Variational Mode Decomposition for NMR Echo Data Denoising

Nuclear magnetic resonance (NMR) relaxometry, a noninvasive and nondestructive method, is a key technique for unconventional reservoir evaluation. Echo data detected 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 article, a variational mode decomposition (VMD) method was proposed for NMR echo data denoising. NMR echo data were 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 numbers. 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 are 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 that a higher denoising quality is achieved by the VMD-based method than by the EMD-based method for NMR echo data.