Improved inverse distance weighting method application considering spatial autocorrelation in 3D geological modeling

Spatial interpolation is a main research method in 3D geological modeling, which has important impacts on 3D geological structure model accuracy. The inverse distance weighting (IDW) method is one of the most commonly used deterministic models, and its calculation accuracy is affected by two parameters: search radius and inverse-distance weight power value. Nevertheless, these two parameters are usually set by humans without scientific basis. To this end, we introduced the concept of “correlation distance” to analyze the correlations between geological borehole elevation values, and calculate the correlation distances for each stratum elevation. The correlation coefficient was defined as the ratio of correlation distance to the sampling interval, which determined the estimation point interpolation neighborhood. We analyzed the distance-decay relationship in the interpolation neighborhood to correct the weight power value. Sampling points were selected to validate the calculations. We concluded that each estimation point should be given a different weight power value according to the distribution of sampling points in the interpolated neighborhood. When the spatial variability was large, the improved IDW method performed better than the general IDW and ordinary kriging methods.