equally likely to occur for aay frequency component. A Kolmogorov- 

 Smimov goodness-of-fit test was performed on several phase spectra, and 

 none were significantly (95%) different from the uniform distribution 

 (Siegle, 1956). 



The spatial consistency of the amplitude spectrum and the uniformly 

 distributed random nature of the phase spectrum of topography indicate 

 that the differences in bathymetric surfaces within statistically homo- 

 geneous provinces simply represent multiple realizations of the same 

 statistical process. The observed changes in the micro topography 

 recorded in Figures 5-3 and 5-4 can be modelled by combining two differ- 

 ent random phase spectra of the same distribution with the known ampli- 

 tude spectrum. With the functional representation of the amplitude 

 spectrum for an area, a "typical" profile or surface can be produced by 

 generating a uniformly distributed set of random numbers to represent 

 the phase spectrum, and performing an inverse Fourier transformation to 

 the space domain. 



The concept of representing the sea floor as a deterministic surface 

 combined with stochastic variability was introduced in an earlier sec- 

 tion. In that discussion, the deterministic components appeared as a 

 smoothed, long wavelength surface which was combined with a higher fre- 

 quency, stochastic roughness component. By describing the higher fre- 

 quency components with a spectral representation, we can now visualize 

 the amplitude spectrum as being determined (by modelling) and the phase 

 spectrum as being a purely random (stochastic) process. 



62 



