Nuclear magnetic resonance (NMR) relaxometry, a non-invasive and non-destructive method, is a key technique for unconventional reservoir evaluation. Echo data detected by from NMR instrument, a kind of weak signal, however, is characterized by a low signal-to-noise ratio (SNR). The achievement of NMR relaxation spectra inversion of a high precision, for echo data with a low SNR, is a challenge, which will also affect the unconventional reservoir evaluation of NMR logging. In this paper, a variational mode decomposition (VMD) method was proposed for NMR echo data denoising. NMR echo data was decomposed into an ensemble of intrinsic mode functions (IMFs) by the VMD method. The IMF number is an important parameter for VMD, and VMD results are different with various IMF number. An optimal selection method for the IMF number was proposed. The decomposed IMFs compose of signals with different frequencies. Noise is from high frequency signal, but valuable data is from low frequency signal. The effective IMFs in VMD were selected and summed as the denoised echo data. Numerical simulations and field NMR logging data processing were undertaken to evaluate the NMR echo data denoising effectiveness and practicality of the proposed VMD-based method. The results showed that the inverted NMR spectra exhibit a higher quality after the VMD-based denoise, compared with those for raw echo data and after the empirical mode decomposition (EMD) denoise. This indicates a higher denoising quality is achieved by the VMD-based method than by the EMD-based method for NMR echo data.

Nuclear magnetic resonance (NMR) technology plays a significant role in petroleum exploration. NMR data can be processed using inversion methods to reflect the relaxation information of all the components. A new double-parameter regularization (DPR) method was proposed for the inversion of NMR data, whose regularization terms consist of Tikhonov regularization and maximum entropy regularization. The objective function for the DPR method was solved using the Levenberg-Marquardt method; the proportional coefficient of the regularization parameter was obtained using an iteration procedure; the optimum regularization parameter of the DPR method was selected using an S-curve. The relationship between the optimum regularization parameter and the signal-to-noise ratio (SNR) of the data was evaluated. Moreover, we compared the results of the NMR inversion obtained from the norm smooth method, the maximum entropy method, and the DPR method for simulated data. We evaluated how the proportional coefficient of the regularization parameter affected the inverted T₂ distributions and processed field NMR log data for a tight sandstone reservoir employing the DPR method. The results showed that the optimum regularization parameter for the DPR method gradually decreases with increasing data SNR. The accuracy is higher for the DPR method than for the norm smooth method and the maximum entropy method under low SNR conditions. It is of great importance to select the proportional coefficient for the DPR method. The inverted T₂ distributions are similar for the DPR method and the norm smooth method when the proportional coefficient is small and similar for the DPR method and the maximum entropy method when the proportional coefficient is large.