Studies of parameter correlations in surface NMR using the Markov chain Monte Carlo method

Surface nuclear magnetic resonance is a technique capable of providing insight into subsurface aquifer properties. To produce estimates of aquifer properties (such as the spatial distribution of water content and parameters controlling the duration of the nuclear magnetic resonance signal), an inversion is required. Essential to the reliable interpretation of the estimated subsurface models is an understanding of the uncertainty and correlation between the parameters in the estimated models. To quantify parameter uncertainty and correlation in the surface nuclear magnetic resonance inversion, a Markov chain Monte Carlo approach is demonstrated. Markov chain Monte Carlo approaches have been previously employed to invert surface nuclear magnetic resonance data, but the primary focus has been on quantifying parameter uncertainty. The focus of this paper is to further investigate whether the parameters in the estimated models exhibit correlation with one another; equally important to building a reliable interpretation of the subsurface is an understanding of the parameter uncertainty. The utility of the Markov chain Monte Carlo approach is demonstrated through the investigation of three questions. The first question investigates whether the parameters describing the water content and thickness of a layer exhibit a strong correlation. This question stems from applying concepts known to electromagnetic surveys (that the layer thickness and layer resistivity parameters are strongly correlated) to the surface nuclear magnetic resonance inversion. A water content–layer thickness correlation in surface nuclear magnetic resonance would not have large effects for quantifying total water content but would affect the ability to identify layer boundaries. The second question examines whether the parameter controlling the duration of the nuclear magnetic resonance signal exhibits a correlation with the water content and layer thickness parameters. The resolution of surface nuclear magnetic resonance typically does not consider the duration of the signal and focuses primarily on the distribution of current amplitudes that form the suite of transmit pulses. It is common to treat regions with short-duration signal with greater uncertainty, but it is important to understand whether the signal duration controls resolution for medium to long duration signals as well. The third question explores if the parameter uncertainty produced by the Markov chain Monte Carlo approach is consistent with that produced by an alternative approach based upon the posterior covariance matrix (for the linearised inversion). The ability of the Markov chain Monte Carlo approach to more thoroughly explore the model space provides a means to improve the reliability of surface nuclear magnetic resonance aquifer characterisations by quantifying parameter uncertainty and correlation.