Mellin transform of CPMG data

This paper describes a new method for computing moments of the transverse relaxation time T2 from measured CPMG data. This new method is based on Mellin transform of the measured data and its time-derivatives. The Mellin transform can also be used to compute the cumulant generating function of ln T2. The moments of relaxation time T2 and ln T2 are related to petro-physical and fluid properties of hydrocarbons in porous media. The performance of the new algorithm is demonstrated on simulated data and compared to results from the traditional inverse Laplace transform. Analytical expressions are also derived for uncertainties in these moments in terms of the signal-to-noise ratio of the data.