A nuclear magnetic resonance echo data filter method based on gray-scale morphology

Nuclear magnetic resonance (NMR) echo data measured in the oil field usually have a very low signal-to-noise ratio (S/N). The low S/N of echo data may affect the accuracy of the inversion results, which further leads to the inaccuracy of derived petrophysical parameter estimates. It is therefore important to filter the echo data to enhance the S/N before inversion. Existing filter methods focus on removing noise by compressing the echo data matrix or processing the echo data in time or frequency domain, which are not very efficient and can be affected by artificial interventions. We have developed a gray-scale morphology filter method based on the morphological difference between the echo data and noise. Either elliptical or triangular structure elements can be used for the morphology filter of NMR echo data. The size of the structure elements should be in the range of 1-5 echo spacings to prevent the echo data from being distorted. Comparing the inversion results of the unfiltered, morphology-filtered, singular value decomposition (SVD)filtered, and wavelet-filtered echo data at different S/Ns, the morphology filter method yields the best results at low S/Ns and the morphology filter method and the wavelet filter method yield similarly good results at high S/Ns. The morphology filter method has the shortest run time compared to the SVD method and the wavelet filter method. Moreover, this morphology filter method is stable to handle random noise and different T-2 distribution models, and it also performs well on NMR well-logging data.