ponent frequency. Oae must, In addition, define the position of each 

 component sinusoid relative to some geographic origin. The location of 

 each sinusoid In space Is expressed by Its phase relative to this geo- 

 graphic origin, and the composite of all component frequencies with 

 their corresponding phases represents the phase spectrum. Since sines 

 and cosines are trigonometric functions, phase Is normally expressed as 

 an angle between - 180° and 180°. 



Results from this study show that within statistically homogeneous 

 provinces, the amplitude spectrtra can be consistently modelled with a 

 single or several power law functions. Although there Is some varia- 

 bility of the measured amplitude around the simplified model, the calcu- 

 lated parameters remain consistent over often large geographic areas. 

 However, any two sample profiles are not necessarily identical or even 

 statistically correlated. The differences In the spatial domain man- 

 ifestations of identical amplitude spectra can only be due to differ- 

 ences In the phase spectra. 



Figure 5-6 Illustrates a typical phase spectrum and the statistical 

 distribution of its phase angles, derived from a single bathymetric pro- 

 file. Several profiles were examined, which represented a variety of 

 geographic locations and geological environments. The variability of 

 phase angle with increasing frequency appeared to be random. A simple 

 one-sample runs test was performed on several phase spectra, and all 

 proved to be randomly ordered to within 95Z confidence limits. The runs 

 test is a non-parametric method (Siegle, 1956), meaning that no proba- 

 bility distribution of the population is assumed. Examination of the 

 distribution of phase angles indicates a uniform statistical distribu- 

 tion; that is, a random distribution in which all phase angles are 



60 



