Gaining insight into the $T\,_2^*$– T 2 relationship in surface NMR free-induction decay measurements
One of the primary shortcomings of the surface nuclear magnetic resonance (NMR) freeinduction decay (FID) measurement is the uncertainty surrounding which mechanism controls the signal’s time dependence. Ideally, the FID-estimated relaxation time T$*\atop{2}$ that describes the signal’s decay carries an intimate link to the geometry of the pore space. In this limit the parameter T$*\atop{2}$ is closely linked to a related parameter T 2 , which is more closely linked to pore-geometry. If T$*\atop{2}$ T 2 the FID can provide valuable insight into relative pore-size and can be used to make quantitative permeability estimates. However, given only FID measurements it is difficult to determine whether T$*\atop{2}$ is linked to pore geometry or whether it has been strongly influenced by background magnetic field inhomogeneity. If the link between an observed T$*\atop{2}$ and the underlying T 2 could be further constrained the utility of the standard surface NMR FID measurement would be greatly improved. We hypothesize that an approach employing an updated surface NMR forward model that solves the full Bloch equations with appropriately weighted relaxation terms can be used to help constrain the T$*\atop{2}$ –T 2 relationship. Weighting the relaxation terms requires estimating the poorly constrained parameters T 2 and T 1 ; to deal with this uncertainty we propose to conduct a parameter search involving multiple inversions that employ a suite of forward models each describing a distinct but plausible T$*\atop{2}$ –T 2 relationship. We hypothesize that forward models given poor T 2 estimates will produce poor data fits when using the complex-inversion, while forward models given reliable T 2 estimates will produce satisfactory data fits. By examining the data fits produced by the suite of plausible forward models, the likely T$*\atop{2}$ –T 2 can be constrained by identifying the range of T 2 estimates that produce reliable data fits. Synthetic and field results are presented to investigate the feasibility of the proposed technique.