tude spectrum (square root of power spectrum) will be used. When 

 properly normalized, the amplitude spectrum allows the amplitude of 

 component sinusoids to be expressed In simple length units, which can be 

 Interpreted more easily than units of length-squared. The method of 

 calculation will follow Davis (1974) with proper windowing, prewhlten- 

 Ing, etc. As will be discussed In later sections, the simple and 

 consistent functional form of spectra of topography allows relatively 

 easy description and manipulation of the model. Also, recent work by 

 Brown (1982, 1983) has shown the value of working In the frequency 

 domain In modelling scattering from rough surfaces. 



Validity of Measurement Over Large Areas 



In generating the variance, autocovarlance, or power spectrum from 

 a discrete sample, only one realization of an Infinite number of possi- 

 ble realizations within the population Is observed. The degree to which 

 this realization Is valid over the entire population depends upon the 

 degree of homogeneity of the process. The condition of spatial homoge- 

 neity Is generally known as "statlonarlty" and the population being 

 described referred to as a "stationary process". The term "process" Is 

 used In the statistical sense of the variation of data with either time 

 or space. In the case of sea-floor topography, the depths vary as a 

 function of space. 



Statlonarlty Is normally defined In two ways (see Chatfleld, 1980; 

 Popoulls, 1962). A spatial series Is said to be "strictly" (or "first- 

 order") stationary If the Joint distribution of the process does not 

 depend upon position. This Implies that the mean and variance do not 



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