clear difference In spectral slope (b(9)), which would not be expected 

 in a simple surface dominated by one process. In fact, the main east- 

 west trend of the fracture zone is produced by tectonic processes which 

 are reflected in profiles collected in a north-south orientation. The 

 various mass-wasting processes acting down this slope produce a differ- 

 ent style of relief which is evident in profiles collected east-west. 

 The bathymetry shown in Figure 6-10 from the continental slope might 

 also be the results of two processes at work. This is reflected in the 

 possible variation of b(6) as shown in Figure 6-11. 



No attempt will be made to derive a general mathematical (geometri- 

 cal) form for the azimuthally-dependent spectra of these multiple com- 

 ponent surfaces. Such a treatment would be beyond the scope of this 

 study. However, an insight into the nature of these surfaces can be 

 gained by examining a few examples. All of the examples following are 

 generated using the same algorithms. First, two random signals of spec- 

 ified spectral characteristics (a and b) are generated using an inverse 

 FFT method. One signal becomes the initial row, and the other the ini- 

 tial column, of a 128 x 128 element matrix. Each element of the matrix 

 is then computed by summing the appropriate row and column element. 

 This method results in a surface which when sampled at 0° azimuth, pro- 

 duces one of the input signals displaced by a random constant. For the 

 90" azimuth, the other input signal is sampled, similarly displaced. To 

 study the spectra of the combined signals in other azimuths, the matri- 

 ces were sampled and analyzed in an identical fashion to the bathymetry 

 grids of Chapter 6. 



Four examples of two spectral component surfaces are shown in Fig- 

 ures E-1 through E-4. A variety of combinations were used. Figure E-1 



203 



