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Electrical Potential Distributions in a Heterogeneous Subsurface in Response to Applied Current

Solution for Circular Inclusions

^a Hydrology and Water Resources Department, University of Arizona, Tucson, AZ 85721
^b Soil, Water, and Environmental Sciences Department, University of Arizona, Tucson, AZ 85721
^c Hydrology and Water Resources Department, University of Arizona, Tucson, AZ 85721

View larger version (10K): [in a new window]   Fig. 1. Schematic diagram of an electrical resistance tomography system.

View larger version (20K): [in a new window]   Fig. 2. Schematic diagram of the solution domain including heterogeneities and images.

View larger version (84K): [in a new window]   Fig. 3. Electrical flow nets for: (a) a homogeneous medium (0), (b) a single circular inclusion at [0.3, -0.3] with K1 = 10 and R0 = 0.1 (I), and (c) a single circular inclusion at [0.3, -0.3] with K1 = 0.1 and R0 = 0.1 (II). Current is applied at [-1, 0] and [1, 0]. Electrical flow nets for: (d) a detailed view of Inclusion I and (e) a detailed view of Inclusion II.

View larger version (93K): [in a new window]   Fig. 4. Change of potential from that in a homogeneous domain due to a single inclusion at [0.3, -0.3] with R0 = 0.1 for (a) K1 = 10 (I) and (b) K1 = 0.1 (II). Current is applied at [-1, 0] and [1, 0]. The streamline passing through each inhomogeneity illustrates the direction of flow.

View larger version (64K): [in a new window]   Fig. 5. Change of potential, compared with a homogeneous domain, resulting from (a) Inclusion III, (b) Inclusion IV, and (c) Inclusion V. The streamline passing through each inhomogeneity illustrates the direction of flow. See Table 1 for inclusion properties.

View larger version (89K): [in a new window]   Fig. 6. Change of potential, compared with a homogeneous domain, resulting from (a) two inclusions (I, III) and (b) three inclusions (I, III, and IV). See Table 1 for inclusion properties.

View larger version (16K): [in a new window]   Fig. 7. The absolute sensitivity of the most sensitive arrays to a conductive perturbation plotted at the location of the perturbation.

View larger version (76K): [in a new window]   Fig. 8. The C-C (A) and P-P (B) separations for the arrays showing the highest sensitivity to a conductive perturbation plotted at the location of the perturbation. The offset (C) and opening (D) of the arrays showing the highest sensitivity to a conductive perturbation plotted at the location of the perturbation.

View larger version (44K): [in a new window]   Fig. 9. The array type (see Table 1 for definitions) of the array showing the highest sensitivity to a conductive perturbation plotted at the location of the perturbation.