The statistical simulation of dataset in 3D area with pentamodel type variogram to Rivne NPP geophysical monitoring
DOI:
https://doi.org/10.17721/1728-2713.111.12Keywords:
Statistical simulation, pentamodel variogram, spectral decomposition, conditional maps, Rivne Nuclear Power Plant (RNPP)Abstract
Background. This paper presents a statistical modeling approach for three-dimensional spatial data using a pentamodel type variogram, which provides an optimal mean-square approximation. The proposed method is applied to supplement geophysical survey data for karst-suffusion processes in monitoring the density of the chalk stratum in the Rivne Nuclear Power Plant (RNPP) area. A comprehensive set of geophysical investigations was conducted in the RNPP site area. Among these investigations, radioisotope measurements of soil density and moisture around the constructed facilities are of primary interest. However, the available observation dataset, derived from 29 wells using radioisotope methods, was insufficient for high-resolution density characterization. To address this limitation, a statistical modeling technique based on the pentamodel variogram was employed, enabling the reconstruction of the random field representing the studied parameter at any point within the 3D domain of interest.
Methods. A statistical model of the averaged density distribution of the chalk stratum within the study area was developed using the spectral decomposition of random fields in 3D space. The algorithm allows for generating realizations of random fields with predefined correlation structures, ensuring spatial discretization consistent with the required accuracy and resolution for geophysical monitoring applications.
Results. An algorithm for statistical modeling of random fields with pentamodel type correlation functions was formulated and implemented. Using the developed software, additional realizations of the random component of the chalk density field were generated on a regular observation grid with the desired level of detail. A comparison of a set of correlation functions for one data set in mean-square was performed. A statistical analysis of the simulated results was performed, including validation against the original observation data and an assessment of the adequacy and convergence of the modeled fields.
Conclusions. The proposed statistical modeling method, based on pentamodel type correlation functions, provides a robust framework for supplementing sparse geophysical datasets with high accuracy. This approach significantly improves the reliability of density distribution estimates and can be effectively applied to geophysical monitoring and the interpretation of spatially distributed geological parameters.
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