Estimation of T2 spectrum in NMR based on OMP algorithm

The Nuclear Magnetic Resonance (NMR) logging is one of the most efficient tools in petroleum exploration, which is used to precisely evaluate the reservoir petrophysical parameters. This paper deals with the reconstruction of T
2
spectra in nuclear magnetic resonance relaxometry. The non-Gaussian noise, the ill-posed character and the large size of this T
2
spectrum estimation problem are the main difficulties to tackle. But conventional methods cannot handle all of these difficulties. In this paper, an improved inversion method is proposed to estimate the T
2
spectrum for large size NMR logging amplitude data with baseline shift and non-Gaussian noise. It has three key contributions. The first contribution is an orthogonal matching pursuit (OMP) algorithm which can calculate the non-zero range of the T
2
spectrum and can resolve the iteration divergence issue in the existence of non-Gaussian noise. In order to further remove the remaining non-Gaussian noise, a baseline shift technique is introduced by appending a baseline shift column at the end of the signal matrix. Then the final T
2
spectrum within the calculated non-zero range is iteratively estimated by combining the regularization method and the SVD algorithm. To verify the effectiveness of the proposed algorithm, multiple groups of NMR logging data are used to test its estimation performance. The estimation results confirm that the proposed algorithm can yield good performance even under very low SNR.