seated as a simple function, this definite Integral could be evaluated 

 analytically to derive the RMS variability for a discrete waveband. 



Having decided to use functional representations as the basis of a 

 stochastic model of sea-floor roughness, the selection of a suitable 

 functional form for the spectra becomes crucial. In order to minimize 

 the size of the model, the simplest functional form which is justified 

 by the data should be the best. An examination of Figure 4-3 as well as 

 many other spectra presented later, would suggest the use of a simple 

 straight line fit to the data. In light of the scatter in this already 

 smoothed data, no higher order functional form is Justified. 



The normal form for fitting a straight line to data is the estima- 

 tion of the coefficients a and b in the equation 



y - b X + a 



Notice in Figure 4-3, however that the data are plotted versus logarith- 

 mic scales. The regression equation would therefore be written, 



log A ■ b log s + log a 



where A » amplitude and s =» frequency. This equation can be rewritten 

 in terms of A as, 



A - a . 8^ 



This inferred relationship between amplitude and frequency is often 

 termed a "power law" or "power function" relationship. Appropriate 



25 



