Computation of parameters in NMR using integral transforms: Tapered areas

This paper describes a method to compute tapered areas of a probability density function by means of integral transforms of its noisy Laplace transform. This problem is directly relevant to Nuclear Magnetic Resonance data for fluid and rock characterization. We describe integral transforms that are directly applicable to the measured magnetisation data, to estimate the tapered areas. In petrophysics, these tapered areas are useful in estimation of fluid saturations and bound and free fluid volumes. Since integral transforms are linear, uncertainty in the tapered areas can be computed as a function of signal-to-noise (SNR) in the data. Performance of these transforms is demonstrated on simulated data and compared to results from the traditional inverse Laplace transform.