title: Noise reduction of nuclear magnetic resonance (NMR) transversal data using improved wavelet transform and exponentially weighted moving average (EWMA).
abstract: NMR logging and core NMR signals acts as an effective way of pore structure evaluation and fluid discrimination, but it is greatly contaminated by noise for samples with low magnetic resonance intensity. Transversal relaxation time (T(2)) spectrum obtained by inversion of decay signals intrigued by Carr-Purcell-Meiboom-Gill (CPMG) sequence may deviate from the truth if the signal-to-noise ratio (SNR) is imperfect. A method of combing the improved wavelet thresholding with the EWMA is proposed for noise reduction of decay data. The wavelet basis function and decomposition level are optimized in consideration of information entropy and white noise estimation firstly. Then a hybrid threshold function is developed to avoid drawbacks of hard and soft threshold functions. To achieve the best thresholding values of different levels, a nonlinear objective function based on SNR and mean square error (MSE) is constructed, transforming the problem to a task of finding optimal solutions. Particle swarm optimization (PSO) is used to ensure the stability and global convergence. EWMA is carried out to eliminate unwanted peaks and sawtooths of the wavelet denoised signal. With validations of numerical simulations and experiments, it is demonstrated that the proposed approach can reduce the noise of T(2) decay data perfectly.
authors.affiliation: School of Geosciences, China University of Petroleum, Qingdao 266580, Shandong, China; CNPC Key Well Logging Laboratory in China University of Petroleum, Qingdao 266580, Shandong, China. Electronic address: gexinmin2002@163.com.
authors.forename: Xinmin
authors.initials: X
authors.lastname: Ge
authors.affiliation: School of Geosciences, China University of Petroleum, Qingdao 266580, Shandong, China; CNPC Key Well Logging Laboratory in China University of Petroleum, Qingdao 266580, Shandong, China.
authors.forename: Yiren
authors.initials: Y
authors.lastname: Fan
authors.affiliation: Research Institute of Exploration and Development, Qinghai Oilfield, CNPC, Dunhuang 736202, Gansu, China.
authors.forename: Jiangtao
authors.initials: J
authors.lastname: Li
authors.affiliation: Department of Earth and Atmospheric Sciences, University of Houston, Houston 77054, TX, USA.
authors.forename: Yang
authors.initials: Y
authors.lastname: Wang
authors.affiliation: School of Geosciences, China University of Petroleum, Qingdao 266580, Shandong, China; CNPC Key Well Logging Laboratory in China University of Petroleum, Qingdao 266580, Shandong, China.
authors.forename: Shaogui
authors.initials: S
authors.lastname: Deng
keywords: Hybrid threshold function; PSO; Simulations; T(2) decay data; Wavelet denoising