Yamada et al. Progress in Earth and Planetary Science (2017) 4:38
DOI 10.1186/s40645-017-0152-7

Progress in Earth andPlanetary Science

RESEARCH ARTICLE

Open Access

Spatial pattern in stress drops of moderatesized earthquakes on the Pacific Plate off
the south-east of Hokkaido, Japan:
implications for the heterogeneity offrictional properties
Takuji Yamada1* , Yu Saito2, Yuichiro Tanioka3 and Jun Kawahara1

Abstract
We show that the spatial heterogeneity in the coseismic displacement of large earthquakes likely reflects the spatial
characteristics of the frictional properties and that it can be inferred from the stress drop of moderate-sized earthquakes.
We analyzed stress drops of 686 earthquakes with magnitudes of 4.0 to 5.0 off the south-east of Hokkaido, Japan, andinvestigated the spatial heterogeneity between the difference of shear strength and dynamic stress level on the PacificPlate. We deconvolved observed P and S waves with those of collocated small earthquakes and derived thesource effect of the earthquakes. We then estimated the corner frequencies of the earthquakes and calculated
stress drops using a circular fault model. The values of stress drops showed a spatial pattern consistent with slip
distributions of historical large earthquakes. Earthquakes that occurred in the area with a large coseismic slip during the1968 Tokachi-oki (MW 8.2) and the 2003 Tokachi-oki (MW 8.0) earthquakes had large values of stress drop, whereas
earthquakes in the afterslip area of the 2003 Tokachi-oki earthquake showed smaller values. In addition, an area
between coseismic ruptures of the 1973 Nemuro-oki (MW 7.8) and the 2003 Tokachi-oki earthquakes had a large
value of stress drop. Ruptures occurred in this area during the 1952 Tokachi-oki earthquake (MW 8.1), and the area
acted as a barrier during the 2003 Tokachi-oki earthquake. These facts suggest that the frictional properties of theplate interface show little temporal change, and their spatial pattern can be monitored by stress drops of moderatesized earthquakes. The spatial heterogeneity provides important information for estimating the slip pattern of a future
large earthquake and discussing a policy for disaster mitigation, especially for regions in which slip patterns of historicallarge earthquakes are unclear.
Keywords: Frictional properties, Spatial heterogeneity, Pacific Plate, Off the south-east coast of Hokkaido, Stress drop

Introduction
Numerous large earthquakes have been observed off thesouth-east of Hokkaido, Japan, due to the subduction of
the Pacific Plate beneath the Okhotsk Plate at a rate of
80–100 mm/year (e.g., DeMets et al. 1990). Previous
studies have suggested that the frictional properties of theplate interface in this region exhibit spatial heterogeneity.

* Correspondence: takuji.yamada.t9sci@vc.ibaraki.ac.jp
1
Department of Earth Sciences, Faculty of Science, Ibaraki University, 2-1-1
Bunkyo, Mito, Ibaraki 310-8512, Japan
Full list of author information is available at the end of the article

Yagi (2004) analyzed the source rupture process of the2003 Tokachi-oki earthquake (in Japanese, X-oki means“off the coast of X”) and found that an area with a large
coseismic slip in the shallower part had a longer risetime than the area in the deeper part of the fault plane.
They pointed out that the difference should be attributed to the spatial variety of the frictional properties.
Miyazaki et al. (2004) analyzed the spatial distribution of
the afterslip following the 2003 Tokachi-oki earthquake
using GNSS data. They found that areas with a significant afterslip were located around the coseismic
rupture area, especially at the shallower plate© The Author(s). 2017 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0
International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, andreproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to
the Creative Commons license, and indicate if changes were made.

Yamada et al. Progress in Earth and Planetary Science (2017) 4:38

interface. Miyazaki et al. (2004) investigated the spatiotemporal evolution of the afterslip in detail. They foundthat the slip-rate history of the afterslip in the coseismicarea during the 2003 Tokachi-oki earthquake was significantly different from that around the area where significant
afterslip was observed. They also concluded that the difference indicated spatial variations in frictional properties.
Ghimire and Tanioka (2011) compiled focal mechanismsof earthquakes on the Pacific Plate off the south-east of
Hokkaido and found a spatial correlation to source areasof historical earthquakes. They pointed out that the angle
between the maximum principal stress direction and thefault normal was between 30° and 45° in coseismic sourceareas of historical earthquakes, whereas it was larger than
45° in other areas, suggesting that the coseismic areas ofhistorical earthquakes have larger frictional coefficients or
higher shear strengths. Azuma et al. (2012) conducted anexperiment using air guns and ocean bottom seismometers off the south-east coast of Hokkaido and investigated
the reflectivity on the interface of the Pacific Plate. They
reported that the reflectivity had lateral heterogeneity,suggesting the lateral variation of the coupling rate andfrictional properties on the plate interface.
As many moderate-sized earthquakes have been taking
place on the subducting Pacific Plate off the south-eastof Hokkaido, Japan, they provide a good opportunity forinvestigating the spatio-temporal distribution of theirstress drops and its implication with respect to the frictional properties of the plate interface. In this study, we
analyzed stress drops of these moderate-sized earthquakes and investigated the correlation of their spatial
pattern with slip distributions of large historical earthquakes. The significance of stress drop analysis is summarized in the next section.

Stress drop and its mechanical significanceStress drop is an important source parameter indicating
the difference between the initial and residual stress levels,that is, the shear stresses before and after earthquake rupture. Stress drops of small and large earthquakes havebeen investigated and have almost confirmed the selfsimilarity of earthquakes (e.g., Kanamori and Anderson
1975; Abercrombie 1995; Prieto et al. 2004; Yamada et al.
2007; Yoshimitsu et al. 2014). This self-similarity is important in that we can treat stress drops of earthquakes as
indicators of the difference between the shear strengthand the dynamic stress level on the fault plane, independent of the earthquake size. Here, we must note that the
self-similarity for a broad range of earthquake sizes is not
fully confirmed and remains a matter of debate. Somepapers have pointed out that earthquakes might have aweak dissimilarity (e.g., Mayeda et al. 2005). However,moderate-sized earthquakes with a narrow magnitude
range, as considered herein, do not show a strong

Page 2 of 12

dissimilarity and their stress drops can be treated as an indicator of frictional characteristics.
The spatio-temporal heterogeneity of stress andstrength has been investigated by stress drops of earthquakes, especially over the last several years. Allmann
and Shearer (2007) analyzed stress drops of small earthquakes near Parkfield, California, and investigated therelationships between their spatial and temporal variations and the source area of the 2004 Parkfield earthquake. They concluded that earthquakes around thesource area of the 2004 Parkfield earthquake had larger
values of stress drop compared to the values of earthquakes outside the region. On an even finer scale,Yamada et al. (2010) investigated stress drops of small
earthquakes that occurred on the fault plane of the 2006
Kīholo Bay earthquake (MW 6.7) and compared thevalues of stress drop to the slip distribution of the earthquake. They found that small earthquakes around large
slip patches of the main shock were likely to have larger
values of stress drop. They concluded that the spatial
pattern of stress drop reflects coherent variations in the
difference between the strength and the residual stresslevel. Urano et al. (2015) conducted a similar analysis of
the 2007 Noto Hanto earthquake and concluded thatstatic stress drops of aftershocks in a large slip area ofthe mainshock are larger than those in a small slip area.
This result also suggests that stress drops of earthquakes
reflect in situ frictional properties, which is the same as
the conclusion of Yamada et al. (2010). Oth (2013) estimated stress drops of earthquakes in Japan and concluded that the values were strongly correlated with heatflow variations. He also pointed out that the lateralstress drop variations of subcrustal earthquakes with a
focal depth larger than 30 km were likely to be consistent with the coupling properties of the plate interface.
Uchide et al. (2014) analyzed stress drops of 1563 small
earthquakes of M3.0-M4.5 in the area east of the Tohoku
region that occurred before the 2011 Tohoku-oki earthquake and found lateral variations in stress drop along the
strike. Yamada et al. (2015) analyzed a cluster of earthquake activity beneath the Tanzawa Mountains, Japan.
They found that the activity included earthquakes with asmall stress drop and showed the hypocenter migration.
They concluded that the activity would be triggered by theincrease of pore pressure due to fluid, that is, the decreaseof the shear strength. Although stress drop estimates generally include some assumptions, such as circular faults
explained in the next section, these previous studies
strongly suggest that the values of stress drop reflect actual
physical characteristics of the fault planes of earthquakes.
On the other hand, some studies raised questions as towhether the estimated stress drop reflects frictional
properties. Shearer et al. (2006) investigated stress dropsof aftershocks of the 1992 Landers earthquake andYamada et al. Progress in Earth and Planetary Science (2017) 4:38

Page 3 of 12

compared their spatial pattern to coseismic displacementson three major segments derived by Wald and Heaton(1994). They pointed out that stress drops of aftershocks
on the northern segment (Camp Rock/Emerson faults)
were consistent with the slip distribution. However, theyalso found that the values on the southern segment(Landers/Johnson Valley faults) showed a weaker correlation and were anti-correlated on the central segment(Homestead Valley fault). Hardebeck and Aron (2009) analyzed stress drops of earthquakes on the Hayward fault.
They found that stress drops had a good correlation with
an applied shear stress but did not directly correlate withthe proposed strength of the wall-rock geology. They
pointed out that this suggests the stress drop gives information on the fault strength, but the relation between thefault strength and the strength of wall rock would be complex. Our result will provide an example of whether or notstress drops derived from seismograms can be used for investigating frictional properties on earthquake faults.

Methods/Experimental
We analyzed stress drops of 686 earthquakes with
4.0 ≤ M ≤ 5.0 off the south-east of Hokkaido, Japan,that took place from June 2002 to December 2015
(Fig. 1). Note that, in this paper, M expresses the magnitude of an earthquake as determined by the Japan
Meteorological Agency (JMA). The hypocenters of the
686 earthquakes were located from 40.5° N to 43.5° N
in latitude and from 141.0° E to 146.5° E in longitudewith a depth of ±15 km from the interface of the46°a2002-2015M ≥ 3.0

Depth (km)
0
10

50°

44°

40°

30°

20°
120° 130° 140° 150°

Latitude (N)Latitu

de (N

)

45°

20
30

43°

40
50

42°

60
80

41°

Longitude (E)

100

M5
M4
M3

40°

300

100 km39°

140° 141° 142° 143° 144° 145° 146° 147°

Longitude (E)
N.TKIH
140°

b

45°

141°

142°

143°

144°

145°

146°

147°

45°
120 kmElevation (m)

80 km
44°

44°

Latitude (N)

40 km
43°

20 km
43°

42°

42°

3500
3000
2500
2000
1500
1000
500
200
100
0
−500
−1000
−2000

41°

41°

−3000
−4000
−5000

40°

40°

−6000
−7000
39°

39°

140°

141°

142°

143°

144°

145°

146°

−8000

147°

Longitude (E)Fig. 1 a Seismicity in the study region from 2002 to 2015. Hypocenters with M greater than or equal to 3.0, as determined by JMA, are plotted.
The color and size of the symbols indicate the depth and magnitude of earthquakes, respectively. We can clearly see that most earthquakes occur on
the subduction interface of the Pacific Plate. b Hypocenters of analyzed earthquakes and seismic stations used in this study. The red circles indicate
hypocenters, and the blue squares indicate seismic stations, including stations of Hi-net (NIED), JMA, and Hokkaido University. The orange lines indicate
the depth of the upper surface of the subducting Pacific Plate (Kita et al. 2010) at intervals of 20 km. Waveforms observed at the station N.TKIH are
shown in Figs. 2 and 3 as examples

Yamada et al. Progress in Earth and Planetary Science (2017) 4:38

Page 4 of 12

Pacific Plate deduced by Kita et al. (2010). The distance of
15 km in depth direction is within the range of uncertainty in the hypocenter determination in the study area
because of the poor azimuthal coverage of seismic stations. We used waveforms observed at stations maintainedby National Research Institute for Earth Science andDisaster Resilience, Japan (NIED), Hokkaido University,
and JMA.
An observed waveform as a function of time W(t) includes the effects of the source S(t), the path from a hypocenter to a receiver P(t), site amplification effects
St(t), and the instrumental features of a seismometer
I(t), that is:
W ðt Þ ¼ S ðt Þ  Pðt Þ  St ðt Þ  I ðt Þ;

ð1Þ

where ∗ denotes convolution. In the frequency domain,
the convolution can be expressed as a scalar product,
and the following equation holds:
W ðf Þ ¼ S ðf ÞP ðf ÞSt ðf ÞI ðf Þ;

ð2Þ

where W(f ), S(f ), P(f ), St(f ), and I(f ) are expressions in
the frequency domain of W(t), S(t), P(t), St(t), and I(t),respectively. If we know the expressions of P(f ), St(f ),and I(f ), we can calculate the Green’s function and estimate the source effect from the observed waveform. As
it is actually difficult to estimate the Green’s function
precisely, we used the method of empirical Green’s function (EGF) (e.g., Hartzell 1978).
The observed waveforms of two earthquakes at a station can be expressed as follows:
W 1 ðf Þ ¼ S 1 ðf ÞP1 ðf ÞSt 1 ðf ÞI ðf Þ;

ð3Þ

W 2 ðf Þ ¼ S 2 ðf ÞP2 ðf ÞSt 2 ðf ÞI ðf Þ:

ð4Þ

If the hypocenters of the two earthquakes are identical, no velocity change takes place during the twoearthquakes, and the soil beneath the station acts
linearly independent of the amplitude of the incoming
waveforms, then the path and site effects are exactly
the same, P1(f) = P2(f) and St1(f) = St2(f). In this case, we
can extract the ratio of the source effect by calculating theratio of the observed waveforms in the frequency domain,
W 1 ðf Þ S 1 ðf ÞP 1 ðf ÞSt 1 ðf ÞI ðf Þ S 1 ðf Þ¼¼:
W 2 ðf Þ S 2 ðf ÞP 2 ðf ÞSt 2 ðf ÞI ðf Þ S 2 ðf Þ

ð5ÞEquation (5) gives the spectral ratio of each pair of ananalyzed earthquake and an EGF earthquake. We assume that source spectrum of an earthquake SC(f ) canbe expressed by the omega-squared model of Boatwright(1978), which is shown as the following equation:()1 = 2
1
C
C
C
;
ð6Þ
S ðf Þ ¼ R ðf ÞM 0 ðf Þ4
1 þ f =f C0

where R, M0, and f0 are the coefficient of the radiation
pattern, the seismic moment, and the corner frequencyof the earthquake, respectively. Here, C indicates thewave type, which is either P or S. This assumptionmeans that we approximated the fault plane as a circularplane.
 C  The deconvolved velocity amplitude spectrau_ ðf Þ can then be expressed as follows:r(4 )1 =2

 C  S CA ðf Þ RCA M 0A 1 þ f =f C0E
u_ ðf Þ¼ 
¼

4
r
S C ðf Þ RC M 
0E
1 þ f =f C0A
EE(¼ RCr M 0r 4 )1 =2
1 þ f =f C0E;
4
1 þ f =f C0A

ð7Þ

where subscripts A and E indicate analyzed and EGF
earthquakes, respectively. Moreover, RCr and M0r express
the relative values of RCA =RCE and M0A/M0E, respectively.
The value of RCr is equal to 1 if the focal mechanisms andhypocenters of the analyzed and EGF earthquakes areexactly the same. The sampling rate of waveforms analyzed in the present study was 100 Hz. We used waveforms of earthquakes in 2004 through 2015 with M3.5
that were closest to the hypocenters of the analyzed earthquakes as EGFs. A list of analyzed and EGF earthquakes isavailable as an Additional file 1 (see eqlist.txt).
We selected earthquakes with M3.5 as EGFs and analyzed earthquakes in a relatively narrow magnitude rangeof 4.0 ≤ M ≤ 5.0 based on the following considerations.
In order to ensure a good signal-to-noise ratio of EGFs,
especially for spectra of lower frequencies, we selectedearthquakes with M3.5 as EGFs. The lower limit (M4.0)of the analyzed earthquakes was fixed in order to maintain a difference in magnitude of 0.5 compared to the
EGFs and to ensure quality in estimating the corner frequencies. As stress drops are estimated for individual
earthquakes, the values for large earthquakes would represent the average characteristics of individual large fault
planes and would not reflect local frictional characteristics. In addition, as waveforms of some large earthquakes
were clipped, we set the upper limit of the earthquake
size to M5.0.
We calculated the spectral ratios of P and S waves forindividual pairs of an earthquake and an EGF. The spectral ratios were calculated for three time windows with alength of 10.23 s, or 1024 data points. The start times ofthe first window were 0.50 s prior to the arrival times
for either the P or S waves. The elapsed times of the two
successive time windows were 1.28 and 2.56 s, respectively.
Taking the logarithm of Eq. (7), the spectral ratio can be approximated as follows: lnu_ Cr ðf Þ≈g f ; f C0A ; f C0E ;ð8ÞYamada et al. Progress in Earth and Planetary Science (2017) 4:38

Page 5 of 12




 1 n

4 o
g f ; f C0A ; f C0E ¼ ln RCr M 0r − ln 1 þ f =f C0A
2

4 o
1 n
:
þ ln 1 þ f =f C0E
2

validity of this assumption in the section “Discussion.”
The seismic moment M0 in newton meters (Nm) can becalculated from MW using the following equation (Hanks
and Kanamori 1979): log10M0 = 1.5MW + 9.1.

ð9Þ

Before fitting each analyzed spectral ratio with the theoretical ratio expressed by Eqs. (8) and (9), we resampled
the frequencies so that the interval was equal to 0.05 on
a log10 scale. As a result, we obtained 20 frequency
bands (data points) for each order of frequency. This
procedure made it possible to treat high- and lowfrequency data equally. We also calculated the standard
deviation of the spectral ratio for each frequency bandand used the value in fitting data, as explained below.
We estimated the values of RCr M 0r , f C0A , and f C0E in
Eq. (9) for each station by a grid search that gave theminimum residual for the spectral ratios of three time
windows, similar to Imanishi and Ellsworth (2006):
res ¼




X lnu_ Cr ðf Þ−g f ; f C0A ; f C0E 2
;
i
σ 2i

ð10Þ

where σi is the standard deviation for each frequency
band calculated in resampling the spectral ratio. All of
the earthquakes have four or more stations available forthe corner frequency estimation. We used data from 0.7
to 20 Hz to calculate the residual in Eq. (10) and estimated corner frequencies by grid search between 0.3
and 20 Hz. This frequency range and the length of thetime window (10.23 s) were selected so that we wereable to analyze corner frequencies of earthquakes with
4.0 ≤ M ≤ 5.0, which would be around 1–3 Hz, as expected by the self-similarity of earthquakes. Figures 2
and 3 show examples of velocity waveforms, their spectra,
deconvolved spectra with a resampling, and the best-fit
curves of spectral ratio that were used for estimating a corner frequency. We also provide examples for another earthquake as supplemental figures (Additional files 2 and 3:
Figures S1 and S2). We can see that waveforms have asignal-to-noise ratio larger than a factor of five even for low
frequencies between 0.7 and 2 Hz for EGF earthquakes.
Finally, we calculated the values of stress drop following Madariaga (1976): C 37f
Δσ ¼ M 0A 0A ;
16
kV S
C

ð11Þ

where VS is the shear wave velocity (=4.5 km/s, from
Matsubara and Obara 2011), and C indicates the wave
type. We used k = 0.32 and k = 0.21 for P and S waves,respectively, assuming that the rupture speed corresponds to 0.9VS (Madariaga 1976). We will discuss theeffect of the value k in the section “Discussion.” We assumed that M is equivalent to the moment magnitude
MW in calculating stress drops. We also discuss the

Results
Figure 4 shows the spatial pattern of stress drop estimated from P and S waves. The results of stress drops
for individual earthquakes are available as Additional
files 4 and 5 (see results_P.txt and results_S.txt). The
spatial patterns of stress drop for the results estimatedfrom both P and S waves suggest correlations with slip
distributions of large earthquakes and an afterslip following the 2003 Tokachi-oki earthquake. Earthquakes that
occurred in the area with a large coseismic slip during the1968 Tokachi-oki (MW 8.2), the 1973 Nemuro-oki (MW7.8), and the 2003 Tokachi-oki (MW 8.0) earthquakes
had large values of stress drop. On the other hand,earthquakes in the afterslip area of the 2003 Tokachi-oki
earthquake, where lower strain was released during thesequence, showed smaller values of stress drop. These results suggest that stress drops of earthquakes represent insitu frictional properties, which is consistent with previous
studies. However, we must also note that slip distributions
derived by the waveform inversion may have large uncertainty (e.g., Mai et al. 2016). We summarize the results forthe three areas in the following subsections. The significance of the results, as well as the discrepancy between
the absolute values of stress drop estimated from P and S
waves are discussed in the section “Discussion.”
Source area of the 1968 Tokachi-oki earthquake

Figure 5a shows a magnified image of the results for the
S wave in this region. The thick gray and thin black lines
indicate the depths of the Pacific Plate and the coseismic
slip of the 1968 Tokachi-oki earthquake, respectively (asin Fig. 4). Refer to the caption of Fig. 5 regarding the intervals of the contours. Earthquakes in an area with acoseismic slip greater than 1 m clearly had higher stressdrops than earthquakes that occurred around the sourcearea of the 1968 earthquake.
We calculated the average values of stress drop in theregion with a coseismic slip larger than 1 m during the1968 earthquake and those in other regions in Fig. 5a. The
values were 64.6 and 20.2 MPa, respectively, and the difference was statistically significant with a 99% confidence
interval from Welch’s t test. This is consistent with the results of Yamada et al. (2010) and Urano et al. (2015), suggesting that the spatial pattern of stress drop reflects thefrictional characteristics of the plate interface.
Moreover, in this region, the area with a high stressdrop and a large slip during the 1968 earthquake corresponds to the kink of the subducting Pacific Plate.
This may imply that the geometry of the subducting

Yamada et al. Progress in Earth and Planetary Science (2017) 4:38

20110726_0758JST(20110725_2258UT)
M4.8
N.TKIH_Ucomp.

5P
0(Noise)
(P0)

-5

10 2
10 1

Amplitude (m)Velocity (10 -4 m/s)aPage 6 of 12

10 0
10 -1
10 -2
10 -3

(P1)
(P2)
10

20

30
40
Time (s)Velocity (10 -5 m/s)

c

50

P
0

(Noise)
(P0)

-5

10 1

Ratio of Amplitude

10 2

20

30
40
Time (s)

e

10 1

10 2

50

60

20061117_2141JST
M3.5 N.TKIH_U

d

10 0
10 -1
10 -2
10 -3

(P1)
10

10 0

10 2

(P2)
0

P0
P1
P2
Noise

Frequency (Hz)20061117_2141JST(20061117_1241UT)
M3.5
N.TKIH_Ucomp.

5

10 -4
10 -1

60

Amplitude (m)020110726_0758JST
M4.8 N.TKIH_U

b

10 -4
10 -1

P0
P1
P2
Noise

10 0

10 1

10 2

Frequency (Hz)20110726_0758JST(20110726_2258UT)
M4.8
N.TKIH_Ucomp.

10 1

P0
P1
P2
SYN

10 0
10 -1

10 0

10 1

10 2

Frequency (Hz)Fig. 2 a Example of an analyzed waveform of an earthquake with M4.8. The color lines indicate the three time windows used in deconvolution,
which were (P0) − 0.50 to 9.73 s, (P1) 0.78 to 11.01 s, and (P2) 2.06 to 12.29 s after the P arrival. The gray line shows a time window from 12.00 to
1.77 s before the arrival time of the P wave, which was used to calculate the spectrum of a noise in (b). Each time window has 1024 data points.
b Spectra of waveforms for the four time windows shown in (a). c Example of a waveform of an M3.5 earthquake that was used for an EGF. Notethat the vertical scales in (a) and (c) are different. d Spectra of waveforms for the four time windows shown in (c). e Deconvolved spectra withthe fitted omega-squared model. The color lines are deconvolved source spectra, that is, (b) divided by (d), for three individual time windows
with a resampling of frequency bands. The black broken line shows the fitted omega-squared model with corner frequencies of 3.98 and 12.6 Hzfor the analyzed and EGF earthquakes, respectively

Pacific Plate plays an important role with regard to
the frictional properties of the upper plate interface of
the Pacific Plate.
Source area of the 2003 Tokachi-oki earthquake

Figure 5b shows the spatial pattern of stress drop ofmoderate-sized earthquakes in this region. Quantitatively investigating the correlation between the spatial
distribution of stress drop values and the coseismic displacement of the 2003 Tokachi-oki earthquake would be
difficult because few earthquakes occurred in the areawith a large coseismic slip. Figure 4c indicates, however,that earthquakes in this area had larger values of stress
drop, suggesting that the difference between the shear
strength and the dynamic stress level is large in this area.

In addition, Fig. 5b shows the correspondence between
the afterslip area following the 2003 earthquake and thestress drop distribution of our results. Miyazaki et al.
(2004) investigated the spatio-temporal distribution ofafterslip following the 2003 Tokachi-oki earthquake andfound that significant afterslip occurred in the adjacentareas to the south and east of the coseismic rupture areaof the 2003 earthquake between the rupture areas of the1968 Tokachi-oki and 1973 Nemuro-oki earthquakes.
The afterslip area is quite consistent with the area with asmaller stress drop in this study. As the afterslip area
had a smaller displacement compared to that in thecoseismic area, this consistency also suggests that the
spatial pattern of the frictional characteristics exhibits little temporal change and can be inferred from the stressYamada et al. Progress in Earth and Planetary Science (2017) 4:38a

520110726_0758JST(20110725_2258UT)
M4.8
N.TKIH_Ncomp.

S

0(Noise)

-5

10 2
10 1

Amplitude (m)Velocity (10 -4 m/s)

10

Page 7 of 12

10 -2

(S2)
10

20

30
40
Time (s)

c

50

S0
S1
S2
Noise

10 0

10 1

10 2

Frequency (Hz)20061117_2141JST(20061117_1241UT)
M3.5
N.TKIH_Ncomp.

S

10 -4
10 -1

60

0

(Noise)10 2
10 1

Amplitude (m)0Velocity (10 -5 m/s)

10 -1

10 -3

(S1)

20061117_2141JST
M3.5 N.TKIH_N

d

10 0
10 -1
10 -2

(S0)
(S2)

0
10 2

10 -3

(S1)

-4

Ratio of Amplitude

10 0

(S0)

-10

4

20110726_0758JST
M4.8 N.TKIH_N

b

10

20

e

30
40
Time (s)

50

60

10 -4
10 -1

S0
S1
S2
Noise

10 0

10 1

10 2

Frequency (Hz)20110726_0758JST(20110725_2258UT)
M4.8
N.TKIH_Ncomp.

10 1

S0
S1
S2
SYN

10 0
10 -1

10 0

10 1

10 2

Frequency (Hz)Fig. 3 a Example of an analyzed waveform of an earthquake with M4.8. The color lines indicate the three time windows used in deconvolution,
which were (S0) − 0.50 to 9.73 s, (S1) 0.78 to 11.01 s, and (S2) 2.06 to 12.29 s after the S arrival. The gray line shows a time window from 12.00 to
1.77 s before the arrival time of the P wave, which was used to calculate the spectrum of a noise in (b). Each time window has 1024 data points.
b Spectra of waveforms for the four time windows shown in (a). c Example of a waveform of an M3.5 earthquake that was used for an EGF. Notethat the vertical scales in (a) and (c) are different. d Spectra of waveforms for the four time windows shown in (c). e Deconvolved spectra with thefitted omega-squared model. The color lines are deconvolved source spectra, that is, (b) divided by (d), for three individual time windows witha resampling of frequency bands. The black broken line shows the fitted omega-squared model with corner frequencies of 3.16 and 12.6 Hz for
analyzed and EGF earthquakes, respectively

drop analysis, supporting the conclusions of Yamada et al.
(2010) and Urano et al. (2015).
However, the afterslip area of the 2003 Tokachi-oki
earthquakes could be also included in the coseismic areaof the 1952 Tokachi-oki earthquake (e.g., Hirata et al.
2003). The spatial resolution of the slip distribution of
the 1952 earthquake would be lower than that of the2003 sequence, which implies that the frictional properties in the region might exhibit significant temporalchange. Further analysis of stress drops for a longer
period may provide a clue for investigating temporalchanges in frictional properties.
Source area of the 1973 Nemuro-oki earthquake

It is difficult to quantitatively investigate the correlation
between the values of stress drop and the coseismic

displacement of large earthquakes in this region. One
reason for this difficulty is that we could not estimate
values of stress drop in most of the area with a large slip
during the 1973 Nemuro-oki earthquake because few
moderate-sized earthquakes occurred in the shallower
part of the coseismic area of the 1973 earthquake from2002 to 2015 (Figs. 1 and 4).
Earthquakes that occurred west of the source area of
the 1973 Nemuro-oki earthquake had larger values ofstress drop. This region corresponds to the seismic gap
between the 2003 Tokachi-oki and the 1973 Nemuro-oki
earthquakes and is included in the coseismic area of the1952 Tokachi-oki earthquake with MW8.1 (Hirata et al.
2003). If the conclusions of Yamada et al. (2010) and
Urano et al. (2015) hold, our result implies that the region
would have acted as a barrier to the 2003 Tokachi-okiYamada et al. Progress in Earth and Planetary Science (2017) 4:38

a 44°

80

Page 8 of 12

km
40

km

20

43°

b 44°

km

Latitude (N)Latitude (N)

M5
M4

C
42°

B

80

43°

C
42°

B
41°

41°

A

A

P

40°

P

100 km40°

141° 142° 143° 144° 145° 146° 147°

141° 142° 143° 144° 145° 146° 147°

Longitude (E)Longitude (E)

m
0k

8

40

M5
M4

20

43°

d 44°

km
km

Latitude (N)c 44°
Latitude (N)

km
km
40
km
20

C
42°

B
41°

80

43°

km
km
40
km
20

C
42°

B
41°

A

A

S

40°

100 km40°

S141° 142° 143° 144° 145° 146° 147°

141° 142° 143° 144° 145° 146° 147°

Longitude (E)Longitude (E)Stress drop
−1.5 −1.0 −0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 (log10 MPa)km
km

Latitude (N)

km

40

80

b 43°

20

Latitude (N)

a 42°

60

km

Fig. 4 a Stress drops for individual earthquakes estimated from P waves. The scale and color of circles indicate the earthquake magnitude andvalue of stress drop, respectively. The thick lines indicate the depth of the upper surface of the subducting Pacific Plate (Kita et al. 2010). Thin
contours A through C show coseismic displacements for the 1968 Tokachi-oki (Nagai et al. 2001), 2003 Tokachi-oki (Yamanaka and Kikuchi 2003),
and 1973 Nemuro-oki earthquakes (Yamanaka 2006), respectively, at intervals of 1 m. b Spatially smoothed stress drop derived from (a) at grid
points at intervals of 0.1 degrees in latitude and longitude. The value at each grid point was calculated as the average of stress drops of earthquakes
within 20 km of the epicentral distance from the grid point. Values were not assigned at grid points with less than four earthquakes within 20 km of
the epicentral distance. c Stress drops estimated from S waves. d Map view of spatially smoothed stress drop derived from (c)

41°

80

42°

Latitude (N)

km
km

143°

144°

145°

Longitude (E)
80

km

60
40
20

43°

42°
144°

km

Afterslip

143°

Longitude (E)

c 44°

20

2003
Tokachi-oki

41°
142°

40°

142°

60

40

1968
Tokachi-oki

141°

km

km
km
km

Stress drop
(log10 MPa)−1.5 −1.0 −0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

1973
Nemuro-oki
145°

146°

147°

Longitude (E)Fig. 5 Magnified images of the three coseismic source areas shown in Fig. 4d for a the 1968 Tokachi-oki (Nagai et al. 2001), b 2003 Tokachi-oki (Yamanaka
and Kikuchi 2003), and c 1973 Nemuro-oki earthquakes (Yamanaka 2006). The interval of the coseismic slip is 1 m (as in Fig. 4). The dominant area of theafterslip following the 2003 Tokachi-oki earthquake is indicated by a broken blue line. Please refer to Miyazaki et al. (2004, 2004) for details

Yamada et al. Progress in Earth and Planetary Science (2017) 4:38

Page 9 of 12

earthquake and would have higher potential for strain release, suggesting that this region may experience larger
displacement during the next large earthquake.
Moreover, as shown in Fig. 4, there is a low stressdrop patch around 42.7° N latitude and 145.0° E longitude. One reason for this would be that the area has alower shear strength. This is consistent with a higher
seismicity in this area, as shown in Fig. 4a, c, because
the subduction rate of the Pacific Plate in this area
should be the same as that for the surrounding areas.

Discussion
Physical background of the spatial pattern of stress drop

As we pointed out in the section “Stress drop and its
mechanical significance,” stress drop is an importantsource parameter indicating the difference between theshear strength and the dynamic stress level. Although
the absolute value of shear strength and the dynamic
stress level cannot be constrained based on waveform
analyses, it is possible to estimate the difference between
the two physical quantities if there is no significant overshoot or undershoot because the initial stress should beequal to the shear strength at the hypocenter, where
the rupture initiates. As each earthquake gives one
value of stress drop that reflects an averaged physicalcharacteristic over a fault plane, the following must be
considered.

First, we must analyze moderate-sized or smaller
earthquakes. If the analyzed earthquakes have large fault
planes, the obtained values of stress drop would not reflect
local physical properties, but rather averaged properties
over the large fault planes. We analyzed earthquakes with
4.0 ≤ M ≤ 5.0, and their fault sizes were on the order of
1 km. In this sense, our results for stress drop can betreated as indicators of the physical properties of the Pacific Plate. Second, as mentioned in the section “Stressdrop and its mechanical significance,” we must consider
the self-similarity of earthquakes independent of theirmagnitudes. We will discuss this point in the following
subsection and will confirm that our results reflect the
spatial characteristics of the frictional properties of the
Pacific Plate.

Stress drop as a function of depth, magnitude, and time

Figure 6a shows stress drops estimated from S waves asa function of focal depth. The red circles indicate average values of stress drop for each depth bin of every
10 km. No clear depth dependence of stress drop is observed between 10 and 80 km, suggesting that the spatial
pattern in Figs. 4 and 5 cannot be explained by the variation in focal depth alone. Oth (2013) found a slight
depth dependence of stress drop for all of Japan, and his
result was different from ours. One reason for this may
be that most inland earthquakes were excluded in ourbStress drop (log10 MPa)

Stress drop (log10 MPa)

a
4

S

3
2
1
0
−1
−2

4

S

3
2
1
0
−1
−2
3.8 4.0 4.2 4.4 4.6 4.8 5.0 5.2

MWStress drop (log10 MPa)

Depth (km)

c
4
3
2
1
0
−1
−2
2002

S

2004

2006

2008

2010

2012

2014

2016

Year
Fig. 6 a Stress drops estimated from S waves as a function of focal depth. The red circles indicate average values for each depth bin for every
10 km. Vertical bars indicate standard errors for individual earthquakes, as calculated from results at individual stations and components. b Stressdrops estimated from S waves as a function of magnitude. The red circles indicate average values for individual magnitude bins. Vertical bars
indicate standard errors (same as (a)). c Estimated values of stress drop as a function of time

Yamada et al. Progress in Earth and Planetary Science (2017) 4:38

analysis. Further investigation may clarify the depth dependence of stress drop.
Values of stress drop as a function of magnitude areshown in Fig. 6b. The red circles indicate average valuesof stress drop for individual magnitude bins. Althoughno significant dependence of stress drop on magnitude
was observed, there may be a weak correlation. Smaller
earthquakes appear to have smaller values of stressdrop. One possible reason for this is that the smallest
value of stress drop can be controlled by the lowest
available frequency, or the length of the time window,
as explained in Fig. 3. Regardless of whether this is an
artifact, this slight dependency of stress drop on theearthquake size can cause an apparent spatial distribution of stress drop. We confirmed that the earthquakes
had no spatial heterogeneity in size and that the observed spatial pattern of stress drop was not an artifact.
Figure 6c shows the estimated stress drops as a function of time from June 2002 to December 2015. Thereis no apparent temporal change with respect to stressdrop.
We would like to emphasize that no significant dependence of stress drop on depth or earthquake size wasobserved in our study. We found no temporal change.
This is very important because we can rule out the possibility that the spatial pattern obtained in Fig. 4 is due
to depth dependence of the estimated stress drop, temporal heterogeneity of earthquake occurrence, or size dependence of the stress drop. Moreover, this confirmsthat the spatial pattern of stress drop shown in Figs. 4
and 5 reflects the spatial heterogeneity of the frictional
properties of the Pacific Plate.

Page 10 of 12

the estimated values of stress drop from P waves in ourstudy are smaller those from S waves, lower rupture
speeds result in the values of stress drop being closer.
In other words, our results suggest that the actual
rupture speed of the analyzed earthquakes would belower than 0.9V S. This is consistent with previous
studies that reported the rupture speed of earthquakes
to be 70–80% of V S, independent of earthquake magnitude (Wald and Heaton 1994, Yamada et al. 2005),
with a few exceptions, such as the 1999 Hector Mine
earthquake, which had a low rupture speed (Ji et al.
2002), and some super-shear earthquakes, including
the 1999 Izmit earthquake (Sekiguchi and Iwata 2002) andthe 2001 Kunlun earthquake (Walker and Shearer 2009).
The estimated values of stress drop from P waves
in Fig. 4b show exactly the same lateral pattern as
the estimated values from S waves in Fig. 4d. Thisstrongly suggests that our results for stress drop arestably estimated and that their lateral pattern indicates the spatial heterogeneity of the frictional properties of the Pacific Plate.
Validity of the assumption of M = MW

We calculated stress drops under the assumption thatthe value of M determined by JMA is equal to MW. As
this assumption might introduce an artifact in our result,
we investigated its validity. Figure 7 shows the relation

ship between M and values of 3:5 þ ð2=3Þ log10 RCr M 0r
in Eq. (7) for individual earthquakes, which correspondto moment magnitudes of analyzed earthquakes if theirfocal mechanisms are identical for individual earthquake
pairs and moment magnitudes of EGF earthquakes with

a

P

5

4

4

5

M

Apparent Magnitude

As each earthquake has one value of stress drop, thevalue of stress drop for an earthquake estimatedfrom P wave should be equal to the value estimatedfrom S wave. Note, however, that the absolute valuesof stress drop estimated from P waves are muchsmaller than the values deduced from S waves inthis study (Fig. 4). This discrepancy originates fromthe assumed rupture speed in the model and hence
provides an insight into the rupture characteristics
of analyzed moderate-sized earthquakes, as describedin detail in the following.
The model of Madariaga (1976) assumes that the rupture initiates from the center of a fault plane and propagates with a certain speed that is lower than the P-wave
velocity. The values of 0.32 and 0.21 for constant k in
Eq. (11) depend on the assumed rupture speed, which
we assumed to be 90% of the S-wave velocity VS. These
factors become smaller for a lower rupture speed, andthe value of k for P wave is much more sensitive to therupture speed than that for S wave (Madariaga 1976). As

Apparent Magnitude

Values of stress drop estimated from P and S waves

b

S

5

4

4

5

M

Fig. 7 Relationships of magnitudes determined by JMA and theapparent magnitude derived as the sum of the magnitude of EGF
earthquakes (3.5) and values of ð2=3Þ log10 RCr M0r in Eq. (7), whichcorresponds to the difference in magnitude between the analyzed
and EGF earthquakes if their focal mechanisms are identical. a and b
show the results for P and S waves, respectively

Yamada et al. Progress in Earth and Planetary Science (2017) 4:38

M3.5 are 3.5 (M3.5 = MW3.5). We herein refer to theabovementioned values as apparent magnitudes. As weused earthquakes with M3.5 as EGFs, Fig. 7 suggests that
MW values would be slightly smaller than M values. Thisimplies that the absolute values of stress drop obtainedin this study might be overestimated. However, we cansee a clear linear relationship between the two parameters with a slope of 1. This strongly suggests that the
spatial pattern in stress drop derived in this study isreliable.

Conclusions
We analyzed stress drops of 686 earthquakes with magnitudes of 4.0 to 5.0 off the south-east of Hokkaido,
Japan, and investigated the spatial heterogeneity of thedifference between the shear strength and the dynamic stress level on the Pacific Plate. Spatial patterns of stress drop for both results estimated from P
and S waves suggest correlations with slip distributions of large historical earthquakes and an afterslip
following the 2003 Tokachi-oki earthquake. Thissuggests that the frictional properties of the plateinterface exhibit little temporal change and their
spatial pattern can be monitored by stress drops ofmoderate-sized earthquakes. The spatial heterogeneity
can be used in estimating the slip pattern of a future
large earthquake and discussing a policy for disastermitigation, especially for regions in which slip patterns of historical large earthquakes are unclear, including the western coast of North America.
Additional files

Page 11 of 12

Acknowledgements
The authors would like to express our sincere thanks to the two reviewers(Adrien Oth and an anonymous reviewer), and the editor, Yuji Yagi, for theirinsightful comments and suggestions, which helped us improve ourmanuscript. We are grateful to Rachel Abercrombie and Takahiko Uchide for
their comments on a draft of this manuscript. We used waveforms fromstations of Hi-net (NIED) as well as Hokkaido Univ. and JMA. The authors
would like to thank the individuals maintaining these seismic stations. We
also used arrival times of P and S waves as determined by JMA. The authors
would also like to thank Yoshiko Yamanaka for providing the results ofcoseismic displacements. Figures were created using Genetic Mapping Tool
software (Wessel and Smith 1991). This study was supported by the Ministryof Education, Culture, Sports, Science and Technology (MEXT) of Japan under
its Earthquake and Volcano Hazards Observation and Research Program.
Funding
This study was supported by the Ministry of Education, Culture, Sports, Scienceand Technology (MEXT) of Japan, under its Earthquake and Volcano Hazards
Observation and Research Program.
Authors’ contributions
TY designed the research project, carried out the analysis, and wrote themanuscript. YS conducted preliminary analyses. YT and JK participated in thediscussion of the results. All of the authors read and approved the final
manuscript.
Competing interests
The authors declare that they have no competing interests.

Publisher’s NoteSpringer Nature remains neutral with regard to jurisdictional claims inpublished maps and institutional affiliations.
Author details
1
Department of Earth Sciences, Faculty of Science, Ibaraki University, 2-1-1
Bunkyo, Mito, Ibaraki 310-8512, Japan. 2Department of Natural History
Sciences, Graduate School of Science, Hokkaido University, Kita 10 Nishi 8,
Kita-ku, Sapporo 060-0810, Japan. 3Institute of Seismology and Volcanology,
Faculty of Science, Hokkaido University, Kita 10 Nishi 8, Kita-ku, Sapporo
060-0810, Japan.
Received: 18 July 2017 Accepted: 23 November 2017

Additional file 1: eqlist. (TXT 65 kb)
Additional file 2: Figure S1. (a) Example of an analyzed P waveformof an earthquake with M4.0 (UD component at station N.SKSH).
The color and gray lines indicate the time windows for calculating
spectra (as in Fig. 2). (b) Spectra of waveforms for the four time
windows shown in (a). (c) Example of a waveform of an M3.5
earthquake that was used for an EGF. Note that the vertical scales in(a) and (c) are different. (d) Spectra of waveforms for the four time
windows shown in (c). (e) Deconvolved spectra with the fitted
omega-squared model. The black broken line shows the fitted
omega-squared model with corner frequencies of 1.58 and 2.51 Hz
for the analyzed and EGF earthquakes, respectively. (EPS 3193 kb)
Additional file 3: Figure S2. (a) Example of an analyzed S waveform of
an earthquake with M4.0 (NS component at station N.SKSH). The
color and gray lines indicate the time windows for calculating
spectra (as in Fig. 2). (b) Spectra of waveforms for the four time
windows shown in (a). (c) Example of a waveform of an M3.5
earthquake that was used for an EGF. Note that the vertical scales in(a) and (c) are different. (d) Spectra of waveforms for the four time
windows shown in (c). (e) Deconvolved spectra with the fitted omegasquared model. The black broken line shows the fitted omega-squaredmodel with corner frequencies of 2.00 and 3.98 Hz for the analyzed and
EGF earthquakes, respectively. (EPS 3181 kb)
Additional file 4: results_P. (TXT 54 kb)
Additional file 5: results_S. (TXT 54 kb)

References
Abercrombie RE (1995) Earthquake source scaling relationships from −1 to 5 ML
using seismograms recorded at 2.5-km depth. J Geophys Res 100:24015–24036
Allmann BP, Shearer PM (2007) Spatial and temporal stress drop variations insmall earthquakes near Parkfield, California. J Geophys Res 112:B04305.
doi:10.1029/2006JB004395
Azuma R, Murai Y, Katsumata K, Nishimura Y, Yamada T, Mochizuki K, Shinohara M(2012) Was the 1952 Tokachi-oki earthquake (MW = 8.1) a typical underthrustearthquake?: plate interface reflectivity measurement by an air gun-ocean
bottom seismometer experiment in the Kuril Trench. Geochem Geophys
Geosyst 13:Q08015. doi:10.1029/2012GC004135
Boatwright J (1978) Detailed spectral analysis of two small New York State
earthquakes. Bull Seismol Soc Am 68:1131–1177
DeMets CR, Gordon R, Argus D, Stein S (1990) Current plate motion. Geophys J
Int 101:425–478
Ghimire S, Tanioka Y (2011) Spatial distribution of stress and frictional strength along
the interplate boundary in northern Japan and its correlation to the locations oflarge earthquakes. Techtonophys 511:1–13. doi:10.1016/j.tecto.2011.08.004
Hanks TC, Kanamori H (1979) A moment magnitude scale. J Geophys Res 84(B5):2348–2350
Hardebeck JL, Aron A (2009) Earthquake stress drops and inferred fault strength
on the Hayward fault, East San Francisco Bay, California. Bull Seismol Soc Am
99:1801–1814. doi:10.1785/0120080242
Hartzell SH (1978) Earthquake aftershocks as Green’s functions. Bull Seismol Soc
Am 68(5):1–4

Yamada et al. Progress in Earth and Planetary Science (2017) 4:38

Hirata K, Geist EL, Satake K, Tanioka Y, Yamaki S (2003) Slip distribution of the 1952
Tokachi-Oki earthquake (M 8.1) along the Kuril Trench deduced from tsunami
waveform inversion. J Geophys Res 108:2196. doi:10.1029/2002JB001976
Imanishi K, Ellsworth WL (2006) Source scaling relationships of microearthquakes
at Parkfield, CA, determined using the SAFOD pilot hole seismic array. In:
Abercrombie RE, McGarr A, Kanamori H, Di Toro G (eds) Earthquakes:
radiated energy and the physics of earthquake faulting, vol 170, Geophys
Monogr Ser. AGU, Washington D.C, pp 81–90
Ji C, Wald DJ, Helmberger DV (2002) Source description of the 1999 Hector Mine,
California, earthquake, part II: complexity of slip history. Bull Seismol Soc Am
92(4):1208–1226
Kanamori H, Anderson DL (1975) Theoretical basis of some empirical relations inseismology. Bull Seismol Soc Am 65:1073–1095
Kita S, Okada T, Hasegawa A, Nakajima J, Matsuzawa T (2010) Anomalous
deepening of a seismic belt in the upper-plane of the double seismic zone
in the Pacific slab beneath the Hokkaido corner: possible evidence forthermal shielding caused by subducted forearc crust materials. Earth Planet
Sci Lett 290:415–426
Madariaga R (1976) Dynamics of an expanding circular fault. Bull Seismol Soc Am
66:639–666
Mai PM, Schorlemmer D, Page M, Ampuero JP, Asano K, Causse M, Custodio S,
Fan W, Festa G, Galis M, Gallovic F, Imperatori W, Käser M, Malytskyy D,
Okuwaki R, Pollitz F, Passone L, Razafindrakoto HNT, Sekiguchi H, Song SG,
Somala SN, Thingbaijam KKS, Twardzik C, van Driel M, Vyas JC, Wang R, Yagi
Y, Zielke O (2016) The earthquake-source inversion validation (SIV) project.
Seismol Res Lett 87:690–708. doi:10.1785/0220150231
Matsubara M, Obara K (2011) The 2011 off the Pacific coast of Tohoku earthquake
related to a strong velocity gradient with the Pacific plate. Earth Planets Space
63:663–667
Mayeda K, Gök R, Walter WR, Hofstetter A (2005) Evidence for non-constantenergy/moment scaling from coda-derived source spectra. Geophys Res Lett
32:L10306. https://doi.org/10.1029/2005GL022405
Miyazaki S, Larson KM, Choi K, Hikima K, Koketsu K, Bodin P, Jaase J, Emore G,
Yamagiwa A (2004) Modeling the rupture process of the 2003 September 25
Tokachi-Oki (Hokkaido) earthquake using 1-Hz GPS data. Geophys Res Lett
31:L21603. doi:10.1029/2004GL021457
Miyazaki S, Segall P, Fukuda J, Kato T (2004) Space time distribution of afterslip
following the 2003 Tokachi-oki earthquake: implications for variations in fault
zone frictional properties. Geophys Res Lett 31:L06623. doi:10.1029/
2003GL019410
Nagai R, Kikuchi M, Yamanaka Y (2001) Comparative study on the source
processes of recurrent large earthquakes in Sanriku-oki region: the 1968
Tokachi-oki earthquake and the 1994 Sanriku-oki earthquake. Zisin ser.2 54:
267–280 (in Japanese with English abstract)
Oth A (2013) On the characteristics of earthquake stress release variations inJapan. Earth Planet Sci Lett 377–378:132–141. doi:10.1016/j.epsl.2013.06.037
Prieto GA, Shearer PM, Vemon FL, Klib D (2004) Earthquake source scaling andself-similarity estimation from stacking P and S spectra. J Geophys Res 109:
B08310. doi:10.1029/2004JB003084
Sekiguchi H, Iwata T (2002) Rupture process of the 1999 Kocaeli, Turkey,
earthquake estimated from strong-motion waveforms. Bull Seismol Soc Am
92(1):300–311
Shearer PM, Prieto GA, Hauksson E (2006) Comprehensive analysis of earthquake
source spectra in Southern California. J Geophys Res 111:B06303. doi:10.1029/
2005JB003979
Uchide T, Shearer PM, Imanishi K (2014) Stress drop variations among small
earthquakes before the 2011 Tohoku-oki, Japan, earthquake and implications
for the main shock. J Geophys Res 119:7164–7174. doi:10.1002/2014JB010943
Urano S, Hiramatsu Y, Yamada T, The Group for the Joint Aftershocks Observationsof the 2007 Noto Hanto Earthquake (2015) Relationship between coseismic slip
and static stress drop of similar aftershocks of the 2007 Noto Hanto earthquake.
Earth Planets Space 67:101. doi:10.1186/s40623-015-0277-0
Wald DJ, Heaton TH (1994) Spatial and temporal distribution of slip for the 1992
Landers, California, earthquake. Bull Seismol Soc Am 84:668–691
Walker KT, Shearer PM (2009) Illuminating the near-sonic rupture velocities of theintracontinental Kokoxili MW7.8 and Denali fault MW7.9 strike-slip earthquakes
with global P wave back projection imaging. J Geophys Res 114:B02304.
doi:10.1029/2008JB005738
Wessel P, Smith W (1991) Free software helps map and display data. EOS TransAGU 72(441):445–446

Page 12 of 12

Yagi Y (2004) Source rupture process of the 2003 Tokachi-oki earthquake
determined by joint inversion of teleseismic body wave and strong groundmotion data. Earth Planets Space 56:311–316
Yamada T, Mori JJ, Ide S, Abercrombie RE, Kawakata H, Nakatani M, Iio Y,
Ogasawara H (2007) Stress drops and radiated seismic energies of
microearthquakes in a South African gold mine. J Geophys Res 112:B03305.
doi:10.1029/2006JB004553
Yamada T, Mori JJ, Ide S, Kawakata H, Iio Y, Ogasawara H (2005) Radiation
efficiency and apparent stress of small earthquakes in a South African gold
mine. J Geophys Res 110:B01305. doi:10.1029/2004JB003221
Yamada T, Okubo PG, Wolfe CJ (2010) Kīholo Bay, Hawaiʻi, earthquake sequenceof 2006: relationship of the main shock slip with locations and source
parameters of aftershocks. J Geophys Res 115:B08304. doi:10.1029/
2009JB006657
Yamada T, Yukutake Y, Terakawa T, Arai R (2015) Migration of earthquakes with asmall stress drop in the Tanzawa Mountains, Japan. Earth Planets Space 67:
175. doi:10.1186/s40623-015-0344-6
Yamanaka Y (2006) Asperity map in Hokkaido and southern Kurile arc. Chikyu
Monthly 28:427–431 (in Japanese)
Yamanaka Y, Kikuchi M (2003) Source process of the recurrent Tokachi-oki
earthquake on September 26, 2003, inferred from teleseismic body waves.
Earth Planets Space 55:e21–e24
Yoshimitsu N, Kawakata H, Takahashi N (2014) Magnitude −7 level earthquakes: a
new lower limit of self-similarity in seismic scaling relationships. Geophys Res
Lett 41:4495–4502. doi:10.1002/2014GL060306