Geophysical Research Letters
Supporting Information for
Activation of very low frequency earthquakes by slow slip events in the Ryukyu
Trench
Mamoru Nakamura and Naoya Sunagawa
Faculty of Science, University of the Ryukyus, Nishihara-cho, Okinawa 9030213, Japan
Contents of this file
Text S1 to S3
Figures S1 to S3
Table S1
Introduction
The data set contains the explanation for error estimation for the epicenter
determination (Text S1 and Figure S1), calculation of the activity in sub-areas (Text S2
and Figure S2), the method for the estimation of the onset of the SSEs (Text S3), a list
of the onsets of SSEs used in this study (Table S1), and the figure for the relations
between magnitude and frequency of the VLFEs (Figure S3).
Text S1.
Estimation of Epicenter Error
To estimate the error of the epicenter of the VLFEs, we determined the epicenter of an
ordinary earthquake (M3.8) that occurred at 20:42 on May 3, 2013. We used the arrival
times of the maximum amplitudes with the inclusion of one wavelength (approximately
15 s) error by mis-picking and changing the number of stations (n-1 stations were used;
here n is number of stations). The estimated epicenter error (1 sigma) in the east–west
direction (parallel to the trench) and north–south direction (perpendicular to the trench)
was approximately 20 and 30 km, respectively (Fig. S1). However, the spread of the
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relocated epicenters covers approximately 100 km (Figs. S1 and S2), which suggests
that the error of the relocated epicenters is of the order of 100 km.
Text S2.
Calculation of VLFE and ordinal earthquakes activity
In Fig. 3, we computed the activation of seismicity in the rectangular area shown in Fig.
4. Then, we divided the area into four areas (NE, SE, NW, and SW quadrants) to
evaluate the degree of local activation (Fig. S3). Notations are the same as those at Fig.
3.
Text S3.
Calculation of onset of SSEs
The List of onset of SSEs is given provided in the Table S1. The onsets were estimated
using the model of SSE [Heki and Kataoka, 2008], which is shown as.
t T 

x  at  b  X 1  exp

 

where x is the coordinate of a component, t is time, b is the simple offset, a is the longterm trend,
represents time constants, X is the displacement of the SSE, and T is the
onset of the SSE. The upper (UCB) and lower (LCB) bounds of T in the model are
evaluated using Akaike’s Information Criterion employing the grid-search method.
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Figure S1. Error estimation for epicenter determination. (a) Map showing earthquake
epicenter (20:42 May 3, 2013, M3.8) (yellow star), relocated epicenter (yellow square),
and epicenters computed using the data containing picking errors (red circles). (b) Map
showing earthquake epicenter and relocated epicenter, which are the same as in (a),
and the epicenters computed using the data containing picking errors and by changing
the number of stations (red circles).
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Figure S2. Activity of VLFEs and ordinary earthquakes in the sub-areas. (b), (e), (h),
and (k) show the time series of the cumulative number of VLFEs. (c), (f), (i), and (l)
denote the cumulative number of ordinary earthquakes. Numbers denote the event
number of the SSEs (Table S1). (a), (d), (g), and (j) show the stacked daily number of
VLFEs (red line), ordinary earthquakes (>M2.0) (dotted blue line), and ordinary
earthquakes when Mw6.7 mainshock on August 17, 2009 and its aftershocks were
eliminated (solid blue line).
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Figure S3. The relations between magnitude and frequency of the VLFEs in YA (a), MI
(the gap area) (b), OK (c), and AM (d). (e) shows the index map. The moment
magnitudes were computed using the amplitude at F-net stations in the Ryukyu arc and
the formula obtained from the empirical relation of moment magnitude versus the
amplitude at station IGK [Ando et al., 2012].
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Onset of SSE
Number
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
Year
Month
2003
2003
2004
2004
2005
2005
2006
2006
2007
2007
2007
2008
2008
2009
2009
2010
2011
2011
2012
2012
2013
2013
4
10
4
11
5
8
1
7
1
2
9
5
10
7
12
8
3
10
4
12
4
7
Day
2
7
19
17
5
8
16
20
1
13
28
4
27
9
22
12
8
6
26
24
15
27
average
LCB
(day)
-2.3
-2.5
-10.1
-2.6
-4.3
-5.7
-2.8
-2.2
-4.8
-2.7
-3.4
-1.4
-4.0
-3.0
-2.7
-2.6
-1.9
-2.2
-2.8
-9.9
-0.8
-2.0
-3.5
UCB
(day)
3.9
2.6
3.3
2.6
3.7
6.4
2.5
2.2
3.5
1.4
5.4
1.6
3.8
2.3
6.5
4.2
1.6
2.3
2.9
13.2
0.8
2.5
3.6
Table S1. List of the onsets of the SSEs used in this study. UCB and LCB show the 95%
upper and lower confidence bounds based on the onsets of SSEs, respectively. The
LCB and UCB of the model (Text S3) are evaluated using Akaike’s Information Criterion.
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