# Joint MT and Gravity Inversion Using Structural Constraints: A Case Study from the Linjiang Copper Mining Area, Jilin, China

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Joint Inversion Methodology

_{1}defines the resistivity Jacobian matrix, which calculates the Jacobian matrix using reciprocity. A

_{2}defines the density Jacobian matrix. ${m}_{1\_0}$ and ${m}_{2\_0}$ are the initial models of resistivity and density, respectively.

## 3. Regularization Inversion Methodology

#### 3.1. L2 Norm Regularization

#### 3.2. L1 Norm Regularization

#### 3.3. Focusing Regularization

#### 3.4. Total Variation Regularization

#### 3.5. Elastic-Net Regularization

_{m}is replaced by diag(Z)·W

_{m}in all of the above equations.

## 4. Synthetic Example

#### 4.1. Comparison Regularization Methods

^{3}.

#### 4.2. Comparison Separate and Joint Inversion

^{3}.

#### 4.3. Noise Effect and Sensitivity Analysis of Elastic-Net Joint Inversion

^{3}. It was found that the model response datasets after adding noise in model 1 could still recover inversion results similar to the true model, as shown in Figure 9a1–h2. This shows that the inversion method has certain anti-noise ability and is suitable for field measurement data processing with high noise. Next, we performed an inversion sensitivity analysis. We reduced the size of the anomalous sources of the model (Figure 9a2,e2) and added 5%, 10%, and 20% random Gaussian nosie to the theoretical model response. The inversion results showed that when the anomalous sources shrank to 0.5 × 0.5 km

^{2}, the inversion method could still recover similar results to the true model. However, when the anomalous sources shrank to 0.2 × 0.2 km

^{2}(Figure 9a3,e3), we found that accurate inversion results might not be obtained with the increase of noise, mainly because the response amplitude of the model was smaller than the noise magnitude, especially the MT method. At this time, our inversion method may not have identified less than 0.2 × 0.2 km

^{2}anomalous sources, so when using this inversion for field data inversion, an anomalous source smaller than 0.2 × 0.2 km

^{2}needs to be interpreted with caution, as it may be a false anomaly. For anomalous sources above 0.2 × 0.2 km

^{2}, the inversion could be accurately identified and identified as a true anomalous source.

## 5. Field Example

#### 5.1. Geologic Background of the Survey Area

#### 5.2. Data Acquisition

#### 5.3. Inversion Models of CSAMT and Gravity Data

^{2.5}Ω·m, 0.0 kg/m

^{3}in rock formation. The models obtained from the separate inversion are shown in Figure 13. The RMS misfit values found after separate inversion were as follows: RMS

_{CSAMT}= 1.39 and RMS

_{GRV}= 0.45. The separate inversion models showed major structural differences, and an interpreter will be faced with difficulties in interpreting them.

_{CSAMT}= 1.39 and RMS

_{GRV}= 0.55. Figure 14 shows the joint inversion results obtained by the smooth regularization method. We found a structural similarity between the density and resistivity models in the results of the smooth joint inversion, which was due to the contribution of the cross-gradient constraints in the objective function. However, the inversion results were relatively smooth, and a large area of divergence was exposed below the anomalous bodies. It was difficult to depict the sharp boundaries of the subsurface geological contact. The corresponding RMS misfit for each data set after the elastic-net joint inversion did not increase significantly and the values attained were: RMS

_{CSAMT}= 1.42 and RMS

_{GRV}= 0.24. Figure 15 shows the joint inversion results obtained by the elastic-net regularization method. We found that the elastic-net joint inversion method could generate much greater detail and a sharper boundary as well as better depth resolution. Compared with the smooth joint inversion results, the large area divergence phenomenon under the anomalous bodies was eliminated, and the fine anomalous bodies boundary appeared in the smooth region. The elastic-net joint inversion method provided more detailed information about the structure of the sources for further analysis than the separate inversion and smooth joint inversion methods.

#### 5.4. Geological Interpretation of the Mining Area

_{1}–F

_{4}) below the survey line. Based on the above inference results, we finally obtained a comprehensive interpretation profile, as shown in Figure 17. The corresponding lithostratigraphic units in Figure 17 are shown in Table 4.

_{1}–F

_{2}), which verified the accuracy of the proposed algorithm. According to the comprehensive interpretation profile results and the deposit formation of the known mining area, we have speculated on the ore-forming target area of other segments. It was preliminarily predicted that the ore-forming target area would be mainly concentrated near the fault structure (F

_{3}–F

_{4}). The interlaminar fault zone is the center of the regional tectonic, magmatic activity, and later ore-forming hydrothermal activities. Prospecting work should pay attention to the mineralization clues of the contact sites between the Mesozoic intrusive rocks and the Precambrian shallow metamorphic strata, particularly the Yanshanian intermediate-acid granites. Mineralization and alteration should also be given sufficient attention, and silicidation and muddy mixtures that are easily overlooked may also have mineralization indication significance. In this paper, the elastic-net joint inversion method could accurately divide the stratum structure and fault zone, and had the ability to find the prospecting target area, which provides a powerful basis for the mining of the deposit.

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**MT separate inversion results obtained using different regularization methods. (

**a**) Resistivity true model; (

**b**) Resistivity inversion model using L2 regularization; (

**c**) Resistivity inversion model using L1 regularization; (

**d**) Resistivity inversion model using elastic-net regularization; (

**e**) Resistivity inversion model using TV regularization; (

**f**) Resistivity inversion model using focusing regularization. The black box indicates the boundary of the anomalous body.

**Figure 2.**Gravity separate inversion results obtained using different regularization methods. (

**a**) Density true model; (

**b**) Density inversion model using L2 regularization; (

**c**) Density inversion model using L1 regularization; (

**d**) Density inversion model using elastic-net regularization; (

**e**) Density inversion model using TV regularization; (

**f**) Density inversion model using focusing regularization. The black box indicates the boundary of the anomalous body.

**Figure 4.**The MT inversion results obtained using separate and joint inversion. (

**a**) Resistivity true model; (

**b**) Resistivity separate inversion model using L2 regularization; (

**c**) Resistivity separate inversion model using elastic-net regularization; (

**d**) Resistivity joint inversion model using L2 regularization; (

**e**) Resistivity joint inversion model using elastic-net regularization. The black box indicates the boundary of the anomalous body.

**Figure 5.**The gravity inversion results obtained using separate and joint inversion. (

**a**) Density true model; (

**b**) Density separate inversion model using L2 regularization; (

**c**) Density separate inversion model using elastic-net regularization; (

**d**) Density joint inversion model using L2 regularization; (

**e**) Density joint inversion model using elastic-net regularization. The black box indicates the boundary of the anomalous body.

**Figure 7.**The true model of MT and gravity methods. Model 1 (

**a**,

**b**); Model 2 (

**c**,

**d**); Model 3 (

**e**,

**f**); Resistivity models (

**a**,

**c**,

**e**) ; Density models (

**b**,

**d**,

**f**).

**Figure 8.**The model response results for three models of resistivity and density. The theoretical model responses of resistivity models obtained by TM mode (

**a1**–

**a3**); The theoretical model responses of density models (

**e1**–

**e3**); The resistivity model responses with 5% noise obtained by TM mode (

**b1**–

**b3**); The density model responses with 5% noise (

**f1**–

**f3**); The resistivity model responses with 10% noise obtained by TM mode (

**c1**–

**c3**); The density model responses with 5% noise. (

**g1**–

**g3**); The resistivity model responses with 20% noise obtained by TM mode (

**d1**–

**d3**); The density model responses with 20% noise (

**h1**–

**h3**).

**Figure 9.**The MT and gravity inversion results obtained using elastic-net joint inversion. Resistivity true model (

**a1**–

**a3**); Density true model (

**e1**–

**e3**); The MT inversion results with 5% noise (

**b1**–

**b3**); The gravity inversion results with 5% noise (

**f1**–

**f3**); The MT inversion results with 10% noise (

**c1**–

**c3**); The gravity inversion results with 10% noise (

**g1**–

**g3**); The MT inversion results with 20% noise (

**d1**–

**d3**); The gravity inversion results with 20% noise (

**h1**–

**h3**).

**Figure 12.**Observation data of the survey line: apparent resistivity in TM mode (

**a**) and residual anomaly (

**b**).

**Figure 14.**The results of joint inversion using smooth regularization: resistivity model (

**a**), residual density model (

**b**).

**Figure 15.**The results of joint inversion using elastic-net regularization: resistivity model (

**a**), residual density model (

**b**).

Unit | Resistivity Model | Residual Density Model |
---|---|---|

A | 1000 Ω·m | −1000 kg/m^{3} |

B | 10 Ω·m | 1000 kg/m^{3} |

C | 100 Ω·m | 0 kg/m^{3} |

Unit | Resistivity Model | Residual Density Model |
---|---|---|

A | 1000 Ω·m | 700 kg/m^{3} |

B | 10 Ω·m | 1000 kg/m^{3} |

C | 100 Ω·m | 0 kg/m^{3} |

Unit | Resistivity Model | Residual Density Model | Size | |
---|---|---|---|---|

A | 10 Ω·m | 1000 kg/m^{3} | 1 × 1 km^{2} | Model 1 |

B | 10 Ω·m | 1000 kg/m^{3} | 1 × 1 km^{2} | |

C | 100 Ω·m | 0 kg/m^{3} | - | |

A | 10 Ω·m | 1000 kg/m^{3} | 0.5 × 0.5 km^{2} | Model 2 |

B | 10 Ω·m | 1000 kg/m^{3} | 0.5 × 0.5 km^{2} | |

C | 100 Ω·m | 0 kg/m^{3} | - | |

A | 10 Ω·m | 1000 kg/m^{3} | 0.2 × 0.2 km^{2} | Model 3 |

B | 10 Ω·m | 1000 kg/m^{3} | 0.2 × 0.2 km^{2} | |

C | 100 Ω·m | 0 kg/m^{3} | - |

Geological Time | Lithostratigraphic Units | Lithology | Density | Resistivity | Unit | |
---|---|---|---|---|---|---|

Era | Period | Formation | Average (g/cm^{3}) | Average (Ω·m) | ||

Cenozoic | Neogene | Junjianshan (N_{2}j) | Basalt | 2.55 | 500 | B |

Chuandishan (N_{1}c) | Basalt | 2.55 | 506 | B | ||

Tumenzi (N_{1}t) | Basalt | 2.57 | 404 | B | ||

Mesozoic | Triassic | Changbai (T_{3}c) | Tuff | 2.6 | 274 | B |

Paleozoic | Ordovician | Majiagou (Q_{2}m) | Limestone | 2.75 | 3386 | |

Liangjiashan (Q_{1}l) | Micrite | 2.65 | 524 | |||

Cambrian | Caomidian (Є_{3}c) | Limestone | 2.70 | 2975 | ||

Gushan (Є_{3}g) | Schist | 2.69 | 2666 | |||

Proterozoic | Sinian | Wanlong (Z_{1}w) | Limestone | 2.72 | 6244 | |

Qingbaikouan | Diaoyutai (Nhd) | Feldspathic quartz sandstone | 2.62 | 3227 | G | |

Paleoproterozoic | Dalizi (Pt_{1}dl) | Eryun schist with marble | 2.75 | 1140 | E | |

Huashan (Pt_{1}h) | Cloud schist | 2.80 | 1957 | A | ||

Zhenzhumen (Pt_{1}z) | Dolomitic marble | 2.78 | 2615 | A |

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**MDPI and ACS Style**

Zhang, R.; Li, T.; Zhou, S.; Deng, X.
Joint MT and Gravity Inversion Using Structural Constraints: A Case Study from the Linjiang Copper Mining Area, Jilin, China. *Minerals* **2019**, *9*, 407.
https://doi.org/10.3390/min9070407

**AMA Style**

Zhang R, Li T, Zhou S, Deng X.
Joint MT and Gravity Inversion Using Structural Constraints: A Case Study from the Linjiang Copper Mining Area, Jilin, China. *Minerals*. 2019; 9(7):407.
https://doi.org/10.3390/min9070407

**Chicago/Turabian Style**

Zhang, Rongzhe, Tonglin Li, Shuai Zhou, and Xinhui Deng.
2019. "Joint MT and Gravity Inversion Using Structural Constraints: A Case Study from the Linjiang Copper Mining Area, Jilin, China" *Minerals* 9, no. 7: 407.
https://doi.org/10.3390/min9070407