## 4 Conclusions  
In this paper, a SF-PPP model based on ionospheric delay and receiver DCB constrained is presented to invert the coseismic deformation and the ionospheric disturbance before and after an earthquake. The GPS data from the 2013 Lushan and 2011 Tohoku-Oki earthquakes were analyzed to assess the proposed method.  
According to the results, (1) the proposed SF-PPP method provided coseismic deformation signals correctly, although its positioning precision was lower than GAMIT/TRACK. (2) On the other hand, compared to GAMIT/TRACK, the proposed SF-PPP was not affected by the selection of the reference station. Thus, it was not degraded by the common mode errors that existed in the GAMIT/TRACK solution, especially during a strong earthquake (i.e., the Tohoku-Oki one). (3) While analyzing the estimated VTEC, it was found that negative VTEC anomalies appeared visibly around the epicenter of Lushan earthquake on the long-term scale, comparing the results in DOY 105 to those in DOY 106. In contrast, on the short-term scale, negative VTEC anomalies appeared during the several hours before and after the earthquake. For the VTEC obtained from GIM data, negative VTEC anomalies appeared visibility in the south area of the epicenter on the day the earthquake occurred. The VTEC calculated by SF-PPP adopted more observation stations in Sichuan; thus, it is possible to present the ionospheric variations in a smaller region and on a shorter time scale. However, the observations of GIM data are sparser than those of SF-PPP. Thus, the variation of VTEC is more obvious in larger regions (e.g., the whole world).  
The presented method has been proved effective for obtaining the deformation and ionospheric disturbance before, during, and after earthquakes. However, it might be  
Figure 12: Distribution of VTEC near the earthquake epicenter from 2:00 UTC to 6:00 UTC on DOY 70, 2011 (the day earthquake happened); subfigures (**a–c**) are the variation process of GIM data; subfigures (**d–f**) are the variation process of SF-PPP.  
challenging to use such a method for accurate natural-hazard monitoring. Currently, there is rapid development of multi-sensor fusion technologies (i.e., GNSS, seismograph, inertial sensors, crack meters, etc.) Meanwhile, the Chinese government is paying more attention to the development of the multi-source data fusion algorithm for contingent nature hazards monitoring and predicting. Thus, our group will carry out more work in those fields in the future.  
Conceptualization, J.L. and Z.G.; data curation, J.L. and Y.W.; funding acquisition, C.Y. and J.P.; investigation, J.L. and Z.G.; software, Z.G.; visualization, C.Y. and J.P.; writing--original draft preparation, J.L.; writing--review and editing, J.L. and Z.G. All authors have read and agreed to the published version of the manuscript.  
This research was partly supported by the National Key Research and Development Program of China (Grant No. 2020 YFB0505802), and the National Natural Science Foundation of China (NSFC) (Grants No. 42074004).  
The datasets adopted in this paper are managed by the School of Land Science and Technology, China University of Geosciences, Beijing, and can be available on request from the corresponding author.  
The authors would like to thank anonymous reviewers who gave valuable suggestion that has helped to improve the quality of the manuscripts.  
The authors declare no conflict of interest.