For a two-dimensional function g(x,y), equation (24) is expanded to 



G(f x , f) - / 7 9t«.r) •"' ^^ + V y> *■ * • («) 



-00 -co 



With g(x,y) consisting of digitized values on a uniform grid covering a finite 

 area R, an estimate of G(f ,f ) may be obtained for the normalized frequency 

 range < f ,f <0.5 cycles/data interval, by use of the discrete two-dimensional 

 fast Fourier transform (FFT) of Cooley and Tukey (1965). This discrete approxima- 

 tion to G(f ,f ) must be interpreted to provide estimates of the three survey 

 parameters; track spacing, sampling rate, and track orientation. The specifica- 

 tion of track orientation requires a knowledge of what happens to trends or 



lineations in the (x,y) domain when they are mapped into the (f ,f ) plane. 



x y 



It has been determined by Fuller (1967) that a trend in the (x,y) plane maps 



into a trend in the (f ,f ) plane in an orthogonal direction. Fuller shows this 

 x y 



simply in the following way. 



Let g(x,o) be an arbitrary function of x defined for y = o. Using this 

 definition, we can construct a function of both x and y, i.e., g(x,y), by 

 shifting g(x,o) a distance Sy in the x direction, with S = -jr— as shown in 

 Figure 2. 



Yt 



.^y 



y\ 



y\ 



Ai 



\ 



/Sy, 



-Y 1 



FIGURE2. THE FUNCTION g(x,y), 

 16 



