## 5 Conclusions  
The TSFs near the epicenter before and after the Yangbi earthquake were inverted by using the FMS around the epicenter. Based on repeated observational data for 27 ground geomagnetic survey vectors within 250 km of the Yangbi earthquake epicenter, an annual variation model of the geomagnetic field around the epicenter from 3 years before the earthquake to 1 month afterwards was constructed. Based on the laboratory meta-instability theoretical model, the annual variation model of the horizontal vector of the geomagnetic field was used to analyze the buildup, occurrence and evolution of the Yangbi earthquake. We reached the following important conclusions:  
1. The azimuth of the maximum principal compressive stress axis of the TSF in the epicentral area was deflected nearly 180 degrees from before to after the Yangbi earthquake.
2. The epicenter was not located in the area with large values of annual anomalous variations in the geomagnetic field but near the area with zero variation and its adjacent area.
3. The area was found to have entered the meta-instability stage one year before the earthquake.  
In the meta-instability stage, the fault is in an irreversible deformation stage, which indicates that an earthquake will inevitably occur. However, the application of meta-instability research from the laboratory to the field is an extension from one-dimensional linear results to a two-dimensional plane. The phase-by-phase variation distribution of the horizontal vector of the geomagnetic field shows that the above four states coexist in the same region, and these four states can be transformed with time in a spatial region. During this transformation, the boundary zone of the \"weak variation region\" of the horizontal vector is the potential epicentral region and is the most easily recognized sign in the field before the area enters the meta-instability stage. The spatiotemporal evolution of the \"weakly variable region\" and the change in the surrounding vector direction are the basic conditions for analyzing whether the epicentral region will enter the meta-instability stage in the future.  
The results are of great value for the study of the earthquake incubation environment and the source of local geomagnetic anomalies, and play a theoretical guiding role in the identification of magnetic field anomalies that are precursors to earthquakes.  
This paper does not present a more in-depth analysis of the corresponding (or quantitative) relationship between the TSF and LGF before and after the earthquake, as this will be covered in future research.  
Data curation, S.C. and S.S.; Formal analysis, Z.W., Z.N. and S.S.; Funding acquisition, J.Y.; Investigation, Z.N. and S.C.; Methodology, Z.W. and Z.N.; Project administration, J.Y.; Resources, Z.W.; Software, Z.W.; Supervision, Z.N.; Validation, S.S. and J.Y.; Visualization, S.C.; Writing--original draft, Z.W. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the National Key Research and Development Program of China, grant number 2018 YFC150330504.  
Not applicable.  
The data presented in this study are available on request from the corresponding author.  
The authors used Generic Mapping Tools to make many of the figures in this article [47]. We thank the Geomagnetic Network of China for providing the geomagnetic field data for this study. We also thank the Harvard University for providing the Global CMT Catalog ([[http://www.globalcmt.org/](http://www.globalcmt.org/)]([http://www.globalcmt.org/](http://www.globalcmt.org/)) (accessed on 16 January 2022)).  
The authors declare no conflict of interest.