As previously stated, the parameter a represents the intercept (In 

 meters) of the functloa with frequency log s » 0, or wavelength A » 1 

 km. The error associated with a (e^) appears as a constant vertical 

 shift of the regression line In log-log space. It Is In fact a multi- 

 plicative factor In linear space and has the effect of multiplying or 

 dividing the A value by [antllog e 1 at any frequency. Since e^ is 

 Independent of frequency, It Is stable over large extrapolations. Since 

 all spectra of topography are red noise, the absolute level of estima- 

 tion error effectively decreases at higher frequencies (lower ampli- 

 tudes). 



The spectral slope parameter b is not Independent of frequency. In 

 log-log space, the dlmenslonless b appears as the slop<^ of the linear 

 regression line. Error associated with b (e^) at s >°- Q, causes &n 

 Increasing prediction error at higher or lower frequencies. The rela- 

 tionship la linear space is also multiplicative and depends on frequency 

 as multiplying or dividing the A value by [antllog ( | log s | • e^) ] . The 

 total error of estimate requires linearly combining the t^c sources e^ 

 and e^, which translates into multiplying or dividing the value A(3) by 

 [antllog (e^ -•■ |log s| * ^i))!* An example of these calculations is 

 Included in the following section. 



Comparison of Surface Ship Sonar Results to Deep-Towed 

 Sonar Results and Results from Bottom Photography 



To quantify accurately the ability of the spectral laodel derlvad 

 from surface ship sonar systems to predict amplitudes at high spatial 

 frequencies requires a large data base of small-scale bathymetry pro- 



112 



