In order to generate a stochastic model of sea-floor topography, we must 

 ensure that the process Is stationary within some limit and over some 

 defined area, with respect to the statistical parameters being calcu- 

 lated. Ideally, this is accomplished by identifying homogeneous prov- 

 inces based upon these criteria. Davis (1974) developed such a "prov- 

 ince picker" for use in geophysical survey design, and his method is 

 illustrated in Figure 4-2. 



By actively defining provinces which are weakly stationary in the 

 frequency band of interest, one improves the validity of the statistical 

 measures generated within each province. In addition, by delineating 

 province boundaries, one can also alleviate the problems associated with 

 the least-squares or averaging nature of Fourier transforms. In gener- 

 ating a power spectrum from a data set, the operator must select the 

 length and location of the sample series to be transformed. The result- 

 ing spectrum will reflect the average frequency composition over the 

 sample. If the sample spanned two distinct statistical processes, the 

 result would provide the average composition of the two provinces, and 

 would accurately represent neither. By confining one's samples within 

 the boundaries of a homogeneous province, one insures a valid and repre- 

 sentative statistic. These concepts will be discussed in detail in 

 Chapter 5. 



Ftinctional Representation of Spectra 



One property which makes the Fourier transform, both continuous and 

 discrete, such a powerful analytical tool is its ability to express a 

 spatial process in the spatial frequency domain both exactly and com- 



19 



