Evaluation of spline and weighted average interpolation algorithms

Abstract

Bivariate polynomial and weighted average interpolations were tested on two data sets. One data set consisted of irregularly spaced Bouguer gravity values. Maps derived from automated interpolation were compared to a manually created map to determine the best computer-generated diagram. For this data set, bivariate polynomial interpolation was inadequate, showing many spurious circular anomalies with extrema greatly exceeding the input values. The greatest distortion occurred near roughly colinear observations and steep field gradients. The computerized map from weighted average interpolation matched the manual map when the number of grid points was roughly nine times the number of input points. Groundwater recharge and discharge rates were used for the second example. The discharge zones are two narrow irrigation ditches, and measurements were along linear traverses. Again, polynomial interpolation produced unreasonably large interpolated values near high field gradients. The weighted average method required a higher ratio of grid points to input data (about 64 to 1) because of the long narrow shape of the discharge zones. The weighted average interpolation method was more reliable than the polynomial method because it was less sensitive to the nature of the data distribution and to the field gradients.