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Book Chapter

Occam’s Inversion of 3-D Electrical Resistivity Tomography

By
Douglas J. LaBrecque
Douglas J. LaBrecque
SteamTech Environmental Services Bakers Field, CA 93309, USA.
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Gianfranco Morelli
Gianfranco Morelli
SteamTech Environmental Services Bakers Field, CA 93309, USA.
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William Daily
William Daily
SteamTech Environmental Services Bakers Field, CA 93309, USA.
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Abelardo Ramirez
Abelardo Ramirez
Lawrence Livermore National Laboratory, L-156, 7000 East Avenue, Livermore, CA 94550, USA.
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Paul Lundegard
Paul Lundegard
UNOCAL CERT, 376 S. Valencia Avenue, Brea, CA 92621, USA.
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Published:
January 01, 1999

Summary

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.

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Contents

Geophysical Developments Series

Three-Dimensional Electromagnetics

Society of Exploration Geophysicists
Volume
7
ISBN electronic:
9781560802154
Publication date:
January 01, 1999

GeoRef

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