Abstract: Two-dimensional (2D) nuclear magnetic resonance (NMR) map commonly refers to a plot of diffusion coefficient (D) vs. transverse relaxation time (T₂), which is often used to characterize materials in porous media. The materials with different D and T₂ can be differentiated by such a map. In this paper, we introduced the physical and mathematical models underlying the inversion of 2D NMR map with a global inversion method. The performances of the traditional singular value decomposition (SVD) method and a improved SVD method in inverting 2D NMR maps were compared. The improved SVD method was shown to have advantages such as faster calculation speed and continued distribution of 2D NMR map. The results suggest that the improved SVD method is especially suitable for inversion of data having high signal-to noise ratio (SNR). Quantitative analysis of 2D NMR map was shown to be feasible when the SNR of the original data was greater than 100, while only qualitative analysis was feasible when 60≤SNR<100. The results also showed that 2D NMR maps can be used to differentiate oil and water directly, suggesting that it may provide a promising new technology for NMR logging.

Key words: NMR logging, relaxation, diffusion, two-dimensional map, singular value decomposition