(doubling) Is constant, the absolute difference decreases exponentially, 

 depending upon the value of b. Since the ability to resolve amplitude 

 is limited, the ability to resolve anisotropy at small scales is also 

 limited and could lead to an erroneous conclusion concerning anisotropy 

 at high frequencies. These relationships do not apply in cases where b 

 varies regularly with azimuth, such as those discussed In Appendix E. 



Estimation of Ttoo-Dimensional Spectra from Randomly 

 Oriented Ship Track 



An alternative method for describing the topographic roughness of a 

 surface over all azimuths Is with the two-dimensional amplitude spec- 

 trum. The method involved is quite similar to that used in the one- 

 dimensional case, but prewhitening requires a circularly sjrmmetric high- 

 pass filter, and a two-dimensional fbst Fourier Transform algorithm is 

 used. Perhaps most important to the practical use of this method is the 

 requirement for a complete two-dimensional array of data (depths) as 

 input. 



As mentioned previously, complete areal bathymetrlc surveys are 

 available in very few areas of the world ocean. To be practical, such 

 surveys must use a oultibeam sonar array such as SASS or SEABEAH, and 

 tracks must be spaced so that adjacent swaths are juxtaposed. Of the 

 areas presented in the previous section, the Gorda Rise survey shown in 

 Figure 6-4 indicated the highest degree of anisotropy and was therefore 

 selected for two-dimensional FFT analysis. 



Figure 6-13 illustrates the results of generating a two-dimensional 

 amplitude spectrum from the gridded bathymetrlc data shown in Figure 



103 



