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Geostatistics and the representative elementary volume of gamma ray tomography attenuation in rock cores

By
J. R. Vogel
J. R. Vogel
US Geological Survey, Water Resources Division, 100 Centennial Mall North, Federal Building Room 406, Lincoln, NE 68508 USA
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G. O. Brown
G. O. Brown
Biosystems and Agricultural Engineering, Oklahoma State University, Stillwater, OK 74078, USA (e-mail: jrvogel@usgs.gov)
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Published:
January 01, 2003

Abstract

Semivariograms of samples of Culebra Dolomite have been determined at two different resolutions for gamma ray computed tomography images. By fitting models to semivariograms, small-scale and large-scale correlation lengths are determined for four samples. Different semivariogram parameters were found for adjacent cores at both resolutions. Relative elementary volume (REV) concepts are related to the stationarity of the sample. A scale disparity factor is defined and is used to determine sample size required for ergodic stationarity with a specified correlation length. This allows for comparison of geostatistical measures and representative elementary volumes. The modifiable areal unit problem is also addressed and used to determine resolution effects on correlation lengths. By changing resolution, a range of correlation lengths can be determined for the same sample. Comparison of voxel volume to the best-fit model correlation length of a single sample at different resolutions reveals a linear scaling effect. Using this relationship, the range of the point value semivariogram is determined. This is the range approached as the voxel size goes to zero. Finally, these results are compared to the regularization theory of point variables for borehole cores and are found to be a better fit for predicting the volume-averaged range.

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Contents

Geological Society, London, Special Publications

Applications of X-ray Computed Tomography in the Geosciences

F. Mees
F. Mees
Ghent University, Belgium
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R. Swennen
R. Swennen
Physico-chemical Geology, K. U. Leuven, Belgium
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M. Van Geet
M. Van Geet
SCK-CEN, Belgium
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P. Jacobs
P. Jacobs
Ghent University, Belgium
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Geological Society of London
Volume
215
ISBN electronic:
9781862394636
Publication date:
January 01, 2003

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