Nanjo and Yoshida Earth, Planets and Space (2017) 69:13
DOI 10.1186/s40623-017-0598-2

Open Access

FULL PAPER

Anomalous decrease in relatively large
shocks and increase in the p and b values
preceding the April 16, 2016, M7.3 earthquake
in Kumamoto, JapanK. Z. Nanjo1*

and A. Yoshida2

Abstract
The 2016 Kumamoto earthquakes in Kyushu, Japan, started with a magnitude (M) 6.5 quake on April 14 on the Hinagu
fault zone (FZ), followed by active seismicity including an M6.4 quake. Eventually, an M7.3 quake occurred on April
16 on the Futagawa FZ. We investigated if any sign indicative of the M7.3 quake could be found in the space–timechanges in seismicity after the M6.5 quake. As a quality control, we determined in advance the threshold magnitude,
above which all earthquakes are completely recorded. We then showed that the occurrence rate of relatively large(M ≥ 3) earthquakes significantly decreased 1 day before the M7.3 quake. Significance of this decrease was evalu‑
ated by one standard deviation of sampled changes in the rate of occurrence. We next confirmed that seismicity
with M ≥ 3 was well modeled by the Omori–Utsu law with p ~ 1.5 ± 0.3, which indicates that the temporal decay ofseismicity was significantly faster than a typical decay with p = 1. The larger p value was obtained when we used dataof the longer time period in the analysis. This significance was confirmed by a bootstrapping approach. Our detailed
analysis shows that the large p value was caused by the rapid decay of the seismicity in the northern area around the
Futagawa FZ. Application of the slope (the b value) of the Gutenberg–Richter frequency–magnitude distribution to
the spatiotemporal change in the seismicity revealed that the b value in the northern area increased significantly, theincrease being Δb = 0.3–0.5. Significance was verified by a statistical test of Δb and a test using bootstrapping errors.
Based on our findings, combined with the results obtained by a stress inversion analysis performed by the National
Research Institute for Earth Science and Disaster Resilience, we suggested that stress near the Futagawa FZ had
reduced just prior to the occurrence of the M7.3 quake. We proposed, with some other observations, that a reduction
in stress might have been induced by growth of the slow slips on the Futagawa FZ.
Keywords: The 2016 Kumamoto earthquakes, p value of the Omori–Utsu law, b value of the Gutenberg–Richter law,
Hinagu fault zone, Futagawa fault zone, Slow slip
Background
Seismicity has become high in almost all parts of Japan
since the 2011 magnitude (M) 9.0 Tohoku-Oki earthquake (e.g., Ishibe et al. 2011; Toda et al. 2011). The 2016
Kumamoto earthquakes occurred under these circumstances, leading to a memorable event that once again*Correspondence: nanjo@u‑shizuoka‑ken.ac.jp
1
Global Center for Asian and Regional Research, University of Shizuoka,
3‑6‑1, Takajo, Aoi, Shizuoka 420‑0839, Japan
Full list of author information is available at the end of the article

caused devastating damage in Japan. The Kumamoto
earthquakes in the Kyusyu district began with an M6.5
quake on April 14, 2016, at 21:26, on the Hinagu fault
zone (FZ), which was followed by numerous shocks
including an M6.4 quake on April 15, at 00:03. Eventually, on April 16, at 01:25, an M7.3 quake occurred on
the Futagawa FZ. The probability of the occurrence of an
M7.0 or so earthquake on the Futagawa FZ had been estimated by the ERC to be 0–0.9% within 30 years (Earthquake Research Committee 2016a), which was rather
high among the probability at active faults in Japan. In a

© The Author(s) 2017. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License(http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium,provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license,
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Nanjo and Yoshida Earth, Planets and Space (2017) 69:13

press conference that was held just after the M6.5 quake,
the Japan Meteorological Agency (JMA) warned of thepossibility of large aftershocks that should bring further damages. However, no information on an increased
probability of M7 or larger quakes was announced by
the JMA during the period between the M6.5 quake andthe M7.3 quake. This is because, according to the ERC(1998) protocol (see also ERC 2016b), the JMA had notconsidered the occurrence of larger earthquakes after an
M6.5 quake. Moreover, it usually takes more than one
day after a mainshock occurrence for the JMA to issue anannouncement of the probability of large aftershocks.
The objective of this study was to investigate if any
indication of the occurrence of the M7.3 quake had notappeared in the space–time changes in the rate of occurrence and magnitude-number distribution of shocks after
the M6.5 quake on April 14. We found that M3 or larger
shocks decreased during the period of one day preceding
the M7.3 quake and that the b value (the ratio of small tolarge events) became pronouncedly high, corresponding
to a decrease in comparatively large shocks, especially inthe area near the hypocenter of the M7.3 quake.
Tremendous efforts have been made to find effective
signatures that indicate a large earthquake occurrencein the near future. A temporal decrease in the b value
may be a candidate (e.g., Suyehiro et al. 1964; Nanjo et al.
2012) while another may be seismic quiescence (e.g.,
Wiemer and Wyss 1994; Sobolev and Tyupkin 1997). It
is known that aftershock activity becomes significantly
quiescent preceding large aftershocks (Mtasu’ura 1986).
However, any signatures ever proposed do not seem tobe universal, since accelerating seismicity (e.g., Bowman
et al. 1998) and an increase in the b value (Smith 1981)
were occasionally reported.
We examined the spatial and temporal trends inthe rate of occurrence of comparatively large (M ≥ 3)
shocks and the b value in the seismic activity following
the M6.5 quake on April 14. We found that the b value
in the activity in the northern area became significantly
high before the M7.3 quake on April 16 and that this feature corresponded to a decrease in large (M ≥ 3) shocks.
We consider that the high b value and the decrease incomparatively large shocks were precursors to the M7.3
quake and propose what caused the observed changes inthe space–time seismicity.

Methods and data
Activity following the M6.5 quake is well modeled by two
statistical laws: the Gutenberg–Richter (GR) frequency–
magnitude law (Gutenberg and Richter 1944) and the
Omori–Utsu (OU) aftershock decay law (Utsu 1961).
The GR law is given as log10N = a − bM, where N is thenumber of earthquakes per unit time with magnitudes

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greater than or equal to M, a describes the productivityof the regional seismicity, and the b value is the ratio ofsmall to large events. A high b value indicates a larger
proportion of small earthquakes, and vice versa. In thelaboratory and in the Earth’s crust, the b value is known
to be inversely dependent on differential stress (Scholz
1968, 2015). In this context, measurements of spatial
temporal changes in the b value could be used to discoverhighly stressed areas where future ruptures are likely
to occur (Schorlemmer and Wiemer 2005; Nanjo et al.
2012). To consistently estimate b values over space andtime, we employed the entire-magnitude-range (EMR)
technique (Woessner and Wiemer 2005), which also
simultaneously calculates the completeness magnitude
Mc, above which all events are considered to be detectedby a seismic network. EMR applies the maximum-likelihood method (Aki 1965) in computing the b value toevents with magnitudes above Mc. Uncertainties in b andMc were computed by bootstrapping (Schorlemmer et al.
2003, 2004).
Any completeness estimation method is subject toerrors, particularly during productive seismicity times
such as investigated in this study. To confirm implications of this study, we compared Mc by the EMR methodwith that by other three methods. Results of the comparison are shown in Appendix 1 and Fig. A1 in Additional
file 1.
The OU law is given as λ = k/(c + t)−p, where t is thetime since a mainshock occurrence, λ is the number ofaftershocks per unit time at t with magnitudes greaterthan or equal to a cutoff M, and c, k, and p are constants.
p = 1 is generally a good approximation (Omori, 1894).
From the view point of the rate- and state-dependent friction law (Dieterich 1994), variability in p can be observed:
p > 1 and p < 1 for rapidly and slowly decreasing stress,
respectively. When stress increases with time, p = 1 att ≫ 0. If this friction law is valid in the Earth’s crust, thenthe p values could be used to infer stress history. Similar to the GR case, we used a maximum-likelihood fit todetermine the parameters for this law. Uncertainties in
the p value were computed by bootstrapping.
Our dataset is the earthquake catalog maintained by
JMA. From this catalog, we separated events associatedwith the 2016 Kumamoto earthquakes after the occurrence of the M6.5 quake on April 14. Owing to a large
increase in the number of borehole seismic stations(Obara et al. 2005), event delectability has been greatly
improved, which lowers the minimum magnitude forcatalog homogeneity (Nanjo et al. 2010). Since 2000, theminimum magnitude is about M = 0–1 in the Kyushu
district.
Small events in clusters such as swarms and aftershocks are often missed in the earthquake catalog, asNanjo and Yoshida Earth, Planets and Space (2017) 69:13

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they are “masked” by the coda of large events and overlap with each other on seismograms. According to previous cases (e.g., Helmstetter et al. 2006; Nanjo et al. 2007),Mc depends on time t. In creating Fig. 1, we used a moving window approach, whereby the window covered 200
events (red). Mc decreased with t from 2.9 and reacheda constant value at around 2.2. Relatively large eventsoccurred early in the sequence, and the mean magnitudeof these events evolved to small values over time (gray).
The time-dependent decrease in Mc is consistent withthe data. To examine if the occurrence of the M6.4 quake
affected completeness, events before the M6.4 quake
were excluded from the dataset and Mc was assigned asa function of t since the M6.4 quake (blue). Immediately
after the M6.4 quake, the estimate of Mc was as high as
2.4. Mc decreased with t and reached a constant value ataround 2.2. We were unable to see any significant deviation of the Mc − t pattern since the M6.4 quake (blue)
from since the M6.5 quake (red). This is interpreted as anindication that the effect of the M6.4 quake on Mc was
weak.

Results
As a preliminary analysis to modeling the OU law, thecumulative number of M ≥ 3 earthquakes was calculated as a function of relative time to the M7.3 quake
over the entire period of activity (Fig. 2a). Taking Mc
in Fig. 1 into consideration, we truncated the catalog
at M = 3 in advance to discard all data that may have87

M and Mc

6
5
4
3
2
1
-1.5

-1

-0.5

0

Relative time to the M7.3 event [days]
Fig. 1 Plot of Mc as a function of relative time to the M7.3 quake(vertical solid line) since the M6.5 quake (red) and since the M6.4
quake (blue) in which a 200-event window was used. Uncertainty
was according to the bootstrapping (Schorlemmer et al. 2003, 2004).
Also included in this figure is a M–time diagram. Vertical dashed lines
indicate the relative times, 0.98 and 0.67 days, to the M7.3 quake. Redstars M6-class quakes (M6.5, M6.4), yellow star M7.3 quake

been inhomogeneous. Visual inspection of the cumulative curve indicates that there are two kinks at the times
0.98 and 0.67 days before the M7.3 quake, suggesting thattransitions to lower occurrence rates of M ≥ 3 shocks
happened twice. We divided all shocks into two groups:
shocks in the northern area (higher than 32.72° in latitude) and those in the southern area (lower than 32.72°
in latitude). We employed the same plotting procedure
as for Fig. 2a to show that there were again two kinks at
0.98 and 0.67 days before the M7.3 quake in both groups(Fig. 2d, g). Figure 2d, g shows that the timing of the
kinks did not correspond to the occurrence of the M6.4
quake (star at 1.05 days preceding the M7.3 quake), indicating that this quake did not affect the seismic activity as
a whole.
We also checked the change in the number (i.e., thechange in the rate of occurrence) of M ≥ 3 shocks. To
do this, we first plotted the number (the rate of occurrence) of M ≥ 3 shocks in the entire area as a functionof relative time to the M7.3 quake in Fig. 2b, where wecounted M ≥ 3 shocks in each time window of 0.08 days.
We then plotted the change in the number (the change inthe rate of occurrence) of those shocks in the same area
as a function of relative time to the M7.3 quake in Fig. 2c.
Also included in this figure are the mean and standard
deviation of the change in the number of M ≥ 3 shocks.
At 0.98 days relative to the M7.3 quake, the change in
the number was negative and smaller than the standard
deviation, while the change at 0.67 days before the M7.3
quake was also at negative but within the margins of thestandard deviation. This shows that the transition to alower occurrence rate at 0.98 days relative to the M7.3
quake was significant, but the transition at 0.67 days
might not have been. The analysis was performed for thenorthern area (Fig. 2e, f ) and southern area (Fig. 2h, i)separately, obtaining the same feature. We confirmed thatthe above-described result is robust, by sampling different time windows (0.10 and 0.05 days) and by noting thatthe general features are the same for all the cases (Fig. A2in Additional file 1). A preliminary analysis of the change
in the number of M ≥ 3 shocks suggests that the decay ofseismic activity over time was faster than that predictedby the OU law, typically with p = 1.
Figure 3 shows a good fit of the OU law with
p = 1.49 ± 0.29 to the activity with M ≥ 3 for the entire
area during the period between the M6.5 and M7.3
quakes (t = 0–1.16 days). Note that this value is significantly larger than a typical value (p = 1). For a short time
period (t = 0–0.18 days, equivalent to 1.16–0.98 days preceding the M7.3 quake), p = 0.46 ± 0.14 is significantly
below 1. For an intermediate period (t = 0–0.49 days,
corresponding to 1.16–0.67 days preceding the M7.3
quake), p = 0.99 ± 0.26 lies between these two p values.

Nanjo and Yoshida Earth, Planets and Space (2017) 69:13

40

aNo. of eq.

160
140
120
100

b

20
0
−1.5

−1

80
60
40
20
0
−1.5

−1

−0.5

10

c

−10

0

−1.5

−1

No. of eq.

80

−0.5

0

Relative time to the M7.3 event [days]

60

20

e

10
0
−1.5

−1

−0.5

0

Relative time to the M7.3 event [days]
40

Change in no.

Cum. number of earthquakes

d

20
0
−1.5

−1

−0.5

0

5

f

0
−5
−1.5

−1

No. of eq.

g

80

20
0
−1.5

−1

−0.5

0

Change in no.

60
40

−0.5

0

Relative time to the M7.3 event [days]

Relative time to the M7.3 event [days]
100

Cum. number of earthquakes

00

Relative time to the M7.3 event [days]
100

−0.5

Relative time to the M7.3 event [days]
Change in no.

Cum. number of earthquakes

180

Page 4 of 8

20

h

10
0
−1.5

5

−1

−0.5

0

−1

−0.5

0

Relative time to the M7.3 event [days]

i

0
−5
−1.5

Relative time to the M7.3 event [days]
Relative time to the M7.3 event [days]
Fig. 2 Plots of the cumulative number (a, d, g), the number (i.e., the rate of occurrence) (b, e, h), and the change in the number (i.e., the change inthe rate of occurrence) (c, f, i) of M ≥ 3 earthquakes as a function of relative time (days) to the M7.3 quake (vertical solid line). a–c seismicity in theentire area, d–f seismicity in the northern area (higher than 32.72° in latitude), and g–i seismicity in the southern area (lower than 32.72° in latitude).
We used a time window of 0.08 days. See also Fig. A2 in Additional file 1 for other time windows of 0.05 and 0.10 days. Vertical dashed lines indicate
relative times 0.98 and 0.67 days to the M7.3 quake

The difference in the p value between the short and long
periods is statistically significant, showing that decayof seismic activity became faster as period increased,
as expected from a preliminary analysis. The influenceof period on p is shown in the inset of Fig. 3 (data inblack). We conducted the same analysis for shocks that
occurred in the northern and southern areas. The results

are plotted in the inset of Fig. 3 (data in cyan and pink,respectively). The difference in the p value between theseareas is significant for periods longer than 0.5 days, where
the p value was not plotted for the southern area for periods longer than one day because the model-fitting analysis did not converge. It can be said that the rapid decreasein the number of M ≥ 3 shocks in the northern area wasNanjo and Yoshida Earth, Planets and Space (2017) 69:13

Fig. 3 Number λ (day−1) of M ≥ 3 earthquakes in the entire area
as a function of t (days) from the M6.5 quake. Fitting of the OU law
to seismicity in the periods t = 0–0.18 (blue), 0–0.49 (green), and
0–1.16 (red) results in (p, c) = (0.46 ± 0.14, 0.00 ± 0.00), (0.99 ± 0.26,
0.02 ± 0.02), and (1.49 ± 0.29, 0.06 ± 0.04), respectively, where c(days) is a constant of the OU law. Inset p value as a function of thelength of the analyzed period (days) since the M6.5 quake for seismic‑
ity in the entire area (black), in the northern area (cyan), and in thesouthern area (pink)

responsible to the rapid decay in the activity observed
over the entire area.
We next examined the spatial distributions in the bvalue for two periods, 1.16–0.98 and 0.98–0 days prior
to the M7.3 quake. The results are shown in Fig. 4a, d,respectively. To create these figures, we calculated b values for events falling within a cylindrical volume with a
5 km radius, centered at each node on a 0.005° × 0.005°
grid and plotted a b value at the corresponding node if
at least 20 events in the cylinder yielded a good fit to
the GR law. We assumed that the characteristic dimension of the node spacing (~500 m) was a larger value
than the value of location uncertainty (typically, 275 m)of the JMA catalog (Richards-Dinger et al. 2010). Distributions in the Mc value that were simultaneously calculated with a b value at each node are shown in Fig. 4b,e. Overall, the b values increased with time. The difference Δb = b1.16−0.98 − b0.98−0 is mostly above 0 (cyan toblue colors in Fig. 4g) and ranges from Δb = −0.05 toΔb = 0.53. A map view shows a zone of large increase in
the b value (Δb ≥ 0.3, blue colors), but only in the northern area. Observed changes in the b value are not considered significant if the test proposed by Utsu (1992,
1999) is not passed, as is shown in Fig. 4h. If logPb, thelogarithm of the probability that the b values are not different, is equal to or smaller than −1.3 (logPb ≤ −1.3),
then the change in b is significant (Schorlemmer et al.
2004). A map of logPb (Fig. 4h) revealed a zone of the

Page 5 of 8

low values (logPb ≤ −1.3, green colors) in the northernarea. This observation is further supported by applying a bootstrapping approach (Schorlemmer et al. 2003,
2004) to the standard deviation of the b values, σ. The
average standard deviation σ of the early period (1.16–
0.98 days prior to the M7.3 quake) is 0.08, and 90% of
the σ values are smaller than 0.10 (Fig. 4c). For the later
period (0.98–0 days prior to the M7.3 quake), σ is 0.12
and 90% of the values are smaller than 0.18. Higher errorsof σ ≥ 0.18 (yellow) were obtained only in the northern area. The sums between σ in the early period and σ
in the late period are at most 0.3. Comparing Δb with σ,
we can say that the increase in the b value in part of thenorthern area is significant. We conducted the same statistical test as shown in for Fig. 4, but calculated b, Mc,and σ values, by sampling the nearest 100 earthquakes at
each node (Fig. A3 in Additional file 1). The general feature remained similar to Fig. 4. Our statistical test demonstrates that the observed changes in the b value were
physically meaningful and not caused by artifacts.
If the b value offers an indicator of stress in the Earth’s
crust, then it is expected to have increased by the time
the M7.3 quake occurred. To examine this possibility, we
compared the b values before the M6.5 quake with the bvalues after the M7.3 quake in a polygon that includes
epicenters of the M6.5, M6.4, and M7.3 quakes (Fig.
A4 in Additional file 1). The b value was almost stable
when b was 0.6–0.8 before the M6.5 quake, consistent
with the results obtained by Nanjo et al. (2016). Though
the b value immediately after the M7.3 quake fluctuated due to many aftershocks following the quake, theb values after this period were significantly larger thanthose before the M6.5 quake. This result indicates thatmeasurement of spatial and temporal changes in the bvalue is useful to infer stress in the Earth’s crust, supporting our interpretation that the significant increasein the b value in Fig. 4 shows a decrease in stress before
the M7.3 quake.

Discussion
We found that the rate of occurrence of comparatively
large shocks with M3 or larger in the seismic activity after
the M6.5 quake on April 14, 2016, decreased significantly
preceding the M7.3 quake on April 16. We further demonstrated that the p and b values increased significantly
before the M7.3 quake, a feature that is consistent withthe decrease in comparatively large shocks. Our analysisof the spatial and temporal changes in the p and b values
indicates that the increase in the p and b values was mostconspicuous in the northern area of the seismic activity
after the M6.5 quake. This finding suggests that stressaround the Futagawa FZ had begun to decrease preceding the M7.3 quake, if we considered that a high p valueNanjo and Yoshida Earth, Planets and Space (2017) 69:13

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Fig. 4 Results from a test of significance of the difference between the periods 1.16–0.98 days and 0.98–0 days prior to the M7.3 quake. a b values,b Mc values, c σ values from 1.16 to 0.98 days. d b values, e Mc values, f σ values from 0.98 to 0 days. g Δb, the difference in b values between the
periods 1.16–0.98 and 0.98–0 days. h log Pb, the logarithm of the probability that the b value for 1.16–0.98 days is different from the b value for
0.98–0 days. Red stars M6-class quakes (M6.5, M6.4), yellow star M7.3 quake, red lines surface traces of active faults, where Hinagu FZ and Futagawa FZ
are designateddeclines an increase in stress (Dieterich 1994) and that ahigh b value indicates low stress (Scholz 1968, 2015).
The reduction in the normal stress at the Futagawa
FZ, i.e., a decrease in compressive stress on the fault, issuggested by an independent observation from the NIED,
the National Research Institute for Earth Science andDisaster Resilience (2016). NIED examined the temporalchange in the stress field by performing a stress inversion

Nanjo and Yoshida Earth, Planets and Space (2017) 69:13

Page 7 of 8

Fig. 5 a The epicentral map of earthquakes that occurred during the period from the M6.5 quake to the M7.3 quake. Events marked by dark graysquares were used to create the cross-sectional view in b and the magnitude–time diagram in c. Red stars M6-class quakes (M6.5, M6.4), yellow starM7.3 quake, red lines surface traces of active faults, where Hinagu FZ and Futagawa FZ are designated. b Cross-sectional view of the seismicity. Apartfrom the majority of the events, outliers (bold squares) can also be observed around the hypocenter of the M7.3 quake. c M as a function of the time(days) until the M7.3 quake (vertical solid line). Outliers seen in b are designated by bold squares. Vertical dashed lines 0.98 days and 0.67 days before
the M7.3 quake

analysis using focal mechanisms of earthquakes in andaround the Kumamoto earthquakes. The minimum compressive stress (σ3) axis lay roughly in a north–south axis
before the M6.5 quake. A comparison between the σ3 axis
after the M6.5 quake and the σ3 axis before this quake
shows that the axis rotated counterclockwise and became
nearly perpendicular to the strike of the Futagawa FZ,
which indicates the normal force operating to the fault
plane reduced.
In the seismic activity after the M6.5 quake, we foundthat earthquakes had occurred near the hypocenter of theM7.3 quake in addition to the majority of the seismicity
around the Hinagu FZ (Fig. 5a). Figure 5b shows a 5-kmwide cross section nearly perpendicular to the strikeof the Futagawa FZ, on which the rupture of the M7.3
quake occurred (ERC 2016a). Note that several events arerecognized close to the hypocenter of the M7.3 quake. In
the magnitude–time diagram (Fig. 5c) where these eventsare designated by bold squares, they occurred 0.98 days
before the M7.3 event. One possible explanation may
be that they were produced by a nucleation process, assuggested by Onaka (1993), of the M7.3 quake. Our finding of the occurrence of earthquakes close to the hypocenter of the M7.3 quake (Fig. 5), combined with the
reduction of normal pressure on the Futagawa FZ (NIED2016), indicates growth of a quasi-static pre-slips before
the M7.3 quake. The pre-slips might have relaxed stressaround the hypocenter of the M7.3 quake. This stressrelaxation provided feedback to reduce the occurrence
rate of larger (M ≥ 3) shocks (Fig. 2), causing a significantly larger p value than p = 1 (Fig. 3) and a significant
increase in the b value (Fig. 4).

Nanjo and Yoshida Earth, Planets and Space (2017) 69:13

Additional file
Additional file 1. Appendix 1, figures A1–A4, and additional references.

Abbreviations
EMR method: entire-magnitude-range method; ERC: Earthquake ResearchCommittee; FZ: fault zone; GR law: Gutenberg–Richter law; JMA: Japan Mete‑orological Agency; NIED: National Research Institute for Earth Science andDisaster Resilience; OU law: Omori–Utsu law.
Authors’ contributions
KZN performed numerical simulations, analyzed data and prepared thefigures. KZN and AY helped to draft the manuscript and participated in inter‑
pretation. KZN wrote the final manuscript. Both authors read and approved
the final manuscript.
Author details
Global Center for Asian and Regional Research, University of Shizuoka,
3‑6‑1, Takajo, Aoi, Shizuoka 420‑0839, Japan. 2 Center for Integrated Researchand Education of Natural Hazards, Shizuoka University, 836, Oya, Suruga,
Shizuoka 422‑8529, Japan.
1

Acknowledgements
We thank the Editor (Matha Savage) and two anonymous reviewers for theirconstructive review.
Competing interests
The authors declare that they have no competing interests.
Received: 1 August 2016 Accepted: 6 January 2017

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