Statistical Considerations 



In order to develop a useful model o£ sea-floor roughness, one must 

 select, from a seemingly infinite variety of available methods, an 

 approach which is both suitable and tractable. In addition to consider- 

 ing the nature of the sea floor itself, one must also consider such 

 aspects as data resolution, computer storage capacity, statistical 

 validity, and compatibility with various applications. Often, the 

 choice of a particular method involves trade-offs between several of 

 these considerations. In the following sections, many of these funda- 

 mental considerations are addressed, and an initial approach to devel- 

 oping this particular model is presented. 



Statistical Measures of Roughness 



If one considers surface roughness to be the variability of heights 

 (or depths), the realm of statistics offers a multitude of measures to 

 describe the roughness of a surface. Perhaps the most fundamental sta- 

 tistic available to describe roughness would be one of the standard 

 measures of data dispersion, such as the root mean square, standard 

 deviation, or variance. These measures have the advantage of producing 

 a simple parameter to describe the variability of depths in a given sam- 

 ple. The major disadvantage of such simple measures is that they do not 

 provide information for roughness in teirms of wavelength, and the sta- 

 tistic derived depends upon the sample spacing and length of sampling as 

 well as the actual roughness of the surface. 



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