provide spot checks of the high frequency structure. This approach will 

 be pursued in Chapter 7. 



Effect of Linear Features 



In generating a Fourier transform of topography within a stationary 

 province, a one-dltaensional statistic is generated from a two- 

 dimensional surface. Provided the surface is isotropic, that is that 

 there Is no significant directional dependence, statistics derived from 

 a one-dimensional sample would be equally valid for any orientation. 

 Even a cursory examination of a deep-sea bathymetrlc chart reveals 

 clearly that the sea floor, at least in the lower spatial frequencies 



presented In a contour chart, is quite anisotropic . There is extensive 



. I 

 evidence that bathymetrlc llneations also exist to some extent in the 



higher spatial frequency roughness of Interest to this study. To com- 

 pletely model sea-floor roughness, It is essential to account for 'any 

 major directional dependence of the topographic features. 



Figure 4-6 Illustrates the effect of sampling a simple two- 

 dimensional periodic function in differing directions. Notice that the 

 true wavelength (X) of the feature is sampled only when the sampling is 

 exactly perpendicular to strike (9 = 0"). Any oblique angle produces an 

 apparent wavelength (A') which is greater than X. At 9 = 90° (a sample 

 taken parallel to strike), the feature is not expressed at all (X' ■ »). 

 The apparent wavelength is related to the true wavelength by 



|co8-l9| . X 



32 



