Three-dimensional electrical resistivity model of a nuclear waste disposal site

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Abstract

A three-dimensional (3D) modeling study was completed on a very large electrical resistivity survey conducted at a nuclear waste site in eastern Washington. The acquisition included 47 pole–pole two-dimensional (2D) resistivity profiles collected along parallel and orthogonal lines over an area of 850 m × 570 m. The data were geo-referenced and inverted using EarthImager3D (EI3D). EI3D runs on a Microsoft 32-bit operating system (e.g. WIN-2K, XP) with a maximum usable memory of 2 GB. The memory limits the size of the domain for the inversion model to 200 m × 200 m, based on the survey electrode density. Therefore, a series of increasing overlapping models were run to evaluate the effectiveness of dividing the survey area into smaller subdomains. The results of the smaller subdomains were compared to the inversion results of a single domain over a larger area using an upgraded form of EI3D that incorporates multi-processing capabilities and 32 GB of RAM memory. The contours from the smaller subdomains showed discontinuity at the boundaries between the adjacent models, which do not match the hydrogeologic expectations given the nature of disposal at the site. At several boundaries, the contours of the low resistivity areas close, leaving the appearance of disconnected plumes or open contours at boundaries are not met with a continuance of the low resistivity plume into the adjacent subdomain. The model results of the single large domain show a continuous monolithic plume within the central and western portion of the site, directly beneath the elongated trenches. It is recommended that where possible, the domain not be subdivided, but instead include as much of the domain as possible given the memory of available computing resources.

Introduction

Numerous authors have noted the problems inherent with resolving geophysical targets using 2D data acquisition techniques over a 3D earth (Dahlin et al., 2002, Bentley and Gharibi, 2004, Gunther et al., 2006). However, the dimensional complexity of the target depends on the scale. In some cases, such as a simple layered earth, arbitrarily choosing a 3D imaging technique may not significantly improve the target resolution, and one can minimize the time spent acquiring data by being mindful of the problem's dimensionality. A class of targets that would likely fall into the 3D category are contaminant plumes (Slater et al., 2000, Slater et al., 2002). These hydrogeologic targets are typically on the order of a few tens of meters on a side and reside in the top 20 m of the surface. The goal of imaging these targets is to understand the source and extent of the plume as well as any time-dependent dynamics that define the fate and transport of the contaminants (e.g. Singha and Gorelick, 2006, Oldenborger et al., 2007).

Acquiring true 3D electrical resistivity data is time-consuming and costly when compared to 2D methods. For 3D acquisition, the metal electrodes used to pass current and measure voltage can be distributed randomly in space, but are commonly placed in a grid pattern on the surface or at multiple depths in several boreholes. Two-dimensional acquisition is conducted along a line of evenly-spaced electrodes. Several suggestions have been made to help migrate 2D techniques to 3D acquisition, including the serpentine roll-along (Loke and Barker, 1996) and the leap frog roll-along (Dahlin and Bernstone, 1997, Dahlin et al., 2002). These enhanced 3D acquisition techniques are an improvement over the traditional methods of running individual wires to the electrodes because they use multi-electrode cables and multi-channeled meters.

The practicality of the 3D roll-along has proven itself to be limited to small problems, as a large number of cables and multiplexors are needed to upscale to larger 3D data acquisition. A technique that does appear suitable for the larger problems is the quasi-3D acquisition, where 2D data are collected but processed using a 3D code. The quasi-3D techniques include a series of closely-spaced parallel lines (Ogilvy et al., 2002), a series of parallel and orthogonal lines within a grid (Friedel et al., 2006, Mansoor and Slater, 2007), radial lines around a common centroid (Nyquist and Roth, 2005), or concentric circles of increasing diameter (Brunner et al., 1999). Less time and equipment are needed to acquire 2D data, equating to a cheaper methodology that still provides a form of 3D interpretation of the subsurface. Gharibi and Bentley (2005) show that data acquired in a quasi-3D manner is suitable for processing and interpretation when using the proper geometric constraints, such as line and electrode spacing.

An analysis of 3D resistivity surveys in the literature (Table 1), shows that the quasi-3D approach of orthogonal line sets is likely the most practical. The table tracks the evolution of the 3D resistivity problem from Park and Van (1991), who used a true 3D grid of acquisition with 25 electrodes (and an estimated 5.5 km of wire) to the most recent paper at the time of this study by Chambers et al. (2007). This last paper, accompanied by the last 4 years of research papers, used the parallel/orthogonal line sets to produce a quasi-3D dataset. In addition to ease of data acquisition, the quasi-3D methodology may have been dictated by simplicity, equipment availability, and array type. For example, several authors chose the Wenner and Schlumberger arrays which are not suitable for pure 3D acquisition. From Table 1, it appears that the electrode arrays more suitable for pure 3D acquisition include pole–pole, pole–dipole, and dipole–dipole.

The 3D resistivity problem has also been limited by computer software and hardware constraints. Resistivity inversion is needed to reconstruct the electrical properties of the subsurface that give rise to the voltage measurements observed in the field. The resistivity inversion problem is non-linear, forcing the solution methodology to be conducted in an iterative procedure (Daily and Owen, 1991, LaBrecque et al., 1996) that solves the forward model many times while changing the subsurface electrical properties. The software and hardware constraint is manifest in the large computer memory requirements needed to store the Jacobian matrix (J) of partial derivatives. The (N × M) J matrix contains the derivative of the simulated data measurements (N) with respect to the model parameters (M) (Gunther et al., 2006). Even on moderately sized problems computing the J matrix can be the most time-consuming step during inversion (Loke and Dahlin, 2002).

Table 1 shows the increase in domain size and electrode number over the past decade, making the need for better and faster inversion codes. Currently, commercial and many academic institutions rely on third party commercial resistivity inversion software like Res3DINV (Geotomo Software — Penang Malaysia http://www.geoelectrical.com) and EarthImager3D (Advanced Geosciences, Inc. — Austin, TX http://www.agiusa.com). These software codes are compiled and run on 32-bit Microsoft Windows platforms (e.g., WIN-2K, XP), limiting available memory to 2 GB of RAM and one CPU core The work by Chambers et al., 2006, Mansoor and Slater, 2007 likely came close to exceeding the memory allotment of these inversion codes. Lately, migration of 32-bit codes to 64-bit platforms has been conducted to take advantage of larger memory and more processors (e.g., EarthImager3DCL by Advanced Geosciences, Inc. and Res3dinvx64 by Geotomo Software).

To overcome software limitations, the inversion codes either need to be scaled to run on computer clusters with large memory capacities, or the domain of large problems needs to be subdivided for inversion and recombined after processing to visualize the final distribution of subsurface electrical properties. This study compares both processing options on a large field resistivity survey to demonstrate that there are trade-offs inherent in both options. The data were acquired with the pole–pole array along a set of orthogonal 2D lines. While accommodating all data over the entire domain is desirable, the computers are expensive and the inversion time can extend over weeks or months. Recombining smaller subdomains into a final interpretation may have limitations, particularly where overlapping areas may differ in resistivity, observed at the boundaries and insensitive regions far from electrode locations. The parameters of the example field study chosen for this paper are summarized in Table 1, which clearly shows that it is a sizeable problem that cannot be inverted with within a single domain without modifications to the computer codes.

Section snippets

Study site

Planned and unplanned radiological releases of liquid waste have occurred to the subsurface within the vadose zone at the Hanford Site in eastern Washington. Several of these releases have resulted in contamination of the local groundwater, which is hydrologically connected to the Columbia River. One of the planned releases occurred at the BC Cribs and Trenches (BCCT) area, a 20-hectare disposal site located south of the 200 East Area (see Fig. 1). The site contains 20 unlined trenches ranging

Geophysical survey method

ERI relies on direct current injection into the ground and subsequent mapping of the potential field as a result of the current flow. To accomplish this, stainless steel electrodes are driven into the ground at regular intervals and a multiconductor cable and switching system is connected so that each electrode can be automatically switched from either current transmission or voltage measuring mode. A full profile is measured by sequencing between all possible transmitter and receiving pairs

Data processing and inversion

The voltage data were first edited to remove noisy measurements by evaluating data collected on all receivers from each transmitter electrode. Array comparisons at the Hanford site indicate that the pole–pole method has a high signal strength when compared to other common inline arrays, falling off as a function of 1/r with r being the distance between transmission source and receiver measurement. Measurements with large deviations from the 1/r relationship, which typically show up as spikes or

Modeling results

An example of model statistics for the eight small subdomains of the 50 m overlap and the larger single domain is shown in Table 2. Four of the eight subdomains completed the inversion with a root-mean-square (RMS) error less than 5% and L2-norm less than 1. The RMS error and L2-norm are “goodness of fit” statistics and are used in the goal seeking process to find the best solution to the inversion problem. Usually, the RMS error should be less than 5%, but the final number should be dependent

Interpretation of results

Using the large single domain model as the guide, it appears from the geophysics that the nuclear waste plume did not reach the water table, located at approximately 103 m below ground surface. Fig. 10 shows a profile through Trench 26, located along the northing at y = 147 m. The profile shows a low resistivity feature contained within the top 50 m of the near surface. Unfortunately, it is difficult to get an exact sense of the depth of penetration by the resistivity method based on the smearing of

Conclusions

The results from two 3D inversion modeling methodologies were compared to demonstrate the importance of inverting whole datasets as one domain for accurate interpretation of hydrogeologic targets. The inversion results from a single large domain of size 570 m × 420 m were compared to a set of increasing overlapping sub domains of about 200 m × 200 m, distributed within the boundaries of the large domain. The degree of overlap investigated was 15 m, 50 m, 100 m, and 150 m. To accommodate the large domain,

Acknowledgements

We gratefully acknowledge the support of Mark Benecke of CH2M Hill and Mark Sweeney of Pacific Northwest National Laboratory. This work was completed under Contract # DE-AC27-99RL14047 for the Department of Energy, Office of River Protection, Richland WA.

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