a(e) - u + V • co8(2 • (e-eg)) 



allows the background, or isotropic, roughness, as well as the degree of 

 anisotropy and its trend to be quantified, and therefore compared in 

 different areas. 



If one assumes this simple model of anisotropy to be true, at least 

 in some cases, an interesting insight into the effect of scale on 

 anisotropy can be seen in the mathematics. The assumption of a constant 

 value of b(6) at all azimuths can be envisioned as a family of lines in 

 log-log space of constant slope whose levels vary with azimuth. The 

 orthogonal azimuths which represent the extremes of anisotropy, would 

 maintain a constant spacing in amplitude at all frequencies in log-log 

 space . That is, if at a given frequency the amplitude in one direction 

 were twice that of the normal azimuth, that relationship would remain 

 constant at all frequencies. 



In examining bathymetry and other geological data, it often appears 

 that anisotropy decreases at shorter wavelengths. Bell (1975) reached 

 that conclusion in studying the aspect ratio of shapes of seamounts of 

 different sizes. Much of the validity of this statement depends upon 

 how anisotropy is defined. As stated above, if a relative doubling of 

 amplitude in the orthogonal direction occurs at one scale, this same 

 doubling should occur at all scales. However, if one considers the 

 absolute difference in amplitudes in orthogonal directions, at long 

 wavelengths the difference between perhaps one and two meters of ampli- 

 tude represents one meter of difference, while at very short wavelengths 

 this same relationship might appear as the difference between one and 

 two centimeters. Although the proportional relationship of amplitude 



102 



