Scaling Relationships of Source Parameters of Inland Crustal Earthquakes in Tectonically

Active Regions

KEN MIYAKOSHI,1 KAZUHIRO SOMEI,1 KUNIKAZU YOSHIDA,1 SUSUMU KURAHASHI,2 KOJIRO IRIKURA,2 and

KATSUHIRO KAMAE3

Abstract—We examined the scaling relationships of inland

crustal earthquakes occurring in tectonically active regions such as

the Japanese Islands. Two important points related to reliable

scaling relationships are discussed empirically: the objective esti-

mation of source parameters such as the seismic moment and

rupture area, and the regionality of the scaling. Rupture areas are

objectively estimated by trimming heterogeneous slip distributions

obtained from waveform inversion. Two trimming procedures have

been proposed to determine effective rupture areas, by Somerville

et al. (Seismol Res Lett 70:59–80, 1999) and Thingbaijam and Mai

(Bull Seismol Soc Am 106:1802–1816, 2016). We confirmed that

both trimmed rupture areas agree well with each other when

applied to the same dataset. The source scaling characteristics are

known to depend on the seismotectonic regime. We investigate the

source scaling relationships of inland crustal earthquakes in Japan

using source parameters obtained from 36 slip models for 22 recent

events (Mw 5.4–7.1) by waveform inversion analysis. We con-

firmed that the source scaling relationships consisting of two stages

were almost the same as those obtained for crustal earthquakes on

the US West Coast by Hanks and Bakun (Bull Seismol Soc Am

92:1841–1846, 2002). For larger earthquakes (Mw [ 7.4) in seis-

mically active regions, Tajima et al. (ZISIN2; J Seismol Soc Jpn

66:31–45, 2013) found saturation of fault displacements showing

the third stage. Combining the earthquake data of Mw 5.4–7.1 in

this study with those of Mw 7.0–8.0 compiled by Murotani et al.

(Pure Appl Geophys 172:1371–1381, 2015), we conclude that the

scaling relationship for rupture area versus seismic moment coin-

cides with the three-stage source scaling relationship using source

parameters extracted from waveform inversions.

Key words: Three-stage scaling relationship, earthquake cat-

egory, waveform inversion, trimming method.

1. Introduction

After the 1995 Hyogo-ken Nanbu earthquake (Mw

6.9) in Japan, dense strong ground motion networks

(K-NET, KiK-net) were installed at about 20-km

intervals by the National Research Institute for Earth

Science and Disaster Resilience (NIED). Using

strong ground motions near the source region, many

heterogeneous slip models have been estimated by

waveform inversion analysis with high-accuracy

velocity structure models. Source parameters (e.g.,

rupture area, average slip, and asperity area) are

extracted from heterogeneous slip models using cer-

tain criteria, and empirical scaling relationships

between source parameters and seismic moment are

evaluated by regression analysis. A three-stage

source scaling relationship between the source rup-

ture area and seismic moment of inland crustal

earthquakes was initially proposed by Irikura and

Miyake (2011) then revised by Murotani et al.

(2015). The Headquarters for Earthquake Research

Promotion (HERP 2017) in Japan adopts such a

three-stage source scaling relationship in predicting

strong ground motions for identified earthquake sce-

narios. Figure 1 shows the schematic source model

for each stage. Irikura and Miyake (2011) proposed a

two-stage scaling relationship of source parameters

for crustal earthquakes occurring mostly on the US

West Coast and some in and around Japan, which

combined source parameters obtained from wave-

form inversion of strong-motion data (Somerville

et al. 1999; Miyakoshi et al. 2000) with those

obtained from geological and geomorphological sur-

veys, selecting only reliable data from the source

parameter catalog compiled by Wells and

Electronic supplementary material The online version of this

article (https://doi.org/10.1007/s00024-019-02160-0) contains sup-

plementary material, which is available to authorized users.

1 Geo-Research Institute, 6F, Kokuminkaikan-Sumitomo-

seimei Bldg., 2-1-2, Otemae, Chuo-ku, Osaka 540-0008, Japan.

E-mail: ken@geor.or.jp2 Aichi Institute of Technology, 1247, Yachigusa, Yakusa-

cho, Toyota, Aichi 470-0392, Japan.3 Institute for Integrated Radiation and Nuclear Science,

Kyoto University, 2, Asashiro-Nishi, Kumatori-cho, Sennan-gun,

Osaka 590-0494, Japan.

Pure Appl. Geophys. 177 (2020), 1917–1929

� 2019 Springer Nature Switzerland AG

https://doi.org/10.1007/s00024-019-02160-0 Pure and Applied Geophysics

Coppersmith (1994). For the first stage, the rupture

area (A) is proportional to Mo2/3 (self-similar scaling)

for earthquakes smaller than Mw 6.5 (Somerville

et al. 1999). For the second stage, A is proportional to

Mo1/2 (the saturation width for the limited thickness

of the seismogenic zone) for earthquakes between

around Mw 6.5 and 7.4 (Irikura and Miyake 2011).

Hashimoto (2007) showed that rupture widths for

inland crustal earthquakes (Mw C around 6.5) satu-

rate at about 16–18 km for the thickness of the

seismogenic zone, using selected reliable data com-

piled by Stirling et al. (2002). Murotani et al. (2015)

proposed the third-stage scaling relationship of

source parameters for large crustal earthquakes in

‘‘megafault’’ systems, including earthquakes with

magnitudes larger than Mw 7.4. They collected

earthquakes that occurred in inland crustal megafault

systems and compiled the source parameters for 11

inland crustal earthquakes, applied analyses of source

rupture processes by waveform inversion as well as

investigation of surface ruptures via

geomorphological surveys. For the third stage, A is

proportional to Mo (the saturation of the slip) for

earthquakes larger than Mw 7.4. Tajima et al. (2013)

showed a saturation of the average slip of about 3 m

in the rupture area of earthquakes (Mw C 7.4) from

datasets of source models with heterogeneous slip

distributions using waveform inversions for inland

crustal earthquakes.

Some researchers (e.g., Wells and Coppersmith

1994; Leonard 2010, 2014) have proposed a self-

similar scaling relationship (where A is proportional

to Mo2/3), just a one-stage scaling relationship, while

others (e.g., Hanks and Bakun 2002; Yen and Ma

2011) have proposed a two-stage scaling relationship.

Hanks and Bakun (2002) showed that A is propor-

tional to Mo2/3 for smaller earthquakes (Mw B 6.7)

but proportional to Mo1/2 for larger earthquakes

(Mw [ 6.7) because of the idea of a constant stress

drop and the limited thickness of the seismogenic

zone. Yen and Ma (2011) showed that A is propor-

tional to Mo1 for seismic moments smaller than

Figure 1Schematic source model for each stage of three-stage scaling relationship

1918 K. Miyakoshi et al. Pure Appl. Geophys.

1020 N m, i.e., non-self-similar scaling, but Mo2/3 for

seismic moments greater than 1020 N m, i.e., self-

similar scaling.

There are some suggestions that source scaling is

affected by the tectonic regionality and focal mech-

anism. Scholz et al. (1986) proposed a classification

into three tectonic earthquake types: I (interplate), II

(intraplate, involving plate boundary-related), and III

(intraplate, involving midplate), on the basis of the

slip rate of the fault. They categorized earthquakes

occurring in inland crust of the Japanese Islands as

intraplate (type II). They also showed the indepen-

dence of faulting regimes for the scaling relationship.

Wells and Coppersmith (1994) proposed a classifi-

cation into two tectonic earthquakes, viz.

stable continental region (SCR) and non-SCR earth-

quakes. Almost all earthquakes in the dataset from

the US West Coast and Japan were categorized as

non-SCR. Their scaling relationships showed a

slightly different dependence on the focal mecha-

nisms. However, Hanks and Bakun (2002) classified

these US West Coast and Japanese earthquakes,

which are categorized into the non-SCR earthquakes

by Wells and Coppersmith (1994), as continental

earthquakes. They showed a bilinear scaling rela-

tionship for saturation of fault widths of 15–20 km

(Mw C 7.5). Leonard (2010, 2012) proposed a clas-

sification into two types of tectonic earthquake, viz.

plate boundary and SCR. The former type includes

interplate and plate boundary-related earthquakes,

including type I and II (Scholz et al. 1986), while the

latter includes mid-continental ones, including

type III (Scholz et al. 1986). Leonard (2010, 2012)

used not only datasets of Wells and Coppersmith

(1994) but also those of Somerville et al. (1999) and

Hanks and Bakun (2002). He categorized earthquakes

occurring in inland crust in both the US West Coast

and the Japanese Islands as interplate. He suggested

that interplate strike–slip earthquakes showed satu-

ration of fault widths of 12–20 km (Figure 2 of

Leonard 2010). Yen and Ma (2011) investigated

source scaling relationships in the collision zone of

Taiwan. Their relationship is influenced by a seis-

mogenic thickness of 35 km, suggesting that stress

drops for small events (Mo B 1020 N m) have some

variation of 1–10 MPa. Another notable feature is

constant slip for seismic moments smaller than

1020 N m. It is suggested that the tectonic regime in

the collision zone of Taiwan is different from that in

the Japanese Archipelago. Stirling et al. (2013)

showed different source scaling relationships

according to different tectonic regimes (e.g., plate

boundary crustal, stable continental, subduction, and

volcanic) and slip types (e.g., strike–slip, reverse, and

normal fault). Besides, plate boundary earthquakes

are classified into two subclasses (fast and slow plate

boundary faults). They concluded the importance of

choosing scaling relationships carefully for seismic

hazard applications in different tectonic environ-

ments. As noted below, the classification of inland

crustal earthquakes in Japan, the transform interplate

and crustal intraplate ones on the US West Coast

should be unified for the same tectonic regionality,

because the source scaling relationships for both are

almost the same.

Wells and Coppersmith (1994) also indicated that

the surface rupture length observed from geological

survey and the subsurface rupture length estimated

from the best-defined aftershock zone are not nec-

essarily consistent with each other. Hence, it is

possible that the reliability of datasets of source

parameters estimated from different measurements

will affect the source scaling relationship. To discuss

source scaling relationships accurately, one must

therefore use source parameters of earthquakes esti-

mated using the same measurement technique in the

same tectonic regionality. Rupture areas have been

estimated highly accurately by waveform inversion

rather than using the aftershock distribution or sur-

face rupture surveys after earthquakes. Inland crustal

earthquakes in the Japanese Archipelago occur in

crustal intraplate regions close to active plate mar-

gins, where the seismicity is very high. The crustal

earthquakes on the US West Coast also occur near

transform interplate and crustal intraplate regions

with high seismicity. We recognized that inland

crustal earthquakes in active regions with high

seismicity in Japan are almost the same as those on

the US West Coast. In this study, we investigated

source scaling relationships of inland crustal earth-

quakes in tectonically active regions using source

parameters obtained from rupture models by wave-

form inversion analysis.

Vol. 177, (2020) Scaling Relationships of Source Parameters of Inland Crustal Earthquakes 1919

2. Earthquake Categorization

Earthquakes occur in different seismotectonic

settings and involve various faulting styles. Firstly,

the seismotectonic setting in which earthquakes occur

must be identified for discussion of source scaling

relationships. The new regulatory guides of the

Nuclear Regulation Authority (NRA) in Japan cate-

gorize earthquakes in and around Japan into three

types (inland crustal earthquakes, interplate earth-

quakes, and oceanic intraplate earthquakes). Our

main targets are the inland crustal earthquakes in

tectonically active regions in Japan and on the US

West Coast. So far, we have categorized the inland

crustal earthquakes compiled by Somerville et al.

(1999) and Miyakoshi et al. (2015). Figure 2 shows

the proposed earthquake categorization referring to

the seismotectonic regime of the IAEA (2016).

Firstly, we divide the earthquakes into two categories,

viz. subduction and nonsubduction earthquakes,

according to the plate tectonic setting. Subduction

earthquakes occur along a subduction interface, in-

slab, and outer-rise (HERP 1999). Secondly, we

divide the nonsubduction earthquake category into

oceanic and continental earthquakes. We do this

because the thicknesses of seismogenic zones are

expected to be different between ocean and conti-

nental crust owing to isostasy. Thirdly, the

continental earthquake category is divided into

stable region earthquakes, such as in Europe, and

active region earthquakes such as in Japan and on the

US West Coast. A stable region is the same as an

SCR (Wells and Coppersmith 1994). Active region

earthquakes include crustal intraplate (inland crustal;

e.g., the 2016 Kumamoto, Japan, earthquake), trans-

form interplate and crustal intraplate events (e.g., the

1989 Loma Prieta, California, earthquake), as shown

in Fig. 2. Our target earthquake category for the

source scaling relationship is inland crustal earth-

quakes in tectonically active regions, as shown in

Fig. 2.

3. Scaling Relationships of Source Parameters Based

on Waveform Inversion Results

Using the waveform inversion results of 36 slip

models for 22 recent inland crustal earthquakes (Mw

Figure 2Earthquake category of inland crustal earthquakes in tectonically active regions referring to the seismotectonic regime of the IAEA (2016)

1920 K. Miyakoshi et al. Pure Appl. Geophys.

Figure 3Distribution of 22 events included in this study and their focal mechanisms (F-net)

Vol. 177, (2020) Scaling Relationships of Source Parameters of Inland Crustal Earthquakes 1921

5.4–7.1) (Fig. 3) that occurred in Japan after the 1995

Hyogo-ken Nanbu earthquake (Mw 6.9), we extracted

the source parameters from the inversion results using

the same criterion as Somerville et al. (1999). These

seismic magnitude ranges (Mw 5.4–7.1) correspond to

the first and second stage of the three-stage source

scaling relationship.

3.1. Trimming Methods for Fault Rupture Area

We calculated the averaged source parameters of

the logarithm using various inversion results for the

same events reported by different authors. Figure 4

shows an example of the waveform inversion result

of the 2016 Kumamoto, Japan, earthquake (Mw 7.1).

In most waveform inversion analysis, the rectangular

dimensions of the fault are chosen to be at least large

enough to accommodate the entire fault rupture as

estimated from the best-defined aftershock zone, and

thus sometimes overestimate the actual dimensions of

the rupture area. To estimate the ‘‘true’’ fault

dimension accurately, Somerville et al. (1999;

S1999) trimmed slip models by removing rows/col-

umns if their average slip was less than 0.3 times the

average slip in rupture area. A part of the Hinagu

segment (‘‘H’’ in Fig. 4), southwest segment of the

Kumamoto earthquake, is removed by the trimming

method of Somerville et al. (1999). Mai and Beroza

(2000; M2000) introduced the concept of effective

source dimensions, based on the autocorrelation

width of the spatially variable slip. Thingbaijam

and Mai (2016; T2016) proposed a new concept of

effective source dimensions extended from M2000.

Thingbaijam et al. (2017) also trimmed slip models

by using the T2016 trimming method and proposed

new scaling relationships. Because both trimming

methods (S1999 and T2016) have the common

purpose of estimating the ‘‘true’’ fault dimension

accurately, one must evaluate whether they can

extract the same source parameters. To do this, we

compare the rupture areas obtained using both

trimming methods, S1999 and T2016.

We used three datasets of inland crustal events

(hereinafter called datasets A, B, and C). Dataset A is

composed of 22 events in Japan, the slip models of

which were trimmed by S1999. Dataset B is com-

posed of 15 events on the US West Coast compiled

by Somerville et al. (1999), the slip models of which

were trimmed by S1999. Dataset C is composed of

133 events compiled by Thingbaijam et al. (2017),

the slip models of which were trimmed by T2016.

There are 11 common events between datasets A and

Figure 4Slip distribution on fault plane of the 2016 Kumamoto, Japan, earthquake (EQ.1, Mw 7.1). Star indicates hypocenter. A part of the Hinagu

segment (‘‘H’’ in this figure), southwest segment of Kumamoto earthquake, is removed by the trimming method of Somerville et al. (1999).

Solid red rectangle shows rupture area obtained by the trimming method of Somerville et al. (1999)

1922 K. Miyakoshi et al. Pure Appl. Geophys.

C, and 13 common events between datasets B and C.

Therefore, we compared the slip models trimmed by

S1999 with those trimmed by T2016 for a total of 24

events, the slip models of which were estimated

independently using both methods. Figure 5 com-

pares the source parameters (rupture length, width,

and area) of the slip models trimmed using the

different methods (S1999 and T2016). The large red

circles in Fig. 5 show the 11 events in Japan that are

common between datasets A (this study) and C

(Thingbaijam et al. 2017). The small blue circles in

Fig. 5 show the 13 events on the US West Coast that

are common between datasets B (Somerville et al.

1999) and C (Thingbaijam et al. 2017). Note that the

Figure 5Comparison between source parameters (rupture length, width, and area) of slip models trimmed using different methods (S1999, Somerville

et al. 1999; T2016, Thingbaijam and Mai 2016). Large red circles show the 11 events in Japan that are common between datasets A (this

study) and C (Thingbaijam et al. 2017). Small blue circles show the 13 events on the US West Coast that are common between datasets B

(Somerville et al. 1999) and C (Thingbaijam et al. 2017). Solid line denotes one-to-one ratio

Vol. 177, (2020) Scaling Relationships of Source Parameters of Inland Crustal Earthquakes 1923

source parameters of the slip models trimmed using

the different methods (S1999 and T2016) are consis-

tent with each other. Although some rupture areas

trimmed using S1999 are smaller than those obtained

using T2016, the discrepancies are small, reaching

about 0.2 (on a log scale) at the maximum. It is

important to note that the different trimming methods

S1999 and T2016 give almost the same source

parameters. This confirms that the trimmed slip

models from this study, Somerville et al. (1999),

and Thingbaijam et al. (2017) can be used to

investigate the source rupture scaling objectively.

3.2. Outer Fault Parameters

We evaluated the source scaling relationships of

inland crustal earthquakes in Japan using the source

parameters obtained from 36 slip models for 22

recent inland crustal earthquakes (Mw 5.4–7.1) by

waveform inversion analysis (Table S1). We also

added earthquake data compiled by Somerville et al.

(1999) and Murotani et al. (2015). Figure 6a, b shows

the relationships between rupture area (A) and seis-

mic moment (Mo) and between rupture length (L) and

seismic moment (Mo), respectively. We used seismic

moment estimated by F-net, NIED. The relation

between the rupture area and seismic moment seems

to bend at around Mw 6.5 due to saturation of fault

width. For larger earthquakes (Mw [ 7.0) in seismi-

cally active regions, we plot source parameters

compiled by Murotani et al. (2015). The relation

(Mw [ 7.4) seems to show another bend due to

saturation of fault displacements (Tajima et al. 2013).

Combining the earthquake data of Mw 5.4–7.1 from

this study with those of Mw 7.0–8.0 (Murotani et al.

2015), we recognize that the scaling relationship of

rupture area versus seismic moment coincides with

the three-stage source scaling relationship (Table S2)

using source parameters extracted from waveform

inversions. The empirical relationship of Leonard

(2014) almost agrees with datasets of estimated

source parameters at the first stage (A is proportional

to Mo2/3) of the three-stage scaling relationship

(Mw \ 6.5) in this paper. The empirical relationship

of Hanks and Bakun (2002) is in agreement with

datasets of source parameters at the first and second

stages (A is proportional to Mo2/3, Mo1/2) of the three-

stage scaling relationship (Mw B 7.4). However, the

rupture area in their empirical relationship is an

underestimate compared with that of our datasets at

the third stage (Mw[ 7.4). The rupture area for a

certain seismic moment obtained from the empirical

relationships by Thingbaijam et al. (2017) tends to be

slightly larger than that of our datasets at the second

and third stages (Mw[ 6.5). On the other hand, the

empirical relationships of Yen and Ma (2011) are not

in agreement with our datasets over a wide range of

seismic moment, suggesting that the tectonic regime

in the collision zone of Taiwan is different from that

in the Japanese Archipelago, as mentioned above. In

conclusion, our datasets for the first stage of the

three-stage scaling relationships are consistent with

the empirical scaling relationships of both Leonard

(2014) and Hanks and Bakun (2002), while those for

the second stage are consistent with the empirical

scaling relationships of Hanks and Bakun (2002).

Note that a clear dependence of the source parameters

on the faulting style cannot be seen in these figures.

Figure 6c shows the relationship between the rupture

width (W) and seismic moment (Mo). It is obvious

that rupture widths are saturated at 16–18 km

(Mw C 6.5–7) for the thickness of the seismogenic

zone in Irikura and Miyake (2001) and Leonard

(2014) in Fig. 6c. However, Thingbaijam et al.

(2017) proposed that the rupture width becomes

wider with increasing seismic moment without sat-

uration. We discuss below whether rupture width

saturates for the inland crustal earthquakes compiled

by Thingbaijam et al. (2017) if appropriate regional-

ity is taken into consideration for scaling of inland

crustal earthquakes.

3.3. Inner Fault Parameters

From the heterogeneous final slip model, we

determined the asperity area following the criterion

proposed by Somerville et al. (1999). The combined

areas of asperities are defined as large slip areas

where slips are more than 1.5 times the average slip

on the entire source fault. The asperity model has one

or several patches with constant large slip velocity

and a background area with less slip (Irikura and

Miyake 2011). The final slip distributions and the

extracted asperity areas for the 2005 Fukuoka, Japan,

1924 K. Miyakoshi et al. Pure Appl. Geophys.

earthquake (Mw 6.6, EQ.8) are shown in Fig. 7 as an

example. The combined area of asperities is an

important source parameter corresponding to the

effective stress drop for the prediction of strong

ground motions (Irikura and Miyake, 2011). Figure 8

shows the relationship between the combined area of

Figure 6Relationships between source parameters and seismic moment. Yellow symbols denote earthquakes included in this study (square: reverse-

slip, triangle: strike-slip, circle: normal-slip). Datasets of source parameters in this study are presented in Table S1. Datasets of Somerville

et al. (1999), Murotani et al. (2015), and Stirling et al. (2002) are also plotted in this figure. Selected datasets of Stirling et al. (2002) by

Murotani et al. (2015) are used in this study. a Relationship between rupture area and seismic moment. Solid black line shows empirical

scaling relationship proposed by HERP (2017). Solid green, gray, orange, and blue lines show empirical scaling relationships of Hanks and

Bakun (2002), Yen and Ma (2011), Leonard (2014), and Thingbaijam et al. (2017), respectively. b Relationship between rupture length and

seismic moment. Solid black lines show empirical scaling relationships proposed by Takemura (1998) (Mo\ 7.5 9 1018 N m) and Irikura

and Miyake (2001) (Mo C 7.5 9 1018 N m), respectively. The other solid lines show the same empirical scaling relationships as in a except

Hanks and Bakun (2002). c Relationship between rupture width and seismic moment. Solid black lines show empirical scaling relationships

proposed by Hashimoto (2007) (Mw C 6.5) and Irikura and Miyake (2001) (L\Wmax), respectively. The other solid lines show the same

empirical scaling relationships as in a except Hanks and Bakun (2002)

Vol. 177, (2020) Scaling Relationships of Source Parameters of Inland Crustal Earthquakes 1925

asperities (Aasp) and seismic moment (Mo). Note that

the slope of the scaling relationship between the

combined area of asperities and seismic moment in

this study coincides with that of Somerville et al.

(1999). If we give weight to recent results for 22

earthquakes, Aasp seems to bend at around Mw 6.5 to

become proportional to Mo1/2 (broken red line in

Fig. 8), keeping effective stress constant.

4. Discussion

4.1. Average Static Stress Drop in Rupture Area

Source scaling is an important issue for earth-

quake source physics. Since Kanamori and Anderson

(1975) proposed empirical relations between source

parameters such as fault length, fault width, fault

displacement, etc., it has been widely accepted that

the stress drop has a constant value independent of

seismic moment. Wells and Coppersmith (1994) and

Leonard (2014) assumed constant stress drop and

proposed a self-similar scaling relationship with

A proportional to Mo2/3 over a wide range of seismic

moment. Hanks and Bakun (2002) assumed increas-

ing stress drop and proposed bilinear scaling

relationships with A proportional to Mo1/2 over a

large seismic moment range (Mw[ 6.7). HERP

(2017) adopts a three-stage source scaling relation-

ship with different slopes between the source rupture

area and seismic moment (where A is proportional to

Mo2/3, Mo1/2, and Mo1). Therefore, whether stress

drop varies over a wide seismic moment range must

be discussed. We estimated the static stress drop in

the rupture area from the heterogeneous final slip of

waveform inversion results using the method devel-

oped by Okada (1992). Figure 9 shows an example of

the static stress drop obtained from the inverted slip

distribution of the 2005 Fukuoka, Japan, earthquake

(Mw6.6, EQ.8) estimated using Okada’s method.

Figure 10 shows the relationship between the average

static stress drop and seismic moment for 19 events

(Table S3). The average static stress drops do not

show such a large difference in the range of the first

Figure 7Slip distribution on fault plane of the 2005 Fukuoka, Japan,

earthquake (Mw6.6, EQ.8). Star indicates hypocenter. Red rectan-

gles denote asperity areas extracted using the criterion of

Somerville et al. (1999)

Figure 8Relationship between combined area of asperities (Aa) and seismic

moment. Datasets of Somerville et al. (1999) are also plotted in this

figure (small circles). Solid blue line shows empirical relationship

of Somerville et al. (1999). Broken red line shows relationship

proportional to Mo1/2 (Mw C 6.5)

Figure 9Static stress drop distribution of the 2005 Fukuoka, Japan,

earthquake (Mw6.6, EQ.8) estimated using the method of Okada

(1992). Star indicates hypocenter

1926 K. Miyakoshi et al. Pure Appl. Geophys.

and second stages of the three-stage source scaling

relationship. The average static stress drops in the

first stage (Mw \ 6.5) fluctuate within 1–4 MPa. The

average stress drop of 2.3 MPa used in the recipe for

strong motion prediction by HERP (2017) is in

approximate agreement with the mean value

(1.7 MPa) of the average static stress drops found

here for the first stage (Mw\ 6.5). Further, the

average static stress drops in the second stage

(6.5 B Mw\ 7.1) also fluctuate within 2–5 MPa.

The static stress drop (3.1 MPa) proposed by Fujii

and Matsu’ura (2000) for strike-slip-type earthquakes

(Mw C around 6.5) approximately agrees with the

mean value (3.1 MPa) of the average static stress

drops found here (6.5 B Mw \ 7.1). We find that the

fluctuation of static stress drops seems to be small

over a very wide range of seismic moment, being

almost constant from Mw 5.4 to 7.1.

4.2. Saturation of Rupture Width

Thingbaijam et al. (2017) proposed a new scaling

relationship for source parameters based on a large

SRCMOD database (Mai and Thingbaijam 2014). As

mentioned above, they showed that the rupture width

becomes longer with increasing seismic moment (or

Mw) and does not saturate for strike-slip-type

earthquakes (Fig. 6c). However, Hashimoto (2007)

and Leonard (2010) proposed that rupture widths for

inland crustal earthquakes (strike-slip, reverse-slip,

and normal-slip type) saturated at about 16–18 km

for the thickness of the seismogenic zone (Fig. 6c).

The saturation of the rupture widths forms the second

and third stages. Our compiled inversion results (e.g.,

Somerville et al. 1999; Miyakoshi et al. 2015)

involve intraplate, transform interplate, and inland

crustal earthquakes in tectonically active regions,

mainly in Japan and on the US West Coast (Fig. 2).

In contrast, Thingbaijam et al. (2017) compiled

strike-slip-type earthquakes, which include oceanic

intraplate earthquakes (Mw[ 7.2), e.g., the 2013

Scotia Sea earthquake (Mw 7.7). To discuss the

source scaling relationship accurately, it is important

to consider earthquakes that occur in the same

seismotectonic setting with high seismic activity, as

described above. Therefore, we try to remove the

oceanic intraplate earthquakes (Mw[ 7.2) compiled

by Thingbaijam et al. (2017). Figure 11 shows the

relationship between rupture width (W) and seismic

moment (Mo) for the dataset from which the oceanic

intraplate earthquakes (Mw [ 7.2) are omitted. We

recognized that rupture widths saturate at about

16–18 km for inland crustal earthquakes with

strike-slip in Fig. 11. The database of inland crustal

earthquakes from SRCMOD, except for the oceanic

intraplate earthquakes (Mw [ 7.2), is in good

Figure 10Relationship between average static stress drop in rupture area and

seismic moment estimated in this study (square: reverse-slip,

triangle: strike-slip, circle: normal-slip). Solid black line shows

self-similar stress drop (2.3 MPa) based on the recipe for strong

ground motion prediction by HERP (2017) (Mw\ 6.5). Broken

and solid grey line shows the static stress drop (3.1 MPa) proposed

by Fujii and Matsu’ura (2000) for strike-slip-type earthquakes

(Mw C around 6.5)

Figure 11Relationship between rupture width and moment magnitude for

inland crustal earthquakes of strike-slip type compiled by Thing-

baijam et al. (2017). Solid blue line shows empirical relationship of

Thingbaijam et al. (2017). ‘‘9’’ denotes oceanic intraplate earth-

quakes compiled by Thingbaijam et al. (2017). Solid black lines

show empirical scaling relationships proposed by Hashimoto

(2007) (Mw ‡ 6.5) and Irikura and Miyake (2001) (L\Wmax),

respectively. Solid orange line shows empirical scaling relation-

ships of Leonard (2014)

Vol. 177, (2020) Scaling Relationships of Source Parameters of Inland Crustal Earthquakes 1927

agreement with the empirical scaling relationship of

Hashimoto (2007) and Leonard (2010) in the second

and third stages.

5. Conclusions

Using waveform inversion results for 22 recent

inland crustal earthquakes (Mw 5.4–7.1) in Japan, we

extracted the source parameters (rupture area, asper-

ity area, etc.) from the inverted heterogeneous slip

distributions following the criterion of Somerville

et al. (1999). We recognized that the scaling rela-

tionship for rupture area (A) versus seismic moment

(Mo) obtained in this study coincide with the three-

stage source scaling relationship (HERP 2017). A

different trimming method for the heterogeneous slip

model by Thingbaijam and Mai (2016) gives almost

the same source parameters as when using that of

Somerville et al. (1999). It is important to note that

trimmed slip models have been used to objectively

investigate the source rupture scaling. We also esti-

mated the average static stress drop in the rupture

area from heterogeneous slip of source inversion

results using the method of Okada (1992). The esti-

mated static stress drops with variation of 1–5 MPa

were in approximate agreement with the self-similar

stress drops (2.3 MPa) based on the recipe used by

HERP (2017) (Mw \ 6.5) and the static stress drop

(3.1 MPa) proposed by Fujii and Matsu’ura (2000)

(Mw C around 6.5). Source parameters of rupture

width compiled by Thingbaijam et al. (2017),

excluding oceanic intraplate earthquakes, showed

saturation at about 16–18 km for inland crustal

earthquakes. We found that source scaling relation-

ships of inland crustal earthquakes are controlled by

the tectonic setting with high seismic activity rather

than faulting style.

Acknowledgements

We used the hypocentral information catalog of the

Japan Meteorological Agency (JMA) in cooperation

with the Ministry of Education, Culture, Sports,

Science, and Technology (MEXT), and source infor-

mation from F-net provided by the National Research

Institute for Earth Science and Disaster Resilience

(NIED). We would like to thank Dr. Asano, K.

(DPRI), Dr. Sekiguchi, H. (DPRI), Prof. Iwata, T.

(DPRI), Dr. Horikawa, H. (AIST), Dr. Kubo, H.

(NIED), Dr. Suzuki, W. (NIED), Dr. Aoi, S. (NIED),

and Dr. Hikima, K. (TEPCO) for provision of

waveform inversion results. Careful reviews and

comments by the editor and two anonymous review-

ers were quite helpful in improving the manuscript.

This study was mainly based on the 2017 & 2018

research project ‘‘Examination for uncertainty of

strong ground motion prediction for the inland crustal

earthquakes’’ by the Secretariat of the Nuclear

Regulation Authority (NRA), Japan.

Publisher’s Note Springer Nature remains neutral

with regard to jurisdictional claims in published maps

and institutional affiliations.

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(Received November 7, 2018, revised March 10, 2019, accepted March 11, 2019, Published online April 16, 2019)

Vol. 177, (2020) Scaling Relationships of Source Parameters of Inland Crustal Earthquakes 1929