## 3 Experiments and Results
### Application in the 2017 Ms 7.0 Juzhaigou Earthquake
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Station** & **Latitude (\({}^{\circ}\))** & **Longitude (\({}^{\circ}\))** & \
\begin{tabular}{c} **Epicentral** \\ **Distance (km)** \\ \end{tabular} &
\begin{tabular}{c} **Station Spacing** \\ **(km)** \\ \end{tabular} \\ \hline GSMX & 34.43 & 104.02 & 137.92 & \\
62 MXT & 34.40 & 104.00 & 134.38 & 3.80 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Information of high-rate GNSS and strong-motion co-located stations. rate. Therefore, VC-AKF can effectively combine the advantages of GNSS and SM, and further capture broadband crustal motion signals directly. (3) The difference between the GNSS-derived and VC-AKF-derived displacements mainly reflects the GNSS noise level, which is within \(1\times 10^{-4}\)mm. This implies that the overall GNSS noise level in the loose integration is relatively stable and homogeneous during the earthquake. Figure 4: (**a**) Displacement time series of GNSS-derived (blue), SM-derived (green), and VC-AKF-derived (red) in the north–south direction of the GSMX/62 MXT station. (**b**) Difference between GNSS-derived and VC-AKF-derived displacements in the same epoch. Figure 3: Acceleration, velocity, and displacement at the 62 MXT station from 13:19:46 (UTC) during the 2017 Jiauzhaigou Ms 7.0 earthquake, in north–south (N), east–west (E), and upward (U) directions. To demonstrate the superiority of the presented VC-AKF in real-time loose integration, Figure 5 shows the comparison of VC-AKF and SKF with different a priori variances \(q\) and \(100q\). In this study, the variance in the pre-event noise of the accelerometer \(q\) is about \(6\times 10^{-5}\)m/s\({}^{2}\) at the 62 MXT station. The time value before the system noise variance \(q\) mainly depends on the intensity of the station motion in practical applications. Figure 5 clearly highlights the following. (1) It is obvious that the derived results of the SKF are heavily dependent on the input of the system noise variance. When a relatively small system noise variance \(q\) is input, the derived results cannot absorb the residual baseline shift of SM well. This problem can be solved by using a larger system noise variance, such as \(100q\). As shown in Figure 5a, the derived displacement time series from SKF-100q are more similar to those of VC-AKF compared to SKF-q, which means that VC-AKF can effectively overcome the influence of the incorrect input system noise variance. (2) The difference between the SKF-derived and VC-AKF-derived displacements mainly reflects the model errors of the system state. The maximum difference between the results of VC-AKF and SKF-q is about 0.91 cm, while the maximum difference between the results of VC-AKF and SKF-100q is about 0.23 cm. The reason for these major discrepancies is the sudden changes in the system variances caused by the occurrences of SM rotation and tilt. Figure 6 indicates the power spectral density (PSD) of the SKF and VC-AKF displacements in the north-south direction of the GSMX/62 MXT station. The PSD of the high-rate GNSS and SM data are also shown for comparison. The inspections from this figure highlights the following. (1) From the frequency domain perspective, the displacements obtained by GNSS are more sensitive to low-frequency signals, and the displacements integrated by SM are more sensitive to high-frequency signals, although they contain the baseline shift. (2) The VC-AKF-derived results not only match the GNSS information well in the low-frequency part but also maintain better consistency with the displacements recovered by SM in the high-frequency part. Therefore, it can be concluded that VC-AKF is able  
Figure 5: (**a**) Comparison of VC-AKF-derived (red solid), SKF-derived with system variance q (green solid), and SKF-derived with system variance 100q (blue solid) displacement time series in the north–south direction of the GSMX/62 MXT station. (**b**) Difference between the displacements from VC-AKF and SKF-q (blue dashed), and VC-AKF and SKF-100q (green dashed) in the same epoch.