Advances in Electrical Resistivity Tomography: Modeling, Electrode Position Errors, Time-Lapse Monitoring of an Injection/Withdrawal Experiment and Solution Appraisal

The electrical resistivity tomography (ERT) experiment is one of a host of geophysical imaging techniques that has great potential for aiding in the minimally invasive, nearly continuous estimation of material properties in near-surface environmental and engineering applications. To fully realize this potential will require an increased understanding of several aspects of the ERT experiment. This dissertation presents a set of advancements to the ERT experiment both in a theoretical and modeling context, and in the context of time-lapse imaging of an injection/withdrawal experiment designed for aquifer characterization and as a proxy for pump-and-treat remediation effort in an unconfined alluvial aquifer. The theoretical and modeling efforts demonstrate that: 1) Source-specific boundary conditions for subsurface electrodes are inexpensive and can provide significant accuracy gains in the face of computational limitations of multi-scale numerical grids. 2) The primary-secondary separation of potential can be used to derive a scattering series in the sparse differential domain with a convergence criterion that accounts for. both the magnitude and distribution of heterogeneity of electrical conductivity. For linearization associated with the Frechet derivative to be valid, the perturbation in electrical conductivity must be small as defined by convergence of the scattered series. A derivation is presented that permits efficient calculation of charge accumulation across contrasts in electrical conductivity by equating accumulated surface charge density to the source of scattered potential in the differential domain. 3) Data error due to electrode mislocations can significantly contaminate ERT data and the reconstructed electrical conductivity. A method is presented to predict systematic data error associated with electrode mislocations and to estimate the resulting artifacts in the reconstructed electrical conductivity images. Both the data error and model artifacts are experiment- and model-dependent. The experimental portion of this dissertation focuses on the outcome of several procedures for incorporating time-lapse information into the inversion of ERT data collected during the injection and sequential withdrawal of a saline proxy contaminant in an unconfined aquifer. Solute mass is consistently under-predicted. However, time-lapse regularization produces the largest changes in model size and results in estimates of solute mass that are closest to actual solute mass. Regardless of regularization scheme, estimates of the change in mass between experimental stages are more accurate than estimates of total solute mass at any particular experimental stage. The volume of investigation index (VOl) is introduced to define regions of reliability for the ERT models. Resolution of the ERT models is quantified using the point-spread function (PSF) which requires development of an efficient computational strategy for the large three-dimensional problem. Both measures of solution appraisal, the VOl and PSF, are model- or time-dependent. The PSF exhibit reasonable resolution, but also significant localization errors that are, as of yet, not well understood