(coastEUCted la cartesian coordinates). The proposed model requires 

 only four parameters (b, u, v and 6^) to describe the surface rough- 

 ness. The two-dimensional spectrum In this case requires a 128 x 128 

 array, or 16,384 parameters. In addition, the four parameters used In 

 the model have physical meaning attached to them which may prove useful 

 In comparisons of different areas. Also, the computer algorithms used 

 to generate the model require far fewer calculations than the direct 

 transform method. 



Perhaps the most relevant advantage In the azlmuthal model con- 

 struction Is that the two dimensional nature of the surface can be esti- 

 mated from randomly oriented ship tracks. Each profile yields a one- 

 dlmenslonal estimate of the amplitude spectrum at the azimuth of the 

 ship's heading. Such estimates can be thought of as cross sections 

 through the surface contoured in Figure 6-13. For example, the profile 

 and amplitude spectrum shown In Figure 6-7 represent a cross section of 

 the two-dimensional surface collected at azimuth NllS^E. Given a suf- 

 ficient number of such randomly oriented tracks over an adequate range 

 of headings, the model can be constructed as described In this chapter. 

 Until a great many more multlbeam surveys have been collected, this 

 method of estimating the anisotropy of bottom roughness will remain the 

 only available method over most of the world oceans. 



106 



