Bootstrap calibration and uncertainty estimation of downhole NMR hydraulic conductivity estimates in an unconsolidated aquifer

Characterization of hydraulic conductivity (K) in aquifers is critical for evaluation, management, and remediation of groundwater resources. While estimates of K have been traditionally obtained using hydraulic tests over discrete intervals in wells, geophysical measurements are emerging as an alternative way to estimate this parameter. Nuclear magnetic resonance (NMR) logging, a technology once largely applied to characterization of deep consolidated rock petroleum reservoirs, is beginning to see use in near-surface unconsolidated aquifers. Using a well-known rock physics relationship-the Schlumberger Doll Research (SDR) equation--K and porosity can be estimated from NMR water content and relaxation time. Calibration of SDR parameters is necessary for this transformation because NMR relaxation properties are, in part, a function of magnetic mineralization and pore space geometry, which are locally variable quantities. Here, we present a statistically based method for calibrating SDR parameters that establishes a range for the estimated parameters and simultaneously estimates the uncertainty of the resulting K values. We used co-located logging NMR and direct K measurements in an unconsolidated fluvial aquifer in Lawrence, Kansas, USA to demonstrate that K can be estimated using logging NMR to a similar level of uncertainty as with traditional direct hydraulic measurements in unconsolidated sediments under field conditions. Results of this study provide a benchmark for future calibrations of NMR to obtain K in unconsolidated sediments and suggest a method for evaluating uncertainty in both K and SDR parameter values.

Adaptive reconstruction of phased array MR imagery

An adaptive implementation of the spatial matched filter and its application to the reconstruction of phased array MR imagery is described. Locally relevant array correlation statistics for the NMR signal and noise processes are derived directly from the set of complex individual coil images, in the form of sample correlation matrices. Eigen-analysis yields an optimal filter vector for the estimated signal and noise array correlation statistics. The technique enables near-optimal reconstruction of multicoil MR imagery without a-priori knowledge of the individual coil field maps or noise correlation structure. Experimental results indicate SNR performance approaching that of the optimal matched filter. Compared to the sum-of-squares technique, the RMS noise level in dark image regions is reduced by as much as the square root of N, where N is the number of coils in the array. The technique is also effective in suppressing localized motion and flow artifacts.

Adaptive reconstruction of phased array MR imagery

An adaptive implementation of the spatial matched filter and its application to the reconstruction of phased array MR imagery is described. Locally relevant array correlation statistics for the NMR signal and noise processes are derived directly from the set of complex individual coil images, in the form of sample correlation matrices. Eigen-analysis yields an optimal filter vector for the estimated signal and noise array correlation statistics. The technique enables near-optimal reconstruction of multicoil MR imagery without a-priori knowledge of the individual coil field maps or noise correlation structure. Experimental results indicate SNR performance approaching that of the optimal matched filter. Compared to the sum-of-squares technique, the RMS noise level in dark image regions is reduced by as much as the square root of N, where N is the number of coils in the array. The technique is also effective in suppressing localized motion and flow artifacts.