# Analysis of Primary Field Shielding Stability for the Weak Coupling Coil Designs

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## Abstract

**:**

## 1. Introduction

## 2. The Primary Field Shielding Leakage

_{1}coil), while the other, having a larger radius, is called the outer receiver coil (RX

_{2}coil). The RX

_{2}coil is in the form of an uneven double “C” connection. These RX coils have the same winding directions. The output of the RX

_{1}coil is connected in series with the input of the RX

_{2}coil. Since the receiver coils RX

_{1}and RX

_{2}are connected across the TX coil, this structure is called the cross-loop design. In this study, the radius of a 10 turn TX coil was set as ${r}_{T}=0.6\text{}\mathrm{m}$, the RX

_{1}coil had ${r}_{1}=0.3\text{}\mathrm{m}$ and 45 turns, while the RX

_{2}coil had ${r}_{2}=0.65\text{}\mathrm{m}$, ${r}_{3}=0.7\text{}\mathrm{m}$, and 33 turns.

_{2}and RX

_{1}coils of the cross-loop design were vertically or horizontally offset by 1 mm, the corresponding ${u}_{P}\left(t-{t}_{1}\right)$ is shown by the red dotted line and the yellow dotted line in Figure 4, respectively.

_{2}coil was vertically offset by 1 mm, the leaked primary field response ${u}_{P}(t<8\text{}\mathsf{\mu}\mathrm{s})\gg {u}_{f}(t8\text{}\mathsf{\mu}\mathrm{s})$. Especially, in the range of $t\le 2.4\text{}\mathsf{\mu}\mathrm{s}$, the magnitude of ${u}_{P}$ was at least 52 times that of the feature signal ${u}_{f}$. Although the leakage of the primary field response was much weaker than that of the non-weak coupling coil design, e.g., the central-loop device, the randomness of its magnitude and polarity still had an unrecoverable impact on the TEM detection data [7]. As an example, Figure 5 reveals that when the RX

_{2}coil exhibited a 5 mm vertical offset, the primary field shielding leakage would lead to as high as 30% apparent resistivity calculation error for a 100 $\Omega \mathrm{m}$ uniform half-space. Therefore, it was necessary to analyze the primary field shielding stability of the weak coupling coil designs.

## 3. Shielding Stability to the Primary Field

#### 3.1. Vertical Stability Coefficient ${\alpha}_{V}$

_{1}was ${r}_{1}=0.3\text{}\mathrm{m}$ and d = +150 mm, the vertical stability test result of the RX

_{1}coil was as shown in Figure 7, in which the output voltage signal of the RX coil corresponding to d = +150 mm is marked by the solid blue line, and the voltage peak during on-time is ${U}_{p}=-1.569\text{}\mathrm{V}$. When d = +151 mm and d = +149 mm, the corresponding output voltage waveform is shown by the red dotted line and the yellow dotted line, and its corresponding voltage peak is ${U}_{p+}=-1.723\text{}\mathrm{V}$ and ${U}_{p-}=-1.416\text{}\mathrm{V}$, respectively. According to Equation (4), the vertical stability coefficient was ${\alpha}_{V}=90.19$%, that is, while RX

_{1}was shifted by 1 mm in the z-axis direction, the output peak voltage was shifted by 9.81% from the zero coupling status.

_{2}located in the z = 0 plane had a vertical stability coefficient ${\alpha}_{V}$ = 98.42% for a 1 mm offset.

_{1}and RX

_{2}coils and the parameter d is shown in Table 1 and Table 2, respectively. It can be seen that the ${\alpha}_{V}$ of the RX

_{1}coil decreased with the increase of d, while the ${\alpha}_{V}$ of the RX

_{2}coil was almost stable at 98.4%. It can be seen from Table 1 and Table 2 that a smaller d value could effectively improve the vertical structural stability of the RX

_{1}coil.

#### 3.2. Horizontal Stability Coefficient ${\alpha}_{H}$

_{1}coil as d = 150 mm as an example, when the RX

_{1}coil was coaxial with the TX coil, the voltage peak ${U}_{p}=-1.569\text{}\mathrm{V}$. When the axis of the RX

_{1}coil was offset by 5 mm from the TX coil, the voltage peak became ${U}_{p+}=-1.567\text{}\mathrm{V}$. According to Equation (4), the horizontal stability of the RX

_{1}coil was ${\alpha}_{H}$ = 99.81%. When the axis of the RX

_{2}coil was offset by 5 mm, the corresponding ${U}_{p+}=-1.873\text{}\mathrm{V}$, so the horizontal stability of the RX

_{2}coil was ${\alpha}_{H}$ = 80.66%.

_{1}and RX

_{2}coils and the parameter d is shown in Table 3 and Table 4, respectively. It can be seen that the ${\alpha}_{H}$ of the RX

_{1}coil increased slightly with the increase of d, so selecting a larger d value could slightly improve the horizontal stability of the RX

_{1}coil. The RX

_{2}coil was relatively close to the TX coil, and its horizontal stability ${\alpha}_{H}$ was almost stable at 81%.

## 4. Shielding Stability Comparison

#### 4.1. The Gradient Design

#### 4.2. The Opposing Design

#### 4.3. The Bucking Design

#### 4.4. The Eccentric-Coils

_{2}coil. Therefore, any RX coils of the weak coupling coil designs should be routed away from the strong primary field.

## 5. Experiment

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Schematic diagram of the transient electromagnetic response signal. ${i}_{T}\left(t\right)$ is the emission current in the TX coil; the secondary field excited by the underground anomalies is mixed with the primary field excited by the emission current in the TX coil and therefore expands the dynamic range of the signal.

**Figure 2.**Schematic diagram of five multi-coil designs. (

**a**) The eccentric coils. (

**b**) The gradient design. (

**c**) The opposing design. (

**d**) The bucking design. (

**e**) The cross-loop design.

**Figure 3.**A simulation model for a resistivity anomaly. The terminal of each coil design is placed on the ground. A conductive cube is placed at $h=10\text{}\mathrm{m}$ below the surface in a uniform half-space with resistivity ${\rho}_{2}=100\text{}\Omega \mathrm{m}$. The resistivity of the cube can be either ${\rho}_{1}=100\text{}\Omega \mathrm{m}$ or ${\rho}_{1}\ne 100\text{}\Omega \mathrm{m}$.

**Figure 4.**A comparison of the leaked primary field response ${u}_{p}$ with the effective detection signal ${u}_{f}$. The change of ${u}_{f}$ caused by a ${\rho}_{1}=1\text{}\Omega \mathrm{m}$ cube is shown by the black solid line, and the leaked primary field response corresponding to the theoretical zero coupling state and in the case of 1 mm vertical or horizontal offset of the RX coil are respectively plotted by the blue dotted line, the red dotted line, and the yellow dotted line.

**Figure 5.**Calculation error of uniform half-space apparent resistivity caused by primary field leakage. When the RX

_{2}coil is in the zero coupling position, the apparent resistivity detection result of the TEM device on the 100 $\Omega \mathrm{m}$ uniform half-space is shown by the blue dotted line, and when the RX

_{2}coil exhibits a 5 mm vertical offset, the primary field shielding leakage will lead to as high as 30% apparent resistivity calculation error, shown by the solid red line.

**Figure 6.**Response model based on a conductive loop. The TX coil is arranged in the z = 0 plane, and a conductive ring used as the secondary field source is coaxially placed in the z = −h plane below the TX coil.

**Figure 7.**Detected signal versus time for three different d values. The output voltage signals of the RX coil corresponding to d = 150 mm, d = 151 mm, and d = 149 mm are respectively plotted by the solid blue line, the red dotted line, and the yellow dotted line, with the peak voltages ${U}_{p}=-1.569\text{}\mathrm{V}$, ${U}_{p+}=-1.723\text{}\mathrm{V}$, and ${U}_{p-}=-1.416\text{}\mathrm{V}$, respectively.

**Figure 8.**Comparison of the stability coefficients of five weak coupling coils. The horizontal stability coefficient ${\alpha}_{H}$ is displayed as a blue histogram, and the vertical stability coefficient ${\alpha}_{V}$ is displayed as an orange histogram. The best performance for the horizontal stability is the opposite design, and the bucking design is relatively disappointing; while the cross-loop design gas the best vertical stability, and the opposite design performs the worst in this respect.

**Figure 9.**A cross-sectional view of the water dissolving cave distribution. (

**a**) The exploration borehole data. (

**b**) The survey result of the electromagnetic wave CT, in which the red color region represents the low resistance body and the blue color region the high resistance body.

**Figure 11.**Apparent resistivity imaging of the water dissolving caves by the cross-loop design. The shape and location of the low resistance water dissolving caves are accurately displayed.

d (mm) | 0 | 50 | 100 | 150 | 200 |
---|---|---|---|---|---|

${\alpha}_{V}$ | 99.86% | 96.26% | 92.71% | 90.19% | 87.94% |

d (mm) | 0 | 50 | 100 | 150 | 200 |
---|---|---|---|---|---|

${\alpha}_{V}$ | 98.51% | 98.6% | 98.37% | 98.42% | 98.6% |

d (mm) | 0 | 50 | 100 | 150 | 200 |
---|---|---|---|---|---|

${\alpha}_{H}$ | 99.56% | 99.57% | 99.67% | 99.81% | 99.95% |

d (mm) | 0 | 50 | 100 | 150 | 200 |
---|---|---|---|---|---|

${\alpha}_{H}$ | 81.81% | 80.4% | 80.65% | 80.66% | 80.46% |

Parameter | Gradient Design | Opposing Design | Bucking Design | Eccentric-Coils | Cross-Loop Design |
---|---|---|---|---|---|

${I}_{TX}$ (A) | 10 | 10 | 10 | 10 | 10 |

${T}_{off}\text{}\left(\mathsf{\mu}\mathrm{s}\right)$ | 14 | 14 | 14 | 14 | 14 |

d (m) | 0.15 | 0.15 | 0 | 0.15 | 0 |

${r}_{TX}$ (m) | 0.6 | 0.6 | 0.6 | 0.6 | 0.6 |

${r}_{RX}$ (m) | 0.25 | 0.25 | 0.25 | 0.25 | RX_{1}: 0.3RX _{2}: 0.65, 0.7 |

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**MDPI and ACS Style**

Huang, J.; Wang, H.; Fu, Z.; Fu, W. Analysis of Primary Field Shielding Stability for the Weak Coupling Coil Designs. *Sensors* **2020**, *20*, 519.
https://doi.org/10.3390/s20020519

**AMA Style**

Huang J, Wang H, Fu Z, Fu W. Analysis of Primary Field Shielding Stability for the Weak Coupling Coil Designs. *Sensors*. 2020; 20(2):519.
https://doi.org/10.3390/s20020519

**Chicago/Turabian Style**

Huang, Jiangbo, Haowen Wang, Zhihong Fu, and Wei Fu. 2020. "Analysis of Primary Field Shielding Stability for the Weak Coupling Coil Designs" *Sensors* 20, no. 2: 519.
https://doi.org/10.3390/s20020519