2. The method is quite sensitive to round-off errors and, except in 

 cases where orthogonalization techniques are used, can become unstable for 

 high degree surfaces. Recent work by Wampler (1969) discusses the problems 

 associated with inverting ill-conditioned matrices using standard procedures. 



3. The technique requires a rather large amount of computer time, 

 although this problem can be minimized through the utilization of recursive 

 linear-regression techniques (Fagin, 1964) when additional data points are 

 added to the set. 



The second general approach which is used to grid survey data is based 

 on interpolation techniques which fit each data value exactly. In this case, 

 it is assumed that any large errors or noise in the data have been removed prior 

 to application of the gridding process, and that the survey coverage is sufficient 

 to minimize aliasing in the data. Historically, this approach has consisted of 

 connecting each pair of data points in such a way as to partition the survey 

 area into non-overlapping triangular sections (Rankin, 1963) and fitting a plane 

 to each of these sections, or by partitioning the survey area into a preliminary 

 rectangular grid and interpolating within each of these areas by an exact-fitting 

 two-dimensional polynomial (Crain and Bhattacharyya, 1967). The principal 

 disadvantage of these methods is that no conditions are imposed on the derivative 

 of the interpolating functions. Except in very smooth areas, this results in the 

 generation of non-realistic gradients. The problem is somewhat reduced by the 

 use of a two-dimensional weighting function of the type developed by Shepard 

 (1968). Shepard's technique generates the data value at a desired grid location 

 by applying a weighting function based upon the distance and direction to the 

 neighboring data points. In addition, estimates of the derivatives at each data 

 point are included. This removes the requirement that the partial derivatives be 

 zero at each data point thus allowing the interpolating function to have extrema 

 anywhere and not just at the original data points. 



