## 3 Results
### Equivalent Source Inversion
#### 3.1.4 Apparent Density Changes of the Sources  
Based on the adjustment results of the mobile gravity observations in the study area, we used the equivalent source inversion method to obtain crustal apparent density values (Figure 6). The geographical elements in this diagram are the same as those in Figure 5. Strictly speaking, the gravity variations are closely related to environmental factors local to each monitoring station, such as the migration of subsurface fluids, soil moisture, vehicle vibration, and elevation changes [12]. These factors, which are difficult to determine, can be uniformly defined as external factors of the sources. They are highly contingent on small-scale drivers and difficult to quantitatively eliminate. Reducing any of them to a fixed value will affect the reliability of the results. In this study, we therefore adopted the equivalent source inversion method and introduced the a priori condition of space-time smoothing into the inversion model to suppress anomalous signals, such as local disturbances and source errors. This allowed us to more accurately extract the anomalous time-varying gravity field signals and determine the parameters of the source model. For the inversion, we selected equivalent crustal density anomalies of 1 km thickness at a depth of 10 km in the study area that could be effectively detected by repeated surface gravity measurements. The characteristics of apparent density variations obtained by inversion are similar to the evolution trends of the gravity values, and the major anomalous regions are consistent. Data (crust1.0) show that the average crustal density in the study area is approximately 2700 kg\(\cdot\)m\({}^{-3}\), and the apparent density variation of the sources in the study area is roughly \(\pm\)3.0 kg\(\cdot\)m\({}^{-3}\). The inverted density variation is about 1% of the crustal density. The time scale of each panel in Figure 6 is the same as that in Figure 5, and the color bar for the time-varying gravity field variation is consistent with that for crustal apparent density variations to allow for a better illustration of the anomalous features revealed by the inversion. Figure 6: _Cont._Figure 6a shows the apparent density variation pattern in the study area from August 2016 to August 2017. Apparent density anomalies were generally distributed along the trend of the tectonic structures, with distinct zoning features. The Urumqi piedmont depression was a region with negative changes, while the foothills of the North Tianshan Mountains showed positive variations. These density changes verified our inference based on the gravity changes described above, i.e., that the crustal media were migrating from the north to the south. There was an incongruuous negative anomaly at the epicenter location, where the density variation contour bends southward, out of line with the tectonic trends. We believe that this feature was not simply caused by noise but very likely constitutes a manifestation of deep crustal material migration before and after the earthquake. According to the theory of isostasy, the regional uplift of the crust will lead to a decrease in its density, thus achieving a state of mass balance among different regions [56]. Therefore, the anomaly shown in Figure 6a may reflect the influence of post-seismic surface deformation and crustal uplift on subsurface media; that is, the seismic activity led to crustal uplift, which induced a decrease in crustal density. The possible reasons for this anomaly are further discussed and verified in combination with the InSAR data in the next section. Figure 6b shows the apparent density change pattern in the study area from August 2017 to August 2018. The region with positive apparent density variation, which was previously distributed along the trend of tectonic structures, significantly expanded toward the north, and the negative anomalies were only distributed in a small area northeast of Urumqi.