2 Designing Surveys

ER and IP data can be collected on the earth surface—including in water bodies, in boreholes, or both. The volume of subsurface sampled, sometimes called the depth or distance of penetration of the current, depends on the (unknown) electrical conductivity structure of the subsurface and the spacing of the electrodes and is, therefore, difficult to quantify or predict prior to data collection and analysis (e.g., Daily and Ramirez, 1995), which partially accounts for variable practices of data collection. Many surface studies successfully image electrical conductivity to depths of a few tens of meters below ground surface. The depth to which a particular survey can image effectively depends on the survey geometry, measurement errors, and the subsurface conductivity structure. The depth of penetration can be interpreted from sensitivity or resolution maps (e.g., Figure 4), or Oldenburg and Li (1999) provided an inversion-based approach (see more on inversion in Section 4) to predicting what they instead termed the depth of investigation (DOI). For DOI calculations, two inversions are performed using two reference models which differ by orders of magnitude, and the resulting images are compared. Depending on the type of regularization used (see Section 4.2 for definitions and details), the images are either differenced or cross-correlated to determine the depth to which the inversion is strongly affected by the reference models, i.e., below this DOI the data provide negligible information. This approach is supported in some inversion software. Simpler approaches to predicting DOI (e.g., Barker, 1989) are based on calculating the measured signal versus depth for a homogeneous half space and identifying the depth corresponding to the maximum, mean, or median signal contribution. These approaches produce simple rules of thumb for various array types and provide practical guidance for survey design. For example, for the popular dipole-dipole array, the median depth of investigation is on the order of 1/5 the maximum electrode spacing in an array (Roy and Apparao, 1971). The important messages here are 1) that some parts of the tomogram will be better resolved than others; 2) there are multiple tools to assess where resolution is expected to be high, and these methods are not absolute measures of accuracy; and 3) there is limit to how far from the electrodes ER and IP can see, which is impossible to determine in advance as it is dependent on the electrical conductivity of the earth and the geometry used to collect data, described below.

Figure showing Cumulative squared sensitivity maps

Figure 4 Cumulative squared sensitivity maps (a proxy for resolution) for surface a) and crosswell b) ERT arrays. These maps are the sum of squared sensitivity (the diagonal of J*J’) where J is the Jacobian matrix and J’ is its transpose. The Jacobian matrix is a matrix of first-order partial derivatives that shows the sensitivity of the model parameters to the data (more details in Section 4.2). c) The absolute sensitivity for a single measurement (i.e., a single row of J); cool colors are negative sensitivity and warm colors are positive (on c only).

Sensitivity is generally highest near the electrodes (Figure 4), whether the electrodes are on the surface or in boreholes. Practitioners are faced with a tradeoff between resolution and spatial coverage. Resolution improves with smaller electrode spacing, but smaller spacing (or well offsets) for a fixed number of electrodes reduces the volume of the subsurface studied. Consequently, when designing a survey, it is important to keep in mind the depth and size of targets. In field surveys and in the presence of heterogeneity, the volume of earth sampled by a particular resistance measurement is unknown—not unlike estimating the volume of earth sampled by a pumping test—and conversion from resistance to electrical conductivity requires inverse modeling. Information on inversion and image reconstruction is outlined in Section 4.

Historically, ER and IP data were collected on the surface using a fixed set of electrode geometries where the two current and two potential electrodes were moved by hand. However, such fieldwork was highly labor intensive. Modern systems are almost always automated using tens to hundreds of electrodes in an array. Some standard array types are often used in the field, such as Wenner, dipole-dipole, or Schlumberger arrays (Figure 5.). Some geometries (e.g., Wenner) are favored for their sensitivity to vertical contrasts in electrical conductivity, whereas other geometries (e.g., dipole-dipole) are favored for sensitivity to lateral changes in electrical conductivity. IP measurements benefit from arrays where the voltage pair are nested between the current pair, as with the Wenner and Schlumberger arrays, because of their high signal-to-noise ratio, although this comes at the expense of additional electromagnetic coupling effects relative to non-nested arrays such as dipole-dipole. By restricting data collection to simple geometries, analytic methods could be used to estimate the subsurface electrical conductivity without numerical modeling and inversion (for example, Zohdy et al., 1974). While selection of an ideal geometry has been the subject of past research, the ability to resolve subsurface structure is dependent not only on the geometry used, but on the electrical-conductivity structure of the subsurface, which is unknown. Optimized sets of measurements based on arbitrary array geometries can now be designed based on considerations of the expected subsurface structure (e.g., Stummer et al., 2004). Modern inversion software is capable of processing ER and IP data in minutes on a low-end PC and does not require that the electrode arrangement corresponds to any of the traditional, standard array types.

Figure showing some common surface electrode geometries

Figure 5 Some common surface electrode geometries for ER and IP, including Wenner, dipole-dipole, and Schlumberger arrays, which have different positioning of current (A,B) and potential (M,N) electrodes, as defined by spacings a and b and n, an integer.

For n electrodes, the number of fully independent 4-electrode measurements (i.e., quadripoles) is n(n3)/2 (Xu and Noel, 1993). Collecting all possible combinations of measurements is often unrealistic in the field given the memory constraints of ER meters and the time required to collect the data. Depending on the speed of data acquisition (i.e., instrument capabilities and measurement times) and whether time-lapse data are required (which may constrain the time allowed for measurements), an appropriate number of quadripoles can be selected. The choice of which quadripoles to collect in the field can be determined by two criteria: (1) geometric factors and (2) signal-to-noise ratios (dependent on the site). Larger electrode spacings will require larger source voltages to get sufficient current into the ground to ensure good data quality. Injected current is limited by the equipment and the resistivity of the ground. With respect to the speed of data collection, new multichannel instrumentation, capable of multiple voltage measurements at once for a given current pair—one voltage measurement at a time per channel—leads to faster data collection than older single-channel tools, although this functionality may only be applicable for certain array types depending on the instrument. To fully capitalize on multi-channel data acquisition, surveys can be designed to minimize the number of unique current injections collected during a given survey.

In borehole surveys, selected quadripoles would ideally combine in-well and cross-well dipoles, i.e., with current pair in one well and potential pair in a second, as well as with current and (or) potential pairs split between wells. In-well dipoles are sensitive to targets located near boreholes, but do not provide much information farther from boreholes. Cross-well dipoles are more sensitive to targets located farther from wells. To collect quality cross-well data, the boreholes should be approximately at least 1.5 times as deep as they are far apart. For much larger offsets, resolution between boreholes becomes highly degraded.


Electrical Imaging for Hydrogeology Copyright © 2022 by Kamini Singha, Timothy C. Johnson, Frederick D. Day Lewis and Lee D. Slater. All Rights Reserved.