geneous province detection. The method used by Davis (1974) was 

 described in Figure 4-2. In this application, the design of optimum 

 survey spacing for marine gravity data collection, the statistic used 

 was the total RMS energy in a particular spatial frequency band. The 

 location of this band in frequency was dictated by later applications of 

 the marine gravity data. Construction of a digital model of oceano- 

 graphic sound speed requires delineating provinces in space and time 

 based on statistics describing the shape of oceanographic profiles (T.M. 

 Davis, personal communication, 1983). 



In order to delineate stationary provinces for the description of 

 sea-floor roughness using frequency spectra, it becomes necessary to 

 make a crude estimate of the amplitude spectrum discretely in the spa- 

 tial domain. Recall that in transforming to the frequency domain, sta- 

 tionarity has already been assumed, and therefore Fourier transform 

 techniques are not appropriate. The method used in this study takes 

 advantage of the relationship between band-limited energy in the spatial 

 and frequency domains (Parseval's Formula), and the inferred power law 

 form of amplitude spectra of topographic surfaces. Just as amplitude 

 spectra represent the amplitude of component sinusoids at discrete fre- 

 quencies, an equivalent estimate can be made in the spatial domain by 

 band-pass filtering the frequency of interest and evaluating its ampli- 

 tude. While the frequency domain estimate represents the least squares 

 average amplitude over the entire length of sample, the amplitude- can be 

 estimated discretely in the spatial domain using the Hilbert Transform. 

 This is very similar to the method developed by Davis (1974) for a sin- 

 gle frequency band. 



47 



