A method for inverting NMR data sets with different signal to noise ratios

The inversion of NMR data set of a T ₂ echo train to obtain a T ₂ amplitude distribution often assumes a constant measurement error for each echo for the whole echo train. However, when the NMR logging tool provides two sets of echo train data, one with a high signal to noise ratio, e.g., short echo trains with a very short recovery time; and another one with a low signal to noise ratio, e.g., long echo trains with an ample recovery time; the measurement error for the two data sets are very different and the inversion of the NMR data with due consideration to both data sets presents a problem. The current approach for inverting the two NMR data sets with drastically different signal to noise ratios uses a splicing technique. The data sets with high and low signal to noise ratios are processed separately with different sets of T ₂ relaxation times. Then, the long T ₂ components for the short echo trains are discarded due to incomplete recovery. The remaining short T ₂ components for the clay-bound water are concatenated with the T ₂ distribution for long echo trains to form the total porosity T ₂ distribution. This splicing technique is computationally fast, simple to implement, and may be appropriate for small numbers of T ₂ relaxation times. However, it can result in discontinuous T ₂ distributions when a large number of T ₂ relaxation times (which allow for a smooth T ₂ display) are used. The discontinuity can occur where the two distributions are spliced. To resolve the discontinuity problem and ensure that no information is lost, we present a new method which accounts for both high and low signal to noise ratio data and processes them simultaneously. The resulting T ₂ distribution is not only smooth throughout, it also reveals subtle features in the short relaxation times which are not observed in the splicing technique. Synthetic, core and log examples are presented to delineate the differences.