NHESSNatural Hazards and Earth System SciencesNHESSNat. Hazards Earth Syst. Sci.1684-9981Copernicus PublicationsGöttingen, Germany10.5194/nhess-17-143-2017Calculation of coseismic displacement from lidar data in the 2016 Kumamoto,
Japan, earthquakeMoyaLuislmoyah@uni.peYamazakiFumioLiuWenChibaTatsuroDepartment of Urban Environment Systems, Chiba University, Chiba
263-8522, JapanResearch and Development Institute, Asian Air Survey Co., Ltd.,
Kawasaki 215-0044, JapanLuis Moya (lmoyah@uni.pe)1February201717114315627September201630September20166December20167January2017This work is licensed under a Creative Commons Attribution 3.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by/3.0/This article is available from https://nhess.copernicus.org/articles/17/143/2017/nhess-17-143-2017.htmlThe full text article is available as a PDF file from https://nhess.copernicus.org/articles/17/143/2017/nhess-17-143-2017.pdf
The spatial distribution of the coseismic displacements
that occurred along the Futagawa fault during the 2016 Kumamoto earthquake
of Mw 7.0 was estimated using airborne light detection and ranging
(lidar) data. In this study, a pair of digital surface models (DSMs)
obtained from the high-density lidar data before and after the mainshock on
16 April 2016 were used. A window matching search approach based on the
correlation coefficient between the two DSMs was used to estimate the
geodetic displacement in the near-field region. The results showed good
agreements with the geodetic displacements calculated from strong-motion
acceleration records and coincided with the fault line surveyed by the
Geological Survey of Japan.
Introduction
On 14 April 2016, an Mw 6.2 earthquake struck Kumamoto Prefecture,
Japan, at 21:26 JST. The epicenter was located at the end of the Hinagu
fault at a shallow depth. After approximately 28 h (at 01:25 on 16 April 2016), another earthquake of Mw 7.0 struck the Futagawa fault, which is
near the Hinagu fault. The first event was designated as the foreshock and
the second one as the mainshock. Both the events occurred in the town of
Mashiki (with a population of approximately 33 000), which is located to
the east of Kumamoto City (with a population of approximately 735 000).
Many aftershocks followed these events, and as of 6 September, 4 months
after the foreshock, the total number of aftershocks (larger than Mw 3.5) is
272. This number is the largest among the recent inland (crustal)
earthquakes in Japan (Japan Meteorological Agency, 2016). This Kumamoto
earthquake sequence triggered secondary effects such as landslides and
liquefaction and caused extensive damage to lifeline systems, buildings,
bridges, and transportation structures. A total of 8550 buildings, mostly in
Kumamoto Prefecture, were seriously damaged or collapsed, and 50 human lives
were lost, mostly because of landslides or the collapse of buildings
(Cabinet Office of Japan, 2016).
Soon after the occurrence of the foreshock, various satellites and airborne
remote sensing technologies were employed to monitor crustal movements and
various damages (Yamazaki and Liu, 2016). The Japan Aerospace Exploration
Agency (JAXA) carried out extensive monitoring of the source area using the
PALSAR-2 sensor on board ALOS-2 satellite. Interferometric synthetic
aperture radar (InSAR) analysis using a pair of imagery data obtained from PALSAR-2
before (pre-event data) and after (post-event data) the mainshock showed the
line-of-sight (LOS) displacements to the satellite direction (Geospatial
Information Authority of Japan, 2016). Using the pre-event data (30 November 2015, 7 March 2016) and the co-event data (7 March, 18 April 2016)
from PALSAR-2, the authors of this paper calculated the spatial
coherence values (International Charter, 2016), which could highlight the
extensive landslides and severe damages to buildings along the Futagawa
fault line.
After the Kumamoto earthquake, government agencies and aerial survey
companies in Japan conducted several aerial surveying flights such as
high-resolution vertical and oblique aerial photography and airborne light
detection and ranging (lidar) surveys (Asia Air Survey Co., Ltd., 2016;
Geospatial Information Authority of Japan, 2016).
The airborne lidar technology is an integrated system consisting of a Global
Navigation Satellite System (GNSS), an inertial navigation system (INS), and
a laser scanner, which sends pulses of laser light towards the ground and
records the return time for calculating the distance between the sensor and
the ground surface (Lillesand et al., 2004). Lidar has many applications in
earthquake engineering, such as landslide detection (Jaboyedoff et al.,
2012) and extraction of building features (Vu et al., 2003,
2009). Lidar data have been used in estimating ground displacement as well.
Muller and Harding (2007) used the elevation of uplifted marine terraces
mapped in the lidar data to estimate the source parameter of the AD 900
Seattle fault earthquake. Sahakian et al. (2016) used lidar data, in
combination with other technologies such as seismic reflection, to identify
a previously unmapped right-lateral strike-slip fault located in the Salton
sea, California, USA. They used the lidar data to constrain the onshore
deformation.
Usually, only post-event lidar data are available; thus, the coseismic
displacement detection is limited to the identification of distortions of
line features such as roads. Li et al. (2016) detected an offset of car
tracks produced during the 2014 Mw 6.9 Yutian earthquake, Tibetan Plateau,
by visual inspection. Chen et al. (2015) extracted two topographic profiles
from lidar data collected after the 1999 Mw 7.1 Hector Mine earthquake,
California. The profiles were parallel to the fault line and located on
either side of the fault in order to estimate the slip during the
earthquake. There are few cases in which lidar data both before and after an
earthquake were available. The first case was in the 2010 Mw 7.2 El
Mayor–Cucapah earthquake. Oskin et al. (2012) performed a simple difference
of elevation to estimate the surface rupture; however, they did not consider
the horizontal displacement. Two more earthquake events, the 2008 Mw 6.9
Iwate–Miyagi earthquake and the 2011 Mw 7.1 Fukushima–Hamadori
earthquake,
were monitored by lidar data acquired before and after the event. Then
Nissen et al. (2014) estimated the 3-D displacement using the Iterative
Closest Point (ICP) algorithm (Nissen et al., 2012). Their results showed a
coherent displacement but with high level of noise in the horizontal
component.
Cross-correlation technique has been used successfully to monitor movements.
Duffy and Hughes-Clarke (2005) applied cross-correlation to monitor the
movements of seafloor dunes using bathymetry data. Liu et al. (2011)
extracted the shifts of vehicles between the panchromatic and multispectral
QuickBird images, which were taken with a time lag of approximately 0.2 s, and then they estimated the vehicles' velocity. Liu and
Yamazaki (2013) calculated the crustal displacement during the 2011 Mw 9.0 Tohoku
earthquake by estimating the shift of undamaged buildings using the
cross-correlation coefficient between the TerraSAR-X intensity images
taken before and after the earthquake. Borsa and Minster (2012) evaluate the
potential use of cross-correlation using lidar data by applying a synthetic
slip to the lidar data of the southern San Andreas fault and then their
result could recover the synthetic slip. Duffy et al. (2013) also used a
pair of lidar data taken before and after the 2010 Mw 7.1 Darfield, New
Zealand, earthquake to calculate the horizontal coseismic displacement.
Measurements of the coseismic displacement in the near field is of great
importance because it can be used to locate the source and to understand the
rupture process. Wang et al. (2013) inverted the coseismic displacement
calculated from GNSS and strong-motion stations to modulate the earthquake
source of the 2011 Mw 9.0 Tohoku earthquake. Earthquake source inversion
methods have become important in the last years because of their potential for
forecasting tsunamis (Melgar and Bock, 2013). The GNSS devices calculate
positions and are nowadays used for continuous monitoring of the earth
crust. Strong-motion devices record acceleration or velocity, and in most of
the cases a baseline correction is required before estimating the correct
displacement time history because the baseline is shifted as a result of
several factors such as ground rotation and rocking movements of the
instrument. The displacement time history can be calculated precisely if the
six components, three translational and three rotational, are recorded
(Graizer, 2010). However, the displacement time history is often estimated
by a double integration of only the translational components with respect to
time. Up to now the source of errors and the rotation components cannot be
quantified and only empirical methods have been proposed in the past to
reduce the effect of the baseline shift and retrieve a reliable displacement
time history. One of the first methods was proposed by Iwan et al. (1985), in
which a bilinear function is used to estimate the velocity trend caused by
the baseline errors. Several modifications of this approach have been
proposed. Wu and Wu (2007) defined the bilinear function in an iterative
process in a way that the displacement time history best fits a ramp
function. Later, Wang et al. (2011) also proposed an iterative procedure,
but they used a step function to constrain the displacement time history.
Moya et al. (2016) used a pair of strong-motion records that were closely
located and perform a simultaneous correction of both records.
Although there have been a great improvement and deployment of GNSS and
strong-motion networks, even the densest network, either GNSS or
strong-motion, has a low spatial resolution. For instance, the nationwide
GNSS network of Japan has one station in an about 20 km interval. Thus, for
an earthquake of moderate magnitude, where the coseismic displacement is
concentrated in a narrow area, it is difficult to depict the spatial pattern
of coseismic displacement. SAR satellite images offer a better spatial
resolution, but SAR requires a pair of images with the same viewing condition
to calculate the coseismic displacement to the LOS of radar.
More pairs of SAR images from different views, which are not very realistic,
are required to obtain 2.5-D or 3-D coseismic displacement.
Map of the near-source area of the 2016 Kumamoto earthquake,
showing the areas of the pre-event DSM (black solid polygon) and the
post-event DSM (black dashed polygon), the distribution of the GNSS and
seismic stations, active fault lines in Japan (red lines), and epicenters
(Mw 6.2 14 April 2016; Mw 7.1 16 April 2016).
Another use of coseismic displacement comes up when the effects of an
earthquake in the near field are estimated using remote sensing techniques.
It is necessary to consider the permanent displacement if an automatic
change detection is applied to extract collapsed buildings or quantify the
mass movement in landslides.
This paper estimates the coseismic displacement due to the mainshock of the
Kumamoto earthquake using the digital surface models (DSMs) obtained from
airborne lidar flights (Asia Air Survey Co., Ltd., 2016). In this case
study, a pair of DSMs, one soon after the foreshock (on 15 April, 15:00–17:00 UTC + 09:00) and another after the mainshock (23 April,
10:00–12:00 UTC + 09:00), corresponding to the town of Mashiki, which includes the
causative Futagawa fault, were used. The obtained results are compared with
the permanent ground displacements estimated from fields surveyed data and
using the acceleration records obtained from KiK-net, K-NET, the
strong-motion seismograph network of Kumamoto Prefecture, and a temporary
observation system (Hata et al., 2016).
Study area and data description
On 15 April 2016, 1 day after the big foreshock, a lidar DSM was acquired
to record the surface rupture and various effects of the earthquake, such as
buildings damaged and landslides (Asia Air Survey Co., Ltd., 2016). The
survey generated a DSM of average point density 1.5–2 points m-2.
Furthermore, because of an unexpected mainshock of Mw 7.0 on 16 April,
a second mission was set up on 23 April to acquire lidar data. The second
survey was able to generate a DSM of average point density 3–4 points m-2. After the rasterization of the raw point clouds, the DSMs
have a data spacing of 50 cm and are registered to the Japan Plane
Rectangular Coordinate System. This data set is one of the few cases in
which pre- and post-event DSMs are acquired by the same pilot using the same
airplane and instrument. For the sake of brevity, we will call the DSMs
acquired on 15 and 23 April the pre-event DSM and the post-event
DSM, respectively.
Figure 1 illustrates the extension of these two DSMs in which the pre-event
DSM extends to a bigger area than the post-event DSM does. The common area
between both the DSMs covers most parts of Mashiki town and a few parts of
Kashima town, Mifune town, and Nishihara village with elevations ranging
from 1 to 500 m (Fig. 2). The entire common
area is composed of residential buildings, agricultural fields, forests, and
a part of the Futagawa fault that caused the mainshock of the Kumamoto
earthquake.
DSMs acquired by Asia Air Survey Co., Ltd. (2016) on 15 April 2016 (pre-event DSM) and 23 April 2016 (post-event DSM).
The Kumamoto earthquake occurred in an area that is sufficiently equipped
with several GNSS instruments that belong to GEONET (Sagiya, 2004) and
strong-motion instruments that belong to KiK-net, K-NET (Aoi et al., 2004),
the strong-motion seismograph network of Kumamoto Prefecture, and a temporal
network deployed by Hata et al. (2016). Figure 1
indicates the location of all the stations within and near the study area.
GEONET consists of approximately 1300 GNSS control stations that cover the
entire territory of Japan with an average interval of 20 km. K-NET consists
of more than 1000 strong-motion accelerometers installed on the ground
surface at every 20 km covering Japan. KiK-net consists of approximately
700 stations and each station has a pair of accelerometers installed on the
ground surface and in a borehole in bedrock. The strong-motion seismograph
network of Kumamoto Prefecture consists of strong-motion accelerometers
installed at the municipality building sites.
Examples of surface ruptures caused by the 2016 Kumamoto
earthquake. Paddy field (P1), river channel (P2), road crossing in Kamijin
and Shimojin districts of the town of Mashiki observed on 17 April 2016 (P3), and crop field in Dozono district of the town of Mashiki observed on
7 June 2016 (P4). The locations of the photographs are shown in Fig. 1.
Example of coseismic displacement extracted from lidar
data: (a) aerial image of buildings near the Mashiki KiK-net station acquired on
15 April 2016; (b) color composite of the post-event (red) and pre-event
(cyan) DSMs for the same area where the yellow arrows depict the direction
and amplitude of the coseismic displacement.
Schematic image of the maximum correlation search algorithm.
Selection of the pre-event DSM (blue) and post-event DSM (red)
windows (a), subpixel discretization of the DSMs (b), and
calculation of correlation coefficient by moving the window of the post-event
DSM over the pre-event one (c).
The evidence of coseismic displacements has been observed in the form of
surface ruptures in agriculture fields, river channels, and roads along the
Futagawa fault line during the Kumamoto earthquake
(Fig. 3). The surface ruptures were caused by the
opposite displacements (right-lateral strike slips) between both the sides
of the fault. A comparison of the pre-event DSM with the post-event DSM
gives a clearer evidence of the coseismic displacements.
Figure 4 shows an overlap of the two DSMs where the
pre- and post-event DSMs are represented by cyan and red colors,
respectively. The gray-colored pixels represent the locations that have the
same elevation in both the pre- and post-event DSMs, whereas the
cyan-colored pixels represent the locations that have a higher elevation in
the pre-event DSM and the red-colored pixels represent the locations that
have a higher elevation in the post-event DSM. Therefore, the colors around
the sides of the houses depicted in Fig. 4b show
that the coseismic displacement occurred to the northeast direction.
Illustration of noise generated in the coseismic displacement for a
window of size 201 × 201 pixels (a) and
101 × 101 pixels (b). The black square in the inset map
shows the area of the main figure.
Methodology
To calculate the horizontal component of the coseismic displacement
distribution in space, we introduced a maximum correlation search algorithm
using a moving window of the post-event DSM within a corresponding larger
area of the pre-event DSM. The method is developed based on the fact that
both the pre- and post-event DSMs cover the same objects, such as
non-damaged buildings. This fact can be used most efficiently for
calculating the spatial cross-correlation between the DSMs. At any location,
the pixel shift necessary to match the pre-event DSM with the post-event DSM
is assumed to be the coseismic displacement at the location. However, the
coseismic displacement is variable in space and has to be calculated using
sub-areas (windows). Figure 5 shows a scheme of the
coseismic displacement search method. First, we consider a square sub-area
of the post-event DSM and a bigger sub-area of the pre-event DSM with their
centers located at the same coordinate (Fig. 5a).
Then, we reduce the pixel size using a cubic convolution method
(Fig. 5b). The post-event window is moved across
the pre-event window, and the cross-correlation coefficient is calculated
for the moving area (Fig. 5c). The location of
the pixel that has the largest correlation value is considered as the
coseismic displacement for that window. The horizontal component of the
coseismic displacement was applied to the post-event DSM to cancel it, and
then the vertical displacement between the two DSMs was calculated. It is
worth mentioning that the cross-correlation was chosen among other
candidates, such as a least-square difference or convolution, mainly because
the peak value was located in a narrower area.
It is not necessary to calculate the correlation for all the locations
because it requires unnecessary computational efforts. A better procedure is
to move the post-event window along the direction in which the
cross-correlation is increasing faster until the peak is reached. This
approach, well known as the steepest method, was applied to calculate the
coseismic displacement for all the study areas. Thus, in this approach, only
the size of the post-event window has to be defined and the rest is done
automatically. However, selecting the size of the post-event window is
crucial because the window should be large enough to include several
distinct objects. For instance, if a post-event window of 1.5 m × 1.5 m (3 × 3 pixels)
is chosen, the peak value of cross-correlation might not be
obtained when the window is located in the middle of a flat building roof or
a big bare land. Therefore, it is recommended to define a window that
includes some buildings or different topography. However, there exists a
trade-off between the size of the window and resolution because the
resolution of the spatial variation of the coseismic displacement decreases
with the increase in the size of the window.
The code for implementing the method was written in Python, an open-source
programming language, in order to use the large collection of scientific
open-source modules. Numpy, a numerical array-programming module, was used
to calculate the cross-correlation. OpenCV (Open Source Computer Vision
Library) was used to reduce the resolution of pixels using the cubic
convolution method. GDAL (Geospatial Data Abstraction Library) was used to
georeference all the inputs and outputs.
Histogram and cumulative distribution of the correlation
coefficient. Only 14 pixels out of 9195 have a correlation coefficient less
than 0.6.
East–west (a) and north–south (b) components of
the coseismic displacement obtained from the maximum cross-correlation search
of the lidar DSMs.
Estimated three-dimensional coseismic displacement produced by the
mainshock of the 2016 Kumamoto earthquake. The arrows indicate the amplitude
and direction of the horizontal displacement at 500 m grid points.
Result of analysis
Using the methodology explained above, we estimated the coseismic
displacements in the common area between the pre- and post-event DSMs, which
is approximately 80 km2. The pixel resolution was increased from 50
to 10 cm by using the cubic convolution method, where a bicubic function is
fitted using a 4 × 4 pixel neighborhood and used to estimate the intermediate
values. The subpixel size was decided based on the computational effort that
is required to detect the peak value of the correlation coefficient. The
size of the window was decided based on the area required to cover several
objects in the DSMs. Figure 6 compares the
east–west coseismic displacement obtained using a window of size
201 × 201 pixels with that obtained using a window of 101 × 101 pixels. The results
obtained using a window of size 101 × 101 pixels indicate increased noise
level in the areas of large agricultural fields because the peak of the
correlation coefficient cannot be identified clearly. In contrast, a
window of size 201 × 201 pixels covers an area large enough to reduce the
noise substantially. Thus, a window of size 201 × 201 pixels (100.5 m × 100.5 m)
was selected for the overall study area. Another issue is to
evaluate the magnitude of the maximum correlation coefficient, which is used
to identify the coseismic displacement. Figure 7
illustrates a histogram of the maximum correlation coefficients detected for
each window. The left vertical axis shows the number of observations per
0.01 intervals of the correlation coefficient and the right vertical axis is
for the cumulative frequency. The figure indicates that most of the results
produced a large correlation coefficient and a closer look revealed that the
areas with a correlation coefficient less than 0.6 showed the results not
consistent with the surrounded areas; however, only 14 cases out of 9195 windows produced a correlation coefficient less than 0.6.
Estimated three-dimensional coseismic displacements estimated along
the eight profile lines in Fig. 9. Vertical break lines show the location of
the known main Futagawa fault line by the GSJ. The location of the secondary
fault line is indicated using dotted lines.
Figure 8 shows the east–west and north–south
components of the coseismic displacement with a certain level of noise,
which is mainly because some objects are not exactly the same after the
earthquake. Several buildings collapsed and landslides occurred as a result
of the mainshock. Besides, the post-event DSM contains certain objects that
were not present in the pre-event DSM, such as the vehicles and tents used
as shelters. However, the general trend of spatial variation of the
coseismic displacement could be depicted adequately. The spatial
distribution of the three-dimensional (3-D) coseismic displacement is shown
in Fig. 9. The black arrows indicate the 2-D
horizontal component and the color shading indicates the vertical
displacement. In order to show only the vertical coseismic displacement and
remove the effect of the collapsed buildings and landslides, a median filter
with a window of the same size (201 × 201 pixels) as the one used for the
matching method was applied. Thus, the resolution of the horizontal
displacement is the same as that of the vertical displacement. Although the
output provided coseismic displacements in a 100.5 m grid, the black arrows
show the displacements only at every 500 m in order to visualize the
orientation of the coseismic displacement efficiently. The change of
direction of the coseismic displacements in both the horizontal and vertical
planes delineates the Futagawa fault line, which is consistent with the
surveyed active faults in Japan and the results of the field investigations
conducted by the Geological Survey of Japan (GSJ, 2016). The observed coseismic
displacement shows eastward movements of up to 2.0 m in the northern area
and 1.2 m in the southern area of the fault line. The legend of the vertical
displacement shows a vertical displacement of up to -3 m; however, this
value corresponds to a narrow area where a large landslide occurred and the
median filter could not remove it completely.
Example of baseline correction procedure for the acceleration
recorded at the Nishihara station. The trend of the uncorrected velocity was
modeled by two straight lines based on the method by Wang et al. (2011) and
was removed from the record. Then, the corrected displacement was calculated
by integrating the acceleration with respect to time. The thick black line in
the displacement time history represents the coseismic displacement
calculated from the lidar DSMs.
A closer look at the general trend shows that a subsidence of up to 2 m
occurred in the northern area and an uplift of up to 0.7 m in the southern
area. Our results are consistent with the coseismic displacement estimated
by using SAR interferometry using ALOS-2 PALSAR-2 imagery (Geospatial
Information Authority of Japan, 2016). Figure 10
shows the coseismic displacement profiles corresponding to the eight dashed
lines that are drawn uniformly along the Futagawa fault (see the locations
in Fig. 9). The changes in the direction of the
displacement for all the components are located almost at the same point,
the surveyed Futagawa fault line. However, the change of sign occurs
gradually because the applied window contained points from the both sides of
the fault line and consequently produced small coseismic displacements. The
main deformation was caused by the slip at the main Futagawa fault line;
however, the profiles GH and IJ show smaller slips caused by the secondary
Futagawa fault line.
Validation of results
The coseismic displacements obtained from the lidar DSMs were compared with
that obtained from the other sources of information. Currently, the GNSS
technology is used to monitor crustal deformation within a centimeter-level
accuracy. Unfortunately, there is no GEONET station in this study area
(Fig. 1). However, several strong-motion
instruments whose results can be used to compare with that of the lidar data
are available. The distribution of six strong-motion stations located within
the study area is shown in Fig. 9. One station,
with code KMMH16, belongs to KiK-net and two stations belong to the
strong-motion seismograph network of the prefecture: one located at the
Mashiki town office (MTO as referred by Hata et al., 2016) and the other at
the Nishihara village office (hereafter, NVO). Three stations, TMP1, TMP2,
and TMP3, belong to a temporary network deployed by Hata et al. (2016) with
the objective of monitoring the aftershocks following the event on 14 April.
The mainshock of Mw 7.0 occurred after the deployment of the temporary
network, and the acceleration records from the stations in this network were
acquired successfully. Furthermore, a K-NET Kumamoto station, with code
KMM006, is located 1 km from the closest point of the study area. Digital
acceleration records obtained from these seven stations could be used to
estimate the coseismic displacement caused by the mainshock.
Comparison of three-dimensional coseismic displacement obtained
from lidar DSMs (thick black line) and those obtained from the acceleration
records at MTO station (a), KMMH16 KiK-net station (b), and KMM006 K-NET
station (c). Red lines in KMMH16 KiK-net station show displacements at the
bedrock (Ground level: -252 m). KMM006 K-NET station is located at 1 km from
the nearest lidar DSM point.
Comparison of three-dimensional coseismic displacement obtained from
lidar DSMs (thick black line) with those obtained from the acceleration
records at TMP1 (a), TMP2 (b), and
TMP3 (c) stations.
Location of surface ruptures (red lines) observed during the field
surveys of the GSJ (2016) and plotted on aerial images acquired by the Asia
Air Co. on 23 April. The black arrow represents the direction and amplitude
of the observed strike slip at each location.
Estimated coseismic displacement parallel to the fault lines along
the 10 profile lines including the locations of the field observation by the
GSJ shown in Fig. 14.
Illustration of collapsed buildings and landslide along with the
difference between the lidar DSMs: location of the sample sites (a),
a heavily damaged residential area (b), and forest including
landslide (c). The top figures in (b) and (c) show
aerial images taken on 23 April while the bottom figures show the differences
between the two DSMs.
The method proposed by Wang et al. (2011) was applied to the acceleration
records obtained from the seven strong-motion stations mentioned above. The
baseline correction procedure estimates a bilinear function from the
uncorrected velocity time history, which is obtained by integrating the
acceleration with respect to time. For instance,
Fig. 11 shows the baseline correction estimated
using the uncorrected velocity obtained from the NVO station. Then the
bilinear function is removed from the uncorrected velocity and the
displacement is calculated. The coseismic displacement calculated from the
lidar data at the same location of the strong-motion station, shown as a
black thick line, is very close to the permanent displacement observed from
the displacement time history. Figure 12 depicts
the coseismic displacements at the MTO, KMMH16, and KMM006 stations obtained
from the acceleration records and the lidar data. The figure reveals that
the coseismic displacements derived from the DSMs are consistent with those
obtained from the strong-motion acceleration records. However, they are not
exactly the same because of the fact that the double integration of
acceleration is empirical and it can provide only an approximation. In the
case of the K-NET Kumamoto station, the results are compared with that
obtained from the closest DSM, which is approximately 1 km away. There were
two accelerometers at the KiK-net KMMH16 station, one on the ground surface
and the other in a borehole (-252 m below the surface). Although the two
permanent displacements were calculated independently, both the results were
similar to that obtained from the lidar data. This fact validates the method
proposed by Wang et al. (2011) and the accuracy of the results obtained from the
lidar DSMs.
On the contrary, the coseismic displacements obtained from the acceleration
records at TMP1, TMP2, and TMP3 were different from those obtained from the
lidar data (Fig. 13). This large discrepancy is because the instruments at
TMP1, TMP2, and TMP3 were placed on the ground surface without foundation.
Thus, they did not have sufficient confinement to avoid movements relative
to the ground, such as rocking or rotation around the vertical axis.
Therefore, the displacements obtained from the temporary network could not
be estimated using just two linear segments in the uncorrected velocity,
which is the method proposed by Wang et al. (2011). These additional
distortions can be easily observed in the north–south component at the three
stations.
Another source of information that can be used to compare our results is the
report of field surveys performed by the GSJ.
In Fig. 14, red lines indicate the surface
ruptures surveyed by the GSJ and the black arrows indicate the direction of
displacement together with the amplitude range of the slip.
Figure 6a illustrates the surface rupture lines
together with our results for the east–west component. Ten profiles, in
which the displacements were measured by the GSJ, were used to calculate the
displacements parallel to the fault lines (Fig. 15).
Discussion
Our result could recover the spatial distribution of the 3-D
(east–west, north–south, and up–down) coseismic displacement and validated
the fault line drawn by the GSJ (Figs. 6, 8 and 9). From the evaluation of the parameters used, the results were found to be
highly sensitive to the window size. Basically, it is crucial that the
windows have to cover several features, such as buildings, trees, and
different topography, in order to obtain a clear peak value in the
correlation coefficient (Fig. 5c). This issue was
our main concern in agricultural fields because large areas have uniform
elevation. In this study, a constant window size was used; however, if the
land use information is available, different window sizes can be applied.
For instance, in urban areas the window size can be smaller than that for
agricultural lands. Therefore, one limitation of the method is the required
window size because the larger the window size, the lower the spatial
resolution of coseismic displacement.
Comparing our result with the InSAR satellite images published by the GSI,
our result provides the 3-D coseismic displacement; while the InSAR results
provide only the displacement to the LOS. But concerning about the
area coverage, satellite sensors can cover a larger area than airborne lidar
sensors do.
The slips calculated from our results are very close to that obtained from
the field observation for most cases (Figs. 14 and 15). It is observed that in the majority of the cases our results are
greater than the measured ones. We believe that the main reason for this is
that the type of soil is cohesive in this area. Cohesive soils have the
ability to exhibit large plastic deformation that depends on the water
content and, as can be seen, the area is mostly used for agricultural
purposes where the soil has high water content. Thus, the surface rupture
measured in the field might not be the total slip. The largest differences
between the GSJ survey and the lidar results are observed in the profiles
“op” and “qr”.
Lidar data are capable of extracting other types of information.
Figure 16 shows two areas: one with collapsed
buildings and the other where a landslide occurred.
Figure 16 also shows the change in elevations
between the DSMs after removing the horizontal coseismic displacement. As
can be observed, the large change in elevations implies that a building
collapsed or a landslide occurred. Therefore, with proper thresholds, these
phenomena can be detected automatically. This issue will be discussed in a
future publication.
Conclusions
The coseismic displacements produced during the mainshock of Mw 7.1 of
the 2016 Kumamoto earthquake were estimated using two DSMs acquired by
high-resolution lidar flights before and after the mainshock on 16 April.
The common area between the DSMs covers approximately 80 km2 including
the Mashiki town section of the known Futagawa fault line. The maximum
cross-correlation coefficient was used with a window matching technique
between the two DSMs to calculate the coseismic displacement. With a window
of size 100 m × 100 m, the maximum cross-correlation value reached more than
0.6 for more than 99.8 % of the all 100 m grid points. Coseismic
horizontal displacements of up to 2 m and subsidence of up to 2 m were
observed in the study area. These values are the largest coseismic
displacements produced during the Kumamoto earthquake, which were not
recorded at any GEONET stations. The results showed good agreement with the
permanent displacements calculated from the double integration of the
strong-motion accelerations at the seven seismic stations. The results were
further compared with the surface ruptures observed by the GSJ, and a
reasonable level of agreement was reached in terms of location and slip
amplitude along the Futagawa fault.
The detailed information of coseismic displacement is indeed useful to
constrain the focal mechanism of the event. Recall that the GSI's
preliminary report estimated a slip of about 24 m in the source zone during
the 2011 Mw 9.0 Tohoku earthquake from an inversion method using the inland
GEONET station records. However, later Sato et al. (2011) observed a
coseismic displacement of 23 m at the ocean bottom and pointed out that this
information could better constrain the focal mechanism. Thus, our results,
which record higher coseismic displacement than those recorded from GNSS
stations, would improve the source estimation. However, this issue is out of
the scope of this paper and will be addressed in a future publication.
As mentioned before, there are only few cases in which lidar data before and
after an earthquake are available. The main reason is a high cost of lidar
surveys. However, this technology can be used properly for a specific region
of interest, such as along fault lines. For instance, the B4 project (Bevis
et al., 2005) collected lidar data of the southern San Andreas and San
Jacinto faults in southern California in order to have a pre-event lidar
data for future earthquakes.
Data availability
Strong-motion data collected from KiK-net and K-NET can be accessed online at
http://www.kyoshin.bosai.go.jp/ (National Research Institute for Earth
Science and Disaster Resilience, 2017) and strong-motion data from the
strong-motion seismograph network of Kumamoto Prefecture were released via
the Japan Meteorological Agency (2017) at
http://www.data.jma.go.jp/svd/eqev/data/kyoshin/jishin/1604160125_kumamoto/index2.html.
The temporary observation records in the town of Mashiki were obtained from
the works of Hata et al. (2016) at
http://wwwcatfish.dpri.kyoto-u.ac.jp/~kumaq (Hata et al., 2017). The
Numpy library can be accessed at http://www.numpy.org/# (Scipy, 2017),
the OpenCV library can be accessed at http://opencv.org/ (OpenCV,
2017), and the GDAL library can be accessed at
http://www.gdal.org/index.html (GDAL, 2017).
The authors declare that they have no conflict of interest.
Edited by: O. Katz
Reviewed by: two anonymous referees
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