NN 5 [m?] 
PROFILE CG | PROFILE IN 
  
  
  
10% x=28 Nu X «23 
  
  
  
10% | - 10^ 
  
  
  
  
lo? ‘| L10* 3 
Kr} 107 ho“ FIT] Q* [o No" Fm 1] 
> | P 
Fig. 2. Fourier-spectra from profiles in Greenland and Norway. 
  
  
  
  
  
  
  
  
  
  
  
  
  
  
The relationship between ag, bg, f and L can be studied by means of the 
power spectrum S. In order to compensate for the influence of the varying 
length L of the profile, the spectrum can be written as function of the 
absolute frequency F = £/L 
S) ss -L:(x «p (2) 
L f f 
or as a function of the wavelength A = 
Fh 
| 
nj [e 
The representation of the terrain in the frequency domain greatly simplifies 
the separation of various surface forms. 
The following model proved to be valid for a large domain of F: 
Sir) = 50 pr" (3) 
where a and E are characteristic parameters for the terrain (Jacobi, 1980). 
The relationship is experimentally verified for our two terrain examples 
1) and the result is shown in Fig. 2. The average spectrum was com- 
for a large number of profiles in both areas. Relationship (3) proves 
for wavelengths l/F ranging from 50 to 10.000 meters. On a double 
i cale log S is linearly related to log F. The slope a of this 
S significantly larger for the Greenland terrain than for Norway 
(2.8 versus 2.3). In general, if the slope a of the spectrum is larger 
e is smooth due to the absence of high amplitudes 
uencies. On the other hand, a slope less than 2.0 indicates 
atively large variations of high frequencies. 
are independent 
landscape looks