Selection of the Value of the Power Distance Exponent for Mapping with the Inverse Distance Weighting Method—Application in Subsurface Porosity Mapping, Northern Croatia Neogene

Abstract

The correct selection of the value of p is a complex and iterative procedure that requires experience in the interpretation of the obtained interpolated maps. Inverse Distance Weighting is a method applied to the porosities of the K and L hydrocarbon reservoirs discovered in the Neogene (Lower Pontian) subsurface sandstones in northern Croatia (Pannonian Basin System). They represent small and large data samples. Also, a standard statistical analysis of the data was made, followed by a qualitative–quantitative analysis of the maps, based on the selection of different values for the power distance exponent (p-value) for the K and L reservoir maps. According to the qualitative analysis, for a small data set, the p-value could be set at 1 or 2, giving the optimal result, while for a large data set, a p value of 3 or 4 could be applied. For quantitative analysis, in the case of a small data set, p = 2 is recommended, resulting in a root mean square error value of 0.03458, a mean absolute error of 0.02013 and a median absolute deviation of 0.00546. In contrast, a p-value of 3 or 4 is selected as appropriate for a large data set, with root mean square errors of 0.02435 and 0.02437, mean square errors of 0.01582 and 0.01509 and median absolute deviations 0.00896 and 0.00444. Eventually for a small data set, it is recommended to use a p-value of 2, and for a large data set, a p-value of 3 or 4.