Backscatter Statistics.

The scattering cross section is proportional to the second moment of received pressure and determines the average bottom reverberation level for a given seafloor. In sonar target detection, it is useful to understand the fluctuations about this average, as strong fluctuations may be interpreted as targets. These fluctuations are usually described in terms of the "probability of false alarm," which is the probability that the received pressure envelope will exceed some preset threshold. It is often assumed that complex scattered pressure is a Gaussian random process, and, in this case, the envelope obeys Rayleigh statistics. While Rayleigh statistics provide a good approximation in many cases, departures from Rayleigh statistics for large envelope values are of interest in setting detection thresholds. Figure 16.1 illustrates the threshold problem using simulated reverberation time series. The upper panel of the figure is a time series for an envelope obeying Rayleigh statistics and the lower panel is an envelope times series obeying Weibull statistics (Sect. 16.3.2). Both series are normalized to have unit mean squares. In these examples, a detection threshold set at the value $$ \sqrt {10} $$ (10 dB above the RMS envelope) produces zero threshold crossings in the displayed time interval for the Rayleigh series while the same threshold produces numerous crossings for the Weibull series. If the sonar designer wishes to set the threshold to achieve a specified rate of false alarms, it is useful to know the statistics obeyed by the reverberation envelope. [ABSTRACT FROM AUTHOR]