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Piezomagnetic Anomalies Associated with the 2021 M_{W} 7.3 Maduo (China) Earthquake

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## Abstract

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_{W}7.3 Maduo earthquake on geomagnetic fields, a piezomagnetic model is constructed based on the coseismic slip to calculate the static coseismic piezomagnetic anomalies (PMs). The PMs are considerable in near-field. However, the PMs are negligible in regions tens of kilometers from the fault rupture. The PMs of our model are consistent with those of other strike-slip earthquakes, indicating that our piezomagnetic model is reasonable. The east component of observed coseismic geomagnetic changes and calculated PMs on a geomagnetic repeat station located about 6 km from fault trace are +4.8 ± 2.2 nanotesla and +4.3 nanotesla, respectively. It seems that the piezomagnetic model can explain the observed data. The PMs are up to 10 nanotesla in the near-field with the initial magnetization of 3 A/m and stress sensitivity of 2 × 10

^{−3}MPa

^{−1}. Consequently, considerable coseismic geomagnetic changes that are above error could be observed along the fault, especially at locations with geometrical complexities.

## 1. Introduction

_{W}> 6.5) in China occurred in this block and its border faults in past twenty years (Figure 1), including the 2001 M

_{W}7.9 Kokoxili earthquake, the 2008 M

_{W}7.8 Wenchuan earthquake, the 2010 Yushu M

_{W}6.9 earthquake, the 2013 M

_{W}6.6 Lushan earthquake, and the 2017 M

_{W}6.5 Jiuzhaigou earthquake. In order to investigate geomagnetic anomalies before, during, and after earthquakes, the China Earthquake Administration operates a geomagnetic network including geomagnetic observatories and geomagnetic repeat stations in the Tibetan Plateau. However, only a repeat station located 26 km from the epicenter of the M

_{W}6.6 Lushan earthquake recorded PMs [29]. PMs can be neglected if the fault rupture is small [30], unless observations are conducted right on faults [3]. However, PMs must be investigated carefully for earthquakes with ruptures larger than 100 km for their huge energy release and strong impact on local and regional geomagnetic fields.

_{W}7.3 Maduo earthquake (herein referred to as Maduo earthquake) occurred at 18:04 UTC on 21 May 2021, with the epicenter located at 98.34° E and 34.59° N (http://www.csi.ac.cn/, accessed on 10 November 2021). Maduo earthquake caused an about 160 km rupture (Figure 1) along the Maduo-Gande fault [31]; however, the tectonic deformation is significantly weak in the region [32]. How does the earthquake disturb geomagnetic fields in the Bayan Har block? Are the piezomagnetic fields localized? More importantly, how will the earthquake impact observations of piezomagnetic fields in the future? To address these questions, in this study, we construct a piezomagnetic model to calculate the static coseismic PMs based on a slip model of the Maduo earthquake. Moreover, observed data of 2019 and 2021 on a repeat station are used to examine the PMs.

## 2. Data and Methods

#### 2.1. Coseismic Slip Model

#### 2.2. Layer Elastic Model

#### 2.3. Piezomagnetic Model

**J**is the change of magnetization,

**S**is the deviatoric stress tensor,

**J**is the initial magnetization, and β is the stress sensitivity.

_{0}, y

_{0}, z

_{0}) due to ∆

**J**of a sub-block with coordinates of (x, y, z) can be expressed as Equation (2) [36], and the PMs can be obtained by differentiating the right-hand side of Equation (2).

**J**, and ρ is the distance between point P and the sub-block,

^{−3}MPa

^{−1}is considered in many studies of seismomagnetic anomalies [3,7,13,19]. However, in some studies, the initial magnetization of 1A/m and stress sensitivity of 1 × 10

^{−3}MPa

^{−1}are too small to explain the observed data [21,25,29]. In our model, an average magnetization of 3 A/m and a stress sensitivity of 2 × 10

^{−3}MPa

^{−1}are assumed. A depth of 16 km was chosen because most of the stress associated with Maduo earthquake released in the upper crust (0–15 km).

## 3. Results

## 4. Discussion

#### 4.1. Validation of Piezomagnetic Model

_{L}7.1 Loma Prieta earthquake [19], the 1992 M

_{W}7.3 Landers earthquake [20], and the 2004 M 6.0 Parkfield earthquake [4]. It should be noticed that the PMs strongly depend on parameters. Therefore, we focus on relative values of PMs here.

^{−3}MPa

^{−1}and 2 × 10

^{−3}MPa

^{−1}are assumed in the piezomagnetic model of Loma Prieta. Here, we choose the maximum PMs of these earthquakes to analyze. The correlation between maximum NPMs and S/Hs is shown in Figure 5. All values of these piezomagnetic models are shown in Table 2. Figure 5 shows that NPMs increase with S/Hs. In other words, given the same β and J, the larger S/Hs is, the larger the PMs are. As shown in Figure 5, NPMs of Maduo earthquake are consistent with those of other strike-slip earthquakes and the Loma Prieta earthquake with stress sensitivity of 2 × 10

^{−3}MPa

^{−1}. It indicates that our piezomagnetic model is reasonable.

#### 4.2. Possible Values of Initial Magnetization and Stress Sensitivity

^{−3}MPa

^{−1}assumed in piezomagnetic model of Maduo earthquake are reasonable.

#### 4.3. Potential Usefulness of Observations along Fault

_{W}7.3 earthquake with a rupture length of 160 km, the geomagnetic field changes that are above the magnetometer accuracy are limited in areas 40 or 50 km from rupture. Considering the error resulting from field observations and data processing, we consider that only magnetometers mounted at a region within 20 km from the fault rupture can observe useful seismomagnetic signals. On the other hand, it also could fail to record seismomagnetic signals even when the magnetometers are mounted in near-field. As our results show, the PMs are small in epicenter area. Thus, only stations that are ideally located can observe the PMs.

## 5. Conclusions

_{W}7.3 Maduo earthquake is assumed to disturb local and regional geomagnetic fields significantly. A piezomagnetic model is constructed to investigate the geomagnetic fields changes due to stress changes resulted from earthquake rupture. We validate the piezomagnetic model by comparing with piezomagnetic changes of other strike-slip earthquakes and observed data before and after earthquake on a geomagnetic repeat station. The PMs of Maduo earthquake seem to appear in areas within 40 km from fault trace. The PMs are larger at the location with bifurcation of slip. The observed geomagnetic field changes before and after Maduo earthquake can be explained by our piezomagnetic model with initial magnetization of 3 A/m and stress sensitivity of 2 × 10

^{−3}MPa

^{−1}. Thus, if there are more observations, we can constrain the detailed magnetic properties and the slip model.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Tectonic setting. Black stars indicate the earthquakes with M

_{W}> 6.5 in the past twenty years. Black triangle is a geomagnetic repeat station. Benchballs indicate earthquake focal mechanism. Bold gray lines are block borders. Thin gray lines are faults. Black lines are fault ruptures of Maduo earthquake from Zhang et al. (2021). The lower inset is the location of target area.

**Figure 3.**Contours of calculated (

**a**) total intensity and (

**b**) east component of PMs obtained from the Maduo earthquake. Contour interval is 1 nT. Focal spheres represent the epicenter. Gray lines are the surface rupture. Dash lines are profiles.

**Figure 4.**East component of PMs on three profiles across fault trace. The dash lines represent fitted PMs instead of calculated ones as the PMs are neglected artificially in order to avoid singularity.

**Figure 5.**Normalized PMs of four earthquakes. Square and star are NPMs of Loma Prieta earthquake with stress sensitivity of 1 × 10

^{−3}Mpa

^{−1}and 2 × 10

^{−3}Mpa

^{−1}. Dashed line is a fitting line of NPMs versus S/Hs for the four earthquakes.

**Figure 6.**Observed data (red dot) and NOC model data from June 2019 to July 2021. (

**a**): the variation of declination. (

**b**): the variation of inclination. (

**c**) the variation of total intensity.

Layers | Depth/km | V_{P}/km·s^{−1} | V_{S}/km·s^{−1} | Density/kg·m^{−3} |
---|---|---|---|---|

1 | 4 | 4.8 | 2.82 | 2600 |

2 | 10 | 5.9 | 3.47 | 2700 |

3 | 20 | 6.1 | 3.59 | 2850 |

4 | 48 | 6.5 | 3.82 | 3000 |

5 | 68 | 7.0 | 4.12 | 3100 |

6 | 100 | 8.1 | 4.76 | 3320 |

Event | Maximum PMs (nT) | Magnetization (A/m) | Stress Sensitivity (10 ^{−3} MPa^{−1}) | S (m) | Hs (km) |
---|---|---|---|---|---|

Maduo | ~10 | 3 | 2 | 8.1 | 6 |

Landers | ~5 | 2 | 2 | 5 | 5 |

Loma Prieta | ~1.5 | 1.5 | 1 or 2 | 2.3 | 6 |

Parkfield | ~0.4 | 2 | 2 | 0.4 | 3 |

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**MDPI and ACS Style**

Song, C.; Zhang, P.; Wang, C.; Chu, F.
Piezomagnetic Anomalies Associated with the 2021 *M*_{W} 7.3 Maduo (China) Earthquake. *Appl. Sci.* **2022**, *12*, 1017.
https://doi.org/10.3390/app12031017

**AMA Style**

Song C, Zhang P, Wang C, Chu F.
Piezomagnetic Anomalies Associated with the 2021 *M*_{W} 7.3 Maduo (China) Earthquake. *Applied Sciences*. 2022; 12(3):1017.
https://doi.org/10.3390/app12031017

**Chicago/Turabian Style**

Song, Chengke, Pengtao Zhang, Can Wang, and Fei Chu.
2022. "Piezomagnetic Anomalies Associated with the 2021 *M*_{W} 7.3 Maduo (China) Earthquake" *Applied Sciences* 12, no. 3: 1017.
https://doi.org/10.3390/app12031017