depead on position. The less restrictive deflaitlon of "weakly" (or 

 "second-order") stationary processes requires the mean to be constant 

 and the autocovar lance function to depend only on lag, not on position. 

 This second definition has somewhat greater application, however. It Is 

 still too restrictive for general use with a spatial process as varied 

 as submarine topography. 



Consider a broadly sloping surface, such as an abyssal fan. The 

 mean depth in this province would by definition vary with position, and 

 therefore would not satisfy the first requirement for statlonarity. Yet 

 if the process is homogeneous in higher spatial frequencies, one might 

 prefer to treat this province as a homogeneous area for modelling. In 

 practice the existing deterministic model could be used to describe the 

 low-frequency trend. The sample data could be high-pass filtered to 

 remove the non-stationary trend before generation of a spectrum. 



The presence of a low-frequency trend in samples of geophysical 

 data is quite typical. In almost any length sample of a natural proc- 

 ess, there are frequency components present with wavelengths greater 

 than the sample length. In most natural systems, there is a finite 

 limit on the rate of change of the process, causing the longer wave- 

 length components to be also of greater amplitude. This typical spec- 

 trum of natural processes was termed a "red-noise" spectrum by Shapiro 

 and Ward (1960), an analogy to the red color of low frequency visible 

 light. 



Although the red-noise spectrum is the usual form in natural sys- 

 tems. Figure 4-1 Illustrates schematically that the presence of non- 

 stationary components (in this case the statistical mean) can occur at 

 any frequency and is dependent upon the horizontal extent of the sample. 



17 



