1 Introduction

On 16 September 2015, an Mw 8.3 earthquake occurred with epicenter to the west of Illapel, Chile, the first megathrust earthquake in central Chile since the 2010 Mw 8.8 Maule earthquake. This earthquake ruptured the Coquimbo seismic gap that has been monitored with a dense space-geodetic network (Vigny et al. 2011). This earthquake resulted in a severe tsunami with run-up as high as 4.5 m (Contreras-López et al. 2016), which struck the Chilean coastal cities and resulted in heavy damage, especially to Socos beach, a famous tourist spot. The earthquake was followed by many large aftershocks, including two >Mw 6.5 on 17 and 21 September. All of the aftershocks for which focal mechanisms were determined are thrust events with gentle dips, similar to the main shock, indicating thrust motion on the subduction interface in Central Chile.

Based on hypocentral location and focal mechanism solution, the Illapel earthquake occurred along the collision zone between the Nazca and South American Plate that converge at a rate of 8 cm year−1 in the N78◦E direction (De Mets et al. 1990). Its tectonic setting is characterized by slightly dextral-oblique convergence between the Nazca and South American Plate margins that has been subducting for the last 20 Ma (Fig. 1; Pardo-Casas et al. 1987; Somoza 1998; Angermann et al. 1999; Cembrano et al. 2009). The plate boundary at these latitudes is characterized by a partitioning of deformation with a large number of destructive thrust earthquakes and resulting tsunamis in the subduction zone (Barrientos et al. 1990; Cisternas et al. 2005; Watt et al. 2009), such as the recent Maule Mw 8.8 earthquake on February 27, 2010 (Vigny et al. 2011) and the Valdivia Mw 9.5 megathrust earthquake on May 23, 1960 (Barrientos and Ward 1990). The Coquimbo-Illapel area (30°–32°S) in Northern part of the Central Chile was the site of major earthquakes in 1730, 1880 and 1943 (Nishenko 1985; Beck et al. 1998). The last major event in this area occurred on 15 October 1997 at a depth of 55 km under the city of Punitaqui (Pardo et al. 2002). As for this most recent earthquake, it released east–west compressional strain accumulated in South America by the eastward subducting Nazca Plate.

Fig. 1
figure 1

Seismotectonic setting of the Andean Cordillera. Red dots show major historical earthquakes along the Chile Trench, and orange dashed ellipses and orange solid lines are their rupture areas and inferred rupture extends, respectively. Circles present the locations of aftershocks >Mw 4 during the following days according to the USGS. The black solid lines present the locking zones. Slip distribution of the Illapel earthquake is also shown, but see more detail in Fig. 3

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This event provides another excellent opportunity to study the source parameters of a megathrust earthquake with high-resolution InSAR measurements, and to assess the risk of continued earthquakes in central Chile. We first obtain the coseismic surface deformation measured through SAR Interferometry (InSAR) of Sentinel-1, using images acquired before and after the Illapel event, which permits a detailed study on the distribution of coseismic fault slip. We invert for a coseismic slip model of the Mw 8.3 Illapel earthquake using this combination of ascending and descending InSAR data. Based on our coseismic fault slip model, we calculate the static Coulomb stress change on two types of representative normal faults to identify whether the main shock has promoted failure of these normal faults, as well as on faults with geometry of the 1922 Mw 8.4 Vallenar earthquake. Finally, we discuss the implications and continued seismic hazards in this area.

2 SAR Data and InSAR Processing

We use six descending Sentinel-1A\IW frames and two ascending Sentinel-1A\IW frame of SAR images immediately after the event, to extrude postseismic deformation and aftershocks as possible as we can. The three descending frames belong to the same track, which is sub-parallel to the Chile coast and thus the descending observing mode of the coseismic deformation covers a larger range than the ascending mode, since we obtain only one frame of the ascending SAR images. The SAR data only measures the terrestrial coseismic displacements (Fig. 2). All of the images are processed with the conventional two-pass differential InSAR method using the GAMMA software package (Wegmüller et al. 1997; Feng et al. 2015). The raw data are transformed into single-look images (SLCs) and then the interferograms are generated through interferometry of the SLC images. We use the SRTM 3 s data to estimate the topographic phases (Farr et al. 2000) and remove them from interferograms. We do not estimate corrections to the orbital geometric phases, due to the high precision of Sentinel-1 orbital data. We unwrap the interferograms with the minimum cost flow algorithm (MCF, Werner et al. 2002). Despite the incomplete deformation field, the quality of the InSAR data is excellent and we obtain clear, smooth and continuous interferograms (Fig. 2).

Fig. 2
figure 2

Interferograms of Mw 8.3 Illapel earthquake. Left the descending interferogram detected by Sentinel-1 SAR data. Right the ascending Interferogram by Sentinel-1 SAR data. Each color cycle represents 10.0 cm line-of-sight (LOS) displacement

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Both the coseismic ascending and descending InSAR measurements reveal that the maximum LOS displacement on continent is >130 cm about 60 km northwest of hypocenter along the Chile coast. The LOS displacements range from 1 to 132 cm along the ascending orbits and −136 to 3 cm along the descending orbits. The InSAR measurements exhibit strong surface displacements, consistent with an Mw 8.3 earthquake. The interferograms reveal no clear phase discontinuities or surface rupture on the continent in this event.

3 Fault Slip Modeling

Inversion of the full data is not tractable due to the large number of pixels in the interferograms (e.g., Simons et al. 2002; Zhang et al. 2011). We down-sample the interferograms and get a more manageable data for inversion using a quad-tree sampling method (e.g., Simons et al. 2002). The total number of LOS measurements that we invert in the descending and the ascending interferograms are about 12,000 and 5000, respectively. In the fault slip modeling, we use a low-angle, anti-listric thrust-slip fault model to approximate the increase of dip of the subduction interface. The fault has a strike of 4° with length and width 520 and 160 km, respectively. Based on trial and error, we find that a fault dip increasing from 15 to 20 degrees along the down-dip direction has the lowest data misfit to the InSAR data. The fault geometry is consistent with the finite fault solution of Ye et al. (2015), as well as coseismic models of previous earthquakes on this subduction bounardy (e.g., Delouis et al. 2010; Tong et al. 2010; Pollitz et al. 2011). To determine a finer slip distribution, the fault plane is further discretized into 10 km × 10 km fault patches and we solve for static fault slip on each patch.

We invert the sub-sampled InSAR measurements, denoted with the vector d, using a constrained least-square method of Wang et al. (2003) which finds a slip model, s, that minimized

$${\text{f}}(s) = \left\| {d - d_{0} - Gs} \right\|^{2} + \beta^{2} \left\| {Hs} \right\|^{2} ,$$
(1)

where G is the Green’s function matrix calculated using slip on a fault in a homogeneous elastic half-space (Okada 1992), assuming a Poisson ratio of 0.25, which describes the relation between the model prediction and InSAR measurement. Because each of the interferograms has a unique starting position for the unwrapping algorithm, there is an unknown constant offset in LOS displacement associated with each of the interferograms. To account for this ambiguity, we include an offset for each of the InSAR interferograms d 0. The inversion is regularized using a Laplacian smoothness constraint on fault slip, where β 2 represents the smoothing factor, H is the Laplacian operator, and \(\left\| {Hs} \right\|\) represents a measure of the slip roughness. The smoothing factor can balance the roughness of fault slip and the data misfit. In this study, the L-curve method is utilized to choose an optimal smoothing factor, which we find to be 0.1 (e.g., Hansen 1992; Feng et al. 2012, 2015; Zhang et al. 2011). Additionally, we constrain the slip rake in each sub-fault within 80°–150° based on historical events mechanisms (where 90° is pure thrust slip). We equally weight both of the ascending and descending InSAR measurements in the inversion.

The slip distribution and its corresponding fit to InSAR data are shown in Fig. 3. The residuals of InSAR LOS displacement are generally smaller than 4 cm away from the coast, although the misfit to the LOS measurements in near the coast are larger, likely due to the having no constraint of InSAR data in the sea (Fig. 3). The average RMS for measurements from the ascending and descending interferograms is about 1.7 cm and about 1.5 cm, respectively. The coseismic slip model reveals primarily reverse fault motion, as expected for this region and from the focal mechanism solutions, with a small component of right lateral strike slip. The maximum thrust slip of 8.3 m at a depth of 1.5 km northwest to the epicenter and the maximum of 1.5 m right-lateral strike slip at the same depth but slightly closer to the epicenter. Because of lack of observations offshore that contain most of the near filed data, the geodetic model probably underestimates the amount of slip at shallower depth. Comparing to the finite-fault models inverted from broadband waveforms (e.g., Ye et al. 2015; http://earthquake.usgs.gov/earthquakes/eventpage/us20003k7a-scientific_finitefault), we find that the maximum slip (about 9.0 m) and rupture zone are similar with our slip model derived from InSAR data. However, our model is more compact and smooth than the results of broadband waveforms, due to different damping strategies applied during inversion. In addition, the seismic data gives an apparent slip gap region surrounded by the major slip patch with large slip magnitude (e.g., Ye et al. 2015), which do not find by InSAR data inversion. Assuming 30 GPa shear modulus, the total estimated moment magnitude is M 0 = 3.28 × 1021 Nm, corresponding to Mw 8.3, which is comparable to GCMT or USGS solutions. The seismic rupture mainly propagated to the north and updip of the hypocenter, with almost no significant slip resolved to the south or down-dip of the hypocenter. Additionally, we find that the early aftershocks mainly occur in the regions with low magnitudes of resolved coseismic fault slip (Fig. 1).

Fig. 3
figure 3

Fault slip distributions of Mw 8.3 Illapel earthquake and InSAR data residuals from optimal inversion. b, c Present the descending and ascending residuals, respectively

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4 Discussion

Our geodetic inversion suggests that the rupture zone is about 400 km long and 140 km wide, sub-parallel to the western coast of South America and extending to about 30 km depth (Fig. 1). The slip mainly concentrates in an area from 40 to 100 km north of the epicenter at depth of 0–17 km, with peak thrust slip up to 8.3 m. At greater depths, slip decreases smoothly and vanishes at about 35 km depth, which is the depth of the Moho interface in Central Chile (Yuan et al. 2002). We also find there was a slight right-lateral component of the Illapel earthquake, which is consistent with northward motion of the Nazca plate. However, the low strike-slip component relative to the northward component of plate convergence indicates slip partitioning in the subduction system here.

Our assumption of a homogeneous elastic half-space and our constraint on rake in the inversion both have some effect on the inferred slip distribution. To assess the degree to which these assumptions influence our final slip model, in the Supplementary Material we present slip inversions assuming either a layered elastic structure or relaxing the rake constraint. While there are some differences in the inferred slip in the supplementary inversions, the main details of the inferred slip is remarkably similar. Using a layered elastic structure, the inferred slip at the trench is slightly lower (the maximum slip assuming a layered model is 12 % lower than when assuming a homogeneous half-space; Figure S1). Relaxing the rake constraint to allow for a component of left-lateral slip in the inversion still results is the thrust slip with a small component of right-lateral slip, as in the model we present in the main text.

The Southern Pacific plate subducts beneath the South American plate, with the subducted plate extending to the mantle and the plate convergence resulting in the Andean cordillera (Burke 1988), intensive volcanoes and a large number of destructive earthquakes. The most recent earthquake ruptured just the shallow portion of the Chilean megathrust. We infer that the rupture started in the region between the locked and creeping zone at about 25 km depth and then propagated unilaterally up-dip and to the north.

In contrast to the Illapel earthquake, there were two separated slip patches in 2010 Mw 8.8 Maule earthquake, both to the north and south of the epicenter along the subduction interface (Aron et al. 2015). To the south of the Illapel epicenter, there have been two major earthquakes during the past four decades: the 1985 Algarrobo Mw 8.0 earthquake (Comte et al. 1986) and the 1971 Mw 7.5 earthquake (Eisenberg et al. 1972). We surmise that the accumulated strain in this region was completely released during those two past earthquakes, and thus rupture did not propagate to the south of the epicenter in the Illapel earthquake. We also find that slip in the Illapel earthquake extended toward the inferred rupture boundary of the 1922 Mw 8.4 Vallenar earthquake (Beck et al. 1998), but did not penetrate into the slip region. This was similar to slip in the 1943 Mw 8.3 Illapel earthquake (Fig. 1), indicating that the 1922 earthquake likely released a significant amount of the accumulated strain in that region of the subduction interface.

There are many normal faults on the hanging wall of the subduction megathrust (Laursen et al. 2002; Moscoso et al. 2011), on which many Mw 4-7 normal earthquakes have been documented (Moscoso et al. 2011). Previous researchers have argued that these normal earthquakes were triggered by the large Coulomb stress change produced by megathrust earthquakes (Farías et al. 2011; Lange et al. 2012; Aron et al. 2015), enhanced by likely fluid presence along weakened zones of the forearc crust as evidenced by high Vp/Vs ratio (Moscoso et al. 2011). However, it is interesting to note that no normal earthquakes were observed following the Illapel earthquake. To explore the triggering effect produced by the great Illapel earthquake on possible extensional faults, we compute the Coulomb stress change exerted by the 2015 Illapel, Chile Mw 8.3 earthquake. Calculations are performed using Coulomb 3.3 (Toda et al. 2005; Lin and Stein 2004), with an effective coefficient of friction of \(\mu\) = 0.4, which is a typical value for subduction zones. Considering the geometry and kinematics of the normal faults (Farías et al. 2011; Aron et al. 2015), we calculate the Coulomb stress change for “receiver faults A” (strike 180°, dip 80°, rake −90°) and “receiver faults B” (strike 30°, dip 60°, rake −90°), corresponding to the representative normal faults. The two “receiver faults” are hypothetical faults, and we set their dips and strikes consistent with the result of Aron et al. (2015). Our results show the latest Chile event increases ~0.5 MPa Coulomb stress on both types of the receiver faults (Fig. 4), which is larger than the typical threshold value needed to trigger earthquakes (e.g., King et al. 1994; Lin and Stein 2004; Harris 1998; Kilb et al. 2000). In the Supplementary Material, we show Coulomb stress changes calculated assuming either lower or higher effective friction coefficients, and while the magnitude of Coulomb stress change is affected by the assumed friction, the sign of the stress change does not vary (Figure S3). In other words, the regions we infer to be positive Coulomb stress change in these calculations are still positive for lower or higher friction. Despite that there are other complex factors in earthquake triggering, the earthquake risk of such normal faulting events in the hanging wall following the Illapel earthquake, where many populated cities are located, is most likely high.

Fig. 4
figure 4

Coulomb stress change caused by Illapel earthquake. a The Coulomb stress change using receiver fault A, presented with map view at 20 km depth. Dashed line is a profile location shown in d. b Same with a, but using receiver fault B. Dashed line is a profile location shown in e. c Coulomb stress change using the source fault of the 1922 Mw 8.4 event as receiver fault, shown in map view at 20 km depth. Dashed line is the profile location show in f. d The cross-section of the Coulomb stress change along the profile shown in a. Arrows and short dotted line show the dip direction and motion of the receiver fault A, respectively. The horizontal dashed line is the map view depth shown in a. e Same with b but using receiver fault B. f The cross-section of the Coulomb stress change along the profile shown in c. In all figures, the white and red stars represent the locations of the 2015 Mw 8.3 and 1922 Mw 8.4 event, respectively

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The pattern of interseismic coupling on subduction interfaces is often used to assess where the next megathrust ruptures are likely to be. The fundamental assumption in these arguments is that the pattern of locking and coseismic slip distribution is similar (Savage et al. 1986; Burgmann et al. 2005; Murrayet et al. 2006; Perfettini et al. 2010). Coseismic slip in the 2010 Mw 8.8 Maule earthquake filled in one of the gaps that was inferred to be coupled (Moreno et al. 2010). We find that the slip distribution of the 2015 Illapel earthquake closely correlates with the pattern of inferred interseismic coupling (Moreno et al. 2010). This suggests that the 2015 Illapel earthquake filled in another portion of the coupled region of the Chilean subduction interface.

Comparing the 2015 Chile megathrust earthquake rupture with earlier events is important for seismic hazard assessment. The 2015 earthquake could be a repeat of the 1943 Mw 8.3 earthquake, which coincides with the estimated recurrence interval of 83 ± 9 years in Central Chile (Comte et al. 1986). If the inter-plate zone were fully locked, as proposed by Khazaradze and Klotz (2003), the slip deficit in the locked interface would be of the order of 5 m (70 years at 6.5 cm/year), which is also the average slip magnitude during the 2015 Chile earthquake. In addition, the 1943 and 2015 earthquakes have the comparable moment magnitude of Mw 8.3 (USGS 2015; Beck et al. 1998), and their epicenters are very close to each other (Fig. 1), lending support to the hypothesis that the Illapel earthquake is a repeat of the 1943 earthquake.

In 1997, the Punitaqui Mw 7.1 earthquake and an offshore earthquake sequence occurred in the central downdip and the northern updip segments of the 1943 rupture zone. These events partially reactivated the Coquimbo seismic gap (Pardo et al. 2002). However, it is interesting that none of the 1943, 1997 and 2015 events ruptured the areas of the 1922 Mw 8.4 Vallenar earthquake, and they were all limited by the rupture zone of the 1922 earthquake. It is natural the rupture of the 1943 Mw 8.3 earthquake could not propagate to the 1922 earthquake, since the accumulated strain since the 1922 Mw 8.5 Vallenar earthquake did not exceed the recurrence time interval of 83 ± 9 years (Comte et al. 1986). Yet the rupture of the 2015 Mw 8.3 earthquake still did not propagate into the zone of 1922 Mw 8.5 earthquake, where the accumulated slip deficit is as high as 6 m following a slip quiescent of 93 years, just outside of the uncertainty of the 83 ± 9 years earthquake recurrence interval. There is a very slight and positive Coulomb stress change (about 0.01 MPa) on the subduction interface from the Illapel earthquake (Fig. 4), which indicates that the most recent earthquake has loaded the megathrust in the region of the 1922 earthquake, albeit to only a small degree. Even given a small Coulomb stress loading and the uncertainty in the estimated recurrence interval, the megathrust in the region of the 1922 rupture is a likely location of the next major subduction thrust earthquake on the Chilean margin, and thus the earthquake potential in this region is urgent.

5 Conclusions

The 2015 Mw 8.3 Illapel earthquake is the latest megathrust earthquake to rupture the subduction interface between the Nazca and South America plates. This latest earthquake ruptured the Coquimbo seismic gap, which has had no destructive events since Mw 8.3 earthquake in 1943. We obtain the surface deformation field of this earthquake using Sentinel-1 InSAR, which we use to estimate the coseismic slip in the Illapel earthquake. Using the estimated coseismic slip model, we calculate the resuling Coulomb stress change. Our conclusions are as follows:

  1. 1.

    The Illapel earthquake is a thrusting event with a slight right-lateral strike slip component. The maximum thrust-slip and right-lateral strike slip reach 8.3 and 1.5 m, respectively. The total seismic moment is 3.28 × 1021 N m, corresponding to a moment magnitude Mw 8.3.

  2. 2.

    The slip distribution correlates closely with the inferred interseismic coupling (Moreno et al. 2010), which indicates that the 2015 Illapel earthquake filled a region of accumulated strain on the shallow megathrust.

  3. 3.

    There is a positive Coulomb stress change caused by Illapel earthquake, favoring failure of the extensional faults in the over-riding South American plate. Though Coulomb stress change increases only slightly in the region of the 1922 megathrust earthquake, the earthquake potential in this region is urgent.