Appendix A.l 



Having concluded that the frequency spectrum of submarine topography 

 conforms to a power law functional foinn, it becomes critical in con- 

 structing a model based on this statistic to ensure a valid regression 

 fit to the data. Such a regression analysis is necessary both in fit- 

 ting the amplitude spectrum itself (amplitude as a function of fre- 

 quency) and in fitting the energy envelopes for various spatial fre- 

 quency bands for use in spatial-domain provincing. We represent our 

 power law function as follows: 



y - f(a,x,b) - ax^ where y ■ dependent variable (amplitude) 



X " independent variable (frequency) 

 a,b > regression coefficients 



Ve can use the property of power law functions that they plot linearly 

 on log-log axes and recast the function in log-log space as follows: 



log(y) - log(a) + b log(x) 



which can be easily solved by a simple linear regression. Upon deriving 

 the coefficients b and log (a), these terms can be reconverted to 

 linear-linear space as, 



b - b 



a > antilog (log(a)) 



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