f (Icos el"^ . x) i:> Icos 9 1 • a • (s • C03 9)^ 



F (a, 6) - |co8 e| • a • (s • cos e)l> 



where F(s, 9) Is the Fourier transform of f(|cosd|~^ • x) expressed 

 in terms of 9 and s. The coefficient a can now be expressed as a func- 

 tion of 9 as 



a(9) - I cose I • a 



which can be generalized to 



a(e) - Ico8(e-e^)| . a 



where 9^ Is the azimuth perpendicular to the linear trend. Notice 

 that for 9 - 9^^ that Is a profile generated perpendicular to trend, 

 |cos(e-e^j)l - 1 and F(s,e) - a • s'', the original function. For 9-9^ - 

 *90°, |co8(9 - 9^) I . 0° and F(s,9) - 0, that Is, for profiles sampled 

 parallel to strike, the series Is a constant (normalized to zero) and 

 therefore contains no energy. The parameter b Is Independent of 9. 



Figure 6-1 illustrates the hypothetical "plane wave" surface that Is 

 used in this simple model. As a test of the above theory, radial tran- 

 sects of the surface were generated and the resulting profiles Input to 

 the standard Fourier transform routines used throughout this study. 

 Figure 6-2 depicts the sampling patterns used to generate the profiles. 



81 



