The study of NMR relaxation time spectra multi-exponential inversion based on Lloyd–Max optimal quantization

The multi-exponential inversion of a NMR relaxation signal plays a key role in core analysis and logging interpretation in the formation of porous media. To find an efficient metod of inverting high-resolution relaxation time spectra rapidly, this paper studies the effect of inversion which is based on the discretization of the original echo in a time domain by using a simulation model. This paper analyzes the ill-condition of discrete equations on the basis of the NMR inversion model and method, determines the appropriate number of discrete echoes and acquires the optimal distribution of discrete echo points by the Lloyd–Max optimal quantization method, in considering the inverse precision and computational complexity comprehensively. The result shows that this method can effectively improve the efficiency of the relaxation time spectra inversion while guaranteeing inversed accuracy. (paper)