Effect of autocorrelation function model on spatial prediction of geological interfaces

This study evaluated the performances of various autocorrelation function (ACF) models in predicting the geological interface using a well-known conditional random field method. Prediction accuracies and uncertainties were compared between a flexible Matérn model and two classical ACF models: the Gaussian model and the single exponential model. The rockhead data of Bukit Timah granite from boreholes at two sites in Singapore as well as simulated data were used for the comparisons. The results showed that the classical models produce a reasonable prediction uncertainty only when its smoothness coefficient is consistent with that of the geological data. Otherwise, the classical models may produce prediction errors much larger than that of the Matérn model. On the other hand, the prediction accuracy of the Matérn model is affected by the spacing of the boreholes. When the borehole spacing is relatively small (< 0.4 scale of fluctuation), the Matérn model can reasonably quantify the prediction uncertainty. However, when the borehole spacing is large, the prediction by the Matérn model becomes less accurate as compared with the prediction using the classical models with the right value of smoothness coefficient due to the large estimation error of the smoothness coefficient.