Differential Spectrum-Based Adaptive Regularization for NMR <i>T</i> ₂ Inversion in Noisy Data

Nuclear magnetic resonance (NMR) logging is widely applied for evaluating the formation porosity, fluid properties, and pore structure. However, inversion of NMR echo signals is an ill-posed problem that is highly sensitive to random noise, often leading to <i>T</i> ₂ spectra that overestimate porosity and misrepresent reservoir characteristics. Analysis of sandstone reservoirs in the Chang 8 Member of the Ordos Basin reveals that, despite low movable water content, the differential spectrum tails show pronounced divergence, and porosity estimates are consistently higher than core measurements due to noise amplification. To address this problem, a locally adaptive regularization inversion method is proposed, which is based on the divergence characteristics of the differential spectrum tail. The method quantifies the degree of tail divergence and dynamically adjusts the regularization parameter, thereby locally constraining the abnormal spectral segments. Tests on Well H*49 demonstrate that the approach effectively suppresses nonphysical pseudopeaks and improves porosity accuracy, reducing mean squared error (MSE) relative to core porosity by an average of 57%. Validation in the adjacent Well H*141 further confirms its adaptability and generalization capability. These results highlight the method's reliability and practical value for NMR logging interpretation under high-noise conditions in complex reservoirs.