# Characterizing Near-Surface Fractured-Rock Aquifers: Insights Provided by the Numerical Analysis of Electrical Resistivity Experiments

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## Abstract

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## 1. Introduction

## 2. Methodological Background

## 3. Results and Discussion

#### 3.1. Sensitivity to Fracture Geometrical Characteristics

#### 3.1.1. Impact of the Fracture Position and Dip Angle

#### 3.1.2. Sensitivity to the Fracture Length

#### 3.2. Impact of Changes in Material Properties

#### 3.2.1. Overburden Properties

#### 3.2.2. Fracture Properties

## 4. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A. Description and Interpretation of ER Profiling Movies Supplementary Materials

#### Appendix A.1. Overall Description of the Supplementary Material

#### Appendix A.2. General Behavior of the Electric Current Flow

#### Appendix A.3. Detailed Description for the Wenner-Schlumberger Array

#### Appendix A.4. Detailed Description for the Dipole-Dipole Array

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**Figure 1.**(

**a**) Single-fracture configuration considered in our simulations with the fracture, bedrock, and overburden represented using blue, white, and brown, respectively. (

**b**) Diagram showing the Wenner-Schlumberger and (

**c**) dipole-dipole electrode arrays, where a is the minimum considered electrode spacing and n is the spacing factor ($n=2$ shown). A and B denote the current electrodes, whereas M and N denote the potential measurement electrodes. The symbols below the arrays indicate the center point of each measurement along with the relative depths of the three considered spacing-factor values, and correspond to the symbols used in Figures 5–8.

**Figure 2.**Diagram showing how the apparent resistivity anomaly, ${\rho}_{a}^{\ast}$, is plotted as a function of the horizontal measurement position, x, and how the anomaly magnitude and width are determined. The anomaly magnitude is defined as the absolute difference between the maximum and minimum observed anomaly values, in %. The anomaly width is defined as the distance between the first and last points where the absolute anomaly value is equal to 5% of the anomaly magnitude, the latter of which is indicated by a red band in the figure. Note that the measurement position corresponds to the midpoint of the considered electrode array.

**Figure 3.**Apparent resistivity anomaly ${\rho}_{a}^{\ast}$ (in %) as a function of horizontal position for a single, 1-mm-aperture fracture having length $\ell =5$ m, electrical resistivity ${\rho}_{f}=10$ $\mathsf{\Omega}\xb7$m, and hosted in bedrock having resistivity ${\rho}_{b}=10,000$ $\mathsf{\Omega}\xb7$m. The fracture is covered by a 1 m thick layer of overburden, having resistivity ${\rho}_{o}=1000$ $\mathsf{\Omega}\xb7$m. Anomalies for fracture angles of ${10}^{\circ}$, ${45}^{\circ}$, and ${80}^{\circ}$ are shown, corresponding to Cases 1, 2, and 3 from Table 1, respectively. Measurement configurations are denoted by WS (Wenner-Schlumberger) or DD (dipole-dipole) followed by the spacing factor ($n=1,2,3$).

**Figure 4.**Apparent resistivity anomaly ${\rho}_{a}^{\ast}$ (in %) as a function of horizontal position for a single, 1-mm-aperture fracture having length $\ell =10$ m, electrical resistivity ${\rho}_{f}=10$ $\mathsf{\Omega}\xb7$m, and hosted in bedrock having resistivity ${\rho}_{b}=10,000$ $\mathsf{\Omega}\xb7$m. The fracture is covered by a 1 m thick layer of overburden, having resistivity ${\rho}_{o}=1000$ $\mathsf{\Omega}\xb7$m. Anomalies for fracture angles of ${10}^{\circ}$, ${45}^{\circ}$, and ${80}^{\circ}$ are shown, corresponding to Cases 4, 5, and 6 from Table 1, respectively. Measurement configurations are denoted by WS (Wenner-Schlumberger) or DD (dipole-dipole) followed by the spacing factor ($n=1,2,3$).

**Figure 5.**Apparent resistivity anomaly magnitude and width as a function of overburden thickness for the case of a single, 1-mm-aperture fracture having length $\ell =5$ m, electrical resistivity ${\rho}_{f}=10$ $\mathsf{\Omega}\xb7$m, and dipping at ${45}^{\circ}$. The fracture is hosted in bedrock having resistivity ${\rho}_{b}=10,000$ $\mathsf{\Omega}\xb7$m, whereas the overburden resistivity is ${\rho}_{o}=1000$ $\mathsf{\Omega}\xb7$m. The measurement configuration is denoted by WS (Wenner-Schlumberger) or DD (dipole-dipole) with spacing factor n. Cases 2, 7, 8, and 9 from Table 1 are considered.

**Figure 6.**Apparent resistivity anomaly magnitude and width as a function of overburden resistivity for the case of a single, 1-mm-aperture fracture having length $\ell =5$ m, electrical resistivity ${\rho}_{f}=10$ $\mathsf{\Omega}\xb7$m, and dipping at ${45}^{\circ}$. The fracture is hosted in bedrock having resistivity ${\rho}_{b}\phantom{\rule{3.33333pt}{0ex}}=\phantom{\rule{3.33333pt}{0ex}}10,000$ $\mathsf{\Omega}\xb7$m. The overburden thickness is 1 m. The measurement configuration is denoted by WS (Wenner-Schlumberger) or DD (dipole-dipole) with spacing factor n. Cases 2, 10, and 11 from Table 1 are considered.

**Figure 7.**Apparent resistivity anomaly magnitude and width as a function of fracture aperture for the case of a single fracture having length $\ell =5$ m, electrical resistivity ${\rho}_{f}=10$ $\mathsf{\Omega}\xb7$m, and dipping at ${45}^{\circ}$. The fracture is hosted in bedrock having resistivity ${\rho}_{b}=10,000$ $\mathsf{\Omega}\xb7$m, whereas the overburden resistivity is ${\rho}_{o}=1000$ $\mathsf{\Omega}\xb7$m. The overburden thickness is 1 m. The measurement configuration is denoted by WS (Wenner-Schlumberger) or DD (dipole-dipole) with spacing factor n. Cases 2, 12, 13, and 14 from Table 1 are considered.

**Figure 8.**Apparent resistivity anomaly magnitude and width as a function of fracture resistivity for the case of a single, 1-mm-aperture fracture having length $\ell =5$ m and dipping at ${45}^{\circ}$. The fracture is hosted in bedrock having electrical resistivity ${\rho}_{b}=10,000$ $\mathsf{\Omega}\xb7$m, whereas the overburden resistivity is ${\rho}_{o}=1000$ $\mathsf{\Omega}\xb7$m. The overburden thickness is 1 m. The measurement configuration is denoted by WS (Wenner-Schlumberger) or DD (dipole-dipole) with spacing factor n. Cases 2, 15, and 16 from Table 1 are considered.

**Table 1.**Parameter values corresponding to the 16 test cases considered in our analysis. For a description of the variables, see Figure 1.

Cases | ${\mathit{\rho}}_{\mathit{b}}$ [$\mathsf{\Omega}\xb7$m] | ${\mathit{\rho}}_{\mathit{f}}$ [$\mathsf{\Omega}\xb7$m] | ${\mathit{\rho}}_{\mathit{o}}$ [$\mathsf{\Omega}\xb7$m] | d [m] | $\mathit{\alpha}$ [${}^{\circ}$] | b [mm] | ℓ [m] |
---|---|---|---|---|---|---|---|

1, 2, 3 | 10,000 | 10 | 1000 | 1 | 10, 45, 80 | 1 | 5 |

4, 5, 6 | 10,000 | 10 | 1000 | 1 | 10, 45, 80 | 1 | 10 |

7, 8, 9 | 10,000 | 10 | 1000 | 0.5, 1.5, 2 | 45 | 1 | 5 |

10, 11 | 10,000 | 10 | 100, 10,000 | 1 | 45 | 1 | 5 |

12, 13, 14 | 10,000 | 10 | 1000 | 1 | 45 | 2, 3, 4 | 5 |

15, 16 | 10,000 | 1, 100 | 1000 | 1 | 45 | 1 | 5 |

**Table 2.**Apparent resistivity anomaly magnitudes (in %) for the test cases described in Table 1. Measurement configurations are denoted by WS (Wenner-Schlumberger) or DD (dipole-dipole) followed by the spacing factor ($n=1,2,3$). Values greater than 2.0% are in bold. See Figure 2 for how these values are determined.

Case | WS-1 | WS-2 | WS-3 | DD-1 | DD-2 | DD-3 |
---|---|---|---|---|---|---|

1 | 3.3 | 4.2 | 4.8 | 5.0 | 5.6 | 6.0 |

2 | 1.4 | 1.7 | 1.8 | 3.3 | 4.5 | 4.7 |

3 | 1.0 | 1.2 | 1.2 | 3.4 | 4.5 | 4.6 |

4 | 3.6 | 4.5 | 4.4 | 5.0 | 7.4 | 7.8 |

5 | 1.4 | 1.8 | 1.9 | 3.3 | 4.7 | 5.0 |

6 | 1.1 | 1.3 | 1.3 | 3.5 | 4.8 | 5.0 |

7 | 2.6 | 3.0 | 3.4 | 6.5 | 7.9 | 8.2 |

8 | 0.8 | 1.1 | 1.2 | 1.7 | 2.9 | 3.2 |

9 | 0.5 | 0.8 | 0.9 | 0.9 | 2.0 | 2.4 |

10 | 0.2 | 0.2 | 0.2 | 0.4 | 0.6 | 0.7 |

11 | 4.5 | 6.0 | 7.1 | 9.2 | 13.2 | 14.4 |

12 | 2.2 | 2.7 | 2.9 | 5.2 | 7.5 | 8.1 |

13 | 2.7 | 3.4 | 3.6 | 6.6 | 9.8 | 10.7 |

14 | 3.1 | 4.0 | 4.2 | 7.7 | 11.7 | 12.8 |

15 | 4.5 | 6.1 | 6.3 | 11.4 | 18.7 | 21.0 |

16 | 0.3 | 0.4 | 0.5 | 0.5 | 0.7 | 0.7 |

Case | WS-1 | WS-2 | WS-3 | DD-1 | DD-2 | DD-3 |
---|---|---|---|---|---|---|

1 | 15.8 | 20.8 | 24.7 | 14.9 | 19.1 | 21.7 |

2 | 17.0 | 22.4 | 26.8 | 13.9 | 17.0 | 19.6 |

3 | 17.8 | 23.4 | 27.1 | 13.4 | 16.7 | 19.6 |

4 | 19.6 | 25.3 | 29.1 | 13.6 | 18.2 | 21.1 |

5 | 19.2 | 25.2 | 29.2 | 15.7 | 19.0 | 21.7 |

6 | 19.4 | 25.5 | 28.8 | 14.4 | 17.9 | 21.0 |

7 | 15.5 | 21.0 | 25.3 | 12.0 | 15.4 | 17.9 |

8 | 18.4 | 23.5 | 27.3 | 15.7 | 18.0 | 20.6 |

9 | 19.8 | 24.3 | 27.8 | 17.5 | 19.2 | 21.9 |

10 | 19.0 | 26.0 | 28.5 | 16.1 | 19.7 | 22.6 |

11 | 13.7 | 19.3 | 23.4 | 7.8 | 11.4 | 14.5 |

12 | 17.4 | 22.8 | 27.0 | 14.1 | 17.1 | 19.5 |

13 | 17.8 | 23.1 | 27.2 | 14.5 | 17.3 | 19.6 |

14 | 18.1 | 23.4 | 27.4 | 14.8 | 17.6 | 19.8 |

15 | 19.1 | 24.2 | 28.1 | 15.6 | 18.0 | 20.4 |

16 | 16.4 | 21.3 | 25.8 | 14.5 | 18.2 | 21.0 |

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**MDPI and ACS Style**

Demirel, S.; Roubinet, D.; Irving, J.; Voytek, E.
Characterizing Near-Surface Fractured-Rock Aquifers: Insights Provided by the Numerical Analysis of Electrical Resistivity Experiments. *Water* **2018**, *10*, 1117.
https://doi.org/10.3390/w10091117

**AMA Style**

Demirel S, Roubinet D, Irving J, Voytek E.
Characterizing Near-Surface Fractured-Rock Aquifers: Insights Provided by the Numerical Analysis of Electrical Resistivity Experiments. *Water*. 2018; 10(9):1117.
https://doi.org/10.3390/w10091117

**Chicago/Turabian Style**

Demirel, Serdar, Delphine Roubinet, James Irving, and Emily Voytek.
2018. "Characterizing Near-Surface Fractured-Rock Aquifers: Insights Provided by the Numerical Analysis of Electrical Resistivity Experiments" *Water* 10, no. 9: 1117.
https://doi.org/10.3390/w10091117