Uncertainty Quantification of Geophysical and Hydrologic Parameters Estimated From Borehole Nuclear Magnetic Resonance Data

Abstract Borehole nuclear magnetic resonance (bNMR) data are typically used to infer in situ hydrologic properties. Partial water content as a function of pore size is estimated by fitting the measured NMR response to a multi‐exponential T 2 distribution, and the sum of estimated T 2 amplitudes equals the total volumetric water content. From these estimated parameters, several empirical relationships are commonly used to infer hydraulic conductivity from the NMR‐estimated water content and T 2 distribution. Often, parameters are estimated through deterministic inversion methods that produce a single best‐fit estimate, but do not reflect uncertainties in model parameters. Here, a Bayesian Markov chain Monte Carlo (McMC) approach for analyzing bNMR data is developed that allows for comprehensive uncertainty quantification of NMR parameters and derived hydrologic properties. The underlying model that describes the T 2 distribution is defined by a set of spline interpolation points. The number of interpolation points is allowed to vary in a trans‐dimensional algorithm that naturally favors simple models with fewer interpolation points, allowing the data to inform the necessary level of model complexity. Additionally, data error is estimated as an unknown parameter. Analysis of the ensemble of models output from the McMC algorithm provides useful details on the range of plausible T 2 distributions that can fit a measured bNMR decay curve, as well as uncertainty estimates of total water content. The ensemble of NMR parameters can also be propagated through commonly used relationships to produce uncertainty estimates on derived parameters such as bound/capillary/mobile water content or hydraulic conductivity.