where A' » apparent wavelength 



\ > true wavelength 



6 « angle of sampling (0° ■• perpendicular 

 to linear trend) 



This relationship can then be combined with the similarity theorem 

 of Fourier Transforms to yield the transform pair 



f (|cos 9 1 • x) r> lcose|"l . p (s/co89) 



Recall that these relationships were formulated for a single component 

 wave form extended to two dimensions. Actual sea-floor topography has a 

 spectrum which is continuous and conforms to a power law functional form 



. «b 



To extend the model to the continuous case, one can envision gener- 

 ating a topographic profile (or other signal with continuous power law 

 form, such as a random walk model), and extending all points on the pro- 

 file to the second dimension. This surface is then sampled in various 

 directions and the spectrum of each profile evaluated for a and b above. 



Combining the above relationships yields 



f(|co8 e| • x) D |cos e|"l . a • (s/cos 9)^ 



or equivalently 



80 



