In order to overcome some of the difficulties associated with these 

 existing techniques and to effectively utilize the computational efficiency 

 afforded by track-type survey data, an interpolation procedure was developed 

 by Bhattacharyya (1969) which makes use of cubic and bicubic splines. The 

 advantage of the cubic spline method, which is a mathematical analog of the 

 draftsman's plastic spline, lies in its ability to not only fit the observed data 

 values but to maintain continuity of the first and second derivatives. This 

 paper concerns the development and testing of a cubic spline technique as 

 applied to the computation of mean gravity anomalies. By utilizing simulated 

 survey data obtained from a model gravity field, it is shown that the spline 

 technique will produce accurate estimates of the mean gravity anomalies 

 provided the original survey is properly designed. The use of a two-dimensional 

 Fourier transform for a solution to the survey design problem is also presented. 



DEVELOPMENT OF THE CUBIC SPLINE ALGORITHM FOR GRIDDING 

 TRACK TYPE SURVEY DATA 



The algorithm presented here is based upon the technique developed 

 by Bhattacharyya (1969) with some modifications to the spline formulation in 

 order to use the boundary conditions and development presented by Pennington 

 (1965). 



Given data values y, y . . . y located at the points x, ,x . . . . x 

 I Z m I 2. m 



where x, < x, 1# we first assume that the second derivative of f(x) is a linear 

 function of x between any pair of adjacent data points. Thus, ifz.,z . ..z 

 are the values of the second derivative of f(x) at the given data points then 

 for the interval x, < x < x, . we have 



f (x) = S-j*- 1 " + z k (1) 



fhere d, = 



k Vl ~ Y 



