Moment-Based Inversions for Electrical Resistivity Tomography - A Problem-Specific Approach to Reducing the Dimensionality

Surface electrical resistivity tomography (ERT) is often used to monitor solute plumes. Inverting the data on a pixel-based grid provides a snapshot of the subsurface conductivity, but even with a large amount of data, the number of model cells outnumbers the amount of independent measurements and sensitivity is variable across the model space. To overcome these problems and converge on a final conductivity image, additional regularization is often imposed, such as smoothness constraints. This regularization can distort the perceived geometry of the plume. Furthermore, extracting information about a plume from a pixelated image requires an additional level of interpretation. In this study, we use moment-based rather than pixel-based parameterization to invert for plume geometry. If we assume a simple Gaussian-shaped plume perturbing the initial background conductivity model, then we can acquire plume location, size, and conductivity value directly from the inversion. Neither regularization nor pixel image interpretation is required. Since we have reduced the dimensionality to only a few model parameters, we are able to explicitly calculate the Jacobian matrix, or the sensitivity of ERT data to model perturbations. If the rows of the Jacobian are independent, each plume moment parameter can be determined uniquely from the data; if they are not independent, parameters can be combined, further reducing dimensionality. By finding the Jacobian with the most independent rows, we can optimize the survey design for plume monitoring.