# A 2D Lithospheric Magnetic Anomaly Field over Egypt Using Gradient Data of Swarm Mission

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## Abstract

**:**

**B**

_{x}and

**B**

_{y}).

## 1. Introduction

**B**

_{x}component. Therefore, in the current work, we have tried to model the whole components using the gradient data from the lower-altitude Swarm satellites. The structure of the current work is as follows: Section 2 presents the data set and the selection criteria in addition to a theoretical discussion of the modelling techniques. Section 3 presents the results of our method in weighted and non-weighted inverted means. Finally, Section 4 presents our conclusions.

## 2. Data Set and Methodology

#### 2.1. Data Set and Selection Criterion

- 1)
- Local nighttime data ($23:00<LocalTime\left(LT\right)06:00$).
- 2)
- Kp $\le $ 1.
- 3)
- The interplanetary magnetic field (IMF) within $-3\le {\mathit{B}}_{z}\le 4$.
- 4)
- The disturbance storm time index within −20 < Dst < 20 daily values.
- 5)
- The regional data observed within [$0\xb0\u201340\xb0\mathsf{N}$] latitude and [$0\xb0\u201340\xb0\mathsf{E}$] longitudes with observational error < 0.3 nT.

#### 2.2. Modeling Techniques

**R**) of the weighted damped least-squares fit method is given by Equation (5):

**m**) and the standard deviation of the misfit of the N–S gradient [32,33]. The misfit has been calculated according to [17]. The black, red, blue, and green lines correspond to the trade-off curves of $\nabla {\mathit{B}}_{x}$, $\nabla {\mathit{B}}_{y}$, $\nabla {\mathit{B}}_{z}$ and $\nabla {\mathit{B}}_{t}$, respectively, where $\nabla {\mathit{B}}_{t}$ is the gradient of the total lithospheric magnetic field. The values of the damping parameters for each trade-off curve are in the order ${10}^{-12},{10}^{-10},{10}^{-9},{10}^{-8},{10}^{-7},{10}^{-6},{10}^{-5},{10}^{-4},{10}^{-3},{10}^{-2},{10}^{-1},{10}^{0},{10}^{1},{10}^{2}.$ We have chosen the damping parameter ${\alpha}^{2}={10}^{-4}$, which locates at the knee of the trade-off curves [32,33].

## 3. Results and Discussions

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**The number of data points with altitude, with the maximum data point concentrated at an altitude of 440 km.

**Figure 2.**The trade-off curve of the north–south $\nabla {\mathit{B}}_{x}$, $\nabla {\mathit{B}}_{y}$, $\nabla {\mathit{B}}_{z}$, and $\nabla {\mathit{B}}_{t}$. The variation of the norm (${\mathit{m}}^{\mathit{T}}$m) with respect to the standard deviation ($\mathit{\sigma}$) of the misfit shows that the knee of the curve is located at the damping parameter, equaling ${10}^{-4}$.

**Figure 3.**The diagonal elements of the resolution matrix at damping parameter ${\alpha}^{2}={10}^{-4}$ with respect to the parameter numbers.

**Figure 4.**The power spectrum of the model with respect to the degree (n), (

**a**) in a linear scale and (

**b**) in a logarithmic scale.

**Figure 5.**The standard deviation of the N–S gradient $\nabla {\mathit{B}}_{t}$ field component binned to regions of the surface area of 2.5 degrees.

**Figure 6.**The $\nabla {\mathit{B}}_{x}$, $\nabla {\mathit{B}}_{y}$, $\nabla {\mathit{B}}_{z}$ and $\nabla {\mathit{B}}_{t}$ components of E–W direction for the observed, modeled, and weighted modeled.

**Figure 7.**Same like Figure 6 but for N-S direction.

**Figure 8.**The lithospheric magnetic anomaly field of the

**B**

_{x}component (

**a**) observed by Swarm A, (

**b**) observed by Swarm C, (

**c**) gradient in the E–W direction, and d) gradient in the N–S direction.

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**MDPI and ACS Style**

Abdellatif, A.; Ghamry, E.; Sobh, M.; Fathy, A.
A 2D Lithospheric Magnetic Anomaly Field over Egypt Using Gradient Data of Swarm Mission. *Universe* **2022**, *8*, 530.
https://doi.org/10.3390/universe8100530

**AMA Style**

Abdellatif A, Ghamry E, Sobh M, Fathy A.
A 2D Lithospheric Magnetic Anomaly Field over Egypt Using Gradient Data of Swarm Mission. *Universe*. 2022; 8(10):530.
https://doi.org/10.3390/universe8100530

**Chicago/Turabian Style**

Abdellatif, Asmaa, Essam Ghamry, Mohamed Sobh, and Adel Fathy.
2022. "A 2D Lithospheric Magnetic Anomaly Field over Egypt Using Gradient Data of Swarm Mission" *Universe* 8, no. 10: 530.
https://doi.org/10.3390/universe8100530