title: Obtaining T1-T2 distribution functions from 1-dimensional T1 and T2 measurements: The pseudo 2-D relaxation model.
abstract: We present the pseudo 2-D relaxation model (P2DRM), a method to estimate multidimensional probability distributions of material parameters from independent 1-D measurements. We illustrate its use on 1-D T1 and T2 relaxation measurements of saturated rock and evaluate it on both simulated and experimental T1-T2 correlation measurement data sets. Results were in excellent agreement with the actual, known 2-D distribution in the case of the simulated data set. In both the simulated and experimental case, the functional relationships between T1 and T2 were in good agreement with the T1-T2 correlation maps from the 2-D inverse Laplace transform of the full 2-D data sets. When a 1-D CPMG experiment is combined with a rapid T1 measurement, the P2DRM provides a double-shot method for obtaining a T1-T2 relationship, with significantly decreased experimental time in comparison to the full T1-T2 correlation measurement.
authors.affiliation: Future Industries Institute, University of South Australia, Mawson Lakes, SA 5095, Australia. Electronic address: nathan.williamson@mymail.unisa.edu.au.
authors.forename: Nathan H
authors.initials: NH
authors.lastname: Williamson
authors.affiliation: SP Food and Bioscience, Frans Perssons väg 6, 402 29 Göteborg, Sweden; School of Energy and Resources, UCL Australia, University College London, 220 Victoria Square, Adelaide, SA 5000, Australia. Electronic address: magnus.roding@sp.se.
authors.forename: Magnus
authors.initials: M
authors.lastname: Röding
authors.affiliation: MacDiarmid Institute for Advanced Materials and Nanotechnology, School of Chemical and Physical Sciences, Victoria University of Wellington, PO Box 600, Wellington, New Zealand. Electronic address: petrik.galvosas@vuw.ac.nz.
authors.forename: Petrik
authors.initials: P
authors.lastname: Galvosas
authors.affiliation: Phenomics and Bioinformatics Research Centre, School of Information Technology and Mathematical Sciences, University of South Australia, Mawson Lakes, SA 5095, Australia. Electronic address: stan.miklavcic@unisa.edu.au.
authors.forename: Stanley J
authors.initials: SJ
authors.lastname: Miklavcic
authors.affiliation: School of Energy and Resources, UCL Australia, University College London, 220 Victoria Square, Adelaide, SA 5000, Australia. Electronic address: m.nyden@ucl.ac.uk.
authors.forename: Magnus
authors.initials: M
authors.lastname: Nydén
keywords: Heterogeneity; Inverse Laplace transform; Inverse-gamma distribution; Lognormal distribution; Multidimensional distribution function; Porous media; Relaxation correlation; T(1); T(2)