A robust method for calculating geometric mean times from multiexponential relaxation data, using only a few data points and only a few elementary operations

A method is presented to compute values of geometric mean time Tg that uses only a few data points equispaced in the logarithm of time (or equispaced in time and weighted by 1t) and a few elementary operations for the computation. The method has been tested on a large number of synthetic relaxation data and on actual NMR relaxation measurements in porous samples, using as few as four points (including the two points needed to normalize the relaxation for decay from 1.0 to 0) on each relaxation curve. This computation of the geometric-mean rate very adequately matches the synthetic data and the results of multiexponential inversion of many (or only a few) data points from NMR measurements. When many computations are needed in short times, as for voxel-by-voxel computations in magnetic resonance imaging (MRI) or for depth-by-depth computation in nuclear magnetism logging (NML) of oilwells, a very quickly computed estimate of Tg should be useful.