Geophysical evaluation of solute plume spatial moments using an adaptive POD algorithm for electrical resistivity imaging

- Center of mass estimates from the adaptive algorithm converge in a common region.
- Compactness of estimated plume morphology improves with increasing updates.
- Direct sampling (DS) moments are dependent on sampling sensitivity and coverage.
- Moments estimation power from DS stabilizes after 12 wells have been installed.
- Resistivity moments are reliable than DS estimates until 6-10 wells are installed.

SummaryWe investigate the potential for characterizing spatial moments of subsurface solute plumes from surface-based electrical resistivity images produced within a Proper Orthogonal Decomposition (POD) inversion framework. The existing POD algorithm is improved here to allow for adaptive conditioning of the POD training images on resistivity measurements. The efficacy of the suggested technique is evaluated with two hypothetical transport scenarios: synthetic #1 is based on the case where the target plume and POD training images follow the same (unimodal) plume morphology, whereas a second source location in synthetic #2 makes the target plume bimodal and inconsistent with the POD training images. The resistivity imaging results indicate that the adaptive algorithm efficiently and robustly updates the POD training images to obtain good quality resistivity images of the target plumes, both in the presence of data noise and when conceptual model inaccuracies exist in the training simulations. Spatial moments of the solute plumes recovered from the resistivity images are also favorable, with relative mass recovery errors in the range of 0.6-4.4%, center of mass errors in the range of 0.6-9.6%, and spatial variance errors in the range of 3.4-45% for cases where the voltage data had 0-10% noise. These results are consistent with or improved upon those reported in the literature. Comparison of the resistivity-based moment estimates to those obtained from direct concentration sampling suggests that for cases with good quality resistivity data (i.e., <3% noise), the imaging results provide more accurate moments until 6-10 multi-level sampling wells are installed. While the specific number of wells will depend on the actual field scenario, we suggest that this finding illustrates the general value of POD-based resistivity imaging techniques for non-invasively estimating the spatial moments of a solute plume.