Supplementary: 2016 Kumamoto Mw = 7.2 earthquake: a significant event in the fault-volcano system

Han Yue1, Zachary E. Ross2, Cunren Liang3, Sylvain Michel2,4, Heresh Fattahi2, Eric Fielding3, Angelyn Moore3, Zhen Liu3, Bo Jia1

1. School of Earth and Space Sciences, Peking University, Beijing, 100871

2. Seismological Laboratory, California Institute of Technology, Pasadena, CA, USA

3. Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA, USA

4. Department of Earth Sciences, University of Cambridge, Cambridge, UK

3D co-seismic ground displacement reconstruction from SAR images

SAR images are considered as the original 3D ground displacement projected to a

particular direction, i.e. line-of-sight direction for interferometry and azimuth

direction for azimuth-offset images. Therefore, the observed data can be presented by

a linear product between the ground displacement and the unit vector.

[ UeUn Uv ]∗[ ENV ]=D

Where E N V represents eastward, northward and vertical ground displacements;

Ue, Un Uv represents the unit vector component in east, north and vertical directions

respectively.

D represents the displacement in the LOS/AZO directions.

If we sort the 3D displacement of each point as one vector, this relationship can be

written as

U∗A=D

U represents the matrix of unit vector

A represents the 3D displacement vector

D represents the projected ground displacement.

To recover 3D displacement for each point as A, we need images projected to more than 3 different directions to ensure the U to be positively determined thus U−1 and U

can be estimated as A=(U ' U )−1 U ' D as a least square problem.

Assume we have approximately 105 data points (~300*300 pixel image), the scale of

U is 105*105 and the calculation of U-1 is quite time consuming. It need to be noticed

that within one image the unit vector doesn’t change significantly, which is of

typically ±1°. For this study, we only aim to shows the pattern of ground

displacements instead of using 3D ground displacement for quantitative calculation

we consider the unit vector as uniform in each SAR image and U matrix is a n*3

matrix, where n represents number of images, which is 4 in this our problem. With this assumption, U †=(U ' U )−1U ', as a 3*4 matrix, can be calculated easily. With

such expression displacement vector A and data vector D has the form of

A=[Ue UnUv ]D= [D1 D2 D 3 D4 ]

A=U † D

This calculation can be realized within seconds using single CPU.

One issue of this method is several pixels of some images may be de-correlated which

is taken as NaN values in the D matrix. Therefore, A matrix also has NaN pixels.

Such decorrelated pixels locate mostly close to the fault surface traces, where co-

seismic displacements are large that the pixels in interferometry tends to be

decorrelated. We smooth correlated pixels out to fill in those pixels to estimate

displacement values at those points.

Fault plane reconstruction from catalog

Relocated catalog is used to identify fault traces at depths to reconstruct fault

geometry at depths. Micro-seismicity lineation is most significant at 12-14 km depths

(figure 2b), thus fault geometry is mainly made reference to the surface and depth

(>12 km depth) traces. Other approaches such as tracing fault segments through fault

cross-sections is also used to identify fault traces, yet we found it is extremely

difficult to follow the aftershock lineation over different cross-sections. Therefore, we

finally used the depth cut catalog to parameterize the fault plane (figure 2). Fault trace

and aftershock cross-sections are plotted in figure S1 for people’s reference.

Figure S1. Seismicity distribution is plotted in the left panel. The fore- and aftershock

loci are marked as dots with the hypocentral depth coded by the filling color.

Boundaries of five profiles are plotted with black boxes. The projected aftershock loci

and fault traces are plotted on the right panels. Fault boundary and traces of three fault

planes are plotted with red, blue and magenta curves in all images.

Data processing and GF computing

Strong motion data

We used three component acceleration waveforms recorded by 7 K-net and KiK-net

stations. Three ground surface (KMM) and four borehole stations (KMMH) stations

are used. Original acceleration waveforms are integrated into velocity recordings. All

waveforms are bandpass filtered with corner frequencies at 0.05 and 0.5 Hz and

down-sampled at 4 sps. Time segment of 0 to 30s reference to the mainshock initial

time is used to cut the waveforms. Green’s functions are computed reference to the

local 1D velocity structure at each station using a frequency-wavenumber integration

method [Zhu and Rivera, 2002]. Displacement Green’s functions are calculated and

differentiated to extract velocity waveforms. The same band-pass filter, down-

sampling and time cut are applied to the Green’s functions.

GPS

We use three component ground displacement recordings recorded by 39 GPS stations

of Geo-net. The original GPS data are process. The high-rate (hr) 5hz GPS time series

were processed using kinematic precise point positioning with GIPSY-OASIS

[Zumberge et al., 1997] and single station ambiguity resolution [Bertiger et al., 2010].

Both standard and high-rate processing fixed the GPS satellite orbits and clocks to the

JPL FLINN final orbit products [Desai et al., 2009]. The IGS antenna phase center

variations were applied to reduce errors due to antenna-specific azimuthal and

elevation dependent changes in the antenna phase center [Schmid et al., 2007]. Hr-

GPS recordings are estimated with 20 min interval. Co-seismic offsets of fore-shock

period are obtained by displacements happened 60 min before the first major

foreshock and 60 min after the second foreshock. Co-seismic offset of the mainshock

are obtained by displacements happened 60 min before and after the mainshock. One

hour time window is used to average the GPS displacement measurement to reduce

data variation. Three component displacements of 11 GPS stations recording the

foreshock displacement and 39 GPS stations recording the mainshock displacement

are used in the inversion to invert for the fore- and mainshock slips simultaneously.

The contribution of each conceptual to the GPS datasets are summarized in Table S2.

SAR images

We consider 6 synthetic aperture radar (SAR) based measurements of the co-seismic

displacement field produced by interferometric SAR (InSAR) and SAR pixel tracking

techniques (Figure 2d). We obtained focused radar images from the Japan Aerospace

Exploration Agency (JAXA) Advanced Land Observing Satellite 2 (ALOS-2) and the

Copernicus Sentinel-1A satellite. We processed the SAR data using

the InSAR Scientific Computing Environment (ISCE) [Rosen et al., 2012] with

prototype extensions for the Sentinel-1 TOPS mode [Fattahi et al, 2017] and ALOS-2

multi-mode images [Liang and Fielding, 2017 a and b]. We consider InSAR data

from three descending ALOS-2 orbits and one ascending Sentinel-1 orbit. Five SAR

measurements recorded the co-seismic deformations of both the main and fore-

shocks, yet one SAR image with a repeat date between the main- and fore-shocks

recorded the deformation happened during the foreshock period (Table S1).  

We coregister Sentinel-1 SAR images using precise orbits and SRTM DEM. We

multilook the interferogram by 3 and 9 looks in azimuth and range directions,

respectively. We then filter each interferogram using Goldstein Filter. Due to the large

near fault deformation, the C-band Sentinel-1 interferogram is less coherent than the

L-band ALOS2 interferograms. Therefore we carefully unwrap the Sentinel-1

interferogram by masking out the incoherent regions and enforce phase unwrapping

passes around the fault rather than crossing the fault. Multiple frames of ALOS-2

images are processed to completely cover the deformation area. Ionospheric phase is

removed by the range split spectrum method [Rosen et al, 2010, Liang and Fielding,

2017 b]. The ALOS-2 images are also used to do SAR pixel tracking. We remove the

topographic effects by doing a geometrical coregistration before pixel tracking.

Table S1 shows a complete list of SAR data used.

These SAR observations provide complete sampling of the three-component static

ground displacement field [Fialko et al., 2001; Pathier et al., 2006]. The InSAR and

SAR pixel offset images are resampled with a resolution based sampling

technique [Lohman and Simons, 2005] which ensures higher sampling density in

regions that best constrain the distribution of slip (Figure 2). Area close to the surface

fault trace presents in-elastic deformation, which can not be modeled with elastic

synthetics. We mask out the sample points located within 2km from the surface fault

trace. Areas with significant surface cracking are also observed to the NW end and

SW end of the co-seismic rupture, that we also mask out these two areas (Figure

S1). A total of 4314 sample points is extracted from these images and used in our

joint inversion. Green’s functions for static ground displacement are based on Wang

et al. [2003]. The three-component ground displacement field is computed and

projected to the satellite line-of-sight (LOS) or azimuth direction for each sample

point. We invert for a quadratic spatial ramp for six SAR deformation

images simultaneously with the model parameters to account for potential artifacts

due to inaccurate orbital information and long wavelength propagation effects.  

Table S1: SAR data information

Satellite TrackEarthquakes

recorded

Reference

DateRepeat Date Interferogram

Azimuth

offset

Δig (days

before

main)

Δps (days

after

main)

ALOS-2D02

3Fore+Main 07-Mar-2016

18-Apr-

20161 4 7 3

ALOS-2D02

Fore+Main 14-Jan-201620-Apr-

20162 5 92 5

Sentinel-1A Fore+Main 08-Apr-201620-Apr-

20163 ✕ 7 5

ALOS-2D02

8Fore 23-Jan-2015

15-Apr-

20166 ✕ 83 -1

Optical Image Offset

We calculated the ground horizontal displacement field from sub-pixel correlation of

pre- and post-earthquake satellite optical images using the COSI-Corr software

(Coregistration of Optical sensed Images and Correlation) [Leprince et al., 2007a;

Ayoub et al., 2009]. Two LandSat-8 panchromatic images (15m resolution) from

2015-05-21 and 2016-05-23 were used, taking into account a time period which

includes the foreshocks, the mainshock and the early post-seismic deformation of the

Kumamoto earthquake. Horizontal offsets across the surface fault trace are obtained

by line fitting the near field displacement on each side of the fault. The fault normal

and parallel components of the displacement at the fault trace are then used in the

inversion to constrain the right lateral and normal slip components of the co-seismic

slip of the foreshocks and mainshock.

Model parameterization

We parameterize the Kumamoto earthquake sequence as three conceptual sub-events,

that the first event represents the kinematic rupture during the mainshock happened on

the main fault plane; the second event represents the static slip happened during the

foreshock period, which happened on the main and third fault planes; the third event

represent the static slips of the mainshock happened on the second and third fault

planes. The status of each subevent and their associated contribution to each dataset

are summarized in Table S2.

Table S2: Slip model parameterization

Subevent

Index

Related

earthquake

Rupture

status

Fault

plane

Strong

motion

GPS

Main

GPS

Fore

SAR1-5 SAR6

1 Mainshock dynamic 1

2 Foreshock

s

Static 1，3

3 Mainshock Static 1，2，3

Data fitting

Fits to all datasets are plotted in figure S2-S5. Variance reduction of 94%, 86%, 91%

and 91% are achieved for the static GPS, strong motion, SAR and pixel offset data

respectively. All datasets are fitted reasonably well.

Figure S2. Waveform fits to strong motion recordings of the mainshock waveforms.

Three component waveforms are plotted in each column, respectively. Observed and

synthetic waveforms are plotted in black and red, respectively.

Figure S3. Co-seismic ground displacement recorded by GPS stations are plotted in

each panel. Co-seismic ground displacements for the mainshock and foreshock period

are plotted in the top and bottom panels, respectively. Horizontal and vertical

displacements are plotted in the right and left panels, respectively. Observed and

synthetic ground displacements are plotted in black and red, respectively.

Figure S4. Observed, residual and orbit corrected ground deformations are plotted in

the left, middle and right columns, respectively. Line of sight (LOS) and azimuth

directions are indicated for each row. Satellites that collected those data and

projection mode are indicated on the right. Events recorded by each image are

indicated on the left.

Figure S5. Displacement maps acquired from correlation of Landsat 8 satellite images. (a) East-West component of displacement. (b) North-South component of displacement. The thick black line corresponds to the fault trace used to get the displacement along the fault.

Figure S6. a,b, right-lateral and normal offsets calculated from the optic image pixel-

tracking technique are plotted in each subplots in the along fault direction (starting

from NE). Observed and synthetic offsets are plotted in red and black, respectively. c.

Lateral offset observed on the ground surface are plotted as arrows along the top edge

of the fault model. Plotting scale for 1m offset is indicated. Significant normal offset

components are observed to the northern end of the fault trace.

Inversion results of fore- and mainshock slips

Figure S7

Co-seismic slip pattern from the joint inversion results are plotted in the map-plane

view. The mainshock and foreshock slips are plotted in the top and bottom panels,

respectively. Three fault planes are plotted in each column. The slip amount is plotted

with a white to black color scale and different saturations are used for the mainshock

and foreshock slips. Slip directions are plotted as black arrows.

Inversion of foreshock slips with/without slips on the main fault plane

Figure S8. a, inversion results of foreshock ruptures with/without slips on the main

fault plane are plotted in the top/bottom panels, respectively. Slip distribution are

plotted with a white-black color scale with respect to different color-scales. b,

residuals of fitted SAR interferometry from two slip models are plotted at the

top/bottom panels, respectively, with identical color scale.

Calculation of topographic stress anomalies

We calculate the stress anomaly introduced by topographic weight using Boussinesq

approximation [Boussinesq, 1885]. The topographic weight is estimated as a vertical

point force load calculated from ρgh, where ρis the rock density (3.3 ×103 kg/m3),

g=9.8 m/s2 and h is the topographic height. For each target depth, we calculate stress

tensors (3*3 stress tensors) in response to point force loading. Distribution of 6

independent components of the stress tensor at 1 km and 5 km in response to a point

loading are plotted in figure S9. The influencing distance scales up with the target

depth. Point force response is then convolved with the 2D topography distribution to

calculate topographic stress anomalies at each depth. Stress tensor distributions is

projected to the receiving fault plane to calculate three stress components including

the fault normal stress and shear stress in two orthogonal directions. Shear stresses are

thus projected to the normal slip direction to calculate the associated shear stress.

Figure S9. Distribution of 6 components of stress tensors (stress kernel) at 1 km and 5

km depths in response to a vertical point force loading at ground surface (130E 32N).

The stress kernel is computed with analytical solution and convolved with the

topographic weight at the ground surface.

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