Correlation between Coulomb stress imparted by the 2011 ...

Geophysical Journal InternationalGeophys. J. Int. (2015) 201, 112–134 doi: 10.1093/gji/ggv001

GJI Seismology

Correlation between Coulomb stress imparted by the 2011Tohoku-Oki earthquake and seismicity rate change in Kanto, Japan

Takeo Ishibe,1 Kenji Satake,1 Shin’ichi Sakai,1 Kunihiko Shimazaki,1 Hiroshi Tsuruoka,1

Yusuke Yokota,2 Shigeki Nakagawa1 and Naoshi Hirata1

1Earthquake Research Institute, the University of Tokyo, 1-1-1, Yayoi, Bunkyo-ku, Tokyo 113-0032, Japan. E-mail: [email protected] and Oceanographic Department, Japan Coast Guard, 2-5-18, Aomi, Koto-ku, Tokyo 135-0064, Japan

Accepted 2015 January 5. Received 2014 December 31; in original form 2014 September 25

S U M M A R YWe studied the seismicity rate increase in the Kanto region around Tokyo following the2011 Tohoku-Oki earthquake (Mw 9.0) to examine whether this increase was correlated withthe static increases in the Coulomb failure function (�CFF) of the Tohoku-Oki earthquakesequence. Because earthquakes in the Kanto region exhibit various focal mechanisms, the re-ceiver faults for the �CFF were assumed to be the focal mechanism solutions for nearly 19 000earthquakes that previously occurred. Our results showed that the number of earthquakes forwhich the mechanism solutions had a positive �CFF (∼12 000) is much larger than those thathad a negative �CFF (∼2000). Comparison of the �CFF values for earthquakes before andafter the Tohoku-Oki earthquake showed that the latter had more positive values; this supportsthe hypothesis that the coseismic stress change transferred from the Tohoku-Oki earthquakesequence is the major contributing factor to the increased seismicity rate in the Kanto region.

Key words: Seismicity and tectonics; Statistical seismology; Asia.

1 I N T RO D U C T I O N

On 2011 March 11, a giant earthquake with a moment magnitude(Mw) of 9.0 occurred off the coast of Miyagi prefecture, wherethe Pacific Plate (PAC) subducts beneath the Okhotsk Plate (OKH;Fig. 1). This earthquake was officially named the ‘2011 off thePacific coast of Tohoku Earthquake’ by the Japan MeteorologicalAgency (JMA) and was the largest earthquake ever recorded byinstruments in Japan. In this paper, we will refer this as the Tohoku-Oki earthquake.

The Global Positioning System Earth Observation Network(GEONET), which is operated by the Geospatial Information Au-thority of Japan, recorded large coseismic displacements along theTohoku coast, with an eastward movement of up to ∼5 m andsubsidence of up to 1.2 m (Ozawa et al. 2011). The coseismic dis-placements were widespread (more than a few hundred kilometresfrom the source region), suggesting that the Tohoku-Oki earthquakehad a substantial impact on the Japanese Islands. Actually, severalmoderate or large earthquakes occurred outside the source regionwithin one month of the main shock (Fig. 1). In addition, abruptchanges in the seismicity rate were observed following the Tohoku-Oki earthquake even in distant regions, as well as active aftershocksin the source region (Hirose et al. 2011; Toda et al. 2011a,b).

The Tokyo metropolis lies in the Kanto region and is located∼300 km southwest of the Tohoku-Oki epicentre. This is an ac-tive seismic region because of its complex tectonic environment;two oceanic plates are subducting beneath the OKH: the PAC from

the east and the Philippine Sea Plate (PHS) from the south (Figs 1and 2a). This region has suffered from various types of large earth-quakes (Usami et al. 2013), including shallow crustal earthquakes;intraslab earthquakes within the PHS or within the PAC and inter-plate earthquakes between the OKH and the PHS, between the OKHand the PAC or between the PHS and the PAC.

The 1923 and 1703 Kanto earthquakes are well known to begreat interplate earthquakes between the PHS and the OKH. The1923 Kanto earthquake (JMA magnitude; MJMA 7.9) caused approx-imately 105 000 casualties, mostly due to a massive fire that wascaused by the main shock (Moroi & Takemura 2004), and the 1703Kanto earthquake with the magnitude (M) of 8.2 also caused muchdestruction and approximately 7000 casualties. A recent palaeo-seismological study indicated that the antepenultimate Kanto earth-quake occurred in 1293 (Shimazaki et al. 2011). The EarthquakeResearch Committee (of the government of Japan) (2014) estimatedthe recurrence interval of the M8-class Kanto earthquakes to be200–400 yr, and calculated the probability of another such earth-quake in the next 30 yr to be approximately 0–5 per cent.

The probability of a large (M ∼ 7) earthquake other than the M8-class Kanto earthquake is much higher (e.g. Grunewald & Stein2006; Stein et al. 2006; Nanjo et al. 2013; Somerville 2014). TheEarthquake Research Committee (2014) calculated the probabil-ity of occurrence of such an earthquake during the next 30 yrto be approximately 70 per cent; this is based on the history ofM ∼ 7 earthquakes since 1703. The Central Disaster PreventionCouncil (government of Japan, under the Cabinet office) estimates

112C© The Authors 2015. Published by Oxford University Press on behalf of The Royal Astronomical Society. This is an Open Access articledistributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permitsunrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited.

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Study of seismicity rate in Kanto region 113

Figure 1. Variable slip model of the 2011 Tohoku-Oki earthquake (green contour), based on a tsunami waveform inversion (Satake et al. 2013). Grey, blackand white stars indicate the epicentres of the foreshock, the Tohoku-Oki earthquake (Mw 9.0), and the large aftershocks (MJMA ≥ 7.0) that occurred within40 minutes, respectively. Orange, yellow, red and blue stars indicate the epicentres of the earthquakes near the boundary between the Nagano and NiigataPrefecture on March 12 (MJMA 6.7), the Eastern Shizuoka earthquake on March 15 (MJMA 6.4), the off-Miyagi earthquake (MJMA 7.2) on April 7, and theFukushima Hama-dori earthquake on April 11 (MJMA 7.0), respectively. Focal mechanism solutions from the Japan Meteorological Agency (JMA) are alsoindicated. Green circles indicate the epicentres of earthquakes (MJMA ≥ 3.0) occurring within seven days following the main shock. The black rectangleindicates the target region of this study, and the grey rectangle indicates the source fault of the 1923 Kanto earthquake (MJMA 7.9; Sato et al. 2005).The red dashed ellipse indicates the region of the Boso slow-slip event. The black dashed lines indicate the prefectural boundaries. Red triangles indicate theQuaternary volcanoes. In the inset, OKH, EUR, PAC and PHS indicate the Okhotsk, Eurasia, Pacific and Philippine Sea plates, and black lines indicate theplate boundaries; data from Bird (2003).

fatalities of up to ∼11 000 and economic losses of 95 trillion yen(∼0.8 trillion US$) if a large earthquake (Mw 7.3) occurs beneaththe Tokyo metropolitan area.

The triggering of earthquakes and changes in the seismicity rateaccompanied by large earthquakes have been investigated usingstatic changes in the Coulomb failure function (�CFF; e.g. Harris& Simpson 1992, 1996; Stein et al. 1992, 1994; Toda et al. 1998;Ogata 2006a, 2007). The �CFF is defined as �CFF = �τ − μ′�σ ,where �τ is the shear stress change on a given failure plane (as-sumed positive in the fault slip direction); �σ is the normal stresschange (assumed positive in the compressive direction); and μ′

is the apparent coefficient of friction, defined as μ′ = e(1 − B).Here, B is Skempton’s coefficient, which varies between 0 and1 (Skempton 1954), and e is the coefficient of friction. Posi-tive values of �CFF promote failures; negative values suppressfailures.

In a previous study (Ishibe et al. 2011a), we calculated the �CFFvalues on receiver faults for focal mechanism solutions of pastearthquakes in the Kanto region. We then retrospectively forecastedthe seismicity rate increase in the southwestern Ibaraki and north-ern Chiba prefectures, where intermediate-depth earthquakes fre-quently occur, and also in the shallow crust of the Izu and Hakoneregions, where hydrothermal activity controls the local stress. Wealso showed that the seismicity rates in these regions actually in-creased following the Tohoku-Oki earthquake, suggesting that ourmethod successfully forecasted the seismicity rate change followingthe Tohoku-Oki earthquake. However, in our previous estimationsof the seismicity rate change, we used the preliminary determina-tion of epicentres (PDE) catalogue provided by the JMA, which didnot include many of small earthquakes during the first 3 weeks afterthe Tohoku-Oki earthquake. Moreover, in our previous study, thenumber of the focal mechanism solutions for earthquakes following

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114 T. Ishibe et al.

Figure 2. (a) The target region in this study. Solid green squares indicate the seismic stations of the JMA (or for which the data is included by the JMA),various universities, Japan Agency for Marine-Earth Science and Technology (JAMSTEC), and the MeSO-net. Isodepth contours of the PAC and PHS slabsare indicated by blue and red dashed lines, respectively (Kasahara 1985). Grey thick dashed lines indicate the western and eastern edges of the area where theupper surface of the PAC slab is in contact with the lower surface of the PHS slab (slab–slab contact zone) (Nakajima et al. 2009). Prefectures are indicated asfollows: Fukushima, Fk; Tochigi, Tc; Gunma, Gm; Ibaraki, Ib; Saitama, Sm; Chiba, Cb; Kanagawa, Kn; Shizuoka, Sz; Yamanashi, Yn and Tokyo metropolis isindicated by Tk. Black rectangles indicate the regions in the subsequent figures (see Table 1 for the details). (b) Durations of five catalogues of focal mechanismsolutions that were used as receiver faults. The vertical dashed line indicates the time at which the Tohoku-Oki earthquake occurred.

the Tohoku-Oki earthquake was insufficient for investigating tem-poral changes in the distribution of focal mechanisms with respectto the �CFF values.

In this study, we thoroughly investigate the seismicity ratechange in the Kanto region by using the unified JMA catalogue(Section 3.1), which has now been updated and extended to 2012

March, and compare this with the �CFF imparted by the foreshockon March 9 and six large aftershocks, as well as with several faultmodels of the main shock. We also examine the temporal changesin �CFF before and after the Tohoku-Oki earthquake to verify thetriggering hypothesis using newly compiled focal mechanism datafrom three seismic networks.

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2 M E T H O D

2.1 Calculation of changes in Coulomb stress

To reduce the uncertainty in the �CFF due to variability in thereceiver faults, we calculated the �CFF on two nodal planes ofthe focal mechanism solutions of past earthquakes. This methodhas been proven to be effective in estimating the �CFF in a het-erogeneous stress field in which earthquakes with various typesof focal mechanism occur (Hardebeck et al. 1998; Imanishi et al.2006; Toda 2008; Ishibe et al. 2011a,b). The �CFF values for thetwo nodal planes differ because the unclamping stresses are not thesame, and we do not know which of these is the actual receiver fault;hence we repeated our analysis for both nodal planes and took thelarger �CFF as the representative value. In calculating the �CFF,we assumed an elastic half-space with a shear modulus of 40 GPaand a Poisson’s ratio of 0.25. We also evaluated the �CFF valuesimparted by the foreshock (MJMA 7.3) on March 9th and six largeshocks following the main shock (Fig. 1), and we added them to the�CFF values from the main shock.

For the apparent coefficient of friction (μ′), we assumed an em-pirically introduced μ′ = 0.4; this minimizes the uncertainty in μ′,as discussed by King et al. (1994). Laboratory rock experiments onfrictional slip indicate higher values, such as 0.5 ≤ μ′ ≤ 0.8 (e.g.Byerlee & Brace 1968). In contrast, fluid injection would causehigh pore-fluid pressure, which would then decrease the apparentcoefficient of friction. Therefore, we also repeated the calculationsfor μ′ = 0.1 and 0.7 in order to examine the sensitivity of the result(see Section 4.2).

We excluded from our discussion the receiver faults for whichthe calculated absolute �CFF values were <0.1 or >15 bars.A lower threshold is commonly adopted in static stress trigger-ing (Reasenberg & Simpson 1992; Hardebeck et al. 1998), be-cause the sign may be easily reversed due to the uncertainties inthe hypocentre locations and/or focal mechanism solutions, andthe number of receiver faults strongly depends on the spatial ex-tent of the target region. Significantly high absolute �CFF values(>15 bars), which are typically calculated near the source fault,may be due to simplified source geometry or the slip distributionof the source fault. Therefore, in this study, positive �CFF valuesmean 0.1 bars ≤ �CFF ≤ 15 bars, and negative �CFF values mean–15 bars ≤ �CFF ≤ –0.1 bars.

2.2 Evaluation of changes in seismicity rates

In order to quantify activation or quiescence following the Tohoku-Oki earthquake, we used the Epidemic-Type Aftershock Sequence(ETAS) model (Ogata 1988, 1989). The intensity function λ (t) forearthquakes in a given time period is defined as

λ(t) = μ +∑

j

K eα{M j −Mc}

(t − t j + c)p, (1)

where μ (shocks per day) is the background seismicity rate and thesummation is taken over every jth aftershock that occurs prior tot (days). The intensity function of the jth aftershock is proportionalto an exponential function of the magnitude Mj, where Mc repre-sents the cut-off magnitude. The coefficient α is the efficiency atwhich a shock generates an aftershock, relative to its magnitude.The parameter K (shocks/day) represents the productivity of the af-tershock activity during a short period just after the main shock. Thenumber of earthquakes during any arbitrary period can be obtainedby integrating the intensity function λ(t) with respect to time.

We used the maximum-likelihood method to estimate the ETASparameters for the pre-seismic period (target period), and comparedthe cumulative number of post-seismic earthquakes predicted bythe ETAS model with the actually observed number of earthquakes.The seismicity during the pre-seismic period (target period) may beaffected by earthquakes that occurred prior to this period, due to thelong-lived nature of aftershock activity. Thus, we considered the ef-fects of aftershocks of earthquakes that occurred during 3 yr prior tothe start of target period (i.e. 1994 October 1–1997 September 30).In regions where the ETAS parameters for the pre-seismic periodclearly changed with time, we used only earthquakes that occurredafter the turning point of seismicity.

We estimated the b-value of the Gutenberg–Richter (G–R) re-lationship (Ishimoto & Iida 1939; Gutenberg & Richter 1944):logN = a − bM, where N is the number of shocks of magnitudeM or larger, and a and b are constants, by using the maximum-likelihood estimate (Aki 1965; Utsu 1965), and determined theirstandard deviations by using the method of Shi & Bolt (1982).

3 DATA

3.1 Earthquake catalogue

We used earthquakes in the unified JMA catalogue, from 1997October 1 to 2012 March 10. We selected those for whichMJMA ≥ 2.0, by considering the completeness magnitude abovewhich all earthquakes are detected (Nanjo et al. 2010). Both thedetection capability and accuracy in hypocentral locations weresignificantly improved after 1997 October, due to the unification ofobservation data into the JMA and the development of a seismicobservation network called the Hi-net (Okada et al. 2004). For esti-mating the ETAS parameters, we defined the pre-seismic period tobe the period from 1997 October 1 to 2011 March 10 except for tworegions (Regions S and G in Table 1) which showed clear turningpoints after 1997 October 1.

3.2 Source faults of the Tohoku-Oki earthquakeand the large earthquakes

For the source fault of the Tohoku-Oki earthquake, we used thevariable slip model obtained from the joint inversion of tsunamiwaveforms, GPS observations, teleseismic waveforms and strong-motion data (Yokota et al. 2011). The various slip distributionsof the main shock showed some variation in the areas in whichlarge slips occurred and in the amount of slip. To examine thesensitivity of the fault models, we also used other models obtainedfrom tsunami waveforms (Satake et al. 2013; Fig. 1a), continuousGPS/Acoustic observations (Ozawa et al. 2011; Yokota et al. 2011),teleseismic waveforms (Yokota et al. 2011) and strong-motion data(Yokota et al. 2011). For the large foreshock and the six largeearthquakes that followed the Tohoku-Oki main shock, we used slipdistributions estimated from near-field strong-motion data and/orfar-field waveforms by the JMA (Japan Meteorological Agency2012a,b; Muto et al. 2014).

3.3 Receiver faults

For the receiver faults, we used five sets of focal mechanism solu-tion catalogues of earthquakes in the Kanto region (Fig. 2b). Twoof these catalogues, Kanto-Tokai Focal Mechanisms and the JapanUniversity Network Earthquake Catalog (JUNEC) of First-Motion

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Tab

le1.

Num

ber

ofM

JMA

≥2.

0ea

rthq

uake

sdu

ring

1yr

prio

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foll

owin

gth

eTo

hoku

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eart

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ke,a

ndse

ism

icit

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tech

ange

sin

each

regi

on.

Reg

ion

nam

eL

ON

_SW

LA

T_S

WL

ON

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LA

T_N

EU

pper

dept

hL

ower

dept

h#

(1yr

befo

re#

(Oct

ober

1997

–#

(1yr

afte

rR

ate

chan

ge(◦

)(◦

)(◦

)(◦

)(k

m)

(km

)To

hoku

-Oki

)To

hoku

-Oki

)To

hoku

-Oki

)(1

yraf

ter/

1yr

befo

re)

FF

ukus

him

a/Ib

arak

i14

0.40

36.6

014

1.00

37.3

00

300

2495

98—

BS

W_I

bara

ki13

9.70

36.0

014

0.15

36.3

040

8011

113

9842

93.

85C

NE

_Chi

ba14

0.60

35.6

014

0.85

35.8

035

5520

464

276

13.7

6U

NW

_Chi

ba14

0.00

35.5

014

0.30

35.7

060

8049

782

172

3.50

KS

E_C

hiba

140.

3035

.30

140.

6035

.50

2070

2336

974

3.21

SS

W_C

hiba

139.

7034

.40

140.

4035

.20

6075

1741

713

67.

98N

Nag

ano/

Nii

gata

138.

4536

.75

138.

7537

.10

020

310

483

427

7.24

GTo

chig

i/G

unm

a13

9.30

36.5

013

9.55

36.9

00

1511

506

169

15.3

2T

Tanz

awa

138.

9035

.40

139.

2035

.60

1030

1830

113

57.

48Z

Shi

zuok

a13

8.65

35.2

513

8.75

35.4

00

201

217

217

1.53

HH

akon

e13

8.95

35.1

513

9.05

35.2

50

100

3944

—I

Izu

138.

9034

.05

139.

6035

.15

030

7719

770

200

2.59

Focal Mechanisms (JUNEC FM2) (described below), contain onlyearthquakes before 2011; recently compiled catalogues from threenetworks, the Full-Range Seismograph Network (F-net), the JMAnetwork and the Metropolitan Seismic Observation network (MeSO-net), cover earthquakes both before and after the Tohoku-Oki earth-quake. The Kanto-Tokai Focal Mechanisms and JUNEC FM2 con-tain a large number of focal mechanism solutions, which we usedas the receiver faults in our retrospective forecast of the changes inthe seismicity rate and the distributions of focal mechanisms. Thecatalogues that contain the focal mechanism solutions for earth-quakes both before and after the Tohoku-Oki earthquake were usedto test the hypothesis that the �CFF imparted by the Tohoku-Okiearthquake sequence triggered a seismicity rate change in the Kantoregion.

The Kanto-Tokai Focal Mechanisms catalogue lists first-motionfocal mechanisms for earthquakes between 1979 July and 2003July, as recorded on the Kanto-Tokai observation network operatedby the National Research Institute for Earth Science and DisasterPrevention (NIED; Matsumura & Observation and Research Groupof Crustal Activities in the Kanto-Tokai District 2002). Among thefocal mechanism solutions for 30 746 events (M ≥ 2.0) within thetarget region (138.0 to 141.5◦E, 34.0 to 37.25◦N, depth 0–100 km;Fig. S1), we used focal mechanism solutions for 18 587 eventsby excluding low-quality solutions with the standard deviationsassociated with the P- and T-axes orientations of >20◦ (Okada1988). The second catalogue is JUNEC FM2 (Ishibe et al. 2014),which includes 935 focal mechanism solutions for earthquakes(M ≥ 2.0) with the assigned quality of A or B (see Hardebeck& Shearer 2002, for detailed descriptions) between 1985 July and1998 December in our target region (Fig. S2).

For the other three network catalogues, we considered that thepre-seismic period began on 2008 April 1. The first of these three isthe F-net (Fukuyama et al. 1998), from which we used 3005 focalmechanism solutions with the variance reductions of ≥80 per centfor earthquakes (M ≥ 2.5) from 1997 October 1 to 2012 March 10(Fig. S3). The second is the JMA network, from which we used 2925first-motion focal mechanism solutions with the scores of ≥90 forearthquakes from 1997 October 1 to 2012 March 10 (Fig. S4).

The third of the three network catalogues is the MeSO-net (Sakai& Hirata 2009), which was constructed under the ‘Special Projectfor Earthquake Disaster Mitigation in the Tokyo Metropolitan Area’during the period of 2007–2011 (Hirata et al. 2009). We obtained thefocal mechanisms using a modified algorithm of HASH version 2(Hardebeck & Shearer 2002), a method of determining focal mech-anisms that takes into consideration possible errors in the hypocen-tres, seismic-velocity structures and observed polarities. Becauseof the low reliability and stability, we excluded earthquakes withreported number of polarities <8. We used the one dimensionalseismic-velocity structure which is routinely used for determininghypocentres by the Earthquake Research Institute. We conductedgrid searches for strike, dip and rake angles at 2◦ intervals. We usedfocal mechanism solutions for 1503 events from 2008 April 1 to2012 March 10 with the quality of focal mechanisms of A or B(Figs S5 and S6).

4 C H A N G E I N C O U L O M B S T R E S S

4.1 Coulomb stress changes in the Kanto region

There were many more receiver faults with positive �CFF valuesthan those with negative �CFF values (Table 2; Figs 3 and S7). This

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Table 2. Numbers and ratios of receiver faults with positive, negative, insignificant or high absolute �CFF values for the Kanto-Tokai FocalMechanisms for three apparent coefficients of friction and six main shock fault models.

Data μ′ +�CFF +�CFF −�CFF −�CFF Insignificant or high Insignificant or high(#) (per cent) (#) (per cent) absolute �CFF (#) absolute �CFF (per cent)

Tsunami waveformsa (ts) 0.1 11 085 59.64 3659 19.69 3843 20.680.4 11 934 64.21 2930 15.76 3723 20.030.7 12 555 67.55 2455 13.21 3577 19.24

GPS observationb (g1) 0.1 11 695 62.92 3812 20.51 3080 16.570.4 13 255 71.31 2524 13.58 2808 15.110.7 14 238 76.60 1688 9.08 2661 14.32

GPS observationc (g2) 0.1 10 732 57.74 3289 17.70 4566 24.570.4 11 681 62.84 2429 13.07 4477 24.090.7 12 385 66.63 1893 10.18 4309 23.18

Strong motionc (sm) 0.1 11 549 62.13 3601 19.37 3437 18.490.4 12 686 68.25 2633 14.17 3268 17.580.7 13 410 72.15 1988 10.70 3189 17.16

Teleseismic waveformsc (te) 0.1 11 828 63.64 3759 20.22 3000 16.140.4 12 962 69.74 2786 14.99 2839 15.270.7 13 610 73.22 2059 11.08 2918 15.70

Jointc (ji) 0.1 10 677 57.44 3251 17.49 4659 25.070.4 11 513 61.94 2434 13.10 4640 24.960.7 12 132 65.27 1864 10.03 4591 24.70

aSatake et al. (2013).bOzawa et al. (2011).cYokota et al. (2011); strong motions, teleseismic, geodetic and tsunami.

implies that the seismicity rate in the Kanto region would increase ifthe distribution of earthquakes and their focal mechanisms remainedconstant. However, this does not necessarily mean that the seismicitylevel in the entire Kanto region would become uniformly higher.

The �CFF distribution is very heterogeneous due to the localstress field, which is possibly controlled by the relative plate mo-tions of the OKH, the PHS and the PAC and the distance from theTohoku-Oki source. The receiver faults with positive �CFF val-ues are concentrated in southwest Ibaraki (Region B), northwestChiba (Region U), northeast Chiba (Region C) and southeast Chiba(Region K), where intermediate-depth earthquakes frequently occurdue to the subduction of the PHS and the PAC, and in the shallowcrustal areas of the western Kanagawa, eastern Shizuoka and south-western Yamanashi prefectures, including geothermal areas suchas Hakone (Region H) and Izu (Region I) regions (Fig. 4). Enescuet al. (2012) have showed the clear impact of static stress changeson seismicity around the Izu Peninsula.

Receiver faults at various focal depths with various focal mecha-nisms had positive �CFF values, while others had negative values(Fig. 5). For example, in the southwest part of the Ibaraki region (Re-gion B), the receiver faults with positive �CFFs are concentrated intwo active seismic clusters (Fig. 6a). The western cluster is locatedat depths of 40–50 km, in an area dominated by WSW–ENE-strikingthrust-type earthquakes driven by the interplate motion between theOKH and the PHS. The eastern cluster is located at depths of 40–80km, in an area dominated by WSW–ENE-striking thrust-type earth-quakes between the OKH and the PHS, and SSE–NNW-strikingones between the PHS and the PAC. In this region, normal-faultingor strike-slip earthquakes are also intermixed. The receiver faultswith typical thrusting focal mechanisms had mostly positive (+1 to2 bars) �CFF values, whereas the �CFF values for strike-slip ornormal-faulting earthquakes are a mixture of positive and negativevalues, depending on the fault strike (Figs 5a–h and 7a). This issimilar for Regions U, C and K, suggesting that the thrust fault-ing (interplate) earthquakes will be particularly activated (Figs 5i–l,7b–d and S8).

In the shallow crust of the Kanto region, �CFF values werepositive for receiver faults in which the T-axes were roughly inthe SW–NE direction, and they were negative for faults in whichthe P-axes were in the SW–NE direction (Figs 5m–p). The re-gions where most of shallow crustal receiver faults have positive�CFF values are western Kanagawa, eastern Shizuoka and south-western Yamanashi prefectures, including Hakone (Region H), Izu(Region I) and Tanzawa (Region T) regions (Figs 8 and S9). Thechanges in Coulomb stress were smaller (<0.5 bars) than those inthe previously discussed regions, due to larger distances from theTohoku-Oki source.

4.2 Insensitivity for slip distributions or apparentcoefficients of friction

Our main conclusion, the overall increase in �CFF, is robust for bothslip-distribution models of the main shock and the assumption ofthe apparent coefficients of friction (Table 2; Fig. 9). The frequencydistribution of the �CFF values were similar for all six fault modelsused for the main shock and for the three different values of theapparent friction coefficients. There were slightly more receiverfaults with positive �CFF values when we used a higher apparentcoefficient of friction. This is probably due to the contribution of thelarge number of receiver faults in Region I (Fig. S9). The dominantreceiver faults in this region were effectively enhanced by a higherapparent coefficient of friction.

5 C O R R E L AT I O N B E T W E E N C H A N G E SI N C O U L O M B S T R E S SA N D S E I S M I C I T Y R AT E

In the entire target region, including the part of the source region ofthe Tohoku-Oki earthquake, the seismicity rate during 1 yr followingthe main shock increased by an order of magnitude compared to thatduring the 1 yr prior to the main shock (Figs 4c–f); increases in the

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Figure 3. (a) Distribution of �CFF values for the Kanto-Tokai Focal Mechanisms (M ≥ 2.0; depth ≤100 km) imparted by the foreshock, the Tohoku-Oki mainshock, and the subsequent six large shocks. The inset shows the histogram of �CFFs. (b) Distribution of �CFF values for the Kanto-Tokai Focal Mechanismsfor different depths.

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Figure 4. (a) Distribution of receiver faults with positive �CFF values for the Kanto-Tokai Focal Mechanisms (M ≥ 2.0; depth ≤ 100 km). Colours indicatethe focal depths. (b) Those with negative �CFF. (c) The hypocentre distribution of earthquakes (MJMA ≥ 2.0; depth ≤ 100 km) for 1yr prior to the Tohoku-Okiearthquake. (d) Those during the 1-yr period following the Tohoku-Oki earthquake. (e) Cumulative magnitude-frequency distribution of earthquakes in theinland Kanto region during the 1 yr prior to (green triangles) and following (purple squares) the Tohoku-Oki earthquake. (f) Cumulative frequency curve (bluesolid line) and bimonthly number of earthquakes (green bar plot). The vertical dashed line indicates the time at which the Tohoku-Oki earthquake occurred.

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Figure 5. Distributions of �CFF calculated for 16 receiver faults among the Kanto-Tokai Focal Mechanisms. The black star indicates the epicentre of theTohoku-Oki earthquake. Green circles indicate the epicentres of each receiver fault.

seismicity rate were also significant outside the Tohoku-Oki sourceregion.

The regions where the seismicity rate drastically increased werewell correlated with the distribution of receiver faults with pos-itive �CFF (Figs 4a–d, 10 and S12), although there were some

exceptions. The seismicity rates in these regions became obviouslyhigher than those predicted by the ETAS model after the Tohoku-Okiearthquake (Fig. 11, Table 3), and this is due to an external source,namely the Tohoku-Oki earthquake, which produces a ‘surplus’ ofseismicity in Kanto due to stress triggering. The result is similar

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Figure 6. (a) Epicentre distribution (upper) and east-west cross section of receiver faults within the region 36.0–36.3◦N (lower) for positive �CFF valuesamong the Kanto-Tokai Focal Mechanisms in the southwestern Ibaraki region (Region B). Typical receiver faults are also shown. The colours in the dilatationof the lower hemisphere indicate the depths of the receiver faults. (b) The same for negative �CFFs. (c) Coloured circles indicate the epicentre (upper) andhypocentre (lower) distribution of earthquakes during 1 yr prior to the Tohoku-Oki earthquake with typical focal mechanism solutions. Open circles show theepicentre (upper) and hypocentre (lower) distributions of earthquakes between 1997 October 1 and 2010 March 10. (d) The same for those for 1 yr followingthe Tohoku-Oki earthquake.

for the analyses using the MJMA ≥ 3.0 earthquakes and thus, thedeviation of observed rates after the Tohoku-Oki earthquake is notresulting from the incomplete detection of small-magnitude earth-quakes. The expected seismicity rate changes can be quantitativelycorrelated with �CFF by the laboratory-based rate/state constitu-tive law (e.g. Dieterich 1994; Toda & Enescu 2011; Toda & Stein2013), while evaluating spatial changes in shear stressing rates andAσ , the constitutive parameter multiplied by the total normal stresson the fault, are not straightforward due to the complicated tectonicstress field in the Kanto region. On the other hand, the b-valuesof the G-R relationship do not show significant changes followingthe Tohoku-Oki earthquake: that is, for MJMA ≥ 2.5 earthquakes,b = 0.785 ± 0.033 for the pre-seismic period and b = 0.785 ±0.008 for the post-seismic period.

At intermediate depths, interplate earthquakes associated withthe subduction of the PHS and the PAC were activated, especiallyin regions B, U, C and K (Figs 6 and S8). Belt-like seismicity thatextended from the southern Miura Peninsula to the southern off-Chiba region through the southern Boso peninsula, at a depth of60–70 km (Region S), was also activated. This region is locatedalong the western edge of the slab-slab contact zone between thePHS and the PAC (Nakajima et al. 2009). A seismic swarm beganat the end of 2011 October and was accompanied by a slow-slipevent near the Boso Peninsula in Chiba Prefecture; this was likelyhastened by the stress transfer from the Tohoku-Oki earthquake(Hirose et al. 2012).

Abrupt increases in the seismicity rate of the shallow crustal re-gions were typically observed in the prefectural boundary regionsbetween Fukushima and Ibaraki (Region F), and between Tochigiand Gunma (Region G) as well as Tanzawa (Region T), Hakone (Re-gion H) and Izu (Region I) regions (Figs 12, S10–S14). In RegionsI and H, swarm-like activity began abruptly following the Tohoku-Oki earthquake. In Region H, the MJMA 4.8 earthquake occurred22 min after the Tohoku-Oki main shock. Furthermore, the Eastern

Shizuoka earthquake (MJMA 6.4) occurred on 2011 March 15, inRegion Z.

Region G lies above the volcanic front, and many Quaternaryvolcanoes are distributed in this area. The activated regions arefound near these volcanoes; this is about 10 km north of an ac-tive seismic cluster during the pre-seismic period (Hagiwara 2012;Kodera et al. 2012). Hypocentral depths (1–5 km) of earthquakesafter the Tohoku-Oki earthquake were shallower than those duringthe pre-seismic period (∼8 km).

In Region T, the seismicity rate immediately following theTohoku-Oki earthquake is comparable with that of the pre-seismicperiod, whereas the MJMA 5.4 earthquake occurred on 2012 January28, and the accompanying aftershocks raised the seismicity rate dur-ing the post-seismic period (Figs 10 and S12). The focal mechanismsolutions for the MJMA 5.4 earthquake and most of the accompany-ing aftershocks have the T-axes striking in the SW–NE direction,and therefore, the transferred stress increase would be expected toenhance the seismicity rate. The seismicity that was activated inRegions T, I and H rapidly decayed, whereas the seismicity rate ofintermediate-depth earthquakes (Regions B, C, U, K and S) remainelevated (Figs 10 and S12).

6 T E M P O R A L C H A N G E S I N F O C A LM E C H A N I S M D I S T R I B U T I O N S W I T HR E S P E C T T O C H A N G E S I N C O U L O M BS T R E S S

If the seismicity change after the Tohoku-Oki earthquake was af-fected by the �CFF imparted by the Tohoku-Oki earthquake aswell as that of the foreshock and six large earthquakes, the focalmechanism solutions of the affected seismicity should have beentemporally shifted toward those with positive �CFF values (e.g.Hardebeck et al. 1998; Toda et al. 2011a). We investigated the

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Figure 7. (a)–(d) Histograms of �CFF values for all receiver faults of the Kanto-Tokai Focal Mechanisms (black), and rates of the �CFF values for thrust-type(blue), normal-fault type (green), strike-slip type (orange) and odd type (grey) of receiver faults in (a) Region B, (b) Region U, (c) Region C and (d) Region K.(e)–(h) Triangle diagrams of focal mechanism solutions (Frohlich 1992) in pre- and post-seismic periods for (e) Region B, (f) Region U, (g) Region C and (h)Region K. The colours in the dilatation of the lower hemisphere indicate the �CFF values.

temporal change in the focal mechanism distribution with respectto �CFF using the data for the three networks.

The focal mechanism solutions of earthquakes in the post-seismicperiod are consistent with receiver faults with positive �CFFs. InRegions B, U, C and K, the predominant focal mechanism solutionsfor earthquakes during the post-seismic period were also of thethrust-faulting type (interplate; Fig. 7), as was expected from stressincreases transferred from the Tohoku-Oki earthquake sequence.In the shallow crustal region (Regions G, T, H and I), the focalmechanism solutions of earthquakes during the post-seismic periodpredominantly have the T-axes striking in the SW–NE direction,which is consistent with that of previous earthquakes in these re-

gions (Figs 12 and S13; e.g. Yukutake et al. 2010, 2012), and thesecan be triggered by sudden increases in stress (Harada et al. 2012).

The histograms of �CFF show that more events in the post-seismic period had positive �CFF values than did those in thepre-seismic period (2008 April 1 to 2011 March 10; Figs 13c–d). Among the 1148 focal mechanism solutions in the pre-seismicperiod, 928 receiver faults indicate significant �CFF, with absolutevalues ≥0.1 bar: 717 receiver faults (77.3 per cent) indicate positive�CFF, while 211 (22.7 per cent) indicate negative �CFF. For thepost-seismic period, 1513 out of 1806 focal mechanism solutionsshow significant �CFF; 1334 receiver faults (88.2 per cent) indicatepositive �CFF, while 179 (11.8 per cent) indicate negative �CFF.

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Figure 8. (a) Distribution of receiver faults with positive �CFFs of the Kanto-Tokai Focal Mechanisms (M ≥ 2.0; depth ≤100 km) in Hakone (Region H;dark grey rectangle) and Tanzawa (Region T; light grey rectangle) regions, and an east-west cross section within 35.15–35.6◦N. The typical focal mechanismsare also shown. (b) Those with negative �CFFs. (c) Azimuthal distributions of P-axes (left-hand side) and T-axes (right-hand side) for receiver faults withpositive �CFFs within the rectangular region in (a). (d) The same for receiver faults with negative �CFFs. (e) (left-hand side) Histogram of �CFF values forall-types (black). (right-hand side) Rates of the �CFF values for thrust-type (blue), normal-fault type (green), strike-slip type (orange) and odd-type (grey)receiver faults within the rectangular region.

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Figure 9. Histograms of �CFFs for the Kanto-Tokai Focal Mechanisms (M ≥ 2.0; depth ≤ 100 km) using various fault models: ts, tsunami waveform (Satakeet al. 2013); g1, GPS observation (Ozawa et al. 2011); g2, GPS observation (Yokota et al. 2011); sm, strong motion (Yokota et al. 2011); te, teleseismicwaveform (Yokota et al. 2011) and ji, joint inversion from tsunami, GPS, teleseismic and strong motion (Yokota et al. 2011), with three apparent coefficientsof friction: (a) μ′ = 0.1, (b) μ′ = 0.4 and (c) μ′ = 0.7.

The result is similar for the longer pre-seismic period, between1997 October 1 and 2011 March 10, for which the focal mechanismsolutions obtained from the F-net and JMA network were used(Fig. S15).

To test the significance of the difference in the distribution of�CFF between pre-seismic and post-seismic periods, we used aMonte Carlo method with bootstrap resampling. As a result, the ratioof positive �CFF randomly resampled from �CFF values in thepre-seismic period never exceeded 83.1 per cent, even after 10 000iterations (Fig. S16). This supports the findings of Toda & Stein(2013); however, our calculation is more reliable than theirs becausewe used a much larger number of focal mechanisms compiled fromthe three networks. It also proves the hypothesis that the static stresschanges transferred from the Tohoku-Oki earthquake sequence areresponsible for the changes in the seismicity rate in the Kanto region.

The remarkable temporal change in the frequency distribution of�CFF results from the increase in the number of receiver faults withpositive �CFF following the Tohoku-Oki earthquake. In the Kantoregion, cumulative Coulomb stress changes abruptly increased fol-lowing the main shock (Figs 13e and S15e). In particular, increasesin the cumulative Coulomb stress changes are obvious in RegionsB, U and F, but they are not clear in Regions C, K and S.

Earthquakes with focal mechanism solutions for which the �CFFvalues were positive drastically increased, while those for whichthe �CFFs were negative showed no obvious changes except forimmediately after the main shock (Figs 13f and S15f). This fault-dependent seismicity change strongly supports the contribution ofthe Coulomb stress transferred from the Tohoku-Oki earthquakesequence to the seismicity rate change in the Kanto region. Im-mediately following the Tohoku-Oki earthquake, earthquakes withall types of focal mechanism solutions were activated in the entireKanto region, but the increased seismicity returned to the back-

ground level within a few months. Short-term increases in the seis-micity rate of earthquakes with focal mechanism solutions for whichthe �CFFs are negative suggest that there may be other contributingfactors; this will be discussed in Section 7.1.

7 D I S C U S S I O N

7.1 Other possible factors affecting the seismicityrate change

There are other possible factors that may be contributing to changesin the seismicity rate and/or the occurrence of future large earth-quakes. The first is the dynamic stress changes due to the pas-sage of seismic waves (Hill et al. 1993; Anderson et al. 1994). In-deed, many remotely triggered local events, whose onset times werewell matched with the passage of P waves and/or large-amplitudeRayleigh or Love waves from the Tohoku-Oki earthquake,were identified from densely distributed seismograms in Japan(Miyazawa 2011, 2012; Yukutake et al. 2011, 2013; Shimojo et al.2014). In geothermal areas with Quaternary volcanoes, such asRegions G, H and I, seismic waves from a distant earthquake mayeffectively trigger small earthquakes by causing changes in the stateof magma bodies (Linde et al. 1994; Hill et al. 2002).

The second factor is the changes in pore-fluid pressure becausedecreases in failure strength due to increases in pore fluid pressurecan also enhance the faulting on the specified fault as well as in-creases in shear stress (e.g. Hubbert & Rubey 1959). Most studiesassumed a constant apparent friction coefficient such as μ′ = 0.4,which minimizes the uncertainty in �CFF as discussed by Kinget al. (1994). However, poro-elastic fluid diffusion model showedthat the occurrence of a large earthquake can drastically change the

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Figure 10. Cumulative frequency curves for the time since 2010 March 11 (blue lines with the scale on the left-hand axis) and magnitude–time diagrams(green bar plots with scale on the right-hand axis) for each region. The rectangles in which the earthquakes were extracted are indicated in Fig. 2(a) and Table 1.The vertical dashed lines indicate the time at which the Tohoku-Oki earthquake occurred. See Fig. S12 for cumulative frequency curves for the time since 1997October 1, and magnitude–time diagrams for each region.

surrounding fields of pore fluid pressure (e.g. Cocco & Rice 2002).Some earthquake swarms induced by the Tohoku-Oki earthquakesuch as those in the prefectural boundary region between Yamagataand Fukushima clearly show temporal expansion of the focal area,which is attributed to fluid diffusion (Okada et al. 2011, 2015;Kosuga 2014). Nakajima et al. (2013) investigated a cluster inRegion S and interpreted it as being caused by fluid-related em-brittlement and the migration of overpressured fluids.

The third factor is the contribution from indirectly triggered earth-quakes; this occurs because the changes in stress due to nearbysmaller earthquakes can be comparable with or even larger thanthose from a distant main shock (e.g. Helmstetter et al. 2005).Felzer et al. (2002) suggested that the 1999 Hector Mine earthquake(Mw 7.1), which occurred seven years after the 1992 Landers(Mw 7.3) earthquake, may have been triggered indirectly by a sec-ondary or higher aftershock of the Landers event, thus indicatingthat small earthquakes may also be important for stress triggering.

The fourth factor is the contribution of post-seismic slip. A re-markable amount of post-seismic slip has been observed by a GPSnetwork along the boundary between the PHS and the PAC; this ismostly in the deeper part of the Tohoku-Oki earthquake source (e.g.Ozawa et al. 2011, 2012; Munekane 2012; Silverii et al. 2014). Inthe eastern off-Chiba region, the total slip during the post-seismicperiod exceeded 1.0 m, and it is still increasing (e.g. Ozawa et al.2012).

The fifth factor is the viscoelastic effect (e.g. Pollitz & Sacks1995; Freed & Lin 1998; Freed et al. 2007). Zeng (2001) showedevidence of stress triggering of the 1999 Hector Mine earthquakedue to viscoelastic flow in the lower crust following the 1992 Lan-ders earthquake. The viscoelastic flow increased the Coulomb stressby more than 1 bar at the hypocentre of the Hector Mine earthquakeover a period of seven years. Our calculations, which assume staticand purely elastic models, may only poorly estimate these longer-term effects, because viscoelastic effects may play an important rolein triggering earthquakes. However, this effect would be negligiblein the period immediately following the Tohoku-Oki earthquake.

7.2 Validity and limitations in utilizing focal mechanismsolutions as receiver faults

This study validated the use of focal mechanism solutions of pastearthquakes as receiver faults for the evaluation of seismicity ratechange following large earthquakes. However, the present methodcannot be applied to evaluate the seismicity rate change in regionsthat have few receiver faults or where focal mechanism solutionsvary with time.

Following the 2011 Tohoku-Oki earthquake, shallow normal-faulting earthquakes abruptly began to occur in Region F(Fig. 14). The largest shock was the Fukushima Hama-dori

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Figure 11. For each region, left-/right-hand panel shows cumulative number of observed (solid red lines) events and theoretical cumulative number predictedby the ETAS model (dashed blue lines) on an ordinary/a transformed timescale. Magnitude–time diagrams are also indicated by green bar plots. In left-handpanels, horizontal axis denotes the elapsed days since the first event after 1994 October 1. Vertical grey and black dashed lines indicate the start time of targetperiod and the time at which the Tohoku-Oki earthquake occurred, respectively.

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Table 3. ETAS parameters in each region, estimated from earthquakes during thepre-seismic period.

Region name μ K c p α

F Fukushima/Ibaraki – – – – –B SW_Ibaraki 0.156 0.002155 0.00019 0.740 1.729C NE_Chiba 0.037 0.006287 0.00510 1.061 1.494U NW_Chiba 0.090 0.002287 0.00124 0.860 1.788K SE_Chiba 0.043 0.011055 0.00823 1.170 1.188S SW_Chiba 0.046a 0.001717a 0.00189a 0.873a 2.041a

N Nagano/Niigata 0.007 0.026054 0.00092 1.018 0.835G Tochigi/Gunma 0.050b 0.004790b 0.00035b 1.091b 1.707b

T Tanzawa 0.050 0.001679 0.00061 0.992 1.835Z Shizuoka – – – – –H Hakone – – – – –I Izu 0.149 0.031659 0.00431 1.362 0.533

aEarthquakes since January 1999 were used.bEarthquakes since January 2002 were used.

Figure 12. (a) Coloured circles indicate the distribution of hypocentres of earthquakes during 1 yr prior to the Tohoku-Oki earthquake in Hakone (Region H;dark grey rectangle) and Tanzawa (Region T; light grey rectangle) regions, and an east–west cross section within 35.15–35.6◦N. Some typical focal mechanismsolutions for earthquakes are also shown. Open circles indicate the hypocentre distributions of earthquakes from 1997 October 1 to 2010 March 10. Therectangle indicates the region where the P- and T-axes are shown in (c). (b) Those during 1 yr following the Tohoku-Oki earthquake with typical focalmechanism solutions. The yellow star indicates the hypocentre of the MJMA 6.4 earthquake of 2011 March 15. The rectangle indicates the region where the P-and T-axes are shown in (d). (c) Azimuthal distributions of P-axes (left-hand side) and T-axes (right-hand side) of the focal mechanism solutions of earthquakesduring the pre-seismic period compiled from three networks. (d) The same for the post-seismic period.

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Figure 13. (a) Distribution of �CFF values for focal mechanism solutions of earthquakes, compiled from the three networks, for the pre-seismic period. Thecolours in the dilatation of the lower hemisphere indicate the �CFF values. (b) Those in the post-seismic period. (c) Histogram of �CFF values for (a). (d)Histogram of �CFF values for (b). Green bars indicate the histogram of �CFF values for receiver faults in the prefectural boundary region between Ibarakiand Fukushima (Region F). (e) Cumulative �CFF values for each region. The vertical dashed line indicates the time at which the Tohoku-Oki earthquakeoccurred. (f) Cumulative number of focal mechanism solutions with positive (solid lines) or negative (dashed lines) �CFFs in each region.

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Figure 14. (a) Distributions of hypocentres of earthquakes in the prefectural boundary region between Ibaraki and Fukushima (Region F) prior to (grey) andfollowing (coloured) the Tohoku-Oki earthquake, with typical focal mechanism solutions compiled from the three networks. The colours in the dilatation ofthe lower hemisphere indicate the hypocentral depths. (b) Magnitude–time diagram (green) and cumulative frequency curve (blue solid line) for earthquakesin Region F. The vertical dashed line indicates the time at which the Tohoku-Oki earthquake occurred. (c) Histograms of �CFFs for the Kanto-Tokai FocalMechanisms and the recently compiled focal mechanisms for Region F.

earthquake (MJMA 7.0) on April 11, 1 month after the Tohoku-Okievent. Normal-faulting earthquakes also followed the main shock atthe prefectural boundary region between Ibaraki and Chiba, and inthe eastern off-Chiba region, where shallow seismicity was inactivebefore the Tohoku-Oki earthquake (Imanishi et al. 2013). This typeof earthquake is not listed in the catalogue of the pre-seismic pe-riod; hence, we cannot apply the present method of estimating thechanges in stress in order to evaluate the changes in seismicity. Wenote, however, that the �CFF values calculated for the focal mech-anism solutions of earthquakes during the post-seismic period aremostly positive; hence, the increased seismicity can be explainedby an increase in stress, which is probably due to the tension of theoverriding plate in the E–W direction.

In the shallow crust of the Tohoku region, strike-slip and normal-faulting earthquakes were activated following the Tohoku-Okiearthquake, whereas thrust-faulting earthquakes, which had beenpredominant due to the compression in the E–W direction, weredeactivated (Fig. S17; e.g. Okada et al. 2011; Kosuga et al. 2012;Kosuga 2014; Suzuki et al. 2014). The �CFFs for most of strike-slip or normal-faulting receiver faults showed significant increases,while the �CFFs for thrusting receiver faults decreased. There-fore, the changes in seismicity in the Tohoku region can be gen-erally interpreted as due to changes in stress due to the Tohoku-Oki earthquake sequence, while some activated seismicity showed

clear counter-evidence against the simplified Coulomb stress trans-fer model assuming an elastic half-space homogeneous mediumwith constant apparent coefficient of friction.

The temporal changes in the distributions of focal mechanismsraise an important question: ‘Can stress regimes easily change dueto perturbations in stress imparted by large earthquakes?’ A possibleexplanation for temporal changes in the focal mechanism distribu-tions is the rotation of optimally oriented faults, due to small amountof differential stress, and this is comparable with the changes instress imparted by the Tohoku-Oki earthquake (e.g. Yoshida et al.2012). Kato et al. (2011) interpreted the activated seismicity in Re-gion F as a wholesale change in the stress regime of the continentalplate, due to a significant reduction in the trench-normal compres-sive stress compared to the trench-parallel stress. This might bepossible near the source region, because the �CFF will be suffi-ciently large and will be comparable with stress drop (10–100 bars;Kanamori & Anderson 1975) associated with an inland earthquake(Hasegawa et al. 2012). However, �CFF values for normal or strike-slip earthquakes, which became more active in the western Tohokuregion following the Tohoku-Oki earthquake, are much smaller thanthe average stress drop.

Another possible explanation for temporal changes in the focalmechanism distributions might be the heterogeneity of the localtectonic stress regime (Toda et al. 2011b) and a recommencement

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of short and immature faults. It is thought that a population offault zones tends to coalesce into a longer and simpler fault asit matures and develops (Wesnousky 1988, 1990, 1999; Lockner1993; Scholz et al. 1993; Shimazaki 1999; Ishibe & Shimazaki2012). Wesnousky (1988) indicated that fault complexities, definedas the number of steps (step width ≥1 km) per unit fault length,decrease as cumulative displacements along faults increase. Thenumber of mapped faults with low slip rates (0.01 mm yr−1 ≤ sliprate <0.1 mm yr−1) is fewer than that expected from the powerlaw distribution and the number of mapped faults with higher sliprates (0.1 mm yr−1 ≤ slip rate) due to incomplete fault mappingby geological/geomorphological studies (e.g. Asada 1991). Fromthese viewpoints, we speculate that there are probably numerousimmature and short faults due to inconsistent fault geometry withthe recent stress regime, especially in the seismically inactive regionprior to the Tohoku-Oki earthquake.

In the shallow crustal areas in Tohoku region, the seismicity ratein most of the activated regions was originally low and shows com-plementary distribution with the hypocentres in the pre-seismic pe-riod (Fig. S17); this was possibly due to an inconsistent local stressregime with a regional E–W compression stress. This interpretationis supported from findings by Imanishi et al. (2012, 2013), whodiscovered that normal-faulting earthquakes occurred at the pre-fectural boundary regions between Ibaraki and Fukushima (RegionF), and between Ibaraki and Chiba before the 2011 Tohoku-Okiearthquake, and suggested that the tectonic stress was originally anormal-faulting regime.

Decreases in failure strength due to increases in pore-fluid pres-sure also cause temporal changes in focal mechanism distributions.Terakawa et al. (2013) examined the effects of pore fluid pressure onseismicity changes following the Tohoku-Oki earthquake by usingthe Coulomb failure criterion to analyse aftershocks far from thesource region, and interpreted that the temporal changes in the focalmechanisms were apparent due to sudden increases in the pressureof the pore fluid. This suggests that the absolute stress level inferredfrom temporal changes in focal mechanisms would be strongly bi-ased if the abrupt changes in the pressure of the pore fluid are notconsidered.

8 C O N C LU D I N G R E M A R K S

The regions where the seismicity rate increased following theTohoku-Oki earthquake are well correlated with areas of positive�CFF values. These areas are southwest Ibaraki, northwest Chiba,northeast Chiba and southeast Chiba, where intermediate-depthearthquakes frequently occur due to the subduction of two oceanicplates, and west Kanagawa, east Shizuoka and southeast Yamanashi,including Izu, Hakone and Tanzawa regions, where shallow crustalearthquakes occur. Following the Tohoku-Oki earthquake, the fre-quency distribution of receiver faults with respect to �CFF valuesshifted toward the positive side. These results strongly indicate thatthe largest factor contributing to changes in the seismicity rate inthe Kanto region was the change in stress that was transferred fromthe Tohoku-Oki earthquake sequence.

A C K N OW L E D G E M E N T S

We thank two anonymous reviewers and the editor Egill Haukssonfor detailed comments which improved our manuscript. The leadauthor thanks Yosihiko Ogata and Masao Nakatani for valuable dis-cussions and Mohammad Heidarzadeh for careful reading of the

manuscript. We used the unified Japan Meteorology Agency (JMA)catalogue, focal mechanisms provided by the NIED and the JMA,as well as variable slip model of the 2011 Tohoku-Oki earthquakebased on GPS observations (Ozawa et al. 2011). For the large fore-shock and six large events that followed the Tohoku-Oki earthquake,we used slip distributions estimated from near-field strong-motiondata and/or far-field waveforms provided by the JMA. We used theGeneric Mapping Tools (Wessel & Smith 1998) for drawing the fig-ures, the TSEIS visualization package (Tsuruoka 1998) for the studyof hypocentre data, the modified HASH algorithm (Hardebeck &Shearer 2002) for determining the first-motion focal mechanisms,a program contained in the Statistical Analysis of Seismicity (SA-Seis2006; Ogata 2006b) to estimate the ETAS parameters, and asubroutine program by Okada (1992) for calculating �CFF. Wethank all the organizations and individuals who provided data andinformation used in this study. This study was supported by theMinistry of Education, Culture, Sports, Science and Technology(MEXT) of Japan, under its Earthquake and Volcano Hazards Ob-servation and Research Program and Special Project for ReducingVulnerability for Urban Mega-earthquake Disasters.

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S U P P O RT I N G I N F O R M AT I O N

Additional Supporting Information may be found in the onlineversion of this article:

Figure S1. (a) Distribution of the Kanto-Tokai Focal Mechanismswith standard deviation for the P- or T-axes orientations of ≤20◦

(1979 July to 2003 July; M ≥ 2.0; depth ≤100 km). The coloursin the focal spheres indicate the hypocentral depth, and the dashedline indicates the prefectural boundary. (b) The cumulative numberof focal mechanism solutions (right-hand axis; solid curves), andhistograms of the annual number in (a) (left-hand axis: blue forscore ≥ 90; green for 80 ≤ score < 90; red for score < 80). (c) Themagnitude frequency distribution of focal mechanism solutions in(a) (black squares), those with score ≥90 (blue squares), 80 ≤ score< 90 (green squares) and < 80 (red squares).Figure S2. (a) Distribution of focal mechanism solutions for earth-quakes between 1985 July and 1998 December of the JUNEC First-Motion Focal Mechanisms (JUNEC FM2; Ishibe et al. 2014). Thesymbols are the same as in Fig. S1. Only focal mechanisms with thequality of A or B, used in this study, are shown. (b) The cumulativenumber of focal mechanism solutions (right-hnd axis; solid curves)and histograms of the annual number in (a) (left-hand axis: bluefor quality A; green for quality B). (c) The magnitude frequencydistribution of focal mechanism solutions within the target region(black squares), those with quality A (blue squares), and quality B(green squares).

Figure S3. (a) Distribution of F-net focal mechanisms duringthe pre-seismic period (left-hand side; 1997 October 1 to 2011March 10), and post-seismic period (right-hand side; 2011 March11 to 2012 March 10). The symbols are the same as in Fig. S1.Only focal mechanisms with the variance reductions of ≥80 percent for earthquakes (M ≥ 2.5), used in this study, are shown. (b)Horizontal projections of the T-axes for focal mechanisms duringthe pre-seismic (left-hand side) and post-seismic (right-hand side)periods. The colours indicate the hypocentral depths. (c) Horizontalprojections of P-axes for focal mechanisms during the pre-seismic(left-hand side) and post-seismic (right-hand side) periods.Figure S4. (a) Distribution of first-motion focal mechanisms withthe scores of ≥90, provided by the Japan Meteorological Agency(JMA) during the pre-seismic period (left-hand side; 1997 October1 to 2011 March 10), and post-seismic period (right-hand side; 2011March 11 to 2012 March 10). The symbols are the same as in Fig. S1.(b) Horizontal projections of the T-axes for focal mechanisms duringthe pre-seismic (left-hand side) and post-seismic (right-hand side)periods. Colours indicate the hypocentral depths. (c) Horizontalprojections of P-axes for focal mechanisms during the pre-seismic(left-hand side) and post-seismic (right-hand side) periods.Figure S5. (a) Distribution of the first-motion focal mechanisms,obtained from the MeSO-net during the pre-seismic period (left-hand side; 2008 April 1 to 2011 March 10), and post-seismic period(right-hand side; 2011 March 11 to 2012 March 10). Only focalmechanisms with the quality of A or B, used in this study, areshown. The symbols are the same as in Fig. S1. (b) Horizontalprojections of T-axes for focal mechanisms during the pre-seismic(left-hand side) and post-seismic (right-hand side) periods. Coloursindicate the hypocentral depths. (c) Horizontal projections of P-axesfor focal mechanisms during the pre-seismic (left-hand side) andpost-seismic (right-hand side) periods.Figure S6. Pairs of the preferred (left-hand side) and acceptable(right-hand side) focal mechanisms obtained from the MeSO-netdata. The letters (A, B and C) indicate their quality. The left mecha-nism of each pair indicates the preferred focal mechanism, togetherwith P-wave first-motion polarity (solid circles, push upward; opencircles, pull downward), and the colours in the dilatation of the lowerhemisphere indicate the hypocentral depths. The right mechanismof each pair indicates 20 acceptable focal mechanism solutions asan indicator of the uncertainty of the focal mechanism solutions.Figure S7. (a) Distribution of the �CFF values for the JUNEC FM2

(M ≥ 2.0; depth ≤100 km). The insert shows the histogram of the�CFFs. (b) Distribution of the �CFFs for different depths.Figure S8. Distribution of receiver faults and hypocentres in theChiba region. East–west cross sections within 35.5–35.8◦N and35.3–35.5◦N are also shown in the middle and lower figures, respec-tively. Symbols are the same as in Fig. 6. (a) Distribution of receiverfaults with positive �CFFs of the Kanto-Tokai Focal Mechanisms.(b) The same for negative �CFFs. (c) Hypocentre distribution ofearthquakes between 1997 October 1 and 2010 March 10 (open cir-cles) and during 1 yr prior to the Tohoku-Oki earthquake (colouredcircles). Some typical focal mechanisms compiled from the threenetworks are also shown. (d) Coloured circles indicate those for 1yr following the Tohoku-Oki earthquake, with some typical focalmechanisms. Open circles are the same as in (c).Figure S9. (a) Distribution of the receiver faults with positive�CFFs in the Izu region (Region I) of the Kanto-Tokai Focal Mech-anisms (M ≥ 2.0; depth ≤ 100 km). Typical focal mechanism solu-tions are also shown. East–west cross sections within the rectangularregions A–A′, B–B′, C–C′, D–D′ and E–E′ are indicated in Fig. S14.Green triangles indicate the distribution of Quaternary volcanoes.

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The thick rectangle indicates the regions where the azimuthal dis-tribution of P- and T-axes is shown in (c). (b) Those with negative�CFFs and typical focal mechanisms. (c) Azimuthal distributionsof P-axis (left-hand side) and T-axis (right-hand side) for receiverfaults with positive �CFFs. (d) The same for negative �CFFs. (e)(left-hand side) Histograms of �CFF values for all-types (black).(right-hand side) Rates of �CFFs for thrust-type (blue), normal-fault type (green), strike-slip type (orange) and odd-type (grey)receiver faults.Figure S10. In each depth, left- and right-hand panels indicatedistribution of hypocentres of earthquakes (MJMA ≥ 2.0) during1 yr periods prior to and following the Tohoku-Oki earthquake,respectively. The colours indicate the hypocentral depths.Figure S11. Seismicity rate changes at different depths for the pe-riod from 1 yr prior to the Tohoku-Oki earthquake to 1 yr followingit. Green circles indicate the hypocentres of earthquakes (MJMA ≥2.0) during the 1 yr period following the Tohoku-Oki earthquake.The target region was divided into grids spacing 0.2◦ × 0.2◦ inlongitudes and latitudes, and 10 km in depths, and seismicity ratechanges were calculated for only grids with the total number ofearthquakes of ≥10.Figure S12. Cumulative frequency curves since 1997 October 1(left-hand axis, blue lines) and magnitude–time diagrams (right-hand axis, green bar plots) for each region. The regions are indicatedin Fig. 2(a) and Table 1. The vertical dashed lines indicate the timeat which the Tohoku-Oki earthquake occurred.Figure S13. (a) Coloured circles indicate the distribution ofhypocentres of earthquakes (MJMA ≥ 2.0) during 1 yr prior to theTohoku-Oki earthquake in Region I. Open circles indicate the distri-butions of hypocentres of earthquakes from 1997 October 1 to 2010March 10. Typical focal mechanism solutions for earthquakes, com-piled from the three networks, are also shown. The thick rectangleindicates the regions where the azimuthal distribution of P- and T-axes is shown in (c). (b) Those during 1 yr following the Tohoku-Okiearthquakes. (c) Azimuthal distribution of P-axis (left-hand side)and T-axis (right-hand side) during the pre-seismic period amongthe focal mechanism solutions compiled from the three networks.(d) The same for the post-seismic period.Figure S14. (a) East–west cross sections of earthquakes with posi-tive �CFFs within the rectangular region A–A′, B–B′, C–C′, D–D′

and E–E′ in Fig. S9. (b) The same for negative �CFFs. (c) East–westcross sections of earthquakes during 1 yr prior to the Tohoku-Okiearthquake (coloured circles) and those between 1997 October 1and 2010 March 10 (open circles). (d) East–west cross sections ofearthquakes during the 1 yr period following the Tohoku-Oki earth-quake (coloured circles) and those between 1997 October 1 and2010 March 10 (open circles).Figure S15. (a) Distribution of the �CFF values for compiled focalmechanism solutions from the F-net and JMA network, in the pre-seismic period (1997 October 1 to 2011 March 10). Colours in thedilatation of the lower hemisphere indicate the �CFF values. (b)Those in the post-seismic period (2011 March 11 to 2012 March10). (c) Histogram of the �CFF values during the pre-seismic pe-riod. (d) Histogram of the �CFF values during the post-seismicperiod. The green bars indicate the histogram of �CFF values forreceiver faults in the prefectural boundary region between Ibarakiand Fukushima (Region F). (e) Cumulative �CFF values in each

region. The vertical dashed line indicates the time at which theTohoku-Oki earthquake occurred. (f) Cumulative number of re-ceiver faults with positive (solid lines) or negative (dashed lines)�CFF values in each region.Figure S16. (a) Cumulative probability curves of focal mecha-nism solutions of earthquakes with respect to �CFF values. Thegreen curves are 100 cumulative probability curves for �CFF val-ues that were randomly resampled from �CFF values for receiverfaults during the pre-seismic period. The blue/red curves are cu-mulative probability curves during the post-seismic period includ-ing/excluding focal mechanism solutions for earthquakes in RegionF. (b) Histogram of rate of positive �CFFs for randomly resam-pled 10 000 times from �CFF values for receiver faults duringthe pre-seismic period (green bar plots). The blue/red dashed linesindicate the rate of positive �CFFs during the post-seismic periodincluding/excluding focal mechanism solutions for earthquakes inRegion F.Figure S17. (a) Distribution of focal mechanisms in the Tohokuregion (depth ≤ 20 km) from the F-net and JMA network for thepre-seismic (left-hand side; 1997 January 1 to 2011 March 10) andpost-seismic (right-hand side; 2011 March 11 to 2012 March 10)periods. The colours in the lower hemisphere indicate the �CFFvalues. The grey circles indicate the hypocentres of earthquakes(MJMA ≥ 2.0; depth ≤20 km) during 1 yr periods prior to (left-handside) and following the Tohoku-Oki earthquake (right-hand side).Green triangles indicate the location of Quaternary volcanoes. (b)Histograms of the �CFF values in the pre-seismic (left-hand side)and post-seismic (right-hand side) periods. (c) Triangle diagramsfor focal mechanism solutions of earthquakes during the pre-seismic(left-hand side) and post-seismic (right-hand side) periods.Figure S18. (a) Distribution of the �CFF values for the Kanto-Tokai Focal Mechanisms (M ≥ 2.0; depth ≤ 100 km) imparted bythe foreshock on 2011 March 9 and the six large aftershocks. Theinset shows the histogram of the �CFFs. (b) Distribution of the�CFFs for different depths.Figure S19. Distributions of the �CFF values for the Kanto-TokaiFocal Mechanisms (M ≥ 2.0; depth ≤ 100 km) imparted by (a) theforeshock (MJMA 7.3) on 2011 March 9; (b) the off-Ibaraki earth-quake (MJMA 7.6) 30 min after the main shock; (c) the earthquakenear the boundary between Nagano and Niigata prefectures (MJMA

6.7) on 2011 March 12; (d) the earthquake in the eastern Shizuokaprefecture (MJMA 6.4) on 2011 March 15; and (e) the FukushimaHama-dori earthquake (MJMA 7.0) on 2011 April 11.Figure S20. Cumulative magnitude–frequency distribution forearthquakes in each region during the pre-seismic (green triangles)and post-seismic (purple squares) periods.Figure S21. Rates of the �CFF values for receiver faults, compiledfrom the three networks, during the pre-seismic (purples) and post-seismic (light greens) periods in each region. Note that overlappedportions of histograms during the pre-seismic and post-seismic pe-riods were indicated as dark green (http://gji.oxfordjournals.org/lookup/suppl/doi:10.1093/gji/ggv001/-/DC1).

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