DAUBIN: STATISTICAL ANALYSIS OF SHIP GENERATED NOISE 



The foreground statistics require an integration time that is 

 long compared with that used for background statistics and short 

 compared with the set stability time. The total time series duration 

 should be long compared with the integration time. 



Figure 3 is taken from Dyer (1970) and shows that the background 

 statistics (calculated in dBs) associated with a single narrow-band 

 source should in theory have a standard deviation of 5.5 dB. When 

 "£" of these sources are at the same strength and are subject to the 

 same average transmission loss, the fluctuation level is predicted 

 to decrease (for 10 sources, it is predicted at about a 1.4 dB 

 standard deviation) . In a later paper Dyer extends this to include 

 noise from sources of different strengths and different frequencies 

 but the sources remain a stable set in the sense that the trans- 

 mission from source to receiver is not intended to change. 



Figure 4 shows the power spectrum derived from the time series 

 of Figure 2. The abscissa is in cycles per day. Note the energy 

 peak at about 0.6 of a cycle per day, which happens to be the inertial 

 period where these data were taken. The task of understanding what 

 is going on involves the prediction of many things, such as the means, 

 the variances, the distributions, and the power spectra. We also 

 want to know the mechanisms that are producing such a distribution 

 of energy. 



Let us focus on the section of the power spectra above one cycle 

 per day. As mentioned before, the decorrelation time of the time 

 series is on the order of 2-1/2 hours or 0.1 days. Its reciprocal 

 is a measure of the maximum frequency for which significant energy 

 appears within this power spectrum. 



Now, the area under the power spectra curves is the variance, 

 as plotted in Figure 5. The time series of Figure 2 corresponds to 



847 



