Smart averaging interpolation algorithm comparative test

In many practical cases, it is necessary to characterize the explored area with a regular set of geodata. Regular matrix data (e.g., ordinary maps) are calculated via existing data interpolation and extrapolation. For low frequency (oversampled) data acquired within a dense profile net (e.g., seismic three‐dimensional structural or gravity mapping), this procedure is mathematically more or less stable and, to a certain extent, unique since we might neglect discrepancies resulting from different interpolations. The situation is quite different for high‐resolution and high‐frequency contaminated data (e.g., raw seismic attributes or geochemistry measurements) represented by sparse profiling. Considering the variety of exploration cases, the investigation of different interpolation algorithm efficiency seems very important. Since it is impossible to compare all algorithms by means of formal mathematics, we have designed a test program. A representative set of seismic attribute maps has been artificially destroyed by introducing blank values (from 20% up to 95%) and then restored by different interpolation algorithms— bicubic, bilinear, nearest neighbor, and “smart averaging.” Smart averaging interpolation is done in a “live” window. The position, form, and size of the window are determined by some mathematical criterion on a trial‐and‐error basis. Discrepancies between restored and initial (true) data have been assessed and analysed. It is shown that the total (absolute) efficiency and comparative (relative) efficiency of the algorithms depend mostly upon the initial interpolant data characteristics. Identifying the best interpolation algorithm for all interpretive cases seems impossible. Some aspects of data processing are discussed in connection with interpolation accuracy.