Differences among the three products
Although GPS, GRACE, and SLM show consistency to a certain extent in monitoring seasonal deformation, there are still evident systematic differences between the three products. For example, the amplitude observed by GRACE and SLM is smaller than that observed by GPS, and the phase lags behind the GPS (Table 1). Figure 7 shows the amplitudes and phases of the seasonal loading deformation calculated using GPS, GRACE, and SLMs at 41 stations. The average annual amplitude of GPS was 9.7 mm (ranging from 5.7 to 14.2 mm), which was 1.3 and 1.6 times higher than that of GRACE (7.4 mm; ranging from 5.3 to 9.8 mm) and SLM (6.1 mm; ranging from 4.0 to 8.6 mm), respectively. Furthermore, a systematic difference was observed in the phase. The mean phases of the three vertical displacement time series, representing the time when the upward peak appeared, were the 91st, 107th, and 113th days for GPS, GRACE, and SLM, respectively, indicating that there was a 16, 22, and 6 day phase lag between GPS and GRACE, GPS and SLM, GRACE and SLM, respectively.
As shown in Fig. 7, the amplitudes estimated by GPS were larger than those estimated by GRACE and SLM possibly due to the uncertainty of the three products. GPS obtains surface deformation with the point measurement mode, which is susceptible to local environmental loading (Nahmani et al. 2012). For example, Gu et al. (2017) noted that the GPS station of YNTH is affected by variations in the nearby river level. The seasonal deformation inferred by GPS is usually contaminated by the thermal expansion of the bedrock and concrete pillar (Fang et al. 2014; Yan et al. 2009). We employed the thermal expansion model derived by Yan et al. (2009) and the global temperature data provided by the National Centers for Environmental Prediction to estimate the thermoelastic deformation at 41 GPS stations. The results show that the average annual amplitude of the thermoelastic deformation was 0.4 mm. The seasonal signals may be affected by errors in GPS data processing. Zhan et al. (2017) indicated that the difference in annual amplitude under different reference frames was approximately 1 mm in this region. Moreover, the annual amplitude of GPS might be overestimated because of the influence of draconitic errors of satellite orbit, multipath effect, etc. (Gu et al. 2017; Rodriguez-Solano et al. 2014; Ray et al. 2007).
In terms of GRACE, the spatial smoothing filter is required to suppress the “north–south” strip error in the processing of GRACE geopotential coefficients. Abundant rainfall means a strong HYDL signal in Southwest China. Coincidentally, regions characterized by such high hydrological signals are susceptible to spatial filtering, causing signal leakage (Chen et al. 2006; Swenson and Wahr, 2011). Using the GSM and GAC monthly solutions of GRACE, we acquired the average annual amplitudes of HYDL and NTAL + NTOL under different filter radii, as shown in Fig. 8a. The results show that, by enhancing the filtering strength, the amplitude of the HYDL is gradually attenuated, indicating that the spatial filtering in this region may cause signal leakage to the adjacent area. The effect of spatial filtering on the annual amplitude of NTAL + NTOL was negligible (< 0.15 mm). In addition, the land water storage estimated by SLM only contains variations in shallow soil moisture, snow depth water equivalent, and plant canopy surface water, but lacks deep soil moisture and groundwater storage changes. Therefore, the land water storage will be underestimated, especially in regions with high HYDL (Scanlon et al. 2019; Mo et al. 2016). Then, the weakened signal attenuates the annual deformation amplitude. In general, other geophysical signals and data processing errors in GPS, the leakage-out errors in GRACE, and the underestimation of land water storage in SLM are jointly responsible for the difference in amplitude among the three products.
In addition to the amplitudes, a systematic phase difference among the three products is shown in Fig. 7. The seasonal deformation in this area is the result of the aforementioned signals of HYDL, NTAL, and NTOL, which we referred to as Shydl, Sntal, and Sntol, respectively, in this section. Because the NTOL is faint, we combined the signals of NTAL and NTOL and marked it as Sa&o in the following content. The seasonal loading deformation in this area was the superposition of Shydl and Sa&o, as shown in Fig. 8b. If Shydl is underestimated (e.g., leakage-out error in GRACE and unmolded components in SLM) or overestimated (e.g., GPS processing errors) when the two annual signals are superimposed, the amplitude of the synthesized signal will be weakened or amplified, respectively, and the phase will change at the same time. We simulated the two signals using a sine function, and set the amplitude (Aa&o) and peak (\(\varphi _{{{\text{a}}\& {\text{o}}}}\)) of Sa&o as 2.8 mm and the 172nd day, and set the peak of Shydl on the 84th day (these parameters were estimated by GRACE and SLM, as shown in “Results”). Then, we set the amplitude of Shydl to 5.2 mm (to simulate SLM), 6.5 mm (to simulate GRACE), and 9.4 mm (to simulate GPS), and combined them with Sa&o to obtain the superimposed signal (Stotal), as shown in Fig. 8c. The results show that the phase delays between GPSsimu/GRACEsimu, GPSsimu/SLMsimu, and GRACEsimu/SLMsimu were 8, 14, and 5 days, respectively. This indicates that approximately 50% (8/16 days), 64% (14/22 days), and 83% (5/6 days) phase difference between GPS/GRACE, GPS/SLM, and GRACE/SLM are caused by the underestimation or overestimation of Shydl. The remaining unexplained difference may be caused by the effects of local loading, the thermal expansion of the crust, and the error in the data processing.
Long-term crustal movement in Southwest China
As an elastic body, variations in the surface loading cause crustal deformation, primarily in the radial direction (Yan et al. 2019). Owing to the environmental mass redistribution (including hydrology and atmosphere), the vertical deformation in Southwest China tends to exhibit a downward tendency in addition to seasonal oscillation. Figure 9a shows the long-term surface mass changes and the resulting deformation estimated by GRACE from 2010 to 2020. In particular, we did not consider the impact of glacial isostatic adjustment in data processing, as Pan et al. (2016) and He et al. (2017) (including their citations) show that the correction model in this region is still controversial, owing to insufficient space geodetic data to restrain it. We assumed that other nontectonic geophysical factors (e.g., polar motion (King and Watson 2014), mantle anelasticity (Ding and Chao 2017)) did not influence loading deformation. Figure 9a shows that, in the study area, except for the northwest, the material in other regions increased at a rate of approximately 5–20 mm/year (in equivalent water height), with a peak increment in the eastern part of Sichuan. Furthermore, long-term vertical loading deformation rates at 41 GPS stations were estimated with the deformation time series acquired by GRACE. The rate ranges from − 0.79 to + 0.1 mm/year, with an average of − 0.58 mm/year, indicating that most areas were under subsidence due to the increased mass loading (Fig. 9a, white vector).
In addition to mass loading, vertical motion is controlled by tectonic activities. The GPS records the vertical displacement caused by tectonic activity and mass variation simultaneously. We obtained the crustal motion rates by subtracting the mass loading deformation rates estimated by GRACE from the linear trend rates of the GPS (Fig. 9b). The corrected rates at 41 stations range from − 3.2 to 2.9 mm/year. As shown in Fig. 9b (three anomalous stations are not presented as they might be affected by local environmental loads), stations in the Sichuan–Yunnan rhombic block (block II in Fig. 9b) that are bounded by the Red river, Anninghe, Xiaojiang, and Jinshajiang faults are uplifted. In particular, the uplift at the Central Yunnan block (block II2 in Fig. 9b) and its eastern boundary are significant, with a upward rate of 1–3 mm/year, which is consistent with the value estimated by precise leveling (Su et al. 2018; Hao et al. 2014). In contrast with the uplifting points in the northeastern wall of the Red river fault, most of the points in the southwestern wall (block III in Fig. 9b) are under subsidence, which may indicate that the Red river fault is the constraining factor for vertical crustal motion in this area.
In addition, to analyze and explain the characteristics of vertical deformation in Southwest China, we collected the GPS horizontal velocity (Fig. 9c) provided by Wang and Shen (2020). The results show that the horizontal velocities rotate at the eastern Himalayan syntaxis; a part of which flows along the southeast direction to the east boundary of Sichhuan–Yunnan rhombic block. Affected by the Xiaojiang fault, the movement component along the fault causes a sinistral strike-slip motion, and the component perpendicular to the fault is blocked by the stable South China block, possibly causing crustal compression and uplift at the eastern boundary of the Central Yunnan block. Similarly, the horizontal crustal movement is affected by the northwest (NW) striking Red river fault. The velocity component along the fault direction causes a dextral strike-slip, and the component perpendicular to the fault direction uplifts the NE wall of the fault. Furthermore, the horizontal velocity in Southwestern Yunnan block (Fig. 9b, block III) featured with extensional movement in EW direction, which coincides with the signs of subsidence in the vertical direction.