A deconvolution-based method for nuclear magnetic resonance T1-T2 inversion.

Nuclear magnetic resonance (NMR) relaxation data are typically analyzed by different methods from simple multi-exponential nonlinear fitting to ill-posed linear inversion. However, linear sampling with a constant echo spacing captures signals from short T2 components only in the first few echoes when measuring samples containing very short T2 components such as organic matter or bitumen. Consequently, fast decay of short relaxation signals leads to incompleteness of short T2 components in two-dimensional Laplace inversion. Based on the conversion of multi-exponential nonlinear fitting to a linear inversion problem, this study further converts the linear inversion problem into a deconvolution problem. A uniform logarithmic fitting and regularized deconvolution (LFD) algorithm is proposed, effectively addressing the incomplete and inaccurate recovery of short T2 components in traditional T1-T2 inversion algorithms. Specifically, the uniform logarithmic fitting method is employed to reconstruct both echo data and the inversion kernel function, which mitigates the ill-conditioned nature of the conventional inversion and improves computational efficiency. Numerical simulations and core experiments indicate that the proposed method significantly improves the accuracy of short T2 component inversion in T1-T2 maps: for the shale model example, the relative error for kerogen saturation decreases from 20.20% to 2.60%, for bitumen from 14.97% to 1.90%, and for clay bound water saturation from 5.85% to 0.90%. Applicable conditions are also discussed.