Introduction

The collision between the Luzon island arc and the Eurasian continental margin brings about large-scale deformation in Taiwan (e.g., Rau and Wu 1995; Takada et al. 2007). Taiwan is one of the fastest growing orogens in the world, which enables us to test many ideas of landscape evolution processes. Southwestern part of Taiwan is characterized by rapid interplate convergence as well as low seismic activity (Fig. 1). We may expect the existence of rapid aseismic deformation, which, in general, can be caused by plate interface locking, postseismic deformation of the past earthquakes, and so forth. Interferometric Synthetic Aperture Radar (InSAR) is a powerful tool to grasp the short-wavelength deformation (e.g., Massonnet et al. 1993) which cannot be detected by nationwide GNSS survey. For southwest Taiwan, previous studies using C-band SAR data reported crustal deformation in and around urban areas (Fruneau et al. 2001; Huang et al. 2009; Huang et al. 2016a), but not successful in the mountainous areas. In this study, we use SAR data of L-band satellites (ALOS and ALOS-2) to obtain coherent images even in the mountainous region covered by dense vegetation. The L-band data are more sensitive to ionospheric and tropospheric disturbances than C- and X-band data. To avoid this disadvantage, we use GNSS data to correct the interferograms. The ALOS image acquisition from descending orbit is very sparse in Taiwan, to which InSAR time series analysis (e.g., Ferretti et al. 2001; Berardino et al. 2002) is not applicable for noise reduction. Thus, the interferogram correction by GNSS is very important to estimate the uplift rates in Taiwan.

Fig. 1
figure 1

Crustal deformation and seismicity in Taiwan. Red rectangle denotes the study area. Red squares stand for, from north to south, Taichung, Tainan, and Kaohsiung, respectively. a Horizontal velocity field with respect to S01R (Paisha, Penghu) obtained by GNSS measurements (Tsai et al. 2015). Ellipsoid indicates 95% confidence interval. b Hypocentral distribution of shallow earthquakes provided by Central Weather Bureau. Radius and color of circles indicate magnitude and depth of earthquakes, respectively. Yellow areas indicate mud diapirs (Lin et al. 2009). Yellow triangles indicate mud volcanoes (Sun et al. 2010). Yellow star indicates epicenter of the Meinong earthquake

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Methods

We made interferograms using ALOS/PALSAR data acquired from ascending orbit (path 447 frame 440) with GAMMA software suite (Wegmüller and Werner 1997). To remove topographic fringes, we adopted the hole-filled Shuttle Radar Topographic Mission (SRTM) 3-arcsecond spacing digital elevation model (DEM) (Jarvis et al. 2008). To raise the signal-to-noise ratio, we created six interferograms taking the temporal baselines (i.e., period between master and slave dates) about 2.5 years (Table 1), by which we can keep perpendicular baseline small and avoid the effect of orbit shift (Additional file 1: Fig. S1). These interferograms are independent of each other with twelve different acquisition dates, which means no systematic errors are commonly included.

Table 1 Interferometric pairs used in this study
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Next, we removed systematic errors included in these interferograms, following the method given by Fukushima and Hooper (2011) with some modifications. To make the corrections effective, we clipped out the area of interest (red frame in Fig. 1) from all interferograms, which increases the GNSS station density and decreases the spatial variability of atmospheric stratification. Then, we removed the height-dependent phase trend from each interferogram using the DEM. To make it precise, we temporarily estimate a bilinear phase ramp as well according to the following equation:

$$\varphi_{i} = a + bx_{i} + cy_{i} + fh_{i}$$
(1)

where \(\varphi_{i}\) is the phase at ith pixel located at (\(x_{i}\), \(y_{i}\)), and \(h_{i}\) is the altitude derived from the DEM. The parameters a, b, c, and f are determined in a least squares manner. Then we only subtract the height-dependent term fh i from each interferogram. As an example, the effect of this correction for an interferogram spanning 874 days is illustrated in Fig. 2a, b, showing that the height-dependent component is very small, possibly due to low altitude of the studied area (~ 300 m above sea level). Next, by assuming GNSS velocity field as correct and steady, we removed the long-wavelength noise. We used the GNSS velocities provided by Tsai et al. (2015). We set Paisha, Penghu SR01 (Fig. 1) as a reference. The error of interferogram at jth GNSS station can be written as

$$d_{j}^{\text{err}} = d_{j} - d_{j}^{\text{GNSS}}$$
(2)

where \(d_{j}\) is the line-of-sight (LOS) velocity obtained by InSAR, \(d_{j}^{\text{GNSS}}\) is the one by GNSS, and \(d_{j}^{\text{err}}\) is the error defined at the GNSS stations (triangles in Fig. 2a). Then we interpolated the error \(d^{\text{err}}\) into all the pixels using bi-cubic spline function (Fig. 2c), by which we obtained final corrected interferogram (Fig. 2d). Comparing Fig. 2a and 2d, a remarkable long-wavelength phase trend, probably due to ionospheric disturbance, is successfully removed. We applied above correction to all the six interferograms, and the corrected interferograms are stacked to further reduce the non-systematic noise. Additional file 1: Figure S2 indicates another five ascending interferograms thus corrected. Strong similarity between these six interferograms (Fig. 2d, Additional file 1: Figure S2) indicates the effectiveness of the noise reduction by GNSS data. Such similarity also results from high signal-to-noise ratio of each interferogram with temporal baseline of ~ 2.5 years. Additional file 1: Figure S3 indicates the corrected interferograms with temporal baseline of 46 days and 3.5 years, respectively. Both of these are very noisy and look completely different each other. Also the temporal decorrelation is remarkable for the latter interferogram.

Fig. 2
figure 2

Interferogram correction for the pair 20071020–20100312 spanning 874 days. Color indicates the length change velocity in the line-of-sight (LOS) direction. a Original interferogram. Black triangle indicates the GNSS station. b Height-dependent component. c Long-wavelength noise. d Corrected interferogram. Colored circle indicates the LOS velocity calculated from the GNSS data

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For descending orbit, we created only one interferogram spanning 644 days due to scare acquisition by ALOS (Table 1), to which the same correction as the ascending interferograms was applied (Additional file 1: Figure S4). Using ascending and descending interferograms thus corrected, we applied the 2.5-dimensional analysis (Fujiwara et al. 2000) to obtain quasi-vertical velocity component (Fig. 3) as well as quasi-horizontal velocity component. In the following part of this paper, we focus on the quasi-vertical component.

Fig. 3
figure 3

Uplift rate calculated from 2.5-dimensional analysis using ALOS data. a Distribution of uplift rate. Colored circle stands for the uplift rate obtained from leveling survey (Ching et al. 2016). Sharp discontinuity in the uplift rate is marked by red arrows. b Uplift rate along the profile A–A′. c Uplift rate along the profile B–B′. Sharp discontinuity in the uplift rate is marked by a shading as well as in Fig. 4c. d Uplift rate measured by InSAR (blue dot) and leveling survey (red dot). We took 5-point running mean for the uplift rates given by InSAR in (b) and (c)

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Results and discussion

Figure 3a shows very rapid uplift in the fold and thrust belt to the east of Tainan city (Fig. 1). The uplifted area takes N–S elongated shape, which stretches ~ 25 km in the N–S direction and ~ 5 km in the E–W direction. Judging from very low seismicity in this area (Fig. 1), we may conclude that this uplift is aseismically proceeding. As an overall trend, the uplift rate increases from south to north, and it reaches ~ 37 mm/year at maximum in the northern part (Fig. 3b). To elaborate the uplift pattern, we took E–W profiles of the quasi-vertical velocity field (Fig. 3b, c). Across the southern part of the uplifted area, Ching et al. (2016) reported a one-dimensional profile of uplift rate by levelling survey (Fig. 3a), showing ~ 18 mm/year at maximum. We compared the uplift rate detected by InSAR with that measured by the levelling survey, and demonstrated that both are consistent with each other (Fig. 3d). We further found that the uplift rate in the E–W profiles indicates a sharp discontinuity at the eastern flank of the uplifted region (shading in Fig. 3c), which is also visible in the plan view (red arrows in Fig. 3a). We interpret that this uplift rate discontinuity results from a hidden active fault steadily creeping under a certain level of shear stress. The location of this fault roughly corresponds to the Lungchuan fault, which is proposed to be a thrust fault (Huang et al. 2004; Ching et al. 2016). The detailed geometry and the precise location of the Lungchuan fault are poorly known, which may be improved from combination of our interferograms and field surveys in the future.

The driving force of this rapid uplift would be the growth of mud diapirs, which is widely distributed from South China Sea to the coastal area of southwest Taiwan (Doo et al. 2015; Lin et al. 2009, Huang et al. 2004) (Fig. 1b). In the uplifted area, active mud volcanoes demonstrate the existence of mud volumes at shallow depth. Ching et al. (2016) tried to construct a fault model to explain the uplift profile obtained by the levelling survey in the southern area (circles in Fig. 3a) and found it as very difficult. Instead, they proposed the mud diapirs as main driving force. In northern part, the uplift rate detected by InSAR takes much higher value than southern part, reaching 37 mm/year (Fig. 3a). This uplift rate is higher than total convergence rate across the study area (Additional file 1: Figure S5), which is unrealistic to be solely explained by fault motion. Based on the gap in the velocity field (Fig. 3), we also constructed a two-dimensional fault model using Okada’s Green’s function (Okada 1985). For the observed horizontal velocity, we removed very long-wavelength component which directly reflects interplate convergence (note that the reference point is S01R in Fig. 1a). We fixed the top of the fault at the surface. As shown in Additional file 1: Figure S6, the optimum fault model with a slip of 55 mm/year on a fault plane dipping 65 degrees down to the west well explains the quasi-east component (Additional file 1: Figure S6a), while we see remarkable misfit (> 15 mm/year) especially at the footwall side (right) in the quasi-vertical component (Additional file 1: Figure S6b); calculated subsidence is too large at the footwall side. Looking at the plan view (Fig. 3a), the foot wall side (east) of this reverse fault is clearly uplifted, which demonstrates that the whole area is raised by a mud diapir located at depth, and the surface offset is caused by the shallow reverse faulting that we found.

To elaborate the rheological property of the aseismic uplift area, we further analyzed the interferograms of the Meinong earthquake (Mw 6.4) that occurred about 20 km east of the uplift area (Fig. 1b) on 5 February 2016 (USGS 2016). Using SAR data acquired by ALOS-2/PALSAR2 (Table 1), we created two interferograms from ascending and descending orbits. Figure 4 shows quasi-vertical displacement associated with the Meinong earthquake. We found a gap in the amount of uplift (red arrows in Fig. 4a, shading in Fig. 4c) at the same location as the gap in the uplift rate before the earthquake (red arrows in Fig. 3a, shading in Fig. 3c). In Additional file 1: Figure S7, clear coherence loss along the gap is commonly observed in both coseismic interferogram of the Meinong earthquake and interseismic interferogram. This coherence loss indicates surface faulting of the hypothetical thrust fault. Huang et al. (2016b) also created the coseismic interferograms of the Meinong earthquake and interpreted this gap as very shallow fault motion. Incidentally, the ALOS-2 interferograms that we used show the same deformation pattern as Sentinel-1 (Huang et al. 2016b). In this study, we demonstrated that this fault slip has aseismically increased at least from 2007 to 2011 when a certain level of shear stress has been statically imposed, as well as at the timing of the Meinong earthquake when a stepwise stress increase is suddenly imposed. Such stable property of the fault slip would be due to the high fluid pressure measured in this area (Huang et al. 2016b). We roughly estimated static Coulomb stress change on the aseismic thrust fault due to coseismic slip of the Meinong earthquake. We assumed slip on the deeper fault of the coseismic fault model proposed by Huang et al. (2016b), which well explains seismic data. We used Coulomb 3.3 to calculate the stress change (Toda et al. 2011). Additional file 1: Figure S8 indicates negative Coulomb stress change on shallower part of the aseismic thrust fault (~ − 0.2 MPa), which, as suggested by previous studies (Ching et al. 2016; Huang et al. 2016b), implies that high fluid pressure observed in this area plays important role for triggering slip on the aseismic thrust fault. Thus, the mechanism of interseismic fault creep was confirmed from crustal response to the Meinong earthquake.

Fig. 4
figure 4

Coseismic uplift due to the Meinong earthquake measured by ALOS-2. a Distribution of coseismic uplift. Gap in the amount of uplift is marked by red arrows. b Amount of uplift along the profile A–A′. c Amount of uplift along the profile B–B′. Gap in the amount of uplift can be seen and is marked by the shading as well as Fig. 3c. Note that both of the profiles A–A′ and B–B′ are the same as those in Fig. 3

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It should be noted that the aseismic fault slip we found (Figs. 3, 4) only adds a short-wavelength perturbation to the whole uplift and/or uplift rate pattern. For the interseismic period, the main driving mechanism of whole surface uplift would be mud diapirs at depth. For the coseismic displacement of the Meinong earthquake, a deep-seated decollement caused long-wavelength surface deformation (Huang et al. 2016b), which, however, is not responsible for the interseismic uplift characterized by short-wavelength deformation (Fig. 3).

Conclusion

We detected very rapid uplift along the fold and thrust belt in southwest Taiwan by L-band SAR data. The interferograms are contaminated mainly by ionospheric disturbances, which are corrected by GNSS data. The rapid uplift is aseismically proceeding judging from the absent of earthquakes. The uplift rate increases from south to north and reaches ~ 37 mm/year in the northern part. In southern part, the uplift rate derived from InSAR is consistent with the one measured by the levelling survey which reaches ~ 18 mm/year at maximum. The main cause of uplift motion would be mud diapirs, but we also identified shallow fault motion along the eastern flank of the uplift area, which moves aseismically before and during the 2016 Meinong earthquake. The shallow fault motion adds a short-wavelength perturbation to the whole uplift pattern.