Application of a New Adaptive Denoising Algorithm Based on Wavelet Transform in NMR Logging Inversion

The echo signal of Nuclear Magnetic Resonance (NMR) logging is easily affected by noise, leading to inaccurate inversion results and, consequently, affecting reservoir evaluation. This paper proposes an adaptive Weighted Energy scoring denoising algorithm based on the energy distribution of approximation coefficients and correlation coefficients. The energy of approximation coefficients is calculated in the algorithm at different wavelet decomposition levels and the correlation coefficients are combined between the original and denoised signals to generate a Weighted Energy Score. The automatic selection of the optimal wavelet basis function combination is performed in our researches, adapting to the complex time-frequency noise characteristics. The researches show that, compared to traditional fixed wavelet basis denoising methods, this algorithm can effectively adapt to different strata signal characteristics, significantly improving wavelet denoising performance under low signal-to-noise ratio (SNR) conditions, and enhancing the resolution of the NMR inversion T2 spectrum for characterizing pore structure. This study provides reliable quantitative evaluation metrics for NMR logging signal denoising, ensuring the fidelity of signal reconstruction, and holds great potential for improving reservoir evaluation through NMR logging.