Fig 1.
Example of soil slice approx. 250μm in thickness, which was scanned by SEM-EDX for chemical mapping.
Fig 2.
Illustration of the sampling grids used in kriging.
Schematic representation of the interpolation layers and the corresponding sampling grids for the selection of the interpolation points. The actual distance between the top and bottom layers, on which the concentration of chemical elements is measured, depends on the cutting and polishing processes, and may be variable.
Fig 3.
Illustration of two consecutive slices and the corresponding layers used in cross-validation.
Schematic representation of two consecutive slices, for which chemical measurements on surface are available. From the two slices, three consecutive layers are used for model development and validation, upper and lower layers (thick black line) are used for model training and interpolation, and middle layer (blue shadowed line) is used for validation of model predictive performance.
Fig 4.
Illustration of SEM-EDX chemical mapping and the corresponding layer within the 3D X-ray CT data.
The intensity of the colour indicates the concentration of the elements, whereas the grayscale intensity of the X-ray CT image reflects the density of the material.
Fig 5.
Variogram model fit for the residuals resulting from the regression tree model.
Fig 6.
Method of selecting the optimum sampling grid based on the analysis of kriging variance.
Representative profile of the kriging variance for a 9 × 9 sampling grid with grid spacing ranging from 1 to 20, when the target point is half way between the two interpolation layers.
Fig 7.
3D prediction of the chemical elements.
Predicted 3D chemical structure by regression tree and regression tree kriging for a 1283 voxels domain and the corresponding 3D X-ray CT measurements.
Fig 8.
Evaluation of predictive performance.
Prediction of the chemical composition of soil on a 2D layer by regression tree and regression tree kriging models, compared to actual measurements.
Table 1.
Summary statistics of chemical values predicted by regression tree and regression tree kriging compared against observed values.
Numbers show Mean and Standard Deviation mean ± SE over n = 8 replicates, on which the models were tested.
Table 2.
Comparison of predictive performance by regression tree and regression tree kriging.
Numbers show RMSE and R2 mean ± SE over n = 8 replicates, on which the models were tested.