Inverting MRI measurements to heterogeneity spectra

Abstract

Spatially resolved MRI measurements of porosity and relaxation time have been performed on a series of sandstone and carbonate rock cores in order to assess spatial heterogeneity in these samples. Geostatistical techniques such as the construction of experimental variograms provide a quantitative measure of heterogeneity, although the interpretation of standard techniques is at times ambiguous. Here, we attempt to resolve some of that ambiguity by addressing the influence of regularization (spatial averaging over the volume of a voxel) on the variogram. Modeling the influence of regularization allows measured variograms to be inverted, yielding a heterogeneity spectrum that shows the extent of spatial heterogeneity as a function of length scale. The current experiment is sensitive to heterogeneity on the 0.3–100 mm length scale, and heterogeneity spectra of carbonates are shown to vary widely from sample to sample over this range. Thus, this analysis is shown to provide a more detailed description of these porous media than the variogram or the first two moments of the porosity distribution provide. The magnetic resonance aspects of this technique are described here, while details of the geostatistical methodology are presented in a companion paper [A.E. Pomerantz, P.G. Tilke, Y.-Q. Song, Math. Geosci., submitted for publication].