Continuous moment estimation of CPMG data using Mellin transform

Abstract This paper provides a theoretical basis to directly estimate moments of transverse relaxation time T 2 from measured CPMG data in grossly inhomogeneous fields. These moments T 2 ω are obtained from Mellin transformation of the measured CPMG data. These moments are useful in computing petro-physical and fluid properties of hydrocarbons in porous media. Compared to the conventional method of estimating moments, the moments obtained from this method are more accurate and have a smaller variance. This method can also be used in other applications of NMR in inhomogeneous fields in characterizing fluids and porous media such as in the determination of hydrocarbon composition, estimation of model parameters describing relationship between fluid composition and measured NMR data, computation of error-bars on estimated parameters, as well as estimation of parameters 〈ln  T 2 〉 and σ ln T 2 often used to characterize rocks. We demonstrate the performance of the method on simulated data.