Nuclear Magnetic inversion is the basis of NMR Resonance （NMR） T2 logging interpretation. The regularization parameter selection of the penalty term directly influences the NMR T2 inversion result. We implemented b...Nuclear Magnetic inversion is the basis of NMR Resonance （NMR） T2 logging interpretation. The regularization parameter selection of the penalty term directly influences the NMR T2 inversion result. We implemented both norm smoothing and curvature smoothing methods for NMR T2 inversion, and compared the inversion results with respect to the optimal regular- ization parameters （（Xopt） which were selected by the dis- crepancy principle （DP）, generalized cross-validation （GCV）, S-curve, L-curve, and the slope of L-curve methods, respectively. The numerical results indicate that the DP method can lead to an oscillating or oversmoothed solution which is caused by an inaccurately estimated noise level. The （Xopt selected by the L-curve method is occa- sionally small or large which causes an undersmoothed or oversmoothed T2 distribution. The inversion results from GCV, S-curve and the slope of L-curve methods show satisfying inversion results. The slope of the L-curve method with less computation is more suitable for NMR T2 inversion. The inverted T2 distribution from norm smoothing is better than that from curvature smoothing when the noise level is high.展开更多
Two-dimensional(2D)nuclear magnetic resonance(NMR)inversion operates with massive echo train data and is an ill-posed problem.It is very important to select a suitable inversion method for the 2D NMR data processing.I...Two-dimensional(2D)nuclear magnetic resonance(NMR)inversion operates with massive echo train data and is an ill-posed problem.It is very important to select a suitable inversion method for the 2D NMR data processing.In this study,we propose a fast,robust,and effective method for 2D NMR inversion that improves the computational efficiency of the inversion process by avoiding estimation of some unneeded regularization parameters.Firstly,a method that combines window averaging(WA)and singular value decomposition(SVD)is used to compress the echo train data and obtain the singular values of the kernel matrix.Subsequently,an optimum regularization parameter in a fast manner using the signal-to-noise ratio(SNR)of the echo train data and the maximum singular value of the kernel matrix are determined.Finally,we use the Butler-Reeds-Dawson(BRD)method and the selected optimum regularization parameter to invert the compressed data to achieve a fast 2D NMR inversion.The numerical simulation results indicate that the proposed method not only achieves satisfactory 2D NMR spectra rapidly from the echo train data of different SNRs but also is insensitive to the number of the final compressed data points.展开更多
基金funded by Shell International Exploration and Production Inc.(PT45371)the National Natural Science Foundation of China-China National Petroleum Corporation Petrochemical Engineering United Fund(U1262114)the National Natural Science Foundation of China(41272163)
文摘Nuclear Magnetic inversion is the basis of NMR Resonance （NMR） T2 logging interpretation. The regularization parameter selection of the penalty term directly influences the NMR T2 inversion result. We implemented both norm smoothing and curvature smoothing methods for NMR T2 inversion, and compared the inversion results with respect to the optimal regular- ization parameters （（Xopt） which were selected by the dis- crepancy principle （DP）, generalized cross-validation （GCV）, S-curve, L-curve, and the slope of L-curve methods, respectively. The numerical results indicate that the DP method can lead to an oscillating or oversmoothed solution which is caused by an inaccurately estimated noise level. The （Xopt selected by the L-curve method is occa- sionally small or large which causes an undersmoothed or oversmoothed T2 distribution. The inversion results from GCV, S-curve and the slope of L-curve methods show satisfying inversion results. The slope of the L-curve method with less computation is more suitable for NMR T2 inversion. The inverted T2 distribution from norm smoothing is better than that from curvature smoothing when the noise level is high.
基金funded by National Science and Technology Major Project of the Ministry of Science and Technology of China(2016ZX05033-003-001).
文摘Two-dimensional(2D)nuclear magnetic resonance(NMR)inversion operates with massive echo train data and is an ill-posed problem.It is very important to select a suitable inversion method for the 2D NMR data processing.In this study,we propose a fast,robust,and effective method for 2D NMR inversion that improves the computational efficiency of the inversion process by avoiding estimation of some unneeded regularization parameters.Firstly,a method that combines window averaging(WA)and singular value decomposition(SVD)is used to compress the echo train data and obtain the singular values of the kernel matrix.Subsequently,an optimum regularization parameter in a fast manner using the signal-to-noise ratio(SNR)of the echo train data and the maximum singular value of the kernel matrix are determined.Finally,we use the Butler-Reeds-Dawson(BRD)method and the selected optimum regularization parameter to invert the compressed data to achieve a fast 2D NMR inversion.The numerical simulation results indicate that the proposed method not only achieves satisfactory 2D NMR spectra rapidly from the echo train data of different SNRs but also is insensitive to the number of the final compressed data points.
