Accounting for a spatial trend in fine-scale ground-penetrating radar data: A comparative case study

In geostatistics, one of the challenges is to account for the spatial trend that is evident in a data-set. Two well-known kriging algorithms, namely universal kriging (UK) and intrinsic random function of order k (IRF-k), are mainly used to deal with the trend apparent in the data-set. These two algorithms differ in the way they account for the trend and they both have different advantages and drawbacks. In this study, the performances of UK, IRF-k, and ordinary kriging (OK) methods are compared on densely sampled ground-penetrating radar (GPR) data acquired to assist in delineation of the ore and waste contact within a laterite-type bauxite deposit. The original GPR data was first pre-processed to generate prediction and validation data sets in order to compare the estimation performance of each kriging algorithm. The structural analysis required for each algorithm was carried out and the resulting variograms and generalized covariance models were verified through cross-validation. The variable representing the elevation of the ore unit base was then estimated at the unknown locations using the prediction data-set. The estimated values were compared against the validation data using mean absolute error (MAE) and mean squared error (MSE) criteria. The results show although IRF-k slightly outperformed OK and UK, all the algorithms produced satisfactory and similar results. MSE values obtained from the comparison with the validation data were 0.1267, 0.1322, and 0.1349 for IRF-k, OK, and UK algorithms respectively. The similarity in the results generated by these algorithms is explained by the existence of a large data-set and the chosen neighbourhood parameters for the kriging technique.