pletely. This complete correspondence between domains allows detailed 

 analyses to be made on the spectra with the assurance that there is an 

 exact analog in the spatial domain. In order to maintain this corres- 

 pondence, it is necessary to retain the complete transform, (both ampli- 

 tude and phase components) in the spatial frequency domain. In the case 

 of discrete data and transforms, it would be necessary to retain all of 

 the degrees of freedom present in the original data set. 



In the creation of a probabilistic model, it makes little sense to 

 retain as much Information in the model as was present in the original 

 data. Presumably, one would prefer to use the original data as a deter- 

 ministic model. Also, the purpose of the model is to describe the gen- 

 eral high frequency structure of the sea floor, rather than to analyze 

 in detail the individual frequency components. Finally, the restric- 

 tions of computer storage space require a limited number of parameters 

 in the model. 



All of the above considerations argue strongly for a severe paring 

 of information in the frequency domain model. The phase spectrum, which 

 requires fully half of the information in the spatial frequency domain, 

 defines the origin in space of all component sinusoids of the amplitude 

 spectrum and adds very little insight into the general structure of the 

 sea-floor. An analysis of bathymetric phase spectra presented in Chap- 

 ter 5 will show that the phase is in fact randomly distributed. For the 

 purpose of this model, no phase spectra will be retained, as none of the 

 previously stated applications require phase information. 



All measured data contain a component of random noise. Remotely 

 sensed data are especially susceptible to measurement noise, the partic- 

 ular noise problems in measuring oceanic depths having been mentioned in 



