Application of the Modified Shepard’s Method (MSM): A Case Study with the Interpolation of Neogene Reservoir Variables in Northern Croatia

Abstract

Interpolation is a procedure that depends on the spatial and/or statistical properties of the analysed variable(s). It is a particularly challenging task for small datasets, such as in those with less than 20 points of data. This problem is common in subsurface geological mapping, i.e., in cases where the data is taken solely from wells. Successful solutions of such mapping problems depend on interpolation methods designed primarily for small datasets and the datasets themselves. Here, we compare two methods, Inverse Distance Weighting and the Modified Shepard’s Method, and apply them to three variables (porosity, permeability, and thickness) measured in the Neogene sandstone hydrocarbon reservoirs (northern Croatia). The results show that cross-validation itself will not provide appropriate map selection, but, in combination with geometrical features, it can help experts eliminate the solutions with low-probable structures/shapes. The Golden Software licensed program Surfer 15 was used for the interpolations in this study.

Recent Advances in Geomathematics in Croatia: Examples from Subsurface Geological Mapping and Biostatistics

“…During 2019 and 2020, broad testing of small datasets mapping has been applied [41,43] to the CPBS. A small subsurface sample set is considered to be a set of measurements which includes [41] less than 20 inputs data.…”

“…The next examples are taken from [43] and compare the differences between the results obtained with the IDW and MSM methods. The IDW does not use weighting coefficient, i.e., each value is "weighted" by a simple (powered) inversely proportional distance from the measured point.…”

“…The numerical cross-validation strongly favoured the IDW (Table 3). The difference resulted from the different mathematical backgrounds of those two methods [43] , because the IDW takes into account all measured points or work with general searching radius (or radii for ellipsoid), but the MSM works with local searching by default. This is why cross-validation was higher for MSM-for porosity 289%, permeability 7%, and thickness 49%.…”

“…However, it was also shown that visual assessment is sometimes the more important criteria than purely numerical cross-validation, what is a crucial conclusion for subsampled reservoirs of the CPBS, and stressed the importance of human and geological expertise, and not purely the application of interpolation algorithms. Consequently, [43] recommended the MSM for subsurface geological mapping of Neogene reservoirs in Northern Croatia in (a) number of samples smaller than 20 measured values, and/or (b) for early exploration phase or later development phase when the number of measurements The difference resulted from the different mathematical backgrounds of those two methods [43], because the IDW takes into account all measured points or work with general searching radius (or radii for ellipsoid), but the MSM works with local searching by default. This is why cross-validation was higher for MSM-for porosity 289%, permeability 7%, and thickness 49%.…”

“…However, it was also shown that visual assessment is sometimes the more important criteria than purely numerical cross-validation, what is a crucial conclusion for subsampled reservoirs of the CPBS, and stressed the importance of human and geological expertise, and not purely the application of interpolation algorithms. Consequently, [43] recommended the MSM for subsurface geological mapping of Neogene reservoirs in Northern Croatia in (a) number of samples smaller than 20 measured values, and/or (b) for early exploration phase or later development phase when the number of measurements of the selected property is small, but a quick insight in the spatial distribution of such variables is necessary.…”