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

Cross borehole electrical resistivity tomography (ERT) was used to image the resistivity distribution before and during two infiltration experiments. In both cases water was introduced into the vadose zone, and the change in resistivity associated with the plume of wetted soil was imaged as a function of time. The primary purpose of this work was to study the capabilities and limitations of ERT to image underground structure and ground water movement in the vadose zone. A secondary goal was to learn specifics of unsaturated flow in a complex geologic setting. Tomographs of electrical resistivity taken before infiltration image coarser, well‐drained soils (sands and gravels) as more resistive zones, whereas finer grained soils (silts and clays), which hold more water by capillarity, are imaged as more conductive. Images of changes in resistivity during infiltration show growth of the water infiltration plume with time that is consistent with known geology. In the ERT images we see the effects of capillary barriers and infer differences between capillary‐driven flow through fine sediments and gravity‐driven flow through very permeable sediments. Images are consistent with numerical flow simulations using hydrological parameter values consistent with soil types inferred from well logs. ERT can be a useful tool to monitor movement of circuitous moisture fronts in a heterogeneous field setting that would go undetected by borehole measurements.

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 ...

[1] A sequential, geostatistical inverse approach was developed for electrical resistivity tomography (ERT). Unlike most ERT inverse approaches, this new approach allows inclusion of our prior knowledge of general geological structures of an area and point electrical resistivity measurements to constrain the estimate of the electrical resistivity field. This approach also permits sequential inclusion of different data sets, mimicking the ERT data collection scheme commonly employed in the field survey. Furthermore, using the conditional variance concept, the inverse model quantifies uncertainty of the estimate caused by spatial variability and measurement errors. Using this approach, numerical experiments were conducted to demonstrate the effects of bedding orientation on ERT surveys and to show both the usefulness and uncertainty associated with the inverse approach for delineating the electrical resistivity distribution using down-hole ERT arrays. A statistical analysis was subsequently undertaken to explore the effects of spatial variability of the electrical resistivity-moisture relation on the interpretation of the change in water content in the vadose zone, using the change in electrical resistivity. Core samples were collected from a field site to investigate the spatial variability of the electrical resistivity-moisture relation. Numerical experiments were subsequently conducted to illustrate how the spatially varying relations affect the level of uncertainty in the interpretation of change of moisture content based on the estimated change in electrical resistivity. Other possible complications are also discussed.

A three-dimensional (3-D) Occam's inversion algorithm for electrical resistivity tomography is modified to allow for inversion on the differences between the background and subsequent data sets. The algorithm is optimized for in situ monitoring applications. The resistivity obtained by the inversion of background data serves as the a priori model in the difference inversion. There are several advantages to this method. First, convergence is fast since the inverse routine needs only to find small perturbations about a good initial guess. Second, systematic errors such as those due to errors in field configuration and discretization errors in the forward modeling algorithm tend to cancel. The result is that we can fit the difference data far more closely than the individual potentials. Better data fits often equate to better resolution with fewer inversion artifacts.The difference inversion technique was applied to monitoring in-situ steam remediation in Portsmouth, Ohio and monitoring of flow in fluid fractures at the Box Canyon site near the Idaho National Engineering Laboratory. Small changes of conductivity were better resolved using the difference inversion method. Difference inversion produced high-quality images with fewer artifacts, and only took 25% to 50% run time of standard Occam's inversion in the Box Canyon case.