Comparison of Neural Network, Ordinary Kriging, and Inverse Distance Weighting Algorithms for Seismic and Well-Derived Depth Data: A Case Study in the Bjelovar Subdepression, Croatia

In subsurface geological mapping, it is more than advisable to compare different solutions obtained with neural and other algorithms. Here, for such comparison, we used the previously published and well-prepared dataset of subsurface data collected from the Bjelovar Subdepression, a 2900 km2 large regional macrounit in the Croatian part of the Pannonian Basin System. Data on depth were obtained for the youngest (the shallowest) Lonja Formation (Pliocene, Quaternary) and mapped using neural network (NN), inverse distance weighting (IDW), and ordinary kriging (OK) algorithms. The obtained maps were compared based on square error (using k-fold cross-validation) and the visual interpretation of isopaches. Two other algorithms were also tested, namely, random forest (RF) and extreme gradient boosting (XGB) algorithms, but they were rejected as inappropriate for this purpose solely based on the visuals of the obtained maps, which did not follow any interpretable geological structures. The results showed that NN is a highly adjustable method for interpolation, with adjustment for numerous hyperparameters. IDW showed its strength as one of the classical interpolators, and its results are always located close to the top if several methods are compared. OK is the relative winner, showing the flexibility of variogram analysis regarding the number of data points and possible clustering. The presented variogram model, even with a relatively high sill and occasional nugget effect, can be well fitted into OK, giving better results than other methods when applied to the presented area and datasets. This was not surprising because kriging is a well-established method used exclusively for interpolation. In contrast, NN and machine learning algorithms are used in many fields, and these algorithms, particularly the fitting of hyperparameters in NN, simply cannot be the best solution for all.