Numerical estimation of choice of the regularization parameter for NMR T2 inversion

作     者：You-Long Zou Ran-Hong Xie Alon Arad 

作者机构：State Key Laboratory of Petroleum Resources and Prospecting China University of Petroleum Beijing 102249China Shell International Exploration and Production Inc.Houston 77079 TX USA 

出 版 物：《Petroleum Science》 (石油科学（英文版）)

年 卷 期：2016年第13卷第2期

页      面：237-246页

核心收录：

学科分类：081801[工学-矿产普查与勘探] 081802[工学-地球探测与信息技术] 0709[理学-地质学] 0819[工学-矿业工程] 0808[工学-电气工程] 08[工学] 0820[工学-石油与天然气工程] 0707[理学-海洋科学] 0817[工学-化学工程与技术] 0818[工学-地质资源与地质工程] 0708[理学-地球物理学] 0807[工学-动力工程及工程热物理] 0815[工学-水利工程] 0816[工学-测绘科学与技术] 0827[工学-核科学与技术] 0703[理学-化学] 0813[工学-建筑学] 0825[工学-航空宇航科学与技术] 0704[理学-天文学] 0814[工学-土木工程] 

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) 

主　　题：NMR T2 inversion Tikhonov regularizationVariable substitution Levenberg-Marquardt method Regularization parameter selection 

摘      要：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.