www.sciencemag.org/content/348/6235/676/suppl/DC1

Supplementary Materials for

Migrating tremor off southern Kyushu as evidence for slow slip of a

shallow subduction interface

Y. Yamashita,* H. Yakiwara, Y. Asano, H. Shimizu, K. Uchida, S. Hirano, K. Umakoshi,

H. Miyamachi, M. Nakamoto, M. Fukui, M. Kamizono, H. Kanehara, T. Yamada, M.

Shinohara, K. Obara

*Corresponding author. E-mail: yamac@eri.u-tokyo.ac.jp

Published 8 May 2015, Science 348, 676 (2015)

DOI: 10.1126/science.aaa4242

This PDF file includes:

Materials and Methods

Figs. S1 to S9

Caption for Data S1

Full Reference List

Other Supplementary Material for this manuscript includes the following:

(available at www.sciencemag.org/content/348/6235/676/suppl/DC1)

Data S1 (Excel file)

Materials and Methods

1. Ocean bottom seismographic observation

Twelve short-period ocean bottom seismometers (OBSs) were deployed on 16–19

April 2013, and recovered on 4–6 July 2013, by the T/S Nagasaki-maru of the Facility of

Fishers, Nagasaki University. All of the OBSs are a pop-up type with an acoustic release

system. Ten OBSs have three-component velocity sensors with a natural frequency of 4.5

Hz (Mark Products, L28-BL) and two OBSs have 1 Hz sensors (Lennartz Co. Ltd., LE-

3D lite). The analog seismic signals were digitized by a 16 bit or 20 bit A/D converter

and recorded continuously on a 40 GB hard drive. The sampling rate is 128 Hz or 200

Hz. The internal clock of each OBS was calibrated just before deployment and after

recovery by comparing it to a GPS clock. Timing is provided by a crystal oscillator and is

estimated to be within 0.05 s. Positions of each OBS on the seafloor were calculated by a

least squares method using acoustic triangulation between the ship and the OBS. The

accuracy of this method is estimated to be tens of meters (31). The spatial interval

between OBSs was approximately 20–50 km. Station 11 was deployed on the Philippine

Sea plate, and the other OBSs were on the overriding continental plate. Although station

2 recorded no data because of technical problems, all other OBSs performed well

throughout the observation period.

2. Tremor source locating by envelope correlation method

Because tremor events do not produce clear P- and S-wave onsets, their source

locations cannot be estimated by standard hypocenter determination methods. Therefore,

we used the envelope correlation method (1) to estimate tremor location. The differential

arrival times between OBS stations were obtained from the lag times with maximum

cross-correlation coefficient between the respective root mean square (RMS) envelopes,

which were converted from a composite waveform of the horizontal components by

applying a 2–8 Hz bandpass filter. RMS envelopes were smoothed by using a 5 s window

and downsampled with a sampling rate of 20 Hz. The time window for calculation of

cross-correlation was set at 2 minutes and calculated every 0.05 s by moving a trace. If

the maximum cross-correlation coefficient for a pair Ci was larger than 0.85, we used the

lag times as the differential time between two stations in estimating the tremor location.

Generally, earthquake hypocenter locations based on P- and S-wave arrival time

data from OBSs must be corrected for travel-time delays due to the differing thicknesses

of the sediment layers directly beneath each OBS station. However, with the envelope

correlation method, travel-time delays that are consistent between OBS stations can be

ignored in locating the tremor source. We tentatively estimated the travel-time delays for

each OBS using the difference in arrival times of P-waves and PS converted waves (32).

The range of estimated delays is 0.6–1.9 s (average 1.3 s) assuming P-wave and S-wave

velocities of 1.8 km/s and 0.6 km/s, respectively, within the sediment layer and 3.5 km/s

and 2.0 km/s, respectively, at the top of the basement layer. The differential delay of 1.3 s

corresponds to a location difference of ~5 km, which is less than the horizontal location

error (Fig. S5). When we compared tremor locations from corrected and uncorrected

data, the horizontal distributions differed only slightly, which confirmed that travel-time

delays are negligible. The estimation of delays included uncertainty due to reading errors

for PS converted waves and to the assumed P- and S-wave velocities. Therefore, we

made no adjustment for delays in the following process.

We calculated RMS residuals between observed and theoretical differential travel

times at a given location on the assumption of a homogeneous S-wave velocity structure.

The assumed S-wave velocity of 3.5 km/s was obtained from a preliminary application of

the envelope correlation method, but we also estimated the appropriate S-wave velocity

for each event. The differences in the horizontal location of tremor sources between the

two velocity structures were smaller than the estimated location error. To estimate the

tremor location, we minimized the RMS residual between the observed and theoretical

differential travel time as

2

1

1

2

1

2,,

N

i

i

N

i

cal

i

obs

ii wdtdtwzyxf , (1)

where x, y, z is the tentative source location, obs

idt and cal

idt are respectively the

observed and theoretical differential travel times of the i th pair of stations, N is the

number of station pairs, and wi is the weight factor for each observation. Here, the weight

factors are defined as

85.00

185.0

i

ii

iC

CCw . (2)

We automatically analyzed the continuous RMS envelope records every 1 min and

calculated the RMS residual from Eq. 1. We found the minimum RMS residual by a grid

search algorithm that evaluated residuals at 1-km intervals throughout the search space

bounded by 29.75° and 32.25°N and 131° and 133.5°E, between 3 and 25 km depth.

Residuals more than two times the standard deviation were considered outliers and

discarded, after which residuals were recalculated using the updated dataset. We repeated

this process four times. In the third and fourth calculation, we also added the threshold

for the residual of a data less than 2 s. After this process, we selected a candidate tremor

hypocenter if the RMS residual was less than 2 s, which corresponds to an estimated

horizontal error less than approximately ± 10 km within the OBS network (Fig. S5). We

then carefully examined the candidate tremor events to distinguish them from ordinary

earthquakes, T-phase signals, or noise. We finalized the tremor catalog (Table S1) after

removing duplicate events caused by overlapping of the moving window.

3. Spatiotemporal distribution of shallow VLFE

VLFE were first detected over a decade ago on the landward side of the Nankai

Trough (9, 10). The long-term spatiotemporal distribution of shallow VLFE (Fig. S2),

which were detected by the method of Asano et al. (10) from tiltmeter data (33), shows

that VLFE have occurred repeatedly in the study area. Considering the spatiotemporal

relationship between shallow tremor and VLFE, shallow tremor is probably ubiquitous in

this area even though it was not previously detected.

4. Waveform characteristics of shallow tremor

The shallow tremor waveforms share five characteristics: 1) P- and S-wave onsets

are unclear (Fig. S3), 2) horizontal components are dominant (Fig. S4), 3) the duration of

tremors ranges from several tens of seconds to a few minutes (Fig. 2A), 4) the dominant

frequency range is around 2 Hz (Figs. 2B and S4). These characteristics are similar to

those found in a previous study of shallow tremor off the Kii Peninsula elsewhere in the

Nankai Trough subduction zone using 4.5 Hz OBS sensors (14), and similar to deep

tremor observed in several subduction zones (1,3). However, the shallow tremor is more

impulsive and shorter in duration, several minutes at most, whereas deep tremor lasts

several dozen minutes to several hours (1). The dominant frequency of shallow tremor

appears to be lower than that of deep tremor (the lower limit of shallow tremor is 0.5 Hz).

Note that these characteristics may include propagation effects and observational

differences between land-based stations and ocean bottom stations. The seismograph of

ocean bottom station is strongly influenced by unconsolidated sediment, which induces

the amplification of signal and attenuation of high frequency range.

Fig. S1.

Seismicity in and around study area. Ordinary earthquakes seismicity during last 15

years detected by Institute of Seismology and Volcanology, Kyushu University, showing

the coseismic slip area of M7-class interplate earthquakes (26, 27) and 1946 Nankai

megathrust earthquake (34) (dark gray) and active volcano (red triangle).

Fig. S2.

Spatiotemporal distribution of shallow VLFE. The event detection and location

method is that of Asano et al. (10), showing the period from 2008 through the study

period in 2013. The activity correlated with the long-term slow slip event (SSE) in the

Bungo Channel reported by Hirose et al. (35) is shown in early 2010.

Fig. S3.

Example waveforms of shallow tremor recorded at OBS stations. Vertical component

waveform (red) is superimposed on a horizontal component (black). Each trace is

normalized by the maximum amplitude of a horizontal component.

Fig. S4.

Comparison with power spectra of shallow and deep tremor. (left) Power spectra of

shallow tremor, ordinary earthquake, and background noise recorded at OBS station 8,

which is same as Fig. 3B. (right) Power spectra of deep tremor and background noise

recorded at N.KWBH, land-based seismic station at the Shikoku, Japan, using north-

south component seismograph. Calculation procedure of power spectra of deep tremor is

same as shallow tremor. Note that the range of power axis is different between shallow

and deep.

Fig. S5.

Uncertainty of shallow tremor locations. Uncertainty is estimated by the standard

deviation of tremor source locations within 10% of the RMS residual. (A) Error in N–S

direction, (B) error in E–W direction, and (C) horizontal errors plotted against RMS

residuals for each event. Gray and red open circles signify events outside and within the

OBS network, respectively. (D) Histograms of horizontal error for each 1 km. Gray and

red bars signify all events and events within OBS network, respectively.

Fig. S6.

Examples of shallow tremor locating by envelope correlation method. RMS residuals

plotted against focal depth at the epicentral location shown. Heavy contours indicate the

RMS residuals at 1 s intervals.

Fig. S7.

Spatiotemporal distribution of shallow tremor for the period 28 May 2013 to 14

June 2013. Open gray circles indicate shallow tremor occurring outside this period.

Other symbols and contours are the same as Fig 1.

Fig. S8

Spatiotemporal distribution of shallow tremor for the period 15 June 2013 to 2 July

2013. Open gray circles indicate shallow tremor occurring outside this period. Other

symbols and contours are the same as Fig 1.

Fig. S9

Spatiotemporal distribution of the two migration sequences. Red and blue circles

indicate shallow tremor of first and second migration sequence, respectively. Other

symbols and contours are the same as Figs 1 and 3.

Additional Data table S1 (separate file)

Shallow low-frequency tremor catalog detected by OBS data. Origin time (time zone

is JST, or UTC + 09:00) indicate the start time of moving time window (2 minutes).

Detail of detection method is shown in Materials and Methods.

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