## 3 Results and Discussion
### Trend Deformation Maps  
Figure 7 represents the linear trend map interpolated from the Kriging method. Based on the trend map, it can be observed that the coastal presented a slight upward trend in the north and northeast zone (i.e., \(\delta up\)\(\sim\)3 mm/year), in blue color. However, in the south and southwest zone, in the case of transverse monitoring of Arauco Bay, it presented a more accentuated upward trend (i.e., \(\delta up\)\(\sim\)24 mm/year), in red color. In addition, a clear deformation pattern is defined along the coast, being greater in the Gulf of Arauco, and Lebu. One study reports [68] the rate of \(\pm\) 1.5 mm/year as the stable zone threshold. In this sense, a rate above this threshold is significant for a possible landslide event or other associated hazards. This trend map already indicates which zones are susceptible to deformation, either in the form of uplift or subsidence. This result related to the identification of risk areas is consistent with the report previously by Ref. [65]. Figure 8 shows the spatial patterns of the deformation for the selected study areas. Studying the entire displacement field depicted in Figure 8a, we observe a slight uplift trend up to longitude 73.0, wherefrom this point, the terrain tends to dip (approximately about \(-\)10 mm/year) (Figure 8b). In Figure 8c, the graph represents the cross section to Arauco Bay, where there is a slight elevation trend. Figure 8d shows that at higher latitudes, starting from latitude 37.0 in a scoutherly direction, the terrain begins to rise. Figure 8a shows that of the municipalities studied, Lota, Arauco, and Lebu have the greatest tendencies to rise when compared to the other municipalities located further north in this study. This pattern is related to the daily seismic activity (see Figure 3), the product of the movement between plates, and the geological faults located in the area. Figure 7: Deformation of tendency map for the study area. This trend behavior was verified previously by [12; 63; 64], which demonstrated the effects of the co-seismic uplift in four peninsulas that make up the region studied, after the 27F earthquake. The retreat of the sea was observed on some beaches, and the dehydration of the Raqui-Tubul wetland in Arauco [69], and the drying up of the Lebu River [63]. Santa Maria island, located in the Arauco Gulf, shows subsidence and uplift tendency patterns in some areas, between \(-14.9\) and \(39.2\) mm/year (Figure 8a). The coastal subsidence trend was also identified by [14], who conducted a study where they recorded that the small island underwent elevation changes between co-seismic cycles between the 1835 and 2010 earthquakes. Therefore, the deformation and tendency maps provide certainty in terms of where hotspots are located, e.g., the most hazardous areas in the study zone. Slopes under seismic excitation are one of the most important problems to consider [70]. In the study area, it was verified in works by [63; 64] that the seismic movements that occurred can generate changes in the relief. These changes occurred under large seismic energy releases. However, it can be observed with the data presented in this study that deformation can also be identified in periods with earthquakes of lower to moderate intensities by using radar techniques. This fact opens a space for future research on potential hazards related to slope stability in areas with potential and active landslides recorded in the study area. Inspired by two studies cited by [55], it was reported that they were intended to model the post seismic displacement that continued to occur at the site after the earthquake. Interferometry played an important role in this study since most of these displacements were aseismic, and therefore went unnoticed by conventional seismological records. Based on their results, it is clear that to capture the smallest displacement structures with ground-based instrumentation, such as GPS receivers, it would be necessary to cover the ground with instruments and that such a density is not realistic.