Geostatistics and the representative elementary volume of gamma ray tomography attenuation in rock cores
J. R. Vogel, G. O. Brown, 2003. "Geostatistics and the representative elementary volume of gamma ray tomography attenuation in rock cores", Applications of X-ray Computed Tomography in the Geosciences, F. Mees, R. Swennen, M. Van Geet, P. Jacobs
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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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X-ray computed tomography (CT) is a technique that allows non-destructive imaging and quantification of internal features of objects. It was originally developed as a medical imaging technique, but it is now also becoming widely used for the study of materials in engineering and the geosciences. X-ray CT reveals differences in density and atomic composition and can therefore be used for the study of porosity, the relative distribution of contrasting solid phases and the penetration of injected solutions. As a non-destructive technique, it is ideally suited for monitoring of processes, such as the movement of solutions and the behaviour of materials under compression. Because large numbers of parallel two-dimensional cross-sections can be obtained, three-dimensional representations of selected features can be created. In this book, various applications of X-ray CT in the geosciences are illustrated by papers covering a wide range of disciplines, including petrology, soil science, petroleum geology, geomechanics and sedimentology.