the Introduction. The presence of noise In the spatial data manifests 

 Itself In two ways in spatial frequency spectra. Inaccuracies of verti- 

 cal measurements in the spatial domain result in the presence of a hori- 

 zontal "white-noise level" in all amplitude or power spectra. This 

 problem will be treated in detail in the following section. Uncertainty 

 in the location of features in the spatial domain results in the scat- 

 tering of amplitude estimates about the true frequency spectrum. These 

 distinctions in the sources of error are somewhat artificial since the 

 vertical and horizontal uncertainties are Interdependent. 



Figure 4-3 reproduces a typical amplitude spectrum of depths. The 

 red-noise character of the distribution as well as the scattering of 

 amplitude values is apparent. The spectrum was derived from data col- 

 lected by the U.S. Naval Oceanographic Office using SASS (Sonar Array 

 Subsystem), and represents the highest resolution ba thyme trie informa- 

 tion currently available from a surface ship (see Glenn, 1970). Control 

 over relative horizontal location (navigational accuracy) of soundings 

 is especially good due to the use of large, stable surveying platforms 

 (in this case, USNS Dutton) and SINS (Ship's Inertlal Navigation 

 System). The degree of scattering of amplitude estimates would pre- 

 sumably be greater in less sophisticated systems. 



Several methods come to mind to smooth this somewhat noisy spec- 

 trum. A simple moving average taken over the amplitude estimates in the 

 frequency spectrum would smooth the data. However, information would be 

 lost from the high and low frequency extremes of the spectrum, while the 

 density of data in the Intermediate frequencies would not be reduced. 

 The use of spectral windows or lag windows could be used both to smooth 

 the spectrum and decrease the data density. The use of data windows in 



22 



