Migration of low frequency tremors revealed from multiple array analyses in western

Shikoku, Japan

Tomotake Ueno, Takuto Maeda*, Kazushige Obara, Youichi Asano, and Tetsuya Takeda

National Research Institute for Earth Science and Disaster Prevention

*Now at the Center for Integrated Disaster Information Research, Interfaculty Initiative in

Information Studies, The University of Tokyo

Short title: MIGRATION OF TREMORS BY MULTIPLE ARRAYS

———————————————

Tomotake Ueno

National Research Institute for Earth Science and Disaster Prevention

3-1 Tennodai, Tsukuba, Ibaraki 305-0006, Japan

(ueno@bosai.go.jp)

1

Abstract

Multiple array observation above a belt-like tremor zone was conducted to

investigate the detailed location and migration of tremor activity in western Shikoku, Japan.

In March 2007, an episodic tremor and slip event occurred, and highly coherent waveforms

were recorded at three arrays. Multiple signal classification analysis for the data from each

array enabled measuring precise arrival directions. The majority of tremor signals

suggested relatively low slowness. The arrival directions of tremor signals were used to

locate tremor sources by the grid search method. Tracking the tremor activity showed that

the tremor migrated within several hours in the northeast-southwest direction over a

distance of 12–15 km, and its migration velocity was 1–2.5 km/h. This migration velocity is

more rapid than the mean velocity of 0.5 km/h over the whole tremor episode lasting

several days. Such a short timescale migration may represent fluctuation of slip

acceleration during the slow slip event. Whenever a tremor migrates southwestward,

very-low-frequency earthquakes occur in the vicinity of the tremor migration terminus.

This indicates that the tremor migration is related to the occurrence of very-low-frequency

earthquakes and slow slip events.

2

1. Introduction

In the Nankai subduction zone in southwest Japan, low-frequency tremors have

been detected [Obara, 2002] with high sensitivity seismograph networks (Hi-net) operated

by the National Research Institute for Earth Science and Disaster Prevention (NIED)

[Okada et al., 2004; Obara et al., 2005]. The tremors are located approximately 30–40 km

deep along the strike of the subducting Philippine Sea plate (PHS). In particular, in the

western Shikoku district, significant tremor episodes recur at six-month intervals, and they

are accompanied by slow slip events (SSEs) [Obara et al., 2004; Hirose and Obara, 2005].

Such episodic tremor and slip are also observed on the Cascadia margin in the northwestern

part of the North American plate [Rogers and Dragert, 2003]. Moreover, similar

phenomena have been detected in some subduction zones, including Costa Rica, Mexico,

Alaska, and New Zealand [e.g., Schwartz and Rokosky, 2007]. In southwest Japan,

very-low-frequency (VLF) earthquakes accompanied by tremors and SSEs have also been

detected [Ito et al., 2007], and they reflect intermediate frictional properties at the deeper

part of the megathrust seismogenic asperity on the subducting plate interface.

During tremor and other coincident phenomena that have a characteristic period of

several days, the tremor sources usually migrate along the strike of the subducting plate

3

with a mean velocity of approximately 10 km/day, which was inferred from the source

locations by the envelope correlation method (ECM) [Obara, 2002]. A similar tremor

migration velocity was estimated at the Cascadia subduction zone [Kao et al., 2006]. On

the other hand, on a very short timescale, low-frequency earthquakes, which are distinct

tremors composed of impulsive signals, migrated along the dip direction of the slab with a

velocity of ~45 km/h during a tremor burst, as measured by waveform correlation analysis

[Shelly et al., 2007]. Such a variation of the estimated velocity suggests that there may exist

a scale dependency of the migration velocity associated with the duration of slow events

[e.g., Ide et al., 2007; Matsuzawa et al., 2009].

The detailed migration of tremor activity is not well understood because the ECM

is based on the smoothed envelope pattern obtained at Hi-net stations separated by a mean

distance of approximately 25 km, and it is spatially limited for the hypocentral location of

tremors. To locate tremor sources with high accuracy, dense seismic array observation is

effective because wavefield analysis can be performed. In Cascadia, La Rocca et al. [2005]

observed well-correlated tremor waveforms with three array observations deployed in the

northern Washington and British Columbia region. La Rocca et al. [2008] pointed out that

small-aperture array analysis is useful to analyze signals from a single tremor source, and

4

more complex and detailed analyses are required to analyze multiple-source tremors. To

analyze the multiple signals in tremor wavetrains, the Multiple Signal Classification

(MUSIC) method [Schmidt, 1986] is suitable, as it is for studying volcanic tremors [e.g.,

Saccorotti et al., 2004].

In the present study, we carried out a dense seismic array observation in western

Shikoku, Japan. We located epicenters of tremor sources using arrival directions estimated

from MUSIC during the episode of March 2007. From the distribution of the tremor

sources, the migration of tremors and the relationship among tremors, VLF earthquakes,

and SSEs are discussed.

2. Data and analysis

2-1. Dense array observation

Western Shikoku is the most active tremor region and SSE area on the belt-like

tremor zone in southwest Japan, and tremor and SSE episodes occur approximately every

six months. To record signals from the tremor sources, dense seismic arrays were deployed

at three sites in western Shikoku separated by approximately 20 km, as shown in Figure 1.

The observation period was from February to May 2007 because a previous tremor episode

5

occurred in September 2006, and we anticipated the next tremor would occur during this

observation period. As expected, a tremor and SSE episode occurred in March 2007. Each

array was composed of 23 vertical-component seismometers with a natural frequency of 2

Hz and 3 three-component seismometers with a natural frequency of 1 Hz. The receiver

configuration of each array is illustrated in Figure 2. The mean spacing between the

receivers was approximately 30 m. The continuous waveform data were recorded at a

sampling interval of 0.01 s.

2-2. Array processing

To detect a coherent signal and arrival direction from dense seismic arrays, various

methods have been developed to estimate the slowness vector [e.g., Niedel and Tarner,

1971; Rost and Thomas, 2002]. Here we adopted a two-step approach to detect the tremor

signal. First, we seek a coherent wave propagating to the array as a candidate for the tremor

signal. Then, the MUSIC method [Schmidt, 1986] is applied to estimate an accurate

backazimuth of the propagation for each tremor signal, which is used to determine the

epicentral location of the tremor. The method of tremor epicenter determination is

described in the section 2-3.

6

2-2-1. Preprocessing

The tremor signal is dominant in the horizontal records compared to the vertical

ones. However, as shown in Figure 3, the tremor signal is clearly coherent and the tremor

amplitude is two or more times larger than the amplitude of background noise in the

vertical records, perhaps because the shear-vertical component of the tremor signals might

be recorded. Therefore, in our analysis, we used only vertical seismometers at each array.

The continuous waveform data observed at the three arrays were processed by a

bandpass filter with a frequency range of 2–8 Hz to eliminate background noise and to

enhance the tremor signal with a dominant frequency of around 2 Hz [Obara and Hirose,

2006]. To detect a coherent wavefield containing the tremor signal, we evaluated the

cross-correlation coefficients of the waveforms recorded at neighboring receivers for each

10-s time window every 2 s. By comparing the waveforms with and without tremor signals,

the averaged cross-correlation coefficients for the tremor signals are much higher than

those without tremors (Figure 3). For the processing described herein, we adopt array

records whose averaged cross-correlation coefficient is higher than 0.75 as candidates for a

tremor signal.

7

2-2-2. Estimation of arrival direction by the MUSIC method

Tremor often occurs at some source locations simultaneously during the time

period of SSE episode. In order to estimate an arrival direction of the coherent waveform

from the strongest tremor source in a given time window, we used the MUSIC method

[Schmidt, 1986] because this method can decompose arrival directions for multiple sources

with high accuracy from a contaminated wavefield [e.g., Goldstein and Archuleta, 1987]. If

we were using other traditional methods in the array analysis, the detection of the most

dominant arrival direction might have been less accurate.

For well-correlated wavetrains in the preprocessing step, we calculated a

cross-covariance matrix for each array’s data in a 10-s time window at a frequency range of

2–8 Hz. Then, eigenvalue decomposition was performed on the cross-covariance matrix. To

decompose the covariance matrix into signal and noise subspaces, the MUSIC method

requires a priori indication of the number of eigenvalues that correspond to signals. For the

case of tremor with ambiguous arrivals, because the difference of eigenvalues between

signal and background noise was small in comparison to a regular earthquake, it was

difficult to determine the number of eigenvalues that correspond to tremor signals. Hence,

8

we have an expedient criterion as follows: the sum of selected eigenvalues from the largest

signal must exceed 95% of the total sum of eigenvalues. Then, we search the MUSIC

spectrum in the slowness space for the most dominant backazimuth and slowness.

An example of the MUSIC spectra from each array at which the coherent signals

were obtained (Figure 3b) are plotted in Figure 4. Regardless of the complexity of the

tremor waveforms, clear peaks in the slowness space appear at each array. In order to

evaluate the error of the MUSIC spectrum, we adapt the delete-1 Jackknife method

[Tichelaar and Ruff, 1989] for the dataset, by removing a waveform recorded at a single

station in each array. Examples of estimated peaks and errors of the MUSIC spectra are

shown with the white circle and bars in the right panel of Figure 4. From this method, we

measure the stability of backazimuth and slowness for incoming waves.

In order to exclude distant signals and coherent noises originating near the surface,

we eliminated the backazimuth and slowness for which the MUSIC spectrum peak is

greater than 0.4 s/km. The uncertainty in the backazimuth of the MUSIC spectrum peak

estimated by the delete-1 Jackknife method tends to increase with decreasing slowness.

Therefore, we choose a well-determined slowness that satisfies the following threshold: the

error in slowness and backazimuth are smaller than 0.2 s/km and 60°, respectively, for peak

9

slowness of more than 0.25 s/km; and these values must be smaller than 0.4 s/km and 140°,

respectively, for peak slowness of less than 0.25 s/km.

2-3. Tremor source detection with multiple array data

We determine the focus point of the three array backazimuths as the epicenter of

the tremor source based on an assumption that tremors occur at the plate interface [Shelly et

al., 2006; Ghosh et al., 2009]. For each time window, the epicenters of tremor sources are

determined by the grid search method. The backazimuths for each grid point are evaluated

using the following equations to estimate the epicentral location:

⎪⎩

⎪⎨⎧

−−

−=Δ

caln

obsn

caln

obsn

nφφ

φφ

360

)180(

)180(

>−

≤−caln

obsn

caln

obsn

φφ

φφ, (1)

∑Δ=Δn

nr2 , (2)

( )∑ Δ−Δ−

=Δn

nsd n2

11 ⎟

⎠

⎞⎜⎝

⎛Δ=Δ ∑

nnn

1, (3)

10

where and denote the observed and calculated backazimuths for the th array,

respectively. denotes the difference between the observed and calculated values.

obsnφ

calnφ n

nΔ rΔ ,

Δ , and denote the sum of squares, the mean value, and the standard deviation of sdΔ nΔ ,

respectively. A point where the minimum value of rΔ and sdΔ are less than 30° and 10°

is treated as an epicenter of a tremor source.

The reliability of the epicentral location decreases as the distance from the three

arrays increases using only backazimuths. Furthermore, some sources are located at the

edge of the search area. Because these sources were focused over 100 km in epicentral

distance, we chose tremor sources less than 100 km from the nearest array determined by

the above location process. Then, to obtain a stable estimate for tracing the tremor

migration, we calculate the centroid of each tremor per hour by averaging individual

epicentral locations with more than 15 events within an hour. The error of this mean

location is evaluated by a bootstrap simulation [Efron and Tibshirani, 1986] using the

following equations:

∑∑= =⋅

=B

b

N

nb nL

nBB

1 1)(1ˆ , (4)

11

1

ˆ)(12

1 1

−⎭⎬⎫

⎩⎨⎧

−=∑ ∑= =

B

BnLN

B

b

N

nb

Bσ , (5)

where is the number of data. denotes the b th bootstrap sample consisting of a

random sample selected from the detected latitudes or longitudes of tremor sources each

hour.

N )(nLb

B denotes the bootstrap frequency, which is 2,000 trials in the present study.

3. Results

The backazimuths of coherent signals estimated well by the MUSIC method at

each array from 9–20 March 2007 are shown in Figure 5. As an indicator of epicentral

locations of tremors and their migration, we adopt a statistical "mode" that is the most

frequent value in the hourly backazimuth dataset within a 10 degree bin. In Figure 5, the

mode is shown by a square, and frequency magnitude indicates tremor activity. Here, we

detect coherent tremor signals continuing to arrive at the three arrays from 13–18 March. In

this period, several tremor signals frequently appeared per minute, as shown in Figure 3b,

even if they were recorded by vertical component seismometers. Out of this tremor period,

many cross-correlation coefficients of incoming waves were less than 0.75, as shown in

12

Figure 3a.

3-1. Characteristics of array estimation

The tremors were clearly detected as coherent signals with wide ranges of

backazimuths and low slowness, indicated by the dark gray region in Figure 5. Before the

afternoon of 13 March, a small number of coherent signals were detected as a weak tremor.

Then coherent signals were clearly detected from the afternoon of the 13th. This indicates

that the active tremor started. In the active tremor period, there were two stages because of

halting of tremor in the evening of the 15th; the first is from the 13th to the 15th and the

second is from the 16th to the 18th.

From the afternoon of the 13th to the morning of the 14th, the mode of

backazimuths clearly migrated from the north (approximately 340°) to the west

(approximately 240°) until the evening of the 14th in array C (Figure 5c). Then, the

migration of backazimuths in Figure 5c repeated in this region until the evening of the 15th.

In the same time period, although scattered backazimuths were obtained in array A, the

mode of backazimuths changed around 200° from 240° on the morning of the 14th, and

scattered between 0° and 60° from the 14th to the 15th (Figure 5a). In array B, tremor

13

signals are mainly distributed around a backazimuth of 0° with a very large mode size on

the 13th, and the signals started to have various backazimuths between 0° and 180° from

the beginning of the 14th (Figure 5b). The wide distribution of backazimuths means that the

sources are located underneath the array, because backazimuth estimation is often unstable

for a near-vertical incident wave. Therefore, the area of deep tremor activity migrated from

the vicinity of array A to array B from the 13th to the 14th. This migration was consistent

with the backazimuth change in array C.

On the evening of the 15th, the tremor activity became weak for a few hours as

shown in Figure 5. On the 16th, active tremor began again. After the evening of the 16th,

many tremor signals were suddenly detected at the three arrays. The tremor activity was

concentrated around a backazimuth of 200° in array B, whereas in arrays A and C the

backazimuth also clustered around 240°. This indicates that the tremor direction of each

array jumped southwestward.

3-2. Epicentral location of tremors determined by multiple arrays

The distributions of polar histograms of backazimuths are illustrated in Figure 6.

The histograms indicate that many signals propagated from between arrays A and B. The

14

centroids of tremor activity were distributed along the strike of the PHS slab [Ueno et al.,

2008], which is 60 km long and 20 km wide in the vicinity of 40 km deep in the depth

contour map of PHS (Figure 7a). The tremor epicenters concentrated between arrays A and

B were well located in our analysis; however other tremors, scattered far from the arrays,

were less accurately located. A similar distribution was also obtained by ECM as shown in

Figure 7b; however, tremor epicenters were relatively more scattered in the vicinity of the

arrays.

The time history of the spatial location of tremors projected on longitude and

latitude axes is presented in Figure 8. The vertical bar shows the error distribution based on

the bootstrap method of equation (5). The tremor activity gradually migrated

southwestward from the northern part of western Shikoku during the episode. The tremor

migrating southwest seems to include a repeated movement along the same route. Such a

migration pattern is reliable because the error in the epicentral locations of tremor during

the period from the 13th to the 16th is half as much as during the other period as shown in

Figure 8. In particular, from the 13th to the 14th and the 14th to the 15th, two

southwestward migrations through a similar route were clearly recognized because the

migration distance exceeds the error estimation. The first migration has a 1 km/h velocity

15

over a distance of 12 km for 12 hours, from the evening of the 13th to the morning of the

14th. The second migration has a 2.5 km/h velocity for six hours over a distance of 15 km

from the evening of the 14th to the morning of the 15th in the same region. And then, on

the evening of the 16th, the tremor started to migrate steeply southwestward, far from the

array stations, as shown in Figures 7 and 8. The steep migration appeared as a jump in the

tremor direction (Figure 5).

4. Discussion

4-1. Scale variation of migrating tremor

The tremor episode in March 2007 is characterized by a horizontal migration of

the epicenters with a mean velocity of roughly 0.5 km/h estimated from the traditional

ECM shown by broken lines in Figure 8b, as in the other tremor episodes in western

Shikoku [Obara, 2009]. We detected a short timescale tremor migration pattern with a

faster velocity of 1–2.5 km/h over a distance of 12–15 km for several hours. The sharp

onset of tremor at the migration front and persisting tremor activity behind the front are

interpreted as the rupture initiation of the SSE [Obara, 2009] and continuation of the slip,

respectively [Obara, 2009; Maeda and Obara, 2009]. In the present study, we found that

16

the tremor activity migrated more than once along the same path within one episode, as

shown in Figures 8. The repeating tremor migration in the short timescale might be a

seismic response to the local stress change caused by the small-scale fluctuation in the

spatio-temporal distribution of the slip velocity at the rupture front of the SSE and/or by the

continued slip after the passage of the rupture front.

Various timescales of tremor migration exist within the same region. An increased

migration velocity for a short time was predicted by a scaling relationship [Ide et al., 2007].

The migration velocity in the short timescale in this study also supports the scaling

relationship between characteristic duration and velocity [Matsuzawa et al., 2009]. The

faster migration of the tremor burst in the same region [Shelly et al., 2007] might provide

an endmember for this scaling relationship.

4-2. Relationship between the tremor and other coincident phenomena

In March 2007, the tremor activity, VLF earthquakes, and the SSE occurred

simultaneously at the western Shikoku region like in other episodes. The spatio-temporal

locations of the VLF earthquakes determined by Ito et al. [2009] and Matsuzawa et al.

[2009] during the SSE are indicated by diamonds in Figures 7 and 8. The VLF earthquake

17

locations appeared to be around the southwestern edge of the tremor activity in the early

mornings of the 14th and the 15th. Comparing the spatio-temporal locations of the tremor

and the VLF earthquakes, the tremor seems to migrate toward the VLF earthquake location,

which is the western edge of the tremor migration shown in Figure 8a. The VLF earthquake

is considered as a seismic slip with slow rupture velocity caused by the stress concentration

at a VLF patch surrounded by a slow slip region [Ito et al., 2007]. Consequently, the stress

was concentrated in a patch at the western edge because of the fluctuation of the SSE

reflected by the repeating tremor migration on 14–15 March, which triggered the VLF

earthquakes at this western edge. A similar situation was observed on the 17th. On the

evening of the 16th, after the tremor abruptly migrated southwestward, VLF earthquakes

occurred at the end of the tremor migration. Our results suggest that the occurrence of VLF

earthquakes is related to the stress concentration caused by small-scale fluctuations of SSE

slips that can be detected by short timescale tremor migration.

Here, we compare the tremor migration and the daily slip rate of the SSE obtained

by time-dependent inversion [Hirose and Obara, 2010] as shown in Figure 9. The

cumulative slip distribution, VLF earthquakes, and tremor activity that occurred in March

2007 are presented in Figure 9a. All of the events were concentrated in the northwest

18

portion of western Shikoku. This result was also consistent with the area exhibiting a

high-energy radiation of tremors [Maeda and Obara, 2009]. Prior to the SSE occurrence

and before the 13th, weak and scattered tremor activity appeared around the northern

portion of array B (Figure 9b–d). Once the slip began and its SSE area became large, the

number of tremor sources also increased (Figure 9d–f). The tremor activity appears to be

located repeatedly along the slow slip contours, and it migrates toward the source area of

the VLF earthquakes, as shown in Figure 9f–i.

On the evening of the 15th, the centroid of the tremor activity could not be

obtained for Figure 8a because the tremor activity abruptly became very weak for a few

hours, and then the tremor became active again as shown in Figure 5. On the evening of the

16th, the tremor activity location abruptly migrated southwestward as if by jumping, as

shown in Figures 5 and 8, and the slip rate contour of the SSE also simultaneously moved

to the southwestern area (Figure 9h and i). These phenomena of halting and jumping were

also found in Cascadia [Kao et al., 2006, 2007].

Since the active area of the VLF earthquakes and the SSE were located far from

our arrays, especially after the 17th as shown by ECM in Figure 8b, the centroid locations

of tremor activity had large uncertainties, as shown in Figures 7a, 8a, and 9i. While the

19

locations are not well-resolved, the migration pattern is still discernible above the errors.

Finally, the tremor activities scattered and gradually ceased after the conclusion of the SSE

(Figures 9j–l). Based on the above discussion, we conclude that the short timescale of

tremor migration is a small-scale fluctuation within the overall slow slips, and it is related

to the occurrence of VLF earthquakes. This type of rupture fluctuation and the relationships

among detailed spatio-temporal distributions of each slow event may be keys to disclosing

a series of slow events.

5. Conclusions

We succeeded in detecting the migration of tremors to investigate the arrival

directions of tremor signals by conducting a multiple array analysis on continuous wave

data. This array experiment was the first such observation and analysis of tremor activity in

the western Shikoku region. Combining the results of the array analyses, we obtained the

following information regarding the March 2007 episode:

1. Highly coherent tremor signals were obtained, and tremor sources were detected

with the multiple array analyses.

2. The majority of the apparent slowness values detected by the three arrays during

20

the active tremor period were relatively low. The incident angles of wavetrains from the

tremor source to the arrays were nearly vertical. The distributions of backazimuths

indicated the direction of the tremor sources.

3. A number of tremor sources were located in northwestern Shikoku. Furthermore,

we obtained a highly reliable distribution of tremor epicenters for each hour. These results

permitted repeating tremor migrations to be detected in a short time. The velocity of the

short timescale tremor migration was approximately 1–2.5 km/h over a distance of 12–15

km for this episode. The migration velocity for the whole episode was roughly 0.5 km/h.

4. The spatio-temporal distribution of the tremor sources was correlated to the VLF

earthquakes and the SSE that occurred in the same region. The short timescale migration of

the tremor suggests a small-scale fluctuation within the overall slow slip that was related to

the occurrences of the VLF earthquake.

21

Acknowledgments

We thank Dr. H. Hirose for providing figures and advice regarding the short term

SSE that occurred in 2007. We also thank Dr. T. Matsuzawa for his advice concerning a

very-low-frequency event and the scaling relationship between characteristic duration and

velocity of a migrating tremor. Dr. Y. Ito helped us prepare and deploy the three arrays and

discussed the relationships among slow events with us. Dr. B. Enescu discussed our work

and provided us with helpful comments. We drew all figures using Generic Mapping Tools

[Wessel and Smith, 1998]. Our study was supported by all Hi-net members. Professor J.

Vidale, an anonymous reviewer, and the associate editor provided useful comments to

improve our manuscript.

22

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Figure captions

Figure 1. Array map and distribution of tremors in southwest Japan. Triangles indicate the

locations of each array, and inverse triangles denote Hi-net stations. Circles indicate the

epicenters of tremors detected using ECM [Obara, 2002] from 9–20 March 2007. The

depth contour map of the upper part of the PHS slab derived from receiver functions [Ueno

et al., 2008] is indicated by dashed lines.

Figure 2. Receiver configurations of each array. An open triangle indicates a vertical sensor.

A filled triangle indicates a 3-component sensor.

Figure 3. Examples of waveform records (a) without and (b) with tremor waveforms

recorded by array A at 22:10 on the 13th and the 14th of March 2007 (JST), respectively, in

upper panels. Lower panels illustrate the averaged correlation coefficient (A.C.), indicated

by triangles. Horizontal axis represents time (s).

Figure 4. Examples of waveforms recorded by arrays A (a), B (b), and C (c). Traces were

recorded at the same time as the upper panel in Figure 3b. Horizontal axes represent time

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(s). Right panels illustrate the MUSIC spectra for unshaded areas above the heavy bars.

Vertical and horizontal axes represent slowness Px (s/km) and Py (s/km), respectively.

White circles and bars show the mean peak of the normalized MUSIC spectrum and its

error estimated by the delete-1 Jackknife method.

Figure 5. Time series of arrival direction for arrays A (a), B (b), and C (c). Slowness values

for each backazimuth are shown in gray scale. Vertical axes represent the backazimuth

(degree). Horizontal axes represent time (day). Dots indicate peak values of the MUSIC

spectrum. Open squares show the backazimuth mode per hour and their size depends on

frequency.

Figure 6. Distribution of tremor sources and polar histograms for each array. Triangles

indicate locations of arrays. Gray dots denote tremor sources that were located using

multiple array analysis. The sector width of the diagram is 10°. The radiated axis is

normalized to unity.

Figure 7. Distribution of tremor activity per hour (circle colored to indicate day) of (a) the

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array analysis in this study, and (b) ECM [Obara, 2002]. VLF earthquakes (diamonds

denote day) and the depth contour map of the upper part of the PHS slab (dashed lines)

[Ueno et al., 2008] are indicated. Black triangles denote locations of arrays.

Figure 8. Changes in tremor sources for longitude (upper panel) and latitude (lower panel)

of (a) the array analysis in this study and (b) ECM [Obara, 2002]. Dots indicate the

centroid location of tremor activity for each hour. White diamonds denote VLF earthquakes.

The error bar was estimated using the bootstrap method. The two velocities of 1 and 2.5

km/h shown in (a) indicate a migrating tremor velocity from the evening of the 13th to the

morning of the 14th and from the evening of the 14th to the morning of the 15th,

respectively. Broken lines in (b) show the migration velocity of 0.5 km/h.

Figure 9. Mean tremor activity per hour and VLF earthquakes for the total study (a) and

each day (b)–(l). For the SSE, (a) illustrates the cumulative slip distribution with contours

in mm and (d)–(j) illustrate the daily slip rate distributions with contours in mm/y [Hirose

and Obara, 2010]. Black triangles indicate array locations. Diamonds and circles denote

VLF earthquakes and tremor activity, respectively. Note that the color scale is different for

30

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(a) (days) and the others (hours).