3 /^ m3 
sim] PROFILE G | se 
Ic? x=28 LIA — IN x=23 
10° M 10° \ 
L10* L 10^ 
103 210? 
- 4l 
gt uo no im A gio 0 Li 
PROFILE IN 
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rj 
ig. 2. Fourier-spectra from profiles in Greenland and Norway. 
The relationship between ag, be, £ 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(F) = s (5) = 1 "rial + pi) (2) 
= ; - L 1 
or as a function of the wavelength A = Te T 
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: 
S(F) 2E -F (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- 
d for a large number of profiles in both areas. Relationship (3) proves 
valid for wavelengths l/F ranging from 50 to 10.000 meters. On a double 
logaritmic scale log S is linearly related to log F. The slope a of this 
i 
line is significantly larger for the Greenland terrain than for Norway 
(2.8 versus 2.3). In general, if the slope à CE the spectrum is larger 
than 2.5, the landscape is smooth due to the absence of high amplitudes 
at high frequencies. On the other hand, a slope less than 2.0 indicates 
a rough surface with relatively large variations of high frequencies. 
Relationship (3) implies that the surface characteristics are independent 
Of the scale of Observation. In particular, for à « 2 the landscape looks 
the same independent cf the scale at which it is observed, the amplitudes 
and wavelengths of the surface details are on the average directly propor- 
tional, 
Based on this model, the suitability of different LIRE POLE ENS methods 
an ed a C f interpol on S depe in the