An Occam's inversion algorithm for crosshole resistivity data that uses a finite-element method forward solution is discussed. For the inverse algorithm, the earth is discretized into a series of parameter blocks, each containing one or more elements. The Occam's inversion finds the smoothest 2-D model for which the Chi-squared statistic equals an a priori value.Synthetic model data are used to show the effects of noise and noise estimates on the resulting 2-D resistivity images. Resolution of the images decreases with increasing noise. The reconstructions are underdetermined so that at low noise levels the images converge to an asymptotic image, not the true geoelectrical section.If the estimated standard deviation is too low, the algorithm cannot achieve an adequate data fit, the

We used electrical resistance tomography (ERT) to map the subsurface distribution of a steam flood as a function of time as part of a prototype environmental restoration process performed by the Dynamic Underground Stripping Project. We evaluated the capability of ERT to monitor changes in the soil resistivity during the steam injection process using a dipole-dipole measurement technique to measure the bulk electrical resistivity distribution in the soil mass. The injected steam caused changes in the soil's resistivity because the steam displaced some of the native pore water, increased the pore water and soil temperatures and changed the ionic content of the pore water. We could detect the effects of steam invasion by mapping changes in the soil resistivity as a function of space and time. The ERT tomographs are compared with induction well logs, formation temperature logs and lithologic logs. These comparisons suggest that the ERT tomographs mapped the formation regions invaded by the steam flood. The data also suggest that steam invasion was limited in vertical extent to a gravel horizon at depth of approximately 43 m. The tomographs show that with time, the steam invasion zone extended laterally to all areas monitored by the ERT technique. us understand the heterogeneous subsurface environment, the factors controlling steam movement in situ, and the steam flow behavior induced by the process. An accurate understanding of the interaction between the steam process and the geologic environment is needed to assess the remediation effectiveness. This underground imaging technique substantially reduces the need for the number of boreholes that would otherwise be required to monitor the process. DESCRIPTION OF ERTTo image the resistivity distribution between two boreholes, we placed a number of electrodes in electrical contact with the soil in each borehole (Figure 1). Using an automatic data collection and switching system (shown schematically in Figure 2), we then applied a known current to any two electrodes and measured the resulting voltage difference between other pairs of electrodes. Each ratio of measured voltage and current is a transfer resistance. Next, we switched to two other electrodes, applied current between two other electrodes and again measured the voltage differences using electrode pairs not being used for the source current. We repeated this process until many combinations were measured which completely encircled the target area. For n electrodes there are n (n -3)/2 linearly independent transfer resistances. A complete set of linearly independent data contains the maximum information content about the target; any additional measurements collected are redundant. This formula does not count reciprocal measurements because a measurement and its reciprocal contain the same information and therefore are only counted as one by the formula. The reciprocal to any original transmitter-receiver pair is one where the original transmitter dipole becomes the receiver dipole and where the original receiver ...

Electrical resistivity tomography (ERT) is a method for determining the electrical resistivity distribution in a volume from discrete measurements of current and voltage made within the volume or on its surface. We have developed an ERT algorithm that is an iterative, modified least squares inversion, based on a finite element forward solution of Laplace’s equation. We report the results of tests on this algorithm designed to determine how resistance measurements made from two boreholes may be used to image the resistivity distribution between them. A number of simple but geophysically significant structures are modeled. These include a single isolated block anomaly, two layers, a thin isolated continuous layer, and a vertical band. The main features of most resistivity models were identifiable in the reconstructions. Limited data accuracy and noise were simulated and found to cause a deterioration of the image. However, even with measurements of only one significant figure accuracy, the algorithm converged toward the desired solution for at least the first iteration and the targets were identifiable in the reconstructions. Imprecision in the data influences convergence as well as image quality; more iterations eventually lead to divergence. Spatial resolution depends on such factors as data errors and the specific target geometry.

Synthetic model data are used to show the effects of noise and noise estimates on Occam' s Inversion of crossborehole resistivity data. Resolution of the images decreases with increasing noise. The reconstructions are underdetermined so that at low noise levels the images converge to an asymptotic image not the true geo-electrical section. For a noise estimate of standard deviation 10% below the correct, value the algorithm achieves an adequate data fit but the image becomes irregular. When the estimated standard deviation is twice the correct value, the resolution decreases substantially.A case history of monitoring at an EOR site is used to illustrate problems in comparing images from a site if the noise level changes. Changes in image resolution can be misinterpreted as actual geo-electrical changes. We suggest one solution to this problem is to perform smoothest but non-Occam' s inversion on later data sets using parameters found from the background data set.

No abstract