THE APPLICATION OF THE VARIOGRAM, COVARIANCE, AND THE SPECTRAL DENSITY FUNCTIONS IN THE GEOSTATISTICAL ANALYSIS OF THE ROCK MICROSTRUCTURES (PREPRINT IBRAE-2013-02)

Preprint IBRAE-2013-02

Savelyeva E., Dinariev O., Svitelman V. 

The adaptation of geostatistical methods for the analysis of microstructural properties on the basis of the Xray microtomographic (μCT) data is discussed in this manuscript. It is shown that the fields of correlation functions contain the information about the structural properties of the rock micromodels, in particular, about the anisotropy at different scales and about inhomogeneity scale sizes. The following techniques are described:

• the anisotropy estimation and classification using the spherical harmonics expansion of the variogram;
• the spectrum of correlation lengths extraction using the spectral representation of the covariance.

These methods represent the mathematical tools required for the geostatistical analysis application to classification and the typification of the three-dimensional μCT models. The techniques are validated on artificially generated samples with various characteristics and applied to the real μCT images

Bibliographical reference

Savelyeva E., Dinariev O., Svitelman V. THE APPLICATION OF THE VARIOGRAM, COVARIANCE, AND THE SPECTRAL DENSITY FUNCTIONS IN THE GEOSTATISTICAL ANALYSIS OF THE ROCK MICROSTRUCTURES. Preprint /Nuclear Safety Institute RAS IBRAE-2013-02 — Moscow: NSI RAS, 2013 — 30 p. — Bibliogr: 27 items