Owing to repeated acquisitions of ALOS-2/PALSAR-2, I obtained spatio-temporal variation in Line-of-Sight (hereafter LOS) displacements after the occurrence of the Kumamoto earthquake sequence. In this chapter, I discuss characteristics of observed LOS displacements from three different viewpoints; i.e., a) spatial distribution of averaged LOS displacements (Figs. 6, 7, 8, 9 and 10b) profiles of displacements along selected sections (Fig. 11c) time series of LOS displacement at selected points (Fig. 12).
Additional file 1: Figures S1–S3 show all flattened filtered non-dispersive components of interferograms for P131-F640, P130-F650, and P23-F2950–2960, respectively. Close-ups of unwrapped interferograms around the source region and Aso caldera are shown in Figs. 6, 7 and 8, where displacement of GEONET stations during the corresponding period projected onto the LOS directions is also shown. All LOC displacements are referred to GEONET 960700 for the paths 131 and 23, 970833 for the path 130, respectively, considering distance from source faults and coherence around them. Coseismic interferograms are also shown in the top left panels of each figure. Comparison of LOS changes with those at GEONET sites with the same reference is given in Additional file 1: Figure S4. Average LOS change rates with GEONET average velocities are in Fig. 9. Time series of InSAR displacement roughly follow GNSS data at most sites with fluctuations. InSAR displacements in summer tend to depart from that of GNSS, which may be attributed to tropospheric disturbances related to heavy precipitation (Precipitation at Kumamoto is shown in Fig. 12f). Because no correction of tropospheric disturbances nor temporal smoothing is applied, jumps appear in InSAR time series when there are storms or torrential rains. Furthermore, all interferograms refer to one specific GEONET site in a scene and local disturbance around it affects entire image. GNSS data is daily averaged coordinate, while InSAR image is an instantaneous one. Therefore, local tropospheric disturbance on interferogram may affect more significantly than GNSS daily coordinates. Discrepancies are large at GEONET sites 950456 and 081169. I suspect soil condition or local topography around these sites affect the movement.
I also compare the present results with that of time series analysis of Sentinel-1 images. I processed Sentinel-1 images during the period from April 20, 2016 to April in 2018 using LiCSBAS developed by Morishita et al. (2020). Additional file 2: Figure S5 shows average LOS displacements of both ascending and descending images. Discrepancies are recognized, but this is attributable to the difference in strategies of analyses. The present result by stacking is the weighted average of changing rate between the first image and others. On the other hand, LiCSBAS calculates average of changing rates of LOS of pairs of consecutive images. Therefore, rapid movement in early stage, if any, may be emphasized in the present result, while LiCSBAS result gives us more slower rates in later stage. Despite this discrepancy, the same features of spatial distribution are recognizable. The most important issue is low coherence in mountainous area on the southeastern side of the Futagawa and Hinagu faults and on northern frank of Aso caldera in Sentinel-1 images. As already known, L-band SAR of ALOS-2/PALSAR-2 gives us higher coherence and can be utilized for the detection of movements.
Figure 10 shows quasi-EW and vertical components of average velocity during the period from the first acquisitions to April 2018. E–W and vertical components of average velocity of GEONET stations are also indicated. For conversion to E–W and U–D components, the same GEONET stations (960700 and 970833) were fixed in the overlapped area of ascending and descending images. In the following section of spatial variation of deformation, I mainly discuss E–W and U–D components in Fig. 10.
Spatial distribution of average rate of postseismic deformation
Coseismic deformations are also shown at the top left in Figs. 6, 7 and 8. Comparing them with following postseismic interferograms, I confirmed that postseismic deformations are concentrated around the source area of the mainshock. However, spatial pattern is significantly different with each other, especially in ascending interferogram (Fig. 6).
Fujiwara et al. (2016) already showed postseismic deformations in early stage, April–May in 2016, with ALOS-2/PALSAR-2 from both ascending and descending orbits. Interferogram from descending orbit is the same as that used in this study (P23; Second left panel of the top raw in Fig. 8). They used pairs of images from a different path with high elevation. There is a little difference in obtained spatial pattern of deformation in ascending interferogram, but the features of obtained postseismic deformations are basically the same. In this study, I put emphasis on their temporal evolution and deformation that arose afterward.
Fujiwara et al. (2016) pointed out several spots of significant LOS changes; (1) deformation along the Futagawa fault, especially near the junction with the Hinagu fault (2) deformation around the Suizenji fault (they mentioned as the Suizenji Park), (3) deformation in the Ozu town. In Fig. 12 of Fujiwara et al. (2016), there are many signals in Aso caldera, but they did not mention in detail. I also recognized the same features and that they were amplified in the following 2.5 years (Figs. 6, 7 and 8). They pointed that there is no clear deformation around the outer rim of Aso caldera, where many surface ruptures were observed in coseismic interferograms. I did not observe clear deformation in later interferograms, neither.
The most prominent one is subsidence along the Futagawa fault and its western extension. Fujiwara et al. (2016) measured less than 10 cm displacement near the junction of the Futagawa and Hinagu faults during the first 2 weeks after the mainshock. Subsidence rate exceeding 6 cm/year in this zone is recognized during 2.5 years despite loss of coherence in most part (arrow a in Fig. 10). Another spot of subsidence is found between the junction and Aso caldera (arrow b). Westward shift is also prevailing in this area. There is a surface rupture along another fault, Idenokuchi fault (Toda et al. 2016). It is noteworthy that this area of subsidence is bounded by the Futagawa and Idenokuchi faults.
Rapid uplift is found on the south side of the Idenokuchi fault (arrow c). In Fig. 12 of Fujiwara et al. (2016), there is not notable signal in this area. Uplift is also recognized on the north side of the Futagawa fault (arrow d). A zone of slight subsidence and westward shift (arrow e) is surrounded by this uplift zone on the north side of the Futagawa fault. It is interesting that the boundary between these uplift and subsided zones nearly coincides with northern edge of a Pleistocene pyroclastic flow deposits (dark green line).
Westward shift is remarkable on the southeastern side of the Hinagu faults, reaching 6 cm/year (arrow f). I also see eastward motion of < 2 cm/year around the epicenter. Further west, I observed subsidence in a fan-shaped zone near the coast (arrow g). It is interesting that its southern boundary roughly coincides with the western extension of the Futagawa fault.
I also found significant deformation off Futagawa and Hinagu faults, which is the same as that of Fujiwara et al. (2016). The most remarkable one is a NW–SE trending zone of subsidence of ~ 4 cm/year in the city of Kumamoto (arrow h). Large subsidence was also detected in coseismic interferograms (Upper left panel in Figs. 6 and 8) (e.g., Fujiwara et al. 2016). The zone of this subsidence coincides with the Suizenji fault zone found by Goto et al. (2017). The present results suggest that postseismic deformation also continued around this fault zone during 2.5 years.
Several spots of subsidence can be observed in Aso caldera, as well. In the northernmost part of this caldera, coseismic surface ruptures were found (Tsuji et al. 2017; Fujiwara et al. 2017). I detected significant subsidence along these surface ruptures during the postseismic period (arrow i), implying continuing movement associated with these ruptures. Another remarkable motion was found on the northern frank of central cone of the Aso volcano (arrow j), where westward shift is also dominant here. Its northern boundary seems to be aligned along a line trending NE–SW.
Significant eastward motion was found at the central cone of Aso volcano (Fig. 10a). There were small explosions during February to May, 2016, and a significant explosion occurred on October 7–8, 2016 (JMA 2016). This eastward motion may be attributed to this activity.
I also found another small spot of westward shift of ~ 4 cm/year and slight subsidence north of Ozu Town, about 10 km north of the Futagawa fault (arrow k). This deformation was already pointed out by Fujiwara et al. (2016). This zone trends in the WNW–ESE direction, which corresponds to local trend of valley where Pleistocene sedimentary rocks are sandwiched by igneous rocks. I did not see any sign of such deformation in preseismic interferogram (Additional file 2: Figure S5). Therefore, this deformation may have been caused by strong shaking due to the Kumamoto earthquake sequence.
LOS displacement profiles along selected sections
It is important to examine temporal variation in deformation for the discussion of mechanism of postseismic deformation. Because timing and frequency of observations are different between descending and ascending orbits, it is impossible to reduce E–W and vertical components at specific epochs. Therefore, I discuss LOS displacements in this section. For this purpose, I prepared two different views of time series of observed deformation. One is the temporal changes along selected profiles. I sampled LOS change from the area within 0.005° on the both sides of a profile and plotted them shifting according to the time of acquisitions of subsequent images. I chose 7 profiles, shown in Fig. 9b, that run through interesting spots of deformation discussed in the previous section, in which I can also grasp the characteristics of spatial distribution of deformation, especially discontinuities in deformation. 5 sections are along meridians, while 2 sections are in the E–W direction. I emphasize that correlation between LOS displacement and topography is not recognized though some sections runs in the areas of rough topography.
The Sect. 1 is the westernmost profile of LOS change, which runs off the main strand of Futagawa and Hinagu faults but crosses the area of local LOS increase around the Suizenji fault zone in Kumamoto City (Fig. 11a, b). I can see local LOS increase around 32.8°N in both interferograms (vertical line) and another local deformation a little bit north of 32.7°N in descending interferogram (red arrow in Fig. 11b). The former corresponds to local subsidence in Kumamoto City, while the latter is signal on the western extension of the Futagawa fault, i.e., the Akitsugawa flexure zone of Goto et al. (2017). These observations suggest that postseismic deformation occurred not only in the vicinity of coseismic faults but off the source. I notice two steps looking closely at the LOS change around 32.8°N in descending interferogram, implying at least two possible faults there (below SZ).
The Sect. 2 runs just west of the junction of the Futagawa and Hinagu faults (Fig. 11c, d). The LOS increase exceeds 30 cm in descending interferogram, the largest in the entire region under study. I observe sharp changes at the northern boundary of this zone of LOS increase (= subsidence) which corresponds to the Akitsugawa flexure zone (vertical line with AF). Southern half of subsidence zone has gradual change in both interferograms, but is limited by the Hinagu fault (vertical line with HF). Comparing the baseline of the last observation (orange lines), discrete shift of far-field displacement is noticeable on the both sides.
The Sect. 3 is a profile running across a smaller local subsidence between the Futagawa and Idenokuchi faults (Fig. 11e, f). There is a spike-like pattern of spatial distribution of LOS changes around 32.8°N (between vertical lines with HF and FF). Its width is much narrower than that found in the Sects. 2 and 4. There is also a shift in the far-field displacement, which is evident in Fig. 11f.
The Sect. 4 shows temporal evolution of LOS changes along the meridian passing the spot of large subsidence between the Futagawa and Idenokuchi faults (Fig. 11g, h). I recognize sharp changes across these two fault and large LOS increase (= subsidence) between them (vertical lines with IF and FF). This LOS change exceeded 10 cm about 1 year after. It is worth noting that the changes across the Idenokuchi fault are larger and sharper than that across the Futagawa fault especially in descending interferograms (Fig. 11h), which implies afterslip on the Idenokuchi fault is more active than on the Futagawa fault, if any. I also noted that there is another gradual step north of the Futagawa fault (red arrow next right of FF), suggesting a minor buried slip. There is another discontinuous change around 32.9°N (red arrow further right), corresponding to the area of westward shift north of Ozu Town in Fig. 10a. I should note convex pattern of the LOS change in ascending interferograms (double-headed arrow in Fig. 11g), while LOS change along the profile is almost flat in descending ones. This convex pattern of LOS change becomes noticeable about 200 days after.
The Sect. 5 runs across the Aso caldera. A sharp discontinuity is obvious around 33.0°N, just south of the northern caldera rim (RP). This point is located a little north of the surface rupture that was formed during the April 16 shock of Mw7.0 (Fujiwara et al. 2016; Fujiwara et al. 2017; Tsuji et al. 2017). I can notice the differential motion evolved according to elapsed time. There were several step-like pattern of deformation during the first 100 days, but most of them died out and the largest one continued for 2 years. LOS changes with relatively short wavelength of ~ 2 km can be seen in ascending interferogram in caldera floor and central cones, while long wavelength deformation is detected with local LOS increase centered around 32.9°N in descending interferogram (red arrow in Fig. 11j).
The Sects. 6 and 7 are LOS displacement profiles along two parallels. The Sect. 6 runs north of the Futagawa fault and northern part of Aso caldera (Fig. 11k, l). A spike-like change of LOS just east of the caldera rim (left red arrow) is related to coseismic surface rupture, the same signal in Sect. 5. Another notable deformation is rapid LOS increase around 131.2°E in the vicinity of central cone, which is as large as 10 cm (right arrow). This change obviously does not correlate with topography. I also recognize difference in level of LOS change between both sides of this zone in both ascending and descending interferograms.
The Sect. 7 crosses local LOS increase in Kumamoto City, junction of the Futagawa and Hinagu faults, and western frank of the Aso caldera. I can find a remarkable deformation on the southeast side of the Futagawa fault in ascending interferogram. This deformation may have been accelerated after the summer of 2016 (double-headed arrow).
Time series of LOS displacement at selected points
The other is the time series of LOS changes at selected points, which is easier to understand the decaying history of deformation. We chose 5 points shown in Fig. 9. Because acquisitions were made frequently from descending orbit (P23) and were less from ascending orbits, I examine only time series of descending interferograms. I sampled LOS change rates in an area of 0.005° × 0.005° centered at the selected points and took average. To estimate characteristic time, I fit an exponential decaying function to observed time series;
$$u = a\left( {1 - { \exp }\left( {{\raise0.7ex\hbox{${ - t}$} \!\mathord{\left/ {\vphantom {{ - t} \tau }}\right.\kern-0pt} \!\lower0.7ex\hbox{$\tau $}}} \right)} \right) + b,$$
(1)
where u is LOS displacement, a and b are constants, t is elapsed time in day from April 16, 2016, τ is characteristic time. Red curves in each panel are estimated decaying time series. It is important to note that the LOS changes till the end of May 2016 are dominant during 2 years at most points, implying much faster motion during this period than this approximation. This fast motion may contribute to the difference between average velocities from stacking of ALOS-2/PALSAR-2 and time series analysis of Sentinel-1.
Point A is located in the middle of local LOS increase in Kumamoto City. LOS changes rapidly decayed till the fall of 2016, though there is a fluctuation in 2017–2018 (Fig. 12a). If I fit exponential decaying function, I obtain characteristic time of only 29 days. Total LOS change amounts to ~ 5 cm.
Point B is located south of the junction of the Futagawa and Hinagu faults, where westward horizontal motion is dominant around this point (Fig. 10a). This point also shows rapid decay with time constant of ~ 50 days and may have reached ~ 6 cm till the winter in 2016, though scatter is a little bit large (Fig. 12b).
On the other hand, points C–E have longer time constant than the previous points. Point C, located in the large subsidence between the Futagawa and Idenokuchi faults, gradually decayed till the beginning of 2017 with time constant of ~ 230 days (Fig. 12c). In 2017, it is stable at the level of 8 cm increase of LOS, and fluctuated in 2018. Point D is in the middle of uplift area on the western frank of the Aso caldera. During the first 2 weeks, this point moved rapidly, but suddenly was decelerated (Fig. 12d). Then, it continues to move in the same direction (= uplift) with slow decay rate of characteristic time of ~ 980 days.
Point E in Aso caldera shows a similar pattern of temporal change to Point C. Characteristic time is almost the same (~ 210 days) (Fig. 12e). Because these two points are located ~ 20 km away from each other, it may be hard to expect the possible mechanical link.
I add daily precipitation at the Japan Meteorological Agency’s (JMA) Kumamoto station in Fig. 12f. Kumamoto area suffered from heavy rain mainly in summer during these 3 years, but the correlation with temporal change in LOS change is not clear at all points.