An Inversion Method for NMR Weak Signals with Short Relaxation Time

This paper proposes an inversion method for nuclear magnetic resonance (NMR) relaxation signals with a low signal-to-noise ratio (SNR) to solve the inversion problem of NMR weak signals with short relaxation components. This method selects a suitable filter factor for inversion by combining the singular value decomposition (SVD) method and the Tikhonov method. Compared with the existing inversion methods, the relaxation time spectrum based on the proposed method is closer to the original spectrum of the NMR simulation signal, especially on short relaxation components when the signal is weak. The reliability of the proposed method under the different SNRs was proved by calculating the uncertainty of the solutions. The ability to obtain precise relaxation times was proved by experimental measurement and inversion analysis of samples with multiple relaxation components. And the changes rule of components in the cement hydration process found by identifying the weak signal with short relaxation components is valid. In conclusion, the inversion method proposed can effectively distinguish the weak NMR signal with short relaxation times, which plays an important role in finding the key components of the sample and characterizing its physical properties, thus promoting the application of NMR relaxation technology.