## 3 Results and Discussion
### MOT Effect on the Long Term Velocity of Global IGS Stations  
Figure 6 shows the spatial distribution of stations' velocity variation rate caused by MOT effect for the U, E and N components.  
Here, we only estimate the velocity of IGS stations with continuous observation span of more than three years, that is 156 GPS weeks, so as to ensure the reliability of the statistics. The basic equation can be written as:  
Figure 6: Spatial distribution of the MOT induced long-term velocity variation rate. From top to bottom are the U, E, and N components. Unit of the variation rate is in percentage (%). The black and white dots in the figure indicate that the velocity variation rate for the station is smaller than the minimum and larger than the maximum value on the scale.  
\[vel\_diff\%_{6}=\frac{vel_{342}-vel_{11}}{vel_{11}}\times 100 \tag{3}\]  
where _vel_diff_ denotes the velocity variation rate for each component, \(vel_{11}\) and \(vel_{342}\) indicate the long-term velocity derived before and after considering the MOT effect respectively. To highlight the impact of MOT on the long-term velocity of the U component, Figure 7 illustrates the percentage of stations with MOT induced vertical velocity variation rate within different ranges.  
From Figure 6, we observe that MOT could only cause very small horizontal velocity change, with 98% of the selected stations' velocity variation smaller than 1% for both the E and N components (middle and bottom panels, Figure 6), and even the maximum variation at the island stations are smaller than 3%, e.g., AOML(Florida, USA). Nevertheless, Figure 7 and the top panel of Figure 6 show that the vertical velocity change caused by MOT is quite big, and there are also obvious spatial characteristics, where the variation rate decreased with stations' distance away from the sea. Those with vertical velocity change larger than 10% account for 42% of the selected stations, including most coastal/island stations, among which the maximum variation rate reaches more than 50%, for example, station TCMS (Taiwan, China), GUAM (Dededo, Guam), AUCK (Whangaparaoa Peninsula, New Zealand), _etc._ Another interesting finding is that all the selected stations in the southwest Pacific exhibit a vertical velocity decrease of more than 10% after considering the MOT effect. This may indicate a more precise data processing strategy for GPS stations in this area that applied in the field of sea level study.  
[PERSON] _et al._, found that the vertical motion of IGS reference stations mainly due to effect of post glacial rebound (PGR) [44]. From our results, however, MOT could also result in considerable vertical velocity change, especially for those along the coast or in ocean areas. For example, the vertical velocity of station REYK in Iceland, together with station VESL, SYOG and MAW1 in Antarctica varied by more than 10% after taking MOT into account. Hence, we conclude that MOT may also be a potential candidate for the vertical motion of global IGS stations. Due to the big vertical velocity change caused by MOT for coastal/island stations, in particular for those in the southwest  
Figure 7: Percentage of stations with MOT induced vertical velocity variation rate inside different ranges. Different color indicates different velocity variation rate range. Unit of variation rate is in percent (%).  
Pacific, we suggest that MOT would be better corrected during high-precision GPS data processing for coastal and ocean regions, so as to obtain more reliable vertical motions for the applications of GPS in geodynamics, such as PGR, sea level studies, _etc._