Influence of adaptive inverse distance weighting method under membership function mapping on the interpolation accuracy of geological boreholes

The adaptive inverse distance weighting (IDW) interpolation method shows improved computational advantages for building high-precision 3D geological models. However, in the case of varying geological borehole distribution characteristics, the statistical range of local adjacent points and the type of membership function are two important factors that affect the adaptive calculation of the weight power value in the IDW method. Therefore, this study attempts to build a general adaptive IDW model unaffected by the spatial distribution of geological boreholes sample data. This study uses a combination of nearest neighbor point statistics and membership function mapping to modify the IDW weights automatically. Moreover, it investigates the accuracy of IDW interpolation under two types of nearest neighbor point statistics ranges (fixed number and area) and three types of membership functions (triangle, trapezoidal, and Gaussian) interactions. The results showed that fixing the search window to determine the local neighbor statistics range and utilizing the triangle membership function to map adjustment weights exhibit strong distribution patterns. The minimum interpolation relative error for 10 sample boreholes reached 0.86%, whereas the average minimum interpolation relative error was 18.80%. Each borehole achieved optimal interpolation accuracy. The research findings significantly impact building adaptive spatial interpolation techniques and high-precision 3D geological models.