BICUBIC SPLINE INTERPOLATION: A QUANTITATIVE TEST OF ACCURACY AND EFFICIENCY * BY K. L. RASMUSSEN and P. V. SHARMA** ABSTRACT RASMUSSEN, K. L., and SHARMA, P. V., 1979, Bicubic Spline Interpolation: A Quantita- tive Test of Accuracy and Efficiency, Geophysical Prospecting 27, 894-408. Two different methods for the construction of an approximation to bicubic splines for interpolating irregularly spaced two-dimensional data are described. These are referred to as the least squares line (LSL) and linear segment (LINSEG) construction procedures. A quantitative test is devised for investigating the absolute accuracy and efficiency of the two spline interpolation procedures. The test involves (i) laying of artificial flight lines on the analytically known field of a model, (ii) interpolation of field values along the flight lines and their subtraction from the original field values to compute the residuals. This test is applied on fields due to four models (three prism models and one dyke model) placed at different depths below the flight lines, and for each case the error estimates (the mean error, the maximum error and the standard deviation) are tabulated. An analysis of the error estimates shows in all cases the LSL interpolation to be more accurate than the LINSEG, although the latter is about 50% faster in computer time. The relative accuracy and efficiency of the LSL interpolation is also tested against a recent method based on harmonization procedure, which shows the latter to be more precise, though much slower in speed. I. INTRODUCTION Since about 1960, spline functions have been used for interpolation of data specified at points spaced irregularly along a line (see e.g. Ahlberg, Nilson, and Walsh 1967). The spline interpolation has been extended successfully to two-dimensional data specified at irregular grids (Bhattacharyya 1969, Hessing, Lee, Pierce, and Powers 1972, Dooley rg76), and several practical examples have been given by the different authors to demonstrate the efficiency of the various approximated spline functions as smooth interpolants for producing contoured maps. These examples of contoured maps of sample data, although qualitatively better than those drawn manually, leave a basic question still unanswered. That is, how precise is the total interpolation in terms of absolute errors (intrinsic spline interpolation errors plus the errors * Received March 1976. ** Institute of Geophysics, University of Copenhagen, Haraldsgade 6, zzoo Copenhagen N, Denmark.