Multi-Segment Rupture Model of the 2016 Kumamoto Earthquake Revealed by InSAR and GPS Data

Abstract

The 2016 Kumamoto earthquake, including two large (Mw ≥ 6.0) foreshocks and an Mw 7.0 mainshock, occurred in the Hinagu and Futagawa fault zones in the middle of Kyushu island, Japan. Here, we obtain the complex coseismic deformation field associated with this earthquake from Advanced Land Observation Satellite-2 (ALOS-2) and Sentinel-1A Interferometric Synthetic Aperture Radar (InSAR) data. These InSAR data, in combination with available Global Positioning System (GPS) data, are then used to determine an optimal four-segment fault geometry with the jRi method, which considers both data misfit and the perturbation error from data noise. Our preferred slip distribution model indicates that the rupture is dominated by right-lateral strike-slip, with a significant normal slip component. The largest asperity is located on the northern segment of the Futagawa fault, with a maximum slip of 5.6 m at a 5–6 km depth. The estimated shallow slips along the Futagawa fault and northern Hinagu fault are consistent with the displacements of surface ruptures from the field investigation, suggesting a shallow slip deficit. The total geodetic moment release is estimated to be 4.89 × 10¹⁹ Nm (Mw 7.09), which is slightly larger than seismological estimates. The calculated static Coulomb stress changes induced by the preferred slip distribution model cannot completely explain the spatial distribution of aftershocks. Sensitivity analysis of Coulomb stress change implies that aftershocks in the stress shadow area may be driven by aseismic creep or triggered by dynamic stress transfer, requiring further investigation.

1. Introduction

In April 2016, a series of shallow earthquakes struck Kumamoto prefecture of Kyushu island, southwest Japan, causing more than 100 fatalities, more than 1000 injuries, and severe destruction to houses and infrastructure. The sequence started with an Mw 6.2 foreshock on 14 April 2016 (UTC), and the Mw 7.0 mainshock, which is thought to be the largest event in central Kyushu island recorded since 1990, occurred approximately 28 h later. The two events generated strong ground motions that reached the maximum seismic intensity of 7 (the largest value on the Japan Meteorological Agency (JMA) scale). Previous studies related to the kinematic rupture process have shown that the mainshock rupture propagated unilaterally to the northeast direction and terminated near the southwest edge of the Aso volcano [1,2,3]. The moment tensor solutions from seismic catalogs (e.g., Global Centroid Moment Tensor (GCMT) [4], United States Geological Survey (USGS) [5], and National Research Institute for Earth Science and Disaster Resilience (NIED) F-net [6]) indicate that the mainshock was dominated by right-lateral motion with significant non-double-couple components, suggesting that rather complex mechanisms were involved in this sequence (Figure 1).

This sequence produced approximately 34 km-long surface ruptures, mainly along the Futagawa fault zone and its eastern extension to the caldera of the Aso volcano, and the northernmost part of the Hinagu fault zone [7]. The Futagawa and Hinagu fault zones belong to part of the western extension of the Median Tectonic Line (MTL), known as the longest right-lateral strike-slip active fault in Japan. These fault zones are located within the Beppu–Shimabara graben, which is dominantly controlled by north–south extension and some northeast–southwest shear modifications from MTL [8]. The oblique subduction of the Philippine Sea Plate (PHS) and the northern extension of the opening Okinawa Trough (OT) are considered to be the sources that drove the formation of the graben structure [9].

The spatial distribution of seismicity and surface ruptures from the field investigation suggest that multi-segment faults ruptured during the earthquake. To better understand the complicated rupture and stress interaction, it is crucial to clarify the source characteristics of this earthquake. Several previous studies [1,2,3,10,11,12,13,14,15] have reported the source models from the inversion of teleseismic, strong-motion, and geodetic datasets, either independently or jointly. However, the fault geometry and maximum slip of various models differ significantly. Typically, Kubo et al. [10] estimated a maximum slip of 3.8 m from strong-motion waveforms with a curved fault model. Their results fitted the waveforms relatively well, yet the maximum slip seemed to be underestimated when compared with the peak slip of 5.7 m from the joint inversion of strong-motion, teleseismic body, and surface waveforms [11]. Fukahata and Hashimoto [12] determined the fault dip angles and slip distribution on two-segment fault planes by inverting the ALOS-2 InSAR data. Their model was well-constrained, but a large misfit (up to 30 cm) occurred near the caldera of Aso volcano, which suggested that their fault model needed to be improved. Additionally, Yue et al. [3] performed the joint inversion of GPS, strong-motion, Synthetic Aperture Radar (SAR) images, and surface offset data with a curved multi-segment fault model. Their results showed the maximum slip exceeding 10 m, which is rare for an Mw 7.0 intraplate event. These studies only assumed northwest-dipping faults, while Ozawa et al. [13], Yoshida et al. [14], and Zhang et al. [15] indicated that a southeast dipping fault within the Aso caldera region might also have ruptured. Therefore, a further study of the fault geometry and slip distribution is required to better understand the source mechanism of this complex earthquake.

In this study, the complex deformation field associated with the 2016 Kumamoto earthquake is firstly derived from both ALOS-2 and Sentinel-1A SAR satellite images. Subsequently, a combination of InSAR and GPS data is utilized to determine the optimal multi-segment fault geometry with the jRi method and to invert the slip distribution on the fault planes. Finally, the Coulomb stress change calculation and its sensitivity analysis are carried out to investigate the possible triggering mechanisms.

2. Coseismic Surface Displacements from InSAR and GPS Data

2.1. InSAR Data

During the 2016 Kumamoto earthquake, both ALOS-2 and Sentinel-1 SAR satellites captured the coseismic surface deformation field covering the entire epicenter area. The ALOS-2 satellite, equipped with the Phased Array type L-band Synthetic Aperture Radar-2 (PALSAR-2) and operated by the Japan Aerospace Exploration Agency (JAXA), provides excellent surface displacement observations. The L-band ALOS-2 satellite can observe the ground surface from the right or left direction and penetrate the heavy vegetation to obtain a high coherent interferogram. The Sentinel-1 satellite is composed of a constellation of two satellites (A and B) maintained by the European Space Agency (ESA) and provides C-band SAR images to detect crustal deformation signals. This constellation operates the novel Terrain Observation with Progressive Scans (TOPS) mode for its standard acquisition, which has a broad swath of up to 400 km wide, with a spatial resolution down to 5 m and a minimum 12-day repeat cycle [16]. In this study, we collected one pair of images from the ALOS-2/PALSAR-2 descending track (P023D) and two pairs of images from both the descending and ascending track (T163D and T156A) of Sentinel-1A, in order to map the coseismic surface deformation. Detailed information on the SAR data used in this study is given in

Table 1. Synthetic aperture radar (SAR) interferometric pairs used in the study.

Track	Sensor	Orbit	Mode	Primary Image (yyyy/mm/dd)	Secondary Image (yyyy/mm/dd)	${\mathit{B}}_{\perp }$ (m)	${\mathit{B}}_{\mathit{T}}$ (days)	$\mathsf{\sigma }$ (cm)	Np
P023D	ALOS-2	Descending	Strip-map	2016/03/07	2016/04/18	81.5	42	2.3	657
T163D	Sentinel-1A	Descending	IW	2016/03/27	2016/04/20	1.9	24	2.5	549
T156A	Sentinel-1A	Ascending	IW	2016/04/08	2016/04/20	65.4	12	3.2	568

$B_{\perp }$ represents the perpendicular baseline between the orbits; $B_T$ is the interval between the master and slave images acquisition dates; Interferometric Wide (IW) swath mode is the main acquisition mode over land; σ, denoting measured error from a combination of various error sources (e.g., ionospheric and atmospheric effects, topographic correction residuals, and orbital and unwrapping errors), was estimated from the far-field area [21]; Np is the number of down-sampling points.

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GAMMA software [17] was utilized to process all SAR images. The interferograms were multi-looked with ratios between the range and azimuth direction of 10:2 and 8:8 for the Sentinel-1A and ALOS-2/PALSAR-2 images, respectively. The 90-m-resolution Digital Elevation Model (DEM) from the Shuttle Radar Topography Mission (SRTM) [18] was used to remove the topographic effects. The interferograms were then filtered with an adaptive-filter method [19] and unwrapped using statistical-cost network-flow approaches [20]. Finally, all interferograms were geocoded to the World Geodetic System (WGS-84) geographic coordinates with a 90 m resolution.

The interferograms obtained from SAR images show significant deformation signals along the mapped active faults associated with the earthquake (Figure 2). Compared with the L-band ALOS-2 interferogram, two C-band Sentinel-1A interferograms can hardly acquire the deformation near the faults due to the worse decorrelation caused by the large displacement gradient, surface ruptures, and landslides. Intensive fringes appear on both the Futagawa fault and the northern part of the Hinagu fault, along which displacement discontinuities can be clearly identified. The unwrapped interferograms of two descending tracks (P023D and T163D) both show three major asymmetric lobes of deformation and detect the line-of-sight subsidence signals at the Aso caldera. Two lobes are located along the mapped Futagawa and Hinagu fault zones, while another is located within the Aso caldera. The observed line-of-sight (LOS) displacements vary from –46 to 18 cm and from –44 to 67 cm for the P023D and T163D tracks, respectively. The slight discrepancy between the two descending tracks arises from the different incidence angles of ALOS-2 (~36°) and Sentinel-1A (~38°) satellite SAR sensors [22]. In the ascending track (T156A), the LOS displacement varies from –97 to 106 cm and the range is much larger than that of the two descending tracks. The LOS displacements on both sides of the Futagawa-Hinagu fault zone display opposite directions, consistent with a strike-slip event. Large displacements of up to 50 cm in the LOS direction are also detected within the Aso caldera.

2.2. GPS Data

In addition to InSAR data, coseismic GPS displacements near the epicentral region from the GPS Earth Observation Network system (GEONET) were also collected. The distribution of GPS stations is shown in Figure 3. The horizontal displacements are consistent with the predominant right-lateral rupture, while the vertical displacements are much more complicated. The largest ~1 m horizontal displacement to the southwest and 0.25 m uplift can be observed at the 960701 station, which is located within kilometers of the mapped fault trace near the Aso caldera. However, this station was not included in the inversion because it is located too close to the fault trace, and the displacement could not be properly modeled by Green’s functions [3]. Moreover, the small displacements with large errors were also not used in the inversion. Consequently, 45 horizontal and six vertical displacements were used to constrain the fault geometry and slip distribution. It is widely known that InSAR measures large-scale line-of-sight displacements with a high spatial resolution, whereas GPS can provide 3-D continuous displacements with a sub-centimeter accuracy. Therefore, a combination of InSAR and GPS datasets can better constrain the fault geometry and slip distribution associated with earthquakes.

3. Model

The surface displacements derived from InSAR and GPS data were modeled using the rectangular dislocations embedded in a homogeneous, isotropic, and elastic half-space [23] and assuming a Poisson’s ratio of 0.25. Millions of highly correlated data points in the unwrapped interferograms were down-sampled with a quadtree sampling method [24] to improve the computational feasibility and efficiency of the model. The InSAR and GPS datasets were weighted equally in the joint inversion, which could fit both datasets quite well, as shown by the relative weight ratio tests (Figure S1).

3.1. Determination of the Fault Geometry with the jRi Method

The surface ruptures, active fault traces, InSAR deformation maps, and seismicity indicate that multi-segment fault planes ruptured during the earthquake. Therefore, four-segment fault planes (hereafter termed F1, F2, F3, and FH) are considered to represent the rupture planes, among which segment F1 is set as a southeast dipping fault plane in the eastward extension of the Futagawa fault zone under the Aso caldera, and the other three northwest dipping segments are located along the Futagawa and northern Hinagu fault zones (Figure 1).

However, determining the fault geometry parameters of multiple segments and the slip distribution on the fault planes simultaneously is computationally expensive [25,26]. In this study, the location and extent of the four-segment fault planes could be identified from geologically-mapped fault traces, surface ruptures, and the seismicity distribution, but the fault dip angles of those segments were difficult to determine, especially for the F1 segment located at a seismic gap of the aftershock. Therefore, we considered fixing the location and extent of the four-segment faults and then searching for the optimal fault dip angles that minimized the data misfit between observed and predicted surface displacements. Regularization errors, such as weight root mean square errors (WRMSE) with the form of ${\Vert C_d^{-1/2}(d-G(\mathsf{\delta })s)\Vert }_2$ or root mean square errors (RMSE) with the form of ${\Vert (d-G(\mathsf{\delta })s)\Vert }_2$, are the most common measures of misfit [25,27,28], and the jRi value [29], including both regularization error and perturbation error from data noise, has also been proposed to find the best-fitting model [30]. The jRi value with respect to fault dip angles can be expressed as:

$$\mathrm{jRi}(\mathsf{\delta })={\Vert C_d^{-1/2}(d-G(\mathsf{\delta })s)\Vert }_2-\frac{1}{k}diag(M{I}_2{M}^T)+\frac{1}{k}diag(M{M}^T),$$

(1)

where $C_d^{-1/2}$ is the weight matrix from Cholesky decomposition of the inverse of the data covariance matrix $C_d$; $G\left(\mathsf{\delta }\right)$ is the assembled matrix of Green’s functions for a vector of dip angle $\mathsf{\delta }$ (with $\mathsf{\delta }=\left[{\mathsf{\delta }}_1,\dots ,{\mathsf{\delta }}_{\mathrm{n}}\right],\mathrm{n}=4$), relating the slip $s$ on a dislocation to the observed data d (i.e., InSAR and GPS datasets); k is the amount of data used in the inversion; $I_2$ is a matrix consisting of $2\times 2 I$ matrices, where $I$ represents a k-by-k identity matrix; and $M=\left[I,-N\right]$, with $N=G\left(\mathsf{\delta }\right)G^{-\mathrm{g}}$. $G^{-\mathrm{g}}$ is the generalized inverse with the following form:

$$G^{-g}={\left({\left[\begin{array}{c}{C}_d^{-1/2}G(\mathsf{\delta })\\ \mathsf{\kappa }L\end{array}\right]}^{\mathrm{T}}\left[\begin{array}{c}{C}_d^{-1/2}G(\mathsf{\delta })\\ \mathsf{\kappa }L\end{array}\right]\right)}^{-1}{\left(C_d^{-1/2}G(\mathsf{\delta })\right)}^{\mathrm{T}},$$

(2)

where L is the Laplacian smoothing matrix and $\mathsf{\kappa }$ is a regularization factor that determines the slip roughness ${\Vert Ls\Vert }_2$. The optimal $\mathsf{\kappa }=2$ can be chosen from the trade-off curve [25] between the data misfit and the average slip roughness or the jRi curve [29], as shown in Figure S2.

It has been demonstrated that the determination of the fault dip angle via the jRi method with geodetic data is more robust than the performance of WRMSE or RMSE in simple one-segment fault scenarios, such as the 2015 Mw 7.9 Gorkha Nepal earthquake [30], but further verification was required for the complex multi-segment fault scenario in this study. Therefore, we extended the jRi method to determine the multi-segment fault dip angles and compared the results with the RMSE method to illustrate the effectiveness of the jRi method. More specifically, the optimal fault dip angles of four segments were iteratively searched, while the slip distributions on the four-segment faults were inverted simultaneously, until the jRi or RMSE value exhibited an insignificant difference. In order to avoid the effect of the imprecise estimation of the slip distribution on the fault planes during searching for optimal dip angles, each fault segment was further discretized into 2 km × 2 km sub-faults.

Figure 4 shows the result of estimating the fault dip angles with the jRi and RMSE methods from InSAR and GPS data. The optimal fault dip angles determined with the jRi method were estimated to be 77°, 57°, 63°, and 74° for the F1, F2, F3, and FH segments, respectively. The fault dip angles of F2, F3, and FH segments were also well-determined with the RMSE method, and only slight differences can be observed when compared with the result from the jRi method. However, the fault dip angle of F1 was poorly determined with the RMSE method, resulting in a shallower dip of 68° compared with the result obtained from the jRi method. The detailed fault parameters of the four-segment fault model used in this study are summarized in

Table 2. Fault parameters of the four-segment fault model used in this study.

Segment	Latitude (°)	Longitude (°)	Depth (km)	Length (km)	Width (km)	Strike (°)	Dip (°)	Max Slip (m)	Moment (Nm)	Mw
F1	131.0178	32.9088	0.2	12	18	40	77	2.3	4.89 × 1019	7.09
F2	130.9222	32.8386	0.2	12	18	236	57	5.6
F3	130.8216	32.7722	0.2	12	18	226	63	3.3
FH	130.7672	32.6918	0.2	16	18	205	74	3.0

The position (latitude, longitude, and depth) indicates the top-center of each fault segment. The rigidity was assumed to be 32 GPa. The fault dip angles were determined with the jRi method.

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3.2. Distributed Slip Model

After the fault geometry parameters of the four segments were determined, a bounded variable least squares method [31] was adopted to invert the distributed slip on each segment. Regarding the limitation on slip, all segments were allowed to include both right-lateral strike-slip and free dip-slip components with a magnitude of less than 10 m, which is a reasonable constraint based on the focal mechanism of the mainshock and previous studies [1,2,6]. Moreover, the Laplacian smoothing constraint was also adopted to avoid non-physical oscillation of the slip distribution.

The preferred slip distribution model reveals a single asperity on each of the four segments, with a maximum slip of 5.6 m on the F2 segment at a 5–6 km depth (Figure 5). The predominant slip occurs at a depth of 0–13 km, which confirms the shallow hypocenters of this earthquake sequence. The relocated aftershocks are mostly located at a depth of between 6 and 15 km, where the slip decays quickly. The slip on the F2 segment is mainly right-lateral strike-slip, but with a significant normal slip of ~2.7 m. The shallowest slip on the F2 segment is characterized by 1–2 m strike-slip, together with 0–1.5 m normal slip, which is consistent with the lateral and vertical displacement components of surface ruptures from the field investigation [7]. On the F3 and FH segments, the slip is almost pure right-lateral, but the maximum slip on the F3 segment (3.3 m) is slightly larger than that on the FH segment (3.0 m). The slip on the southeast dipping F1 segment exhibits a dominant normal slip, but smaller magnitude than the other three segments, and the maximum slip is less than 2.5 m. The total geodetic moment release was estimated to be 4.89 × 10¹⁹ Nm, which is equivalent to a Mw 7.09 event, assuming a shear modulus of 32 GPa. The estimated moment release is in general agreement with that of Zhang et al. [15], but slightly larger than the seismic moment derived from teleseismic data [4,5,6] or regional strong-motion data [2]. Note that InSAR data cover the largest foreshock (Mw 6.0) and four days of aftershocks, which may explain the slightly higher moment release.

Figure 6 shows a comparison of observed and predicted InSAR data from our best-fitting slip model, as well as the corresponding residuals. The general deformation patterns from both ALOS-2 and Sentinel-1A observations can be interpreted well by the preferred model. However, there are some near-fault residuals for ALOS-2 descending track P023D with maximum misfit of up to 10 cm, which may be attributed to a combination of complicated near-field deformation and possible nontectonic influences of liquefaction, landslides, and inelastic deformation [32]. The histograms of the residual distribution of each InSAR track are illustrated in Figure 7. The RMSEs were estimated to be 5.64, 2,75, and 2.74 cm for P023D, T163D, and T156A tracks, respectively. The preferred model provides a good fit to the GPS horizontal and vertical displacements shown in Figure 3. A detailed comparison of three components of the observed and predicted GPS displacements is shown in Figure 7. The fits to horizontal displacements are relatively better than those to vertical displacements, with RMSEs of 1.70, 2.35, and 4.38 cm for east, north, and vertical components, respectively.

4. Coulomb Stress Change Analysis

Numerous previous studies have shown that the Coulomb stress changes caused by an earthquake may trigger subsequent events, change the seismicity rate, and affect the state of nearby faults through stress transfer [33,34,35]. Based on the Coulomb failure criterion, the change in Coulomb failure stress (ΔCFS) due to an earthquake on the receiver faults can be calculated as follows:

$$\Delta \mathrm{CFS}=\Delta {\mathsf{\tau }}_{\mathrm{s}}+{\mathsf{\mu }}^{\prime }\Delta {\mathsf{\sigma }}_{\mathrm{n}},$$

(3)

where $\Delta {\mathsf{\tau }}_{\mathrm{s}}$ is the shear stress change parallel to the slip direction; ${\mathsf{\mu }}^{\prime }$ is the effective friction coefficient, varying between 0 and 0.8, with a moderate value of 0.4 used as default; and $\Delta {\mathsf{\sigma }}_{\mathrm{n}}$ is the normal stress change (positive for tension). Positive values of $\Delta \mathrm{CFS}$ on the receiver faults with a typical triggering threshold of ~0.1 bar (0.01 MPa) are more likely to promote failure and increase regional seismicity, while negative ones may inhabit failure and decrease seismicity [36].

In order to investigate the possible triggering mechanism of the sequence, the static stress changes were calculated based on the distributed slip model in this study. The calculations were performed using Coulomb 3.4 software [37], with an effective friction coefficient of 0.4 and a shear modulus of 32 GPa. Receiver fault parameters (i.e., strike, dip, and rake) were specified as 220°, 68°, and −165°, respectively, and were derived from the equivalent focal mechanism of our preferred model, which shows a slight discrepancy with focal mechanisms of GCMT [4], USGS [5], and NIED [6] F-net (Table S1). Static stress changes at various depths between 0 and 20 km were compared with the locations of Mw > 3.0 aftershocks that occurred before 30 April 2016. Only large and early aftershocks were selected in our analysis to reduce possible location errors and multiple interactions between aftershocks.

Figure 8 shows the static Coulomb stress, shear stress, and normal stress changes at different depths with an interval of 5 km, compared with the spatial distribution of Mw > 3.0 aftershocks. The localized pattern of Coulomb stress changes is significantly observed in the vicinity of fault zones and dominated by shear stress changes. At a depth of 2.5 km, the calculated Coulomb stress increases larger than 10 bars are mainly located near the most northeastern and southwestern ends of the fault zone, where aftershocks primarily occurred. The pattern of stress changes at a 7.5 km depth is similar to that at a 2.5 km depth, but is more complicated at a 12.5 km depth. The area with positive Coulomb stress changes at a 12.5 km depth is larger than that at a shallower depth, but the majority of aftershocks do not concentrate on the Coulomb stress increase regions. As the depth increases to 17.5 km, the positive ΔCFS area has only a few aftershocks and may have a potential seismic risk in the future. Additionally, if focal mechanisms are available, a more stringent calculation that resolves Coulomb stress changes on the nodal planes associated with the aftershocks can be conducted to assess whether or not the nodal planes are brought closer to failure. The focal mechanisms of aftershocks with Mw >5.0 from NIED F-net were selected to calculate Coulomb stress changes on the two conjugate planes at each hypocenter. The result highlights that six out of the seven aftershocks are positively affected by a Coulomb stress increase on at least one conjugate plane (

Table 3. Coulomb stress changes at the hypocenter resolved on the two conjugate nodal planes of the focal mechanisms of aftershocks with Mw >5.0.

ID	Origin Time (UTC)		Hypocenter			Mw	Nodal Plane 1		Nodal Plane 2
	yyyy/mm/dd	dd:mm	Latitude (°)	Longitude (°)	Depth (km)		Strike/Dip/Rake	$\Delta {\mathrm{CFS}}^1$ $\left(\mathbf{bar}\right)$	Strike/Dip/Rake	$\Delta {\mathrm{CFS}}^2$ $\left(\mathbf{bar}\right)$
1	2016/04/15	16:45	32.8632	130.8990	10.55	5.7	286/35/–70	−18.15	81/57/–104	–20.11
2	2016/04/15	18:03	32.9638	131.0868	6.89	5.5	209/60/–174	7.35	116/85/–30	7.79
3	2016/04/15	18:55	33.0265	131.1910	10.89	5.5	220/72/–167	1.09	126/78/–19	2.02
4	2016/04/16	00:48	32.8470	130.8350	15.91	5.2	230/38/–112	−4.43	77/55/–73	6.95
5	2016/04/16	07:02	32.6992	130.7200	12.30	5.1	255/30/–88	3.24	72/60/–91	–2.78
6	2016/04/18	11:41	33.0020	131.1998	8.64	5.4	314/86/3	2.38	224/87/176	1.07
7	2016/04/19	08:52	32.5352	130.6353	9.96	5.3	221/60/–169	2.45	126/81/–30	1.51

Coulomb stress changes were evaluated using our preferred slip distribution model and an efficient coefficient of friction of 0.4. The focal mechanisms originated from the F-net catalog of the National Research Institute for Earth Science and Disaster Resilience (NIED), Japan.

). Intriguingly, the largest aftershock (event 1) occurred just 20 min after the mainshock, but the Coulomb stress changes resolved on both conjugate planes show negative values. In general, static Coulomb stress triggering can explain the majority of Mw >5.0 aftershocks, but there are also some Mw >3.0 aftershocks within the stress shadow zone that may be triggered by other factors, which will be discussed in the following section.

5. Discussion

5.1. Seismogenic Fault Geometry

The fault model proposed in this study is composed of four-segment fault planes, including three northwest dipping planes (F2, F3, and FH) along the Futagawa and northern Hinagu faults and one southeast dipping plane (F1) along the northeastward extension of the Futagawa fault under the Aso caldera. The FH segment along the Hinagu fault zone has a strike of N205° and an estimated dip angle of 75°, in good agreement with other previous models [2,12]. The F3 segment with a strike of N226° connects the Futagawa and Hinagu faults, while the F2 segment has a strike of N236° along the Futagawa fault. The dip angles were estimated to be 63° and 57° for the F3 segment and F2 segment, respectively. The F1 segment with a strike of N40° and an optimal dip angle of 77° is located at the northeastward extension of the Futagawa fault, where dextral displacements exceeding 100 cm were observed in the field investigation [7]. Our preferred fault model is generally consistent with previous studies based on surface displacements and/or strong-motion waveforms [12,15]. For example, Fukahata and Hashimoto [12] obtained the dip angles of two faults, attaining values of 61° ± 6° for the Futagawa fault and 74° ± 12° for the Hinagu fault by inverting InSAR data. Zhang et al. [15] combined InSAR, GPS, and strong-motion data to construct a three-segment model, in which the Futagawa fault segment dips 60° to the northwest, the Hinagu fault segment dips 70° to the northwest, and a southeast dipping fault segment near the Aso volcano has a dip angle of 80°.

However, there are several studies proposing northwest dipping fault models in the Aso caldera region based on teleseismic and/or strong-motion data [10,38]. Is a southeast dipping fault model more reasonable than a northwest dipping one? We carried out additional tests to compare the RMSE and jRi values for the southeast dipping fault F1 and the northwest dipping one. The results (Figure S3) indicate that a southeast dipping fault F1 can better fit the observed data than a northwest dipping one. Ozawa et al. [13] suggested that a southeast dipping fault plane near the Aso caldera region should be considered to explain the complex deformation pattern obtained from SAR images. Yoshida et al. [14] also confirmed that the model with a southeast dipping fault predicted the observed subsidence around the central cones of Aso volcano better than a northwest dipping one. The vertical displacements calculated from our preferred model were utilized to confirm the predictive performance by comparing the data with those of previous models. The result (Figure S4) indicates that our four-segment model with a southeast dipping F1 segment can better explain the subsidence around the Aso volcano from the decomposition of InSAR data [3,39].

5.2. Comparison with Previous Slip Distribution Models

The checkerboard and jackknife tests (Appendix A) show that the slip distribution model on each segment is well-constrained by the combination of InSAR and GPS data. Our preferred model is in general agreement with previous models based on teleseismic waveforms [1], strong-motion data [2,10], geodetic data [39,40], or combinations of them [3,11,15]. Consensus has been reached on at least three things, which are: (1) multi-segment faults with varying fault geometries ruptured during this earthquake; (2) the ruptures initiated at the Hinagu segment and propagated unilaterally to the northeastern extension of the Futagawa fault under the Aso caldera; and (3) the slip on the Hinagu fault (FH) was almost purely right-lateral strike-slip, and the Futagawa fault (F2 and F3) was dominated by right-lateral strike-slip, along with a significant normal slip component. However, there are some inconsistencies in the maximum slip and slip pattern. Our preferred slip distribution model shows that each segment has a concentrated slip area (asperity) and the largest asperity is located on the F2 segment, with a peak slip of 5.6 m at a 5–6 km depth. The maximum slip (5.6 m) is similar to the results of [1,2,11,12], but smaller than those of [3] (~10 m), [15] (7.4 m), and [41] (6.9 m). The slip pattern discrepancy may be attributed to the different data sets, model regularizations, and parameterizations employed. For example, Yue et al. [3] combined GPS, strong-motion, InSAR data from both ALOS-2 and Sentinel-1A images, and surface offsets to invert the kinematic rupture process on the curved multi-segment fault planes. They selected a smaller smoothing factor based on the consistency between the calculated Coulomb stress and aftershock distribution, which might overestimate the peak slip. Using Sentinel-1A imagery, GPS, and strong motion data, Zhang et al. [15] also inverted the slip distribution on the three-segment fault planes. Compared with our model, Zhang et al. [15] constructed the fault model with a similar southeast-dipping fault near the Aso volcano and generated a rougher slip pattern, choosing a smaller smoothing factor with the L-curve method. In our model, the Futagawa fault is parameterized into two segments (F2 and F3) and has two different asperities, which are consistent with the third and fourth asperity locations in Yue et al.’s model [3]. In summary, based on adequate constraints of InSAR (both ALOS-2 and Sentinel-1A images) and GPS datasets, our preferred model selects an optimal smoothing factor with the jRi method and presents a more plausible slip pattern.

5.3. Shallow Slip Deficit

The estimated slips on the shallowest sub-faults along the Futagawa and northern Hinagu faults are consistent with the displacements of surface ruptures from the field investigation [7] (Figure 5). On the F2 segment, the estimated slip has a peak of 5.6 m at a 5–6 km depth and diminishes to an average of 2 m near the surface, which implies a shallow slip deficit (SSD) of ~65% (Figure 5). A similar SSD also occurred on the other three segments. Previous studies have demonstrated that SSD might be caused by velocity-strengthening friction at a shallow depth that can be recovered through shallow afterslip [42,43] or distributed coseismic brittle damage in the uppermost crust layer [44,45]. Moreover, some studies have shown that SSD can also arise from artifacts due to a lack of near-fault data [46] or from model uncertainties [47]. However, the SSD in this study is real because the slip near the surface was estimated well in the inversion, and a similar SSD was also obtained using near-fault data in several previous studies [3,41]. Interestingly, Yue at al. [3] and Moore et al. [48] both observed significant post-seismic deformation close to the faults, which might arise from afterslip at a shallow depth. Therefore, velocity-strengthening friction at shallow depths is more likely to be the mechanism that produces significant SSD, but the “distributed brittle failure” explanation cannot be ruled out from the currently available observations.

5.4. Sensitivity Analysis of Coulomb Stress Change

Although the majority of Mw > 5.0 aftershocks with available focal mechanisms support static Coulomb stress triggering, the entire aftershock sequence cannot be explained well by the calculated Coulomb stress changes on the receiver fault that is parallel to the seismogenic fault of the mainshock. A few aftershocks occurred in the stress shadow regions characterized by negative stress changes. Given that the calculation of Coulomb stress change involves three variables ($\Delta {\mathsf{\tau }}_{\mathrm{s}}$, $\Delta {\mathsf{\sigma }}_{\mathrm{n}}$, and ${\mathsf{\mu }}^{\prime }$ in Equation (3)), the sensitivity of Coulomb stress calculations to the effective coefficient of friction, receiver fault, and source model also needs to be investigated. The effective coefficient of friction varies from 0.2 to 0.8 for different types of fault. The mainshock focal mechanisms from NIED, GCMT, USGS W-phase, and this study were adopted to define receiver faults in four different scenarios, respectively. Furthermore, six available finite fault slip models inverted from different datasets shown in Table S1 were collected to address the sensitivity of the source model. The result of the sensitivity tests (Figures S5–S7) indicates that the source model plays a more important role in the Coulomb stress calculations, especially in the case of a complex rupture event, while the receiver fault geometry and effective friction coefficient have a slight effect on the size of the Coulomb stress change area. A comparison of Coulomb stress changes calculated with different source models shows that the differences are apparent near the faults, and source models (i.e., Yue et al. [3], Zhang et al. [15], and our study) inverted from various datasets jointly can generate a more detailed stress change pattern which can better explain the spatial distribution of seismicity. In all scenarios, there are some common features in that the static Coulomb stress increase significantly triggers aftershocks located in the northern part of the Aso volcano, and a few aftershocks in a stress shadow area may be driven by aseismic creep [3,49] or triggered by dynamic stress transfer [50], which requires further investigation.

6. Conclusions

The complex coseismic deformation field associated with the 2016 Kumamoto earthquake sequence is derived from Sentinel-1A and ALOS-2 SAR images. Together with GPS data, InSAR data provide powerful constraints on the fault geometry and slip distribution of the seismogenic fault. Based on surface ruptures, active fault traces, InSAR deformation maps, and seismicity, we constructed a four-segment fault model with one southeast-dipping fault plane and three northwest-dipping fault planes. The fault dip angles of the four segments were determined well with the jRi method, which exhibited a better performance than the conventional RMSE method. Our preferred slip distribution model reveals a single asperity on each segment with a maximum slip of 5.6 m on the F2 segment and suggests a significant shallow slip deficit that may be caused by velocity-strengthening friction at shallow depths. Areas with large slips are spatially complementary to the distribution of aftershocks. The total geodetic moment release was estimated to be 4.89 × 10¹⁹ Nm, equivalent to an Mw 7.09 event. The Coulomb stress calculation and its sensitivity analysis indicate that static Coulomb stress triggering can only explain part of the aftershock sequence, while aftershocks that occurred in a stress shadow area may be triggered by other factors, such as aseismic creep or dynamic stress transfer.