Data, fault model, and method
The source process is estimated using a multiple-time-window linear
kinematic waveform inversion methodology explained in detail by Sekiguchi et al.
(2000) and Suzuki et al.
(2010), who followed the
approaches of Olson and Apsel (1982) and Hartzell and Heaton (1983).
We use strong-motion waveforms at 20 stations (Fig. 1a): 14 KiK-net stations in borehole, 4 K-NET
stations on ground surface, and 2 F-net (Okada et al. 2004; NIED 2019a) stations in vault. At the F-net stations, we use data
observed by velocity-type strong-motion seismographs. Although three components
of the seismogram are used at most of the stations, only the horizontal
components are used at IBUH03, because the data of the up-down seismograph in
the borehole had some problems at the time of the mainshock. Except for data
from the F-net stations, where original data are velocity waveforms, the
original acceleration waveforms are numerically integrated in the time domain
into velocity. The velocity waveforms are band-pass filtered between 0.05 and
0.5 Hz, resampled to 5 Hz, and windowed from 1 s before S-wave arrival for
25 s.
The spatial distribution of the aftershocks shows that the strike
angle of the earthquake gradually changed along the strike direction
(Fig. 1b). This indicates that it is
unreasonable to express the source fault of this event by a single rectangular
plane. Consequently, we use a more realistic fault model in the source
inversion. Based on the spatial distribution of the aftershocks and the moment
tensor solution of F-net, we develop a curved fault model that is approximated
by multiple rectangular subfaults (Fig. 1b and c). The curved fault model is described by multiple
planes, each with a width of 20 km, a top depth of approximately 22 km, and a
dip angle of 65°, and various strike angles. The dip angle is based on the F-net
moment tensor solution. The assumed strike angle of the planes changes gradually
along the strike direction: 15° in the northern part, − 20° in the central part,
and 40° in the southern part (Fig. 1c).
The rupture starting point is set at 42.6908°N, 142.0067°E, at a depth of
37.04 km, which is the hypocenter determined by JMA. The fault model is divided
into 15 rectangle subfaults along the strike direction and 10 subfaults along
the dip direction. The maximum subfault size is 2 × 2 km. The top and bottom
lengths of the fault model are approximately 22.2 km and 25.4 km, respectively.
The total area of the fault model is approximately
476.6 km2. At an extension of the fault model
along the up-dip direction, there exists the active fault zone along the eastern
margin of the Ishikari Lowland extending in an NS direction (Fig. 1a); however, the assumed dip angle of this
active fault is low at depths greater than 3 km (HERP 2010), which is inconsistent with the high
dip angle of this earthquake (65° in F-net).
The slip time history of each subfault is discretized using eight
smoothed ramp functions (time-windows) progressively delayed by 0.4 s, and
having a duration of 0.8 s each. The number of time-windows is determined using
a trial-and-error process, so that the source time function at each subfault can
be explained properly. The first time-window starting time is defined as the
time prescribed by a circular rupture propagation of constant speed, Vftw. Hence, the rupture
process and seismic waveforms are linearly related via Green’s functions. The
slip within each time-window at each subfault is derived by minimizing the
difference between the observed and synthetic waveforms using a least-squares
method. To stabilize the inversion, the slip angle is allowed to vary
within ± 45° centered at 107°, which is the rake angle of the F-net moment
tensor solution, using the non-negative least-squares scheme (Lawson and Hanson
1974). In addition, we impose a
spatiotemporal smoothing constraint on slips (Sekiguchi et al. 2000). The weight of the smoothing
constraint is determined based on Akaike’s Bayesian Information Criterion
(Akaike 1980).
Green’s functions are calculated using the discrete wavenumber
method (Bouchon 1981) and the reflection/transmission matrix method (Kennett and
Kerry 1979) with a one-dimensional
(1-D) layered velocity structure model. The 1-D velocity structure models are
obtained for each station from the 3-D velocity structure model (Fujiwara et al.
2009). Logging data is also
referred to for the KiK-net stations. Although a 1-D structure model used for
calculating Green’s functions differs among stations, the models have a common
structure at depth deeper than 13 km where the assumed fault model is located.
To consider the rupture propagation effect in each subfault, 25 point sources
are uniformly distributed over each subfault to calculate the Green’s functions
(e.g., Wald et al. 1991). For
stations near the fault (IBUH02, HDKH01, HDKH04, IBUH03, and IBUH01), weights
that are two times larger than those for the other stations are used.
Results and discussion
Figure 2a, b shows the
total slip distribution of the 2018 Iburi earthquake by map projection and the
rupture progression, whereas Additional file 1: Figures S1 and S2 show the total slip distribution by
planar projection and the slip-velocity time function of each subfault. The
seismic moment is 2.9 × 1019 Nm (Mw 6.9), which is larger
than those estimated by F-net and GCMT (1.0 × 1019 Nm
and 1.2 × 1019 Nm). One likely reason for this is
that a portion of slips in the source model are derived to reproduce some part
of later phases which are produced by the lateral heterogeneity of the actual
velocity structure and which cannot be fully reproduced with the 1-D velocity
structure model. One way to approach this issue is further calibration of the
velocity structure model for Green’s functions. The maximum final slip is 4.8 m.Vftw is set to
1.3 km/s, providing the smallest misfit solution among all solutions forVftw varying from
0.8 to 4.0 km/s. The large slips are mostly found at 25–30 km depth in the
up-dip direction from the hypocenter. The horizontal extent of this large-slip
area along the strike direction is approximately 10 km. During the first 6 s,
the rupture slowly grows around the hypocenter with small slips. Subsequently,
the rupture develops with a large moment release between 6 s and 12 s in the
large-slip area. The total rupture duration is approximately 20 s.
The slow rupture growth during the initial moment of this
earthquake is supported by the observed waveforms. Figure 2c shows the waveforms recorded at HDKH04 and
IBUH01 during the mainshock and of an MJMA 5.4 aftershock that occurred at 6:11
on September 6, 2018 (JST). The latter occurred near the mainshock hypocenter
(Fig. 1a), and its focal depth
(37.67 km) is practically the same as that of the mainshock. This waveform
comparison indicates that although the shape of the main S-wave of the mainshock
is similar to that of the aftershock, the main phases of the mainshock arrived
several seconds later than those of the aftershock. This suggests that the
radiation of seismic waveforms was not significant during the initial moment of
this earthquake, which is consistent with the source model derived in this
study.
Figure 2a shows the spatial
distribution of the aftershocks as well as the total slip distribution. Most
aftershocks occurred at a depth of approximately 30–35 km, whereas only a few
aftershocks occurred within the large-slip area. This pattern has also been
noted in other crustal earthquakes such as the 1992 Landers earthquake (e.g.,
Cohee and Beroza 1994), the 1995
south Hyogo (Kobe) earthquake (e.g., Ide et al. 1996), the 1999 Chi–Chi earthquake (e.g., Wu et al.
2001), the 2002 Denali
earthquake (e.g., Asano et al. 2005), the 2016 Kumamoto earthquakes (e.g., Kubo et al.
2016), and the 2016 Central
Tottori earthquake (e.g., Kubo et al. 2017).
Figure 3 shows a comparison
between the observed and synthetic waveforms. The waveform fit is
satisfactory.