DAUBIN: STATISTICAL ANALYSIS OF SHIP GENERATED NOISE 



high noise period or "hump" in the middle of these data, which exists 

 for the order of 3 hours, is the effect of the passage of a ship. 



Figure 2 is a time series of data from the Caribbean. Note that 

 these data cover a period of 10 days, while the previous data covered 

 a few hours. There are four separate 1/3-octave bands, each displayed 

 as a time series of 1-minute energy averages of these data. Within 

 each time series there are several high-noise humps similar to that 

 in Figure 1. To the left of each series is the distribution of these 

 data from the time series. 



If we expand a section of a time series from Figure 2, we find 

 a series of these humps on the order of 2 to 4 hours in duration, 

 typically 2-1/2 hours, riding on a background consisting of two parts: 

 very rapid fluctuations and long-term trends. To consider the analysis 

 of such a time series, we must partition it into sets, called statis- 

 tical sets: Background statistics and foreground statistics, classi- 

 fied according to the integration used to obtain the individual data 

 samples and to the time duration of the set of samples. 



The background statistics are those of the type that Ira Dyer 

 has covered extensively for narrow bands, but in our 1/3-octave 

 representation, v;e see a summation of many such bands. These narrow- 

 band statistics should represent an integration that is long compared 

 with the period of the acoustic signal, yet short compared with the 

 period of the fade of the narrow-band signal, or, alternatively, short 

 compared with the decorrelation time of the narrow-band signal. The 

 duration of such a set should be short compared with a number that I 

 call the set stability time, which in a sense is the decorrelation 

 time of that main time series. For the time series of Figure 2, the 

 stability time is on the order of 2-1/2 hours, which is probably 

 indicative of the fact that the area was heavily trafficked. 



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