Uncertainty estimates for surface nuclear magnetic resonance water content and relaxation time profiles from bootstrap statistics

A method for estimating uncertainty in surface nuclear magnetic resonance (NMR) water content and relaxation times utilizing bootstrapping statistics is presented. Bootstrapping is particularly well suited for assigning uncertainty to the surface NMR data set due to the primary factor that degrades surface NMR data quality: ambient electromagnetic noise. We use synthetic forward modeled data with various noise levels applied (the “known uncertainty”), and then demonstrate that a bootstrap resampling of the observed synthetic data can produce an uncertainty estimate that closely represents the “known uncertainty”. Finally, we present two field data sets collected under different magnitude ambient noise levels as examples illustrating the result of this approach under realistic noise conditions. This approach for estimating uncertainty is computationally intensive, but straightforward to implement and produces useful uncertainty estimates on both water content and relaxation time results for smooth surface NMR sounding models.