vldually describes the roughness in all directions. The need for a 

 dlrectlonally dependent function is obvious. The two-dimensional 

 Fourier transform might appear to be appropriate, since it describes the 

 two-dimensional roughness of a surface. However, its calculation 

 requires a complete two-dimensional grid of data values which is gener- 

 ally unavailable. The double Fourier transform, well described in Davis 

 (1973), is calculated from two orthogonal one-dimensional spectra. This 

 method, especially without the retention of the phase spectra, can not 

 unambiguously Identify the orientation of trend. Both the two-dimen- 

 sional and double Fourier transforms require a large two-dimensional 

 matrix to be retained in the model. 



McDonald and Katz (1969) describe a method for estimating autocor- 

 relation functions as a function of azimuth 6. A similar approach will 

 be attempted here for use with amplitude spectra. By studying the azl- 

 muthally dependent distribution of the coefficients derived from the 

 power law regression, a and b, it Is anticipated that some functional 

 form or forms will be revealed to allow modelling of the entire process 

 as a function of both spatial frequency (s) and true azimuth (6). If 

 a=-f3(e) and b-f^(e) then 



F(e,3) - fa(e) . s 



fbO) 



With this functional form, Input into the model of simple compass 

 direction for a given location would return the unique spatial- 

 frequency-dependent function coefficients for the amplitude spectrum in 

 that particular direction. Evaluation of these 6 dependent functions 

 should provide a simple measure of the degree and direction of bottom 



anisotropy. 



40 



