# Optimizing Semi-Airborne Electromagnetic Survey Design for Mineral Exploration

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Methodology

#### 2.1. Scheme

#### 2.2. Forward Problem and Inversion

_{e}is the source-current density. The custEM implements a finite-element discretization on unstructured meshes and Nédélec basis functions in collaboration with the direct solver MUMPS. The time-harmonic curl-curl equation was used for the electric field with the common quasi-static approximation for the frequency range of CSEM methods reads. Finally, we solved a linear system of equations AE = b for each frequency and calculated the magnetic field using Equation (2) [26,27].

_{d}is the error-weighting matrix with inverse errors, and W

_{m}is the smoothness operator. The inverse solver also involves the model and data transformations, whose inner derivatives are used to scale the model, data, and the Jacobian matrix. We use a two-sided logarithmic transformation [31] to constrain the resistivity between ${\rho}_{a}=1$ and ${\rho}_{b}=\mathrm{10,000}$ Ωm (Equation (4)).

#### 2.3. Synthetic Experiments

^{2}(3 km × 3.2 km).

## 3. Single- and Multi-Component Inversion

^{®}PowerEdge R940 server with four Intel

^{®}Xeon

^{®}2 Gold 6154 processors and 48 LRDIMM 64 GB, DDR4-2666 Quad Ranks with shared random access memory (RAM). Figure 2 shows the inversion results; Figure 2a–d represent the case of a single component inversion, and Figure 2a,b represent the x-component results, better describing the edges of the body in the x direction. The anomaly of the body was less inclined towards the transmitter, but on the other hand, the effect of the body reached the surface. In the same way, in Figure 2c,d (z-component result), the resistivity was more limited to the edges in the z direction but tended more towards the transmitter. We could recover the body properly with a lower resistivity resolution. Figure 2e,f show that, using multi-component inversion, the block edges were better recovered in all directions; moreover, the maximum resistivity values were higher. Another way to confirm our conclusion here was that all subfigures showed the minimum (min) and mean of the resistivity of cells located inside of the target. For example, by using only a single component, the X minimum of the resistivity was 76 Ωm and the mean of resistivity of the cells inside the body was 108 Ωm; in the case of multi-component inversion, these numbers dropped down to 27 and 66 Ωm and became closer to the synthetic model. Our results were in agreement with those of Ke et al. [21], who were studying multi-component inversion. As a result, all of the other modellings you will see hereafter are multi-component inversion results.

## 4. Survey Parameters

#### 4.1. Surveying Data Density

#### 4.2. Transmitter Length

#### 4.3. Transmitter Orientation with Respect to the Block

#### 4.4. Using More Than One Transmitter

#### 4.5. Transmitter Orientation with Respect to Each Other

#### 4.6. The Distance of the Transmitters from Each Other

#### 4.7. Anomalies under the Transmitter

## 5. Discussion

^{2}with high resolution (inside of the 2 × 2 transmitter square) and a total area of 84 km

^{2}(outside). The optional transmitters (green lines) will further improve the resolution, particularly in cases of unknown strike direction, and increase this area to 144 km

^{2}. It is worth noting that this scheme can be arbitrarily extended to larger survey areas by moving the transmitter combinations by increments of 3 km in all directions.

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Appendix A

**Figure A1.**Synthetic data of one flight line over a homogeneous half space at 300 Ωm. Frequency was 512 Hz. (

**a**) Data without noise; (

**b**) noisy data.

**Figure A2.**Sketch of the model using two transmitters perpendicular to each other. Red line is the Transmitter 1 and green line is Transmitter 2.

**Figure A3.**Sketch of the dipping plate using two transmitters perpendicular to each other. Plane views are 45 degrees in x–y plane. Red line is Transmitter 1 and green line is Transmitter 2.

**Figure A4.**Sketch of the model using two transmitter parallel to each other. Red line is Transmitter 1 and green line is Transmitter 2.

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**Figure 1.**Sketch of the 3D SAEM model. White points are receivers (50 m in the air); red line is the ground transmitter. Data points are removed within a distance of 400 m from the transmitter. The resistivities of the block and background were 1 and 300 m.

**Figure 2.**Cross-sections (y–z and x–z planes) of inversion results for different components: (

**a**,

**b**) x-component; (

**c**,

**d**) z-component; and (

**e**,

**f**) xyz (multi)-component. In all figures in this paper, when the transmitter was perpendicular to the plane, it is shown as a red circle, whereas it is shown as a red straight line when it was parallel to the plane. In the title, the minimum and mean resistivity values inside of the target dimensions (blue rectangles) are provided as a quantitative measure of resolution.

**Figure 3.**Inversion results for different measuring grid sizes: (

**a**,

**b**) 100 m × 100 m; (

**c**,

**d**) 200 m × 100 m; (

**e,f**) 200 m × 200 m. Blue dots are receiver positions.

**Figure 4.**Inversion results for different transmitter lengths: (

**a**,

**b**) 1 km; (

**c**,

**d**) 2 km; (

**e**,

**f**) 3 km. The conductive body is located: (

**a**,

**c**,

**e**) 1 km from the transmitter; (

**b**,

**d**,

**f**) 2 km from the transmitter.

**Figure 5.**Inversion results for different transmitter lengths ((

**a**) 1 km, (

**b**) 2 km, (

**c**) 3 km, (

**d**) 4 km), in this case, the conductive body was located 3 km away from the transmitter.

**Figure 6.**Inversion results of transmitter at different distances of (

**a,b**) 1 km away from the center of the conductive body; and (

**c,d**) 2 km away from the center of the conductive body. Transmitter was perpendicular to the general strike of the body.

**Figure 7.**Inversion result for using single and double transmitters, the first transmitter (Tx1) is displayed in red and the second transmitter (Tx2) is displayed in green. Inversion results of (

**a**) two conductive bodies and one transmitter; and (

**b**) two conductive bodies and two transmitters on both sides.

**Figure 8.**Inversion results of using two transmitters perpendicular to each other. Cross-sections (

**a**) y–z plane and (

**b**) x–z plane of inversion results.

**Figure 9.**Inversion results of using two transmitters perpendicular to each other; in this case, the conductive body is a dipping plate. Cross-sections (

**a**) front view and (

**b**) side view of inversion results. For a better understanding of the plane views, please refer to the Appendix A, Figure A3.

**Figure 10.**Inversion results for a body located at different depths: (

**a**–

**c**) 150 m; (

**d**–

**f**) 300 m; and (

**g**–

**i**) 500 m from the surface, and for different transmitter distances: (

**a**,

**d**,

**g**) 2 km; (

**b**,

**e**,

**h**) 3 km; and (

**c**,

**f**,

**i**) 4 km.

**Figure 11.**Inversion results using a body located under the transmitter and different depths below the surface: (

**a**,

**b**) 150 m; (

**c**,

**d**) 300 m; and (

**e**,

**f**) 500 m.

**Figure 12.**Inversion results using a body located under two transmitter and different depths of (

**a**,

**b**) 150 m; (

**c**,

**d**) 300 m; and (

**e**,

**f**). 500 m. In this case, the body was located exactly under the transmitter, Tx1, and 2 km away from transmitter, Tx2.

**Figure 13.**Recommended optimized survey layout (to be adapted to field conditions). The length of all transmitters and spacing between parallel transmitters was 3 km, using common groundings that reduced logistic effort. Three of the overlapping flight patches are given as examples (each covering an area of 24 km

^{2}): (

**A**) over the lower-left Tx (dashed blue), (

**B**) over the lower-right Tx (solid blue), and (

**C**) over the optional Tx (dashed green).

Grid Size (m) | Number of Data Points | Runtime (h) |
---|---|---|

100 × 100 | 1023 | 19 |

200 × 100 | 528 | 6 |

200 × 200 | 272 | 3 |

**Table 2.**Numerical analyses of results for different parameters: the minimum (min) and mean resistivity value inside of the target dimensions is provided as a quantitative measure of resolution. Recommended values of parameters are highlighted.

Figures | Parameter | Mean Cells (Ωm) | Min Cells (Ωm) | Anomaly Gain (%) |
---|---|---|---|---|

3. Single and multi-component inversion | ||||

Figure 2a,b | X | 108 | 76 | 24 |

Y | 167 | 125 | 15 | |

Figure 2c,d | Z | 112 | 72 | 25 |

Figure 2e,f | XYZ | 66 | 27 | 42 |

4.1. Surveying data density | ||||

Figure 3a,b | 100 × 100 m | 44 | 15 | 53 |

Figure 3c,d | 200 × 100 m | 66 | 27 | 42 |

Figure 3e,f | 200 × 200 m | 89 | 52 | 31 |

4.2. Transmitter length | ||||

Figure 4a | 1KmTx1kmfromblock | 40 | 11 | 58 |

Figure 4c | 2KmTx1kmfromblock | 35 | 10 | 60 |

Figure 4e | 3KmTx1kmfromblock | 34 | 7 | 66 |

Figure 4b | 1KmTx2kmfromblock | 112 | 71 | 25 |

Figure 4d | 2KmTx2kmfromblock | 68 | 22 | 46 |

Figure 4f | 3KmTx2kmfromblock | 60 | 19 | 48 |

Figure 5a | 1KmTx3kmfromblock | 245 | 192 | 8 |

Figure 5b | 2KmTx3kmfromblock | 191 | 157 | 11 |

Figure 5c | 3KmTx3kmfromblock | 111 | 68 | 26 |

Figure 5d | 4KmTx3kmfromblock | 99 | 50 | 31 |

4.6. The distance of the transmitters from each other | ||||

Figure 10a | 150mDepth2kmTx | 40 | 11 | 58 |

Figure 10b | 150mDepth3kmTx | 80 | 36 | 37 |

Figure 10c | 150mDepth4kmTx | 134 | 72 | 25 |

Figure 10d | 300mDepth2kmTx | 71 | 36 | 37 |

Figure 10e | 300mDepth3kmTx | 126 | 91 | 21 |

Figure 10f | 300mDepth4kmTx | 192 | 142 | 13 |

Figure 10g | 500mDepth2kmTx | 149 | 121 | 16 |

Figure 10h | 500mDepth3kmTx | 204 | 151 | 12 |

Figure 10i | 500mDepth4kmTx | 255 | 152 | 12 |

4.7. Anomalies under the transmitter | ||||

Figure 11a,b | Under1Tx150mDepth | 34 | 4 | 76 |

Figure 11c,d | Under1Tx300mDepth | 80 | 41 | 35 |

Figure 11e,f | Under1Tx500mDepth | 213 | 188 | 8 |

Figure 12a,b | Under2Tx150mDepth | 36 | 5 | 72 |

Figure 12c,d | Under2Tx300mDepth | 75 | 42 | 34 |

Figure 12e,f | Under2Tx500mDepth | 161 | 140 | 13 |

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**MDPI and ACS Style**

Nazari, S.; Rochlitz, R.; Günther, T.
Optimizing Semi-Airborne Electromagnetic Survey Design for Mineral Exploration. *Minerals* **2023**, *13*, 796.
https://doi.org/10.3390/min13060796

**AMA Style**

Nazari S, Rochlitz R, Günther T.
Optimizing Semi-Airborne Electromagnetic Survey Design for Mineral Exploration. *Minerals*. 2023; 13(6):796.
https://doi.org/10.3390/min13060796

**Chicago/Turabian Style**

Nazari, Saeed, Raphael Rochlitz, and Thomas Günther.
2023. "Optimizing Semi-Airborne Electromagnetic Survey Design for Mineral Exploration" *Minerals* 13, no. 6: 796.
https://doi.org/10.3390/min13060796