurement time and temporal coherence. As a result, the well known 5.6-dB transmission loss ~TL! standard deviation of Dyer is found to be a special case of a more general TL standard deviation that approximates 4.34 sqrt~1/m! dB when the time-bandwidth product m is large. Therefore, the TL standard deviation approaches zero for increasing m, as it must in the deterministic limit of an arbitrarily large sample size. A similar generalization is obtained for the TL mean, from which it is found that the sonar equation must be corrected for a m-dependent bias that vanishes in the deterministic limit of large m. Additionally, asymptotic analysis shows that intensity statistics in the saturated region converge to a log-normal distribution, where m.4 is typically sufficient for the log-normal approximation to be made.