Prediction of the Spatial Distribution of Petrophysical Properties of Sediment Formations Using Multidimensional Splines

The spatial variability of properties in sedimentary deposits can be assessed using approximation methods. A small number of direct measurements or their extremely uneven distribution leads to significant model errors. This article explores the possibility of using multidimensional approximation and regression splines, both considering spatially referenced direct observation data and using well log curves statistically linked to the modeled variables. It is possible to significantly reduce the forecast error by utilizing indirect data. The results can be computed for individual wells as for inter-well space, allowing for the creation of geological cross-sections of predicted properties and 3D models of their distribution. In order to demonstrate the effectiveness of the proposed approach, computational experiments were conducted using data from the stratigraphic range of the Georgievskaya and Vasyuganskaya formations in the Kazan field in southeastern West Siberia. Comparing the obtained forecast with the real, unknown values of the modeled variable at the time of its implementation showed a high quality model with determination coefficients up to 0.9.