Occam’s Inversion of 3-D Electrical Resistivity Tomography
Douglas J. LaBrecque, Gianfranco Morelli, William Daily, Abelardo Ramirez, Paul Lundegard, 1999. "Occam’s Inversion of 3-D Electrical Resistivity Tomography", Three-Dimensional Electromagnetics, Michael Oristaglio, Brian Spies
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Electrical resistivity tomography (ERT) images the electrical properties of the subsurface from dc resistivity measurements between surface and borehole electrodes. We experiment with 3-D inversion of ERT using finite-element forward solution and a conjugate-gradient inverse routine. The algorithm finds the smoothest model (Occam’s inversion) that fits the data to a given prior error level. The algorithm takes 10 to 20 iterations to converge but requires only a single forward solution per iteration and does not require direct solution of a large system of equations.
Inversion of data from two sites is shown. The first site tests the ability of ERT to monitor leaks around large metal tanks at the Hanford Reservation in Washington State. Data were collected and inverted from 16 wells placed around a circular tank. The tank is of heavy-gauge steel covered with concrete, is 15 m in diameter, and extends 2 m below the ground surface. The 3-D algorithm was modified to allow the smoothness operator to be decreased at the tank boundary. The 3-D inversion was necessary to produce an accurate picture of the leak.
At a second site, ERT was used to monitor the injection of air from a vertical well at a shallow petroleum remediation site. Using a cone penetrometer, three electrode strings were placed in the ground on the corners of a right triangle. The background of the site was assumed to be layered. Results of 3-D and 2-D inversion agreed well when the regions of interest were approximately 2-D. Air injection caused large changes in resistivity. At early times, these were confined to an area near the injection point. Later, the changes were along a dipping, tabular region. At the latest times, there is evidence of mixing of brackish water at the depth of the injection point with freshwater in a shallower aquifer on the site. This mixing would have decreased the resistivity and thus the apparent size and magnitude of the zone of influence of sparging.