About ten years ago, one of the first field experiments using cross-well electrical resistivity (ER) to monitor saline tracer migration and quantify transport characteristics was conducted at Massachusetts Military Reservation on Cape Cod, Massachusetts. This study, conducted in the F626 wellfield near the site of the long-term natural gradient tracer test, consisted of a two-well pumping-injection experiment where 2200 mg/L of sodium chloride was injected for 9 hours. ER data sets were collected from four corner-point wells surrounding the injection and extraction wells every 6 hours for 20 days. More than 180,000 resistance measurements were collected during the test. Each ER data set was inverted to produce a sequence of 3-D snapshot maps, known as tomograms, that track the plume.

The goal of the experiment was to estimate properties of plume movement, such as tracer mass, center of mass, and spatial variance without having the large number of wells often required to calculate these spatial moments. Using modified moment analysis of the electrical conductivity tomograms, these properties were calculated using only four wells. Although the tomograms provide valuable insights into field-scale tracer migration behavior and aquifer heterogeneity, and the center of mass estimated from the ER inversions coincided with that given by migration of the tracer plume using 3-D advective-dispersion simulation, standard tomographic inversion lead to some complicating factors: underestimation of tracer mass and overestimation of spatial variance. Such issues were attributed to (1) reduced measurement sensitivity to electrical conductivity values with distance from the electrodes and (2) spatial smoothing (regularization) from tomographic inversion.

This work prompted the development of new inversion techniques for electrical imaging that focus on inversion for plume moments. Capitalizing on the mathematical analogy between moment-based descriptors of plumes and the moment-based parameters of probability distributions, a new inverse problem was designed that describes plumes by only a few parameters (rather than many thousands, as is used in the state-of-the-practice), producing tomograms consistent with expected plume behavior and requiring comparatively few data to achieve reasonable model estimates.