# The Potential of the Horizontal Component TEM Data in the Detection of Polarizable Mineral: Synthetic Cases

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

_{0}describes the DC resistivity of the earth, and m

_{0}is the chargeability, which describes the degree of charge accumulation of the earth. τ

_{ρ}is the relaxation time, which describes the time required for charge accumulation to reach equilibrium; c is the frequency exponent, which describes the broadness of the relaxation time distribution; τ

_{ρ}and c define the rate of charge accumulation, but the impact of c is smaller compared with τ

_{ρ}. Determined by these parameters, the IP effect manifests sign reversals in the TEM data. Many researchers have theoretically studied the vertical component under the ungrounded-TEM system and found m

_{0}, τ

_{ρ}, and c greatly affect the occurrence time of sign reversal (Time of SR) and the maximum amplitude of negative responses (max of NR) [25]. In theory, when m

_{0}is larger, τ

_{ρ}is smaller and c is around 0.5, which means the medium has a strong ability to accumulate electric charges and a faster rate of charge accumulation; therefore, the Time of SR occurs earlier and the amplitudes of NR are larger [26]. Several locations where IP effects are reported and recorded demonstrated that the range of each parameter varies hugely. Some minerals present strong IP effects, such as disseminated sulfide, clay layers, and shallow frozen rocks [27], that are likely to present the IP features apparently. Conversely, some mediums with relatively weak IP effects (m

_{0}is below 0.1) usually cause the EM data not to show the IP features [28]. Once the IP information is missing, it will be tough to recover the parameters accurately, especially for the weak IP effects [29].

## 2. Methods

#### 2.1. The tTEM System and Noise Level

^{2}

_{uni}represents the uniform noise, and V

_{noise}represents the background noise contribution. STD, the uniform standard, is set to 3% for dB/dt responses typically, which accounts for the instrument and other non-specified noise contributions. The background noise that decreases with t

^{−1/2}in transients is given by,

^{2}and b = 1.6 nV/m

^{2}at 1 ms for z and x components, respectively.

#### 2.2. Forward Modeling Process

_{max}represents the maximum phase angle of the Cole–Cole model and τ

_{φ}is the inverse of the frequency at which φ

_{max}is reached. The relaxation time τ

_{φ}is linked to τ

_{ρ}though m

_{0}and c, as follows: ${\tau}_{\phi}={\tau}_{\rho}(1-{m}_{0}{)}^{1/2c}$.

_{z}/dt) and horizontal fields (dB

_{x}/dt) of 1D layered models with or without the IP effects. To analyze the behavior of different EM components, we compared the negative value and slope of TEM responses and quantified the influence of the IP effects on the EM data by calculating the direct impact ratio [29]:

_{IP}represents the EM data with the IP effects (IP responses), and M

_{non-IP}represents the EM data without the IP effects (non-IP responses). If the ratio is around 1, the difference between IP responses and non-IP responses is little and, thus, the response is barely affected by the IP effects. If sign reversal appears, the value will drop to negative values. Figure 2 shows an example of the IP responses of a three-layer chargeable model.

#### 2.3. 1D Laterally Constrained Inversion Scheme

**d**

_{obs}denotes the observed data,

**e**

_{obs}denotes the error on the observed data and

**g**is the forward mapping. The Jacobian matrix

**G**contains the partial derivative of the forward mapping with respect to the model parameters. The previous method introduced a single vertical component to the Jacobian matrix

**G**; however, we have made a little improvement on the basis of previous work by introducing both vertical and horizontal components into

**G**for the joint inversion. Equation (8) also can be written as

**d**

_{obs}represents the differences between observed data and forward data. The covariance matrix for the observation errors

**C**

_{obs}can be calculated by

**d**

_{obs}and

**g**(

**m**

_{ref}).

**e**

_{r}is the errors on the constraints between adjacent points with 0 as the expected value; δ

**r**= −

**Rm**

_{ref}provides the identity between the parameters tied by constraints in the roughening matrix

**R**, containing 1 and −1 for the constrained parameters, 0 in all other places. The variance, or strength of the constraints, is described in the covariance matrix

**C**

_{R}. Practical experiments showed that constraint values between 1.1 and 1.3 were good starting options. Roughly speaking, a constraint value of 1.1 meant those model parameters were allowed to vary by 10% between neighboring models. Thus, if we combine Equations (9) and (10), we can find

**C**′ that contains

**C**

_{obs}and

**C**

_{R}is written as:

**d**′ contains δ

**d**

_{obs}and δ

**r**, while N

_{d}, N

_{m}, and N

_{r}represent the number of data points, model parameters, and constraints. The data misfit χ can be calculated by

_{z}/dt and dB

_{x}/dt, calculated δ

**d**′ covariance matrix

**C**′ to obtain Q*, and updated the estimated model finally.

#### 2.4. The Synthetic Models and Sounding Layout

_{0}was the largest and τ was the smallest for the strong chargeable medium, while m

_{0}was the smallest and τ was the largest for the subtle chargeable medium. The parameters in the moderate chargeable medium were at the middle level.

## 3. Results and Discussion

#### 3.1. Comparison of between Horizontal and Vertical Components of Forward Modeling

#### 3.1.1. Synthetic Model 1: Strong Chargeable Medium

^{2}(SNR = 40 dB), whereas that of the z-data is 0.025 µV/m

^{2}(SNR = 34 dB). The horizontal component shows the IP features more clearly.

_{IP}is larger than M

_{non-IP}; over time, ξ decreases to one, which means M

_{IP}≈ M

_{non-IP}. ξ then decreases to zero or even negative values, which means M

_{IP}is a negative value. The x component shows a wide range of ξ varying from 3 to −10 and the z component ranges from 3 to −3. The degree of polarization influence is proportional to the difference between ξ and 1. Hence, compared with the conventionally measured vertical component, the horizontal component is more susceptible to the IP effects and shows IP features more obviously.

#### 3.1.2. Synthetic Model 2: Moderate Chargeable Medium

#### 3.1.3. Synthetic Model 3: Subtle Chargeable Medium

#### 3.2. Resolution of x-Only, z-Only, and Joint Inversion

_{0}; (2) choosing a low or moderate value (10–30 mrad) as the starting φ

_{max}; (3) setting the starting value for c to 0.5, i.e., an intermediate value; (4) selecting a value in the interval 10 μs to 0.1 s for τ

_{φ}based on the appearance time of sign reversal. For the first two synthetic models, in which ρ

_{0}varies between 10 Ωm and 300 Ωm and φ

_{max}varies between 50 mrad and 100 mrad, τ

_{φ}= 0.1 ms and c = 0.5; thus, the starting model is ρ

_{0}= 100 Ωm, φ

_{max}= 30 mrad, c = 0.5, and τ

_{φ}= 0.1 ms due to the fact that the sign reversals have arisen early on. For the second model, in which ρ

_{0}varies between 30 Ωm and 100 Ωm and φ

_{max}varies between 10 mrad and 30 mrad, τ

_{φ}= 100 ms and c = 0.5 and the starting model is ρ

_{0}= 100 Ωm, φ

_{max}= 10 mrad, c = 0.5, and τ

_{φ}= 10 ms because the sign reversal appeared late. However, in some cases the resistivity of the starting model can be hard to retrieve automatically and has to be manually set. We also implemented a robust concept for the calculation of the depth of investigation (DOI) that is valid for any 1D EM geophysical model [46]. The DOI is crucial for interpreting the geophysical models, as the validity of the model varies considerably with data noise and parameter distribution. Therefore, we plotted the inverted results together with DOI information. The DOI visualization was performed by lining the model with a low relative threshold value of 2% (deep).

#### 3.2.1. Synthetic Model 1: Strong Chargeable Medium

_{max}shows that the estimated values in the third layer are smaller than the true values. The residuals of z-data and joint inversions are lower than the residuals of x-data inversion. From Figure 9b, we learn that the magnitude of resistivity in the third layer is inaccurate, while the DOIs in φ

_{max}, τ

_{φ}, and c are the most shallow (almost 30 m). Comparing Figure 9c,d, we can see that although the residuals are very close (both are around one), the estimated values show differences. The results of φ

_{max}and ρ

_{0}in the joint inversion show the three-layered structure more clearly, while in the z-data inversion results the boundary between the first and second layers is blurred. It seems that joint inversion will improve the precision of the shallow layer.

#### 3.2.2. Synthetic Model 2: Moderate Chargeable Medium

_{max}of the shallow layer in the joint inversion is closer to the true model.

#### 3.2.3. Synthetic Model 3: Subtle Chargeable Medium

_{max}in Figure 15d shows differences compared to the background φ

_{max}. The estimated model of the most chargeable layer of the joint inversion is close to the true model, compared with the x-only and z-only inversion. The residuals of the MPA inversion are lower. For the subtle chargeable media, although resistivity inversion can achieve good fitting, we can still perform the MPA inversion by setting a lower value for chargeability, which is also effective in showing the chargeability.

#### 3.3. Discussion on the Recovering Capability of the Joint Inversion

_{0}is 100 Ωm, φ

_{max}is 10 mrad, τ is 100 ms, and c is 0.5. As the second layer was more chargeable and conductive, we set chargeability as 30, 50, 70, 100, 200, 300 mrad, respectively, while ρ

_{0}was 5 Ωm, τ was 100 ms, and c was 0.5. We performed forward modeling and inversion for each model and compared the resolution. The start values for each model used in the inversion process were the following: ρ0 was 100 Ωm, φ

_{max}was 10 mrad, τ was 100 ms, and c was 0.5.

_{max}of Model 1′ is 13 mrad, which is similar to the background value (10 mrad) due to the little polarization information contained. The estimated φ

_{max}of model 2′ begins to show changes compared to the background value, though the values (around 25 mrad) are lower than the true model. Nevertheless, this contrast reveals the subtle polarization medium. The results of Model 3′ (70 mrad) and 4′ (100 mrad) approach the true models’ values and show significant differences. In terms of 200 and 300 mrad, the estimated values are close to the true models. From the results, we concluded that the minimum chargeability that can be recovered by the joint inversion is roughly 30 to 50 mrad.

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 2.**IP responses for a three-layer model. (

**a**) The three-layer model. (

**b**) The time derivatives of the magnetic fields, where red curves represent dB

_{x}/dt with the errorbar, blue curves represent dB

_{z}/dt with the errorbar; and the negative values are marked with green circles or cyan circles, respectively. Moreover, the green and cyan lines show the noise levels: b takes 1.6 and 0.2 nV/m

^{2}at 1 ms for x and z components, respectively. The errorbars are connected with the noise model described in Equation (2).

**Figure 3.**Synthetic models and sounding points. For example, the blue boxes present model 1 and model 5.

**Figure 4.**Results of forward modeling for the strong chargeable medium: (

**a**) non-IP responses and (

**b**) IP responses, where red curves represent dB

_{x}/dt, blue curves represent dB

_{z}/dt (the color becomes darker from W to E), and negative values are marked with green circles or cyan circles, respectively. Moreover, the green and cyan lines show the noise levels for x- and z-components, respectively; (

**c**) ξ for the x- component; and (

**d**) ξ for the z-component, where the area under the red curve represents the data below the noise level.

**Figure 5.**Results of forward modeling for the moderate chargeable medium: (

**a**) non-IP responses and (

**b**) IP responses; (

**c**) ξ for the x-component; and (

**d**) ξ for the z-component. The meanings of the curves and area are the same as in Figure 4.

**Figure 6.**Results of forward modeling for the subtle chargeable medium: (

**a**) non-IP responses and (

**b**) IP responses; (

**c**) ξ of x-component; and (

**d**) ξ of z-component. The meanings of the curves and area are the same as in Figure 4.

**Figure 7.**Comparison between the true resistivity value (

**a**) and resistivity inversion results of the IP responses of the strong chargeable medium: by x-data only (

**b**); z-data only (

**c**); and x and z data (

**d**). White line shows the DOI curve and circles the areas of the models below the DOI, while red and blue curves represent the misfits of x data and z data.

**Figure 8.**Comparison between the true resistivity value (

**a**) and resistivity inversion results of the non-IP responses of the strong chargeable medium: by x-data only (

**b**); z-data only (

**c**); and x and z data (

**d**). The meanings of the curves and the area are the same as in Figure 7.

**Figure 9.**Comparison between the true model (

**a**) and estimated MPA parameters of the strong chargeable medium by x-data only (

**b**); z-data only (

**c**); and x and z data (

**d**). The meanings of the curves and the area are the same as in Figure 7.

**Figure 10.**Comparison between the true resistivity value (

**a**) and resistivity-inversion results of the IP responses of the moderate chargeable medium: by x-data only (

**b**); z-data only (

**c**); and x and z data (

**d**). The meanings of the curves and the area are the same as in Figure 7.

**Figure 11.**Comparison between the true resistivity value (

**a**) and resistivity-inversion results of the non-IP responses of the moderate chargeable medium: x-data only (

**b**); z-data only (

**c**); and x and z data (

**d**). The meanings of the curves and the area are the same as in Figure 7.

**Figure 12.**Comparison between the true model (

**a**) and estimated MPA parameters of the moderate chargeable medium: by x-data only (

**b**); z-data only (

**c**); and x and z data (

**d**). The meanings of the curves and the area are the same as in Figure 7.

**Figure 13.**Comparison between the true resistivity value (

**a**) and resistivity inversion results of the IP responses of the subtle chargeable medium: by x-data only (

**b**); z-data only (

**c**); and x and z data. (

**d**) The meanings of the curves and the area are the same as in Figure 7.

**Figure 14.**Comparison between the true resistivity value (

**a**) and resistivity inversion results of the non-IP responses of the subtle chargeable medium: by x-data only (

**b**); z-data only (

**c**); and x and z data (

**d**). The meanings of the curves and the area are the same as in Figure 7.

**Figure 15.**Comparison between the true model (

**a**) and estimated MPA parameters of the subtle chargeable medium by x-data only (

**b**); z-data only (

**c**); and x and z data (

**d**). The meanings of the curves and the area are the same as in Figure 7.

**Figure 16.**The recovering ability of the joint inversion for different chargeabilities: φ

_{max}takes 30, 50, 70, 100, 200, and 300 mrad, respectively.

MPA Parameters | Layer | ρ_{0} (Ωm) | φ_{max}(mrad) | τ_{φ} (ms) | c |
---|---|---|---|---|---|

Strong chargeable medium | 1 | 100 | 100 | 0.1 | 0.5 |

2 | 300 | 50 | 0.1 | 0.5 | |

3 | 50 | 300 | 0.1 | 0.5 | |

Moderate chargeable medium | 1 | 150 | 80 | 0.1 | 0.5 |

2 | 300 | 50 | 0.1 | 0.5 | |

3 | 10 | 100 | 0.1 | 0.5 | |

Subtle chargeable medium | 1 | 100 | 10 | 100 | 0.5 |

2 | 30 | 30 | 100 | 0.5 | |

3 | 100 | 10 | 100 | 0.5 |

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## Share and Cite

**MDPI and ACS Style**

Wu, Y.; Xie, H.; Ji, Y.; Zhao, P.; Wang, Y.
The Potential of the Horizontal Component TEM Data in the Detection of Polarizable Mineral: Synthetic Cases. *Minerals* **2023**, *13*, 523.
https://doi.org/10.3390/min13040523

**AMA Style**

Wu Y, Xie H, Ji Y, Zhao P, Wang Y.
The Potential of the Horizontal Component TEM Data in the Detection of Polarizable Mineral: Synthetic Cases. *Minerals*. 2023; 13(4):523.
https://doi.org/10.3390/min13040523

**Chicago/Turabian Style**

Wu, Yanqi, Huilin Xie, Yanju Ji, Peng Zhao, and Yuebing Wang.
2023. "The Potential of the Horizontal Component TEM Data in the Detection of Polarizable Mineral: Synthetic Cases" *Minerals* 13, no. 4: 523.
https://doi.org/10.3390/min13040523