represents a simple scaling factor for roughness. For a given frequency 

 (s) and exponent (b), the amplitude (A) Is proportioned to a. IXie to 

 the method of calculation of this expression, the actual value of a cor- 

 responds to the amplitude of the component sinusoid with a wavelength of 

 one kilometer and Is usually expressed In meters or kilometers. This 

 particular normalization was selected because the one kilometer wave- 

 length falls within the sampling of most surface sonar data. For exam- 

 ple, the required 0.5 km sample rate would be obtained with a 1 minute 

 sonar ping rate on a ship traveling 30 km/hr (or 16 knots). The value 

 of a does not necessarily correspond to any particular features In the 

 signal, but only to the amplitude of the component sinusoid. 



The Interpretation of the exponential parameter (b) Is somewhat 

 less Intuitive. For the case of b «• 0, the amplitude of all component 

 frequencies Is constant and equal to a. This Is the well-known "white 

 noise" associated with random series such as Instrument noise. Such a 

 value for b would customarily be interpreted as instrument noise in any 

 spectra from sea-floor topography. Values of b > imply that ampli- 

 tudes increase at shorter wavelengths, a condition that has never been 

 observed in bathymetric data. What is consistently observed is the case 

 where b < 0, the previously mentioned "red-noise" spectrum, in which 

 amplitudes of component sinusoids increase with decreasing spatial fre- 

 quency (longer wavelength). This indicates simply that broader features 

 have greater height. 



An interesting special case occurs when b ■ -1. The expression 



52 



