6. Anlsotropy of Surfaces 



The necessity of dlrectlooally treating anisotropic surfaces was 

 Introduced In Oiapter 4. Any statistic generated from a one-dlmenslonal 

 profile of a two-dimensional surface is only valid in all directions if 

 that surface is isotropic. This chapter examines the importance of 

 anlsotropy in detail. A simplified theoretical model of the effect of 

 anlsotropy on the frequency spectra of directionally sampled profiles is 

 formulated and tested. Such spectra are generated for two areas of the 

 sea floor where complete, two-dimensional ba thyme trie data are available 

 from multlbeam sonar. An identical study is performed on data from 

 side-scan sonar. These results are then compared to the theoretical 

 model. Next, the posslbili^ of estimating such two-dimensional func- 

 tions from randbmly oriented bathyraetric profile data is discussed. 



Theoretical Model 



Before examining the effect of anlsotropy on measured frequency 

 spectra derived from actual ba thyme trie profiles, it is instructive to 

 examine a very simple theoretical model of this effect. Several of the 

 concepts introduced in Chapter 4 will be utilized. There it was shown 

 that the effect of one-dlmensionally sampling a sinusoid which has been 

 extended to two dimensions (see Figure 4-6), is to stretch the true 

 wavelength as. 



X' - |cos~le| • X 



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