# Piezomagnetic Anomalies Associated with the 2021 \(M_{\text{W}}\) 7.3 Maduo (China) Earthquake
## 4 Discussion
### Possible Values of Initial Magnetization and Stress Sensitivity  
Undoubtedly, we cannot obtain a completely correct estimation of PMs using uniform parameters in a piezomagnetic model [12]. The precise structure of magnetization is not easy to determine. Nevertheless, we still attempt to evaluate the initial magnetization and stress sensitivity assumed in our piezomagnetic model. We examined the observed geomagnetic data on a geomagnetic repeat station (MD) located about 6 km from the fault trace, as shown in Figure 1. A non-magnetic plastic plate was set on the repeat station to ensure that the magnetometers were mounted on the same position every time. The preseismic observation was conducted at 06:09 to 06:41 UTC on 19 June 2019 to investigate the regional geomagnetic fields. The repeat observation was conducted at 06:05 to 06:31 UTC on 27 June 2021 to investigate the geomagnetic field changes associated with the Maduo earthquake. The \(K\)p indices (the planetary 3-h-range \(K\)p index was designed to measure solar particle radiation by its magnetic effects) were both 1 at two observations times, respectively, which suggests that there were no strong magnetic disturbances, solar flares, or solar storms. The geomagnetic vector data were obtained including declination (\(D\)), inclination (\(I\)), and total intensity (\(F\)). GSM-19T proton magnetometer with an accuracy of 0.2 nT was used to measure \(F\). Flux-gate theodolite with an accuracy of 0.2 arcmin was used to measure \(D\) and \(I\). \(Y\) was calculated according to \(D\), \(I\), and \(F\), as \(Y=F\) cos \(I\) sin \(D\). In order to calculate the geomagnetic field changes, we must eliminate the secular and diurnal variations, which are more than a few tens of nanotesla [39]. The methods introduced by [PERSON] et al. [40] including diurnal reduction and secular reduction are used to correct the raw data. The changes of \(F\) and \(Y\) between 2019 and 2021 are \(-0.55\) nT and \(+4.8\) nT, respectively, which seem to be large enough to be detected by magnetometers. Here, we must investigate the error of repeat observation by analyzing the mounting error of magnetometers, diurnal reduction error, and secular reduction error. The maximum magnetic gradient of MD is 0.2 nT/m. Thus, the mounting error resulting from position deformation can be neglected. The larger RMS of diurnal reduction in 2019 and 2021 observed data are 0.11 arcmin, 0.03 arcmin, and 0.18 nT for \(D\), \(I\), and \(F\), respectively, which can be regarded as the error of diurnal reduction. The sixth-order natural orthogonal component (NOC) of the geomagnetic fields from June 2019 to July 2021 is used to correct the secular variation. Figure 6 depicts the observed data in 72 quietest days and the values of NOC model from June 2019 to July 2021 on Jiayuguan geomagnetic observatory, which is one of the observatories used in the NOC model. The RMS of difference between observed data and NOC model is 0.08 arcmin, 0.1 arcmin, and 0.75 nT for \(D\), \(I\), and \(F\), respectively, which can be regarded as the error of secular reduction. The total error can be calculated by the accuracy of instruments, diurnal reduction error, and secular reduction error, which  
Figure 5: Normalized PMs of four earthquakes. Square and star are NPMs of Loma Prieta earthquake with stress sensitivity of \(1\times 10^{-3}\) Mpa\({}^{-1}\) and \(2\times 10^{-3}\) Mpa\({}^{-1}\). Dashed line is a fitting line of NPMs versus \(S/H\)s for the four earthquakes. are 0.24 arcmin, 0.22 arcmin, and 0.80 nT for \(D\), \(I\), and \(F\), respectively. As \(Y\) is primarily dependent on \(D\), the total error of \(Y\) can represent by the error of \(D\), which is about 2.2 nT in MD for 0.24 arcmin. Since the observed \(F\) (\(-\)0.55 nT) is less than the error (0.80 nT), we do not compare it with calculated \(F\) changes. As the observed \(Y\) is about twice the error, we believe it was reasonable and authentic. The observed and predicted \(Y\) at MD are +4.8 \(\pm\) 2.2 nT and +4.3 nT, respectively.