Nuclear Magnetic Resonance(NMR) T_2inversion is the basis of NMR logging interpretation.The regularization parameter selection of the penalty term directly influences the NMR T_2 inversion result.We implemented both norm smoothing and curvature smoothing methods for NMR T_2 inversion,and compared the inversion results with respect to the optimal regularization parameters(α_(opt)) which were selected by the discrepancy principle(DP),generalized cross-validation(GCV).S-curve,L-curve.and the slope of L-curve methods,respectively.The numerical results indicate that the DP method can lead to an oscillating or oversmoothed solution which is caused by an inaccurately estimated noise level.The α_(opt) selected by the L-curve method is occasionally small or large which causes an undersmoothed or oversmoothed T_2 distribution.The inversion results from GCV,S-curve and the slope of L-curve methods show satisfying inversion results.The slope of the L-curve method with less computation is more suitable for NMR T_2inversion.The inverted T_2 distribution from norm smoothing is better than that from curvature smoothing when the noise level is high. Nuclear Magnetic Resonance (NMR) T_2inversion is the basis of NMR logging interpretation. The regularization parameter selection of the penalty term directly affects the NMR T_2 inversion result. Both implemented both norm smoothing and curvature smoothing methods for NMR T_2 inversion, and compared to the inversion results with respect to the optimal regularization parameters (α_ (opt)) which were selected by the discrepancy principle (DP), generalized cross-validation (GCV). S-curve, L-curve and the slope of L-curve methods, respectively . The numerical results indicate that the DP method can lead to an oscillating or oversmoothed solution which is caused by an inaccurately estimated noise level. The α_ (opt) selected by the L-curve method is occasionally small or large which causes an undersmoothed or oversmoothed T_2 distribution. The inversion results from GCV, S-curve and the slope of L-curve methods show satisfying inversion results. The slope of the L-curve method with less computation is more su itable for NMR T_2inversion. The inverted T_2 distribution from norm smoothing is better than that from curvature smoothing when the noise level is high.