An improved non-stationary geostatistical method for three-dimensional interpolation of Benzo(a)pyrene at a contaminated site

Intense industrial activities and complex hydrogeological conditions at contaminated sites make accurate three-dimensional (3D) mapping challenging. The cause is the non-stationarity in the variance of soil pollutants in geographical space (G-space), making the stationary hypothesis required by the Kriging method unsatisfactory. To handle the variance non-stationarity, a Variance-Octree-Kriging (VOK) method was proposed. VOK is a spatial deformation method that constructs a stationary deformation space (D-space) by stretching and shrinking the G-spaces with low and high spatial correlation, respectively. VOK method consists of 3D stratification in G-space, space scaling and transformation, and ordinary Kriging (OK) in D-space. 3D stratification uses variance octree (VOT) to generate a set of anchor points in the G-space. The spatial scaling and transformation use the virtual force algorithm (VFA) and thin-plate spline to evenly distribute the anchor points and obtain the D-space, where the OK is implemented. The method was applied to predict the distribution of soil Benzo(a)pyrene (BaP) at a contaminated site in North China Plain. The results show that the interpolation accuracy of VOK was 9% higher than that of OK. The VOK method also changed the spatial structure from anisotropic to isotropic. The root mean squared error (RMSE) of fill, silt and clay layers decreased by 4.67%, 11.39%, and 20.46%, respectively. This method is applicable to the 3D interpolation of pollutants at contaminated sites, with the advantages of high interpolation accuracy and the ability to handle the non-stationarity in variance.