Implementing a New and Rigorous Technique for 1-D NMR Inversion: Slope of L-curve and Adaptive Pruning
1-D NMR data inversion is the process of obtaining T2 amplitude distribution from NMR spin echo trains. NMR inversion is an ill-posed problem, the noise in the data allows for many possible solutions. We solve for the amplitudes on an equally spaced logarithmic scale, representing a typical pore system distribution. If a least square method is used the solution is highly unstable, so we adopted a technique, Tikhonov-Regularization to restrict the range of possible solutions. A stable version of this algorithm was developed and a detailed parametric studies was performed. Two different L-cure parametrizations, the slope of the L-curve method and adaptive pruning was adopted. We generated forward models for the T2 echo train, using an assumption of multiply peaked amplitude distributions with varying levels of Gaussian noise. The forward models were then inverted using the developed algorithm to examine how much of the original information was lost. We conclude with a discussion of the limitations of NMR inversion and the relative merits of each L-curve parametrization.