Geostatistics‐Based Inverse Distance Weighted Interpolation Method for Geological Boreholes

ABSTRACT The adaptive inverse distance weighted interpolation technique significantly enhances the calculation accuracy of geological boreholes by employing membership functions to adaptively compute interpolation weights. However, these functions typically utilize conventional mathematical forms, and identifying more suitable membership functions based on the sample distribution pattern remains a critical research area for improving computational accuracy. This study introduces a geostatistical method to examine the spatial distribution characteristics of geological information and establishes corresponding membership functions for position weight mapping calculations. A high‐precision geological borehole geostatistics‐based inverse distance weighted (GIDW) interpolation method is subsequently developed. The results showed that using the correlation distance as the interpolation search neighborhood radius to define the interpolation range for the points to be estimated can optimize interpolation accuracy. The minimum absolute interpolation error for 10 sample boreholes is recorded at 2.12%, with an average minimum error of 21.07%. In addition, the membership function, designed based on the actual drilling conditions in the statistical area, proved more accurate and suitable for calculations. The GIDW method demonstrates robust stability and minimizes the error introduced by abrupt feature points within the area. These results offer valuable insights for developing high‐precision interpolation methods suitable for geological data.