title: The generalized Phillips-Twomey method for NMR relaxation time inversion.
abstract: The inversion of NMR relaxation time involves the Fredholm integral equation of the first kind. Due to its ill-posedness, numerical solutions to this type of equations are often found much less accurate and bear little resemblance to the true solution. There has been a strong interest in finding a well-posed method for this ill-posed problem since 1950s. In this paper, we prove the existence, the uniqueness, the stability and the convergence of the generalized Phillips-Twomey regularization method for solving this type of equations. Numerical simulations and core analyses arising from NMR transverse relaxation time inversion are conducted to show the effectiveness of the generalized Phillips-Twomey method. Both the simulation results and the core analyses agree well with the model and the realities.
authors: State Key Laboratory of Petroleum Resources and Prospecting, China University of Petroleum, Beijing 102249, China; College of Science, China University of Petroleum, Beijing 102249, China. Electronic address: gaoyang1203@163.com.
authors: Yang
authors: Y
authors: Gao
authors: State Key Laboratory of Petroleum Resources and Prospecting, China University of Petroleum, Beijing 102249, China.
authors: Lizhi
authors: L
authors: Xiao
authors: College of Science, China University of Petroleum, Beijing 102249, China.
authors: Yi
authors: Y
authors: Zhang
authors: Key Laboratory of Shale Gas Exploration, Ministry of Land and Resources, Chongqing Institute of Geology and Mineral Resources, Chongqing 400042, China.
authors: Qingming
authors: Q
authors: Xie
keywords: Core analysis; Generalized Phillips-Twomey method; Ill-posedness; NMR relaxation time inversion; Numerical simulation