# Exploration of Seafloor Massive Sulfide Deposits with Fixed-Offset Marine Controlled Source Electromagnetic Method: Numerical Simulations and the Effects of Electrical Anisotropy

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## Abstract

**:**

## 1. Introduction

^{7}tonnes in easily accessible SMS deposits [6].

## 2. CSEM Modeling Approach

**E**and magnetic flux

**B**obey the respective Faraday’s law and Ampere’s law for a 3-D distribution of anisotropic electrical conductivity $\underset{\_}{\underset{\_}{\sigma}}$ excited by an impressed current source ${J}_{s}$

_{0}is the magnetic permeability that is assumed to be constant over the domain, ω is the angular frequency. For a general anisotropic medium, the electrical conductivity is a 3 × 3 tensor

**R**(α),

**R**(β) and

**R**(γ) are defined by

**A**is the vector potential and ϕ the scalar potential, they are also known as the magnetic and electric potentials, respectively. Inserting Equation (8) into Equations (6) and (7) leads to

**n**is the unit normal vector on the boundary.

**W**is the weighting function.

**M**is a sparse symmetric complex matrix,

**u**is the vector of unknowns associated with nodes and edges of the tetrahedral elements, and

**S**is the vector from volume integration of the source terms over the mesh. The linear system of Equation (16) is solved iteratively using the quasi-minimal residual method (QMR) with an incomplete LU preconditioning [43].

## 3. Numerical Experiments

#### 3.1. Validation of the Modeling Scheme

#### 3.2. SMS Model Studies

## 4. Summary and Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Schematic representation of the fixed-offset controlled-source electromagnetic method (CSEM) system [34] applied in exploration of seafloor massive sulfide (SMS) deposits. A horizontal electric dipole source is towed close to the seafloor, and the electromagnetic fields are recorded by receivers towed behind the transmitter.

**Figure 2.**Degrees of freedom associated with a tetrahedral element. The vector potential is constructed by linear interpolation of the tangential component on each edge, while the scalar potential is constructed by linear interpolation of the scalar value on each node.

**Figure 3.**A deep-water layered anisotropic model with a conductive SMS layer covered by seafloor sediments.

**Figure 4.**Comparison between the finite element (FE) (symbols) and quasi-analytic (lines) solutions for the deep-water layered anisotropic model. Amplitude (

**a**) and phase (

**b**) of the Ex and Ez components denoted by circles and squares, respectively. Corresponding relative amplitude errors (

**c**) and phase differences (

**d**) between the FE and quasi-analytic solutions.

**Figure 5.**Illustration of a saddle model used for 3-D forward modeling studies, water depth is 2000 m. (

**a**) 3-D view of the saddle structure. (

**b**) Schematic of the model dimensions in the x-z plane at y = 0 m.

**Figure 6.**2-D cross-section (x-z plane) through the submarine knoll center of the four 3-D conductivity models investigated in forward modeling studies. During the survey, the CSEM system is towed from left to right along the surveying line with the transmitter on the right. The four considered conductivity models are illustrated in (

**a**–

**d**).

**Figure 7.**Amplitude of the inline electric fields at a frequency of 2 Hz for four considered models (model 1 to 4) are displayed in (

**a**–

**d**), and amplitude of the vertical electric fields in (

**e**–

**h**). Note that the fields are plotted at the midpoint of the transmitter and receiver.

**Figure 8.**Phase of the inline electric fields at a frequency of 2 Hz for four considered models (model 1 to 4) are displayed in (

**a**–

**d**), and phase of the vertical electrical fields in (

**e**–

**h**). Note that the fields are plotted at the midpoint of the transmitter and receiver.

**Figure 9.**The normalized amplitude response of model 2 with respect to model 1 is calculated for Ex (

**a**) and Ez (

**b**), and corresponding phase difference for Ex (

**c**) and Ez (

**d**).

**Figure 10.**The normalized amplitude response of model 3 with respect to model 1 is calculated for Ex (

**a**) and Ez (

**b**), and that of model 3 with respect to model 2 for Ex (

**c**) and Ez (

**d**).

**Figure 11.**The phase difference of model 3 with respect to model 1 is calculated for Ex (

**a**) and Ez (

**b**); and that of model 3 with respect to model 2 for Ex (

**c**) and Ez (

**d**).

**Figure 12.**The normalized amplitude response of model 4 with respect to model 3 is calculated for Ex (

**a**) and Ez (

**b**), and corresponding phase difference for Ex (

**c**) and Ez (

**d**) to quantify the effects of dipping electrical anisotropy.

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Peng, R.; Han, B.; Hu, X.
Exploration of Seafloor Massive Sulfide Deposits with Fixed-Offset Marine Controlled Source Electromagnetic Method: Numerical Simulations and the Effects of Electrical Anisotropy. *Minerals* **2020**, *10*, 457.
https://doi.org/10.3390/min10050457

**AMA Style**

Peng R, Han B, Hu X.
Exploration of Seafloor Massive Sulfide Deposits with Fixed-Offset Marine Controlled Source Electromagnetic Method: Numerical Simulations and the Effects of Electrical Anisotropy. *Minerals*. 2020; 10(5):457.
https://doi.org/10.3390/min10050457

**Chicago/Turabian Style**

Peng, Ronghua, Bo Han, and Xiangyun Hu.
2020. "Exploration of Seafloor Massive Sulfide Deposits with Fixed-Offset Marine Controlled Source Electromagnetic Method: Numerical Simulations and the Effects of Electrical Anisotropy" *Minerals* 10, no. 5: 457.
https://doi.org/10.3390/min10050457