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The El Salvador and Philippines Tsunamis of August 2012: Insights from Sea Level Data
Analysis and Numerical Modeling
MOHAMMAD HEIDARZADEH
1,2
and KENJI SATAKE
1
Abstract—We studied two tsunamis from 2012, one generated
by the El Salvador earthquake of 27 August (Mw 7.3) and the other
generated by the Philippines earthquake of 31 August (Mw 7.6),
using sea level data analysis and numerical modeling. For the El
Salvador tsunami, the largest wave height was observed in Baltra,
Galapagos Islands (71.1 cm) located about 1,400 km away from
the source. The tsunami governing periods were around 9 and
19 min. Numerical modeling indicated that most of the tsunami
energy was directed towards the Galapagos Islands, explaining the
relatively large wave height there. For the Philippines tsunami, the
maximum wave height of 30.5 cm was observed at Kushimoto in
Japan located about 2,700 km away from the source. The tsunami
governing periods were around 8, 12 and 29 min. Numerical
modeling showed that a significant part of the far-field tsunami
energy was directed towards the southern coast of Japan. Fourier
and wavelet analyses as well as numerical modeling suggested that
the dominant period of the first wave at stations normal to the fault
strike is related to the fault width, while the period of the first wave
at stations in the direction of fault strike is representative of the
fault length.
Key words: Tsunami, earthquake, DART, tide gauge, spectral
analysis, Fourier analysis, wavelet analysis, numerical modeling, El
Salvador earthquake, Philippines earthquake.
1. Introduction
We studied two small tsunamis occurring in the
Pacific basin in August 2012, generated by submarine
earthquakes offshore El Salvador and Philippines
(Fig. 1). According to the United States Geological
Survey (USGS 2012a), the El Salvador earthquake
occurred on 27 August 2012 at 04:37:20 GMT. The
epicenter of this Mw-7.3 earthquake was at 12.278°Nand
88.528°W at the depth of around 20 km, producing
almost no damage or casualty in the region (REUTERS
2012a). However, it generated a small tsunami in the
Pacific Ocean whose wave amplitude was reported
around 10 cm along the coastlines (CNN 2012a). A Field
survey by BORRERO et al.(2014) showed that the tsunami
generated a maximum runup of 6 m in the near-field,
injuring several people. The first information bulletin
about this tsunami was issued around 8 min after the
earthquake occurrence, by the Pacific Tsunami Warning
Center (PTWC) (PTWC 2012a). Following this early
information, a tsunami warning was issued at 04:58
GMT (around 20 min after the earthquake) for the region
(PTWC 2012b),andwascancelledaround110minafter
the earthquake (PTWC 2012c).
The Philippines tsunami was slightly larger than the
El Salvador one, having been produced by a slightly
larger earthquake (Mw 7.6). According to the USGS
(2012b), the origin time of the Philippines earthquake
was at 12:47:34 GMT on 31 August 2012. The epicenter
was at 10.838°N and126.704°E at a depth of around
35 km (USGS 2012b). This offshore earthquake caused
little damage and one death in the Philippines (REUTERS
2012b). Following this large submarine earthquake, a
tsunami warning was issued at 12:55 GMT (around
8 min after the earthquake) for the region (PTWC 2012d).
No damage was reported from the tsunami. Finally, the
tsunami warning was cancelled at 14:54 GMT, about
2 h after the earthquake (PTWC 2012e).
In the following, we perform statistical, Fourier
and wavelet analyses on the sea level records of these
tsunamis in order to characterize the tsunami waves.
In addition, numerical modeling of tsunami is con-
ducted to give us insights into the propagation pattern
of tsunami waves in the Pacific Basin.
1
Earthquake Research Institute (ERI), The University of
Tokyo, 1-1-1 Yayoi, Bunkyo-ku, Tokyo 113-0032, Japan. E-mail:
mheidar@eri.u-tokyo.ac.jp
2
Cluster of Excellence ‘‘The Future Ocean’’, Christian-Al-
brechts University of Kiel, Kiel, Germany.
Pure Appl. Geophys.
Ó2014 Springer Basel
DOI 10.1007/s00024-014-0790-2 Pure and Applied Geophysics
2. Sea level data
We report and analyze 25 sea level records of
the aforesaid tsunamis consisting of both tide gau-
ges and Deep-ocean Assessment and Reporting of
Tsunamis (DART) records (Fig. 1; Tables 1,2).
The sea level data were provided by the USA
National Oceanographic and Atmospheric Admin-
istration (NOAA 2012) and the UNESCO
Intergovernmental Oceanographic Commission (IOC
2012). The sampling interval for all of the sea level
data is 1 min.
Figure 1
General location map of the Pacific Basin showing the locations of the El Salvador tsunami of 27 August 2012 (right asterisk) and the
Philippines tsunami of 31 August 2012 (left asterisk). Solid circles and triangles represent the locations of tide gauge and DART stations,
respectively. Abbreviations are: LG Legaspi, MK Malakal, YI Yap Island, AH Apra Harbor, IS Ishigakijima, NH Naha, TS Tosashimizu, AB
Aburatsu, KS Kushimoto, CH Chichijima, MR Mera, and Ph. Sea Philippine Sea
Table 1
Sea level stations used to study the El Salvador tsunami of 27 August 2012
No. Sea level station Country (state) Longitude Latitude Distance to the
source (km)
Tide gauge stations
1 La Union El Salvador 87.82°W 13.31°N 140
2 Acajutla El Salvador 89.84°W 13.57°N 206
3 Baltra Ecuador 90.28°W 00.43°S 1,433
4 Santa Cruz Ecuador 90.31°W 00.75°S 1,468
5 La Libertad Ecuador 80.91°W 02.22°S 1,829
6 Easter Chile 109.45°W 27.15°S 4,985
DART stations
7 43413 SW of Acapulco, Mexico 99.85°W 11.07°N 1,271
8 32413 NW of Lima, Peru 93.50°W 07.40°S 2,267
M. Heidarzadeh, K. Satake Pure Appl. Geophys.
3. Methods of Waveform Analyses
3.1. Tsunami Waveform Detection
The following steps were employed to detect the
tsunami signal from the sea level records: (1) quality
control, and (2) removing low-frequency signals like
tides by high-pass filtering. The Butterworth IIR
digital filter (MATHWORKS 2012) was employed to
remove low frequency signals for which a cut-off
frequency of 0.0003 Hz (about 1 h) was chosen. To
examine whether the Butterworth digital filter gener-
ates a spurious leading depression wave or not in our
analyses, we performed tidal harmonic analysis for
selected waveforms (Sect. 4.1).
3.2. Statistical Analysis
We calculated the following physical parameters
of the tsunami (HEIDARZADEH and SATAKE 2013a): (1)
the arrival time of the first tsunami wave, (2) the
polarity of the first wave, (3) the arrival time of the
maximum wave, (4) the maximum trough-to-crest
wave height, (5) the number of waves before the
arrival of the maximum wave, and (6) duration of
tsunami.
3.3. Spectral Analysis
The spectral content of a tsunami record is mostly
dictated by two factors: (1) the effect of local and
regional bathymetric features like continental shelves
and coastal harbors/bays, and (2) the effect of
tsunami source and dimensions of the seafloor
deformation. In this context, a tide gauge record of
a tsunami usually includes both of the aforesaid
effects, because tide gauges are deployed in coastal
areas and hence bathymetric features play an impor-
tant role in their records. In contrast, DART records
mostly reflect tsunami source characteristics, as they
are deep-water instruments and hence are free from
shallow bathymetric effects. To separate tsunami
source and bathymetric effects in a tide gauge record,
RABINOVICH (1997) proposed to compare spectral
peaks computed from tsunami water level data
recorded at different locations and then to pick the
common spectral peaks contained within different
water level spectra from a particular tsunami. We
applied this method to separate source and bathy-
metric effects in our tide gauge data. In this study, we
applied two methods to investigate the spectral
content of the tsunami signals: Fourier and wavelet
analyses.
Table 2
Sea level stations used to study the Philippines tsunami of 31 August 2012
No. Sea level station Country (state) Longitude Latitude Distance to the
source (km)
Tide gauge stations
1 Legaspi Philippines (Albay) 123.76°E 13.15°N 417
2 Malakal Palau Islands 134.45°E 07.33°N 949
3 Yap Island Micronesia 138.12°E 09.51°N 1,283
4 Ishigakijima Japan (Okinawa) 124.10°E 24.20°N 1,520
5 Naha Japan (Okinawa) 127.67°E 26.22°N 1,721
6 Aburatsu Japan 131.41°E 31.58°N 2,376
7 Chichijima Japan 142.19°E 27.09°N 2,507
8 Tosashimizu Japan (Kochi) 132.97°E 32.78°N 2,548
9 Kushimoto Japan 135.77°E 33.48°N 2,724
10 Mera Japan 139.83°E 34.92°N 3,063
11 Wake Island USA (Wake Island) 166.62°E 19.28°N 4,557
12 Kwajalein Marshall Islands 167.73°E 08.73°N 4,588
DART stations
13 52405 West of Pacific Ocean, Guam 132.33°E 12.88°N 669
14 52403 West of Pacific Ocean, Truk 145.59°E 04.05°N 2,241
15 52402 NW of Kwajalein 154.04°E 11.87°N 3,055
16 52401 NE of Saipan 155.77°E 19.26°N 3,380
17 21413 SE of Tokyo, Japan 152.12°E 30.52°N 3,590
Analysis of the El Salvador and Philippines Tsunamis of August 2012
3.3.1 Fourier Analysis
For Fourier analysis, we used Welch’s averaged-
modified-periodogram method of spectral estimation
by considering Hamming window and overlaps
(WELCH 1967). Calculation of the signal spectrum
was done using the Welch algorithm from the signal
processing toolbox in Matlab program (MATHWORKS
2012).
3.3.2 Wavelet Analysis
Wavelet analysis, also known as the frequency-time
(f–t) analysis, has been used in tsunami research for
studying the temporal changes of tsunami energy
(RABINOVICH and THOMSON 2007;HEIDARZADEH and
SATAKE 2013a;BORRERO and GREER 2013). Since a
tsunami is a non-stationary signal, its spectral content
varies in strength and peak frequency over time.
Wavelet analysis presents the distribution of tsunami
energy in different frequency bands (f) over time (t).
In other words, wavelet analysis shows in which
period band tsunami energy is concentrated at a
particular time, and hence can be considered as a
complementary analysis for Fourier analysis. Because
a tsunami is a non-stationary signal, the use of
wavelet analysis allows for the analysis of the
frequency content of a tsunami wave train as it
changes over time. More details about wavelet
analysis is given in TORRENCE and COMPO (1998)
and HEIDARZADEH and SATAKE (2013a,b).
4. Results of the Analyses
4.1. Tsunami Waveforms
Figure 2presents the original and filtered signals
for the El Salvador tsunami of 27 August 2012
(Fig. 2a) and the Philippines tsunami of 31 August
2012 (Fig. 2b, c). It can be seen that the tsunami
signal is clear in most of the analyzed tide gauge
records. The El Salvador tsunami was recorded on
five coastal tide gauges and two DART stations
(DARTs 43413 and 32413). The Philippine tsunami
was recorded on ten coastal tide gauges and on two
DART stations of 52405 and 52403 with 1-min
temporal resolution. While the tsunami was possibly
recorded on DART stations 52402, 52401 and 21413,
the tsunami arrival occurred after the station had been
switched from 1-min sampling to 15 min sampling.
Under-sampled traces of seismic waves are also
present in the DART records of both events and are
evident in the figures.
Figure 2d compares the results of Butterworth
digital filter (middle panel) with those of tidal
harmonic analysis (right panel) for four stations
recording the Philippines tsunami. We applied the
tidal analysis package Tidal Analysis Software Kit
(TASK) for tidal analysis (BELL et al.2000).
Figure 2d shows that both of the analyses yield
almost the same results, indicating that the applied
digital filter is not producing spurious leading
depression waves.
4.2. Statistical Properties of the Tsunamis
Based on the filtered tsunami signals (Fig. 2), the
main physical properties are summarized in Tables 3
and 4.
4.2.1 El Salvador Tsunami
Among the analyzed sea level stations for the El
Salvador tsunami, the Acajutla tide gauge was the
first one to receive the tsunami. The first arrival in La
Union can be distinguished by taking into consider-
ation the fact that the period of tsunami is larger than
that of noise signals. The time interval between the
first tsunami peak (asterisk in Fig. 2a) and the next
peak is around 16 min for the La Union record. It will
be shown later that the 16-min signal is one of the
governing signals of the El Salvador tsunami. The
largest trough-to-crest wave height is 71.1 cm
recorded at the Baltra tide gauge station at a distance
of around 1,400 km from the tsunami source
(Table 3). At other far-field stations like Santa Cruz
and La Libertad, wave heights of 34.4 and 35.6 cm
were recorded, respectively, though the Santa Cruz
station is located in the far-field on the lee side of the
Galapagos island system relative to the direction of
incidence of the tsunami (Fig. 1). The far-field wave
heights are about five times larger than the near-field
wave heights (e.g., La Union station). Comparison of
average values for the DART and tide gauge
M. Heidarzadeh, K. Satake Pure Appl. Geophys.
waveforms (Table 3) indicate three main differences
between tsunami records on DARTs and tide gauges:
(1) Duration of tsunami oscillations on tide gauges is
about four times longer than that on DARTs, (2) the
maximum wave height on tide gauges is 14 times
larger than that on DARTs, and (3) the first wave is
the largest one in DART records, whereas the second,
third or later wave is the largest in tide gauge records.
Figure 2
Sea level records of the El Salvador tsunami of 27 August 2012 (a) and the Philippines tsunami of 31 August 2012 (b,c). The left and middle
panels show the original and filtered signals, respectively. In the right panel, only a small part of the filtered signal is enlarged. The letters
Eand Trepresent Earthquake and Tsunami, respectively. The dashed rectangle shows part of the data enlarged in the neighboring panel.
Small insets show the respective waveforms with a better resolution. Asterisks show the arrival times of the first wave. dComparison of the
results of waveform analysis performed by the Butterworth digital filter (middle panel) and the tidal harmonic analysis (right panel). Tide
predictions are shown by blue curves in the left panel. The red-vertical line represent the time of the earthquake occurrence
Analysis of the El Salvador and Philippines Tsunamis of August 2012
4.2.2 Philippines Tsunami
The largest wave height was 30.5 cm, recorded at
Kushimoto (Japan) for the Philippines tsunami.
Similar to the El Salvador tsunami, among the
analyzed sea level stations for the Philippines
tsunami (Table 4), the near-field wave heights are
significantly smaller than the far-field ones. Accord-
ing to Table 4, deep water tsunami waves recorded at
DART 52405 have smaller amplitudes and last for a
shorter time compared to those recorded by tide
gauges.
4.3. Spectral Peaks
Fourier analysis of the tsunami waveforms iden-
tified a few peaks, which are shown by asterisks in
Fig. 3and are summarized in Tables 5,6.We
performed Fourier analysis for both the entire
tsunami waveform (Fig. 3/left panels) and for the
first 2 h (Fig. 3/right panels), and then the peak
periods were picked from the latter spectra. It is
expected that the 2-h-long spectra are less influenced
by coastal bathymetric features. In general, a clear
difference can be seen between the tsunami spectra of
DARTs and those of tide gauges. Tsunami spectrum
is usually simple and consists of only one peak for
DARTs, whereas it is relatively complicated and
includes several peaks for tide gauges.
4.3.1 El Salvador Tsunami
The analysis suggests spectral peaks at approximately
19 and 9 min for the El Salvador tsunami (Fig. 3a;
Figure 2
continued
M. Heidarzadeh, K. Satake Pure Appl. Geophys.
Table 3
Statistical properties of the El Salvador tsunami of 27 August 2012
No. Sea level station First wave Maximum wave Duration (h)
Arrival time (GMT)
(dd/mm-HH:MM)
Travel time
a
(h:min)
Sign
b
Arrival time
(GMT) dd/mm-HH:MM)
Travel time
a
(h:min)
Observed max.
wave height (cm)
c
No. of the
max. wave
1 La Union 27/08-05:39 01:02 (?) 27/08-06:11 01:34 4.5 3 10
2 Acajutla 27/08-05:23 00:46 (-) 27/08-09:29 04:52 12.5 23 14
3 Baltra 27/08-07:08 02:31 (?) 27/08-07:21 02:44 71.1 2 10
4 Santa Cruz 27/08-07:25 02:48 (?) 27/08-07:34 02:57 34.4 2 7
5 La Libertad 27/08-08:11 03:44 (?) 27/08-11:23 06:46 35.6 17 10
6 Easter NA
d
NA NA NA NA NA NA NA
Average 31.6 9 10.2
7 DART 43413 27/08-06:15 01:38 (?) 27/08-06:19 01:42 2.3 1 2
8 DART 32413 NA NA NA 27/08-08:15 03:38 2.2 1 2.8
Average 2.25 1 2.4
a
Compared to the earthquake origin time (27/08/2012 04:370:2000 GMT)
b
(-)and(?) represent leading depression and elevation waves, respectively
c
Maximum trough-to-crest wave height
d
Not Applicable
Analysis of the El Salvador and Philippines Tsunamis of August 2012
Table 4
Statistical properties of the Philippines tsunami of 31 August 2012
No. Sea level station First wave Maximum wave Duration (h)
Arrival time (GMT)
(dd/mm-HH:MM)
Travel time
a
(h:min)
Sign
b
Arrival time (GMT)
(dd/mm-HH:MM)
Travel time
a
(h:min)
Observed max.
wave height (cm)
c
No. of the
max. wave
1 Legaspi 31/08-13:23 00:36 (?) 31/08-13:43 00:56 4.2 2 9
2 Malakal NA
d
NA NA NA NA NA NA NA
3 Yap Island 31/08-14:28 01:41 (?) 31/08-15:04 02:17 3.2 6 2
4 Ishigakijima 31/08-14:45 01:58 (?) 31/08-16:59 04:12 9.8 11 10
5 Naha 31/08-15:05 02:18 (?) 31/08-17:00 04:13 10.5 5 5
6 Aburatsu NA NA NA 31/08- 20:53 08:06 7.3 NA 6
7 Chichijima 31/08-15:52 03:07 (?) 31/08-16:57 04:10 24 5 13
8 Tosashimizu 31/08-16:19 03:32 (?) 31/08-16:37 03:50 17.9 2 2
9 Kushimoto 31/08-16:25 03:38 (?) 31/08-16:38 03:51 30.5 2 10
10 Mera 31/08-17:36 04:49 (?) 31/08-18:34 05:47 23.9 5 6
11 Wake Island 31/08-18:36 05:49 (?) 31/08-19:05 06:18 7.5 3 3
12 Kwajalein NA NA NA NA NA NA NA NA
Average 13.9 5 6.6
13 DART 52405 31/08-13:31 00:44 (?) 31/08-13:33 00:46 5.8 1 1
14 DART 52403 31/08-15:50 03:03 (?) 31/08-15:50 03:03 1.01 1 –
a
Compared to the earthquake origin time (31/08/2012 12:470:3400 GMT)
b
(-)and(?) represent leading depression and elevation waves, respectively
c
Maximum trough-to-crest wave height
d
Not applicable
M. Heidarzadeh, K. Satake Pure Appl. Geophys.
Table 5); these are possibly the main tsunami source
periods. The most governing signal is possibly the
one with the period of around 9 min, because this
signal is the one that is most common in Table 5.
4.3.2 Philippines Tsunami
For the Philippines tsunami, the governing periods
are 29, 12, and 8 min (Fig. 3b, c; Table 6), among
which the 12-min period seems to be the strongest
one because it is the most common signal in
different stations (Table 6). The period of the
tsunami recorded at the DART 52403 is also
12 min (Fig. 2c). Some unusual observations can
be seen in the tsunami spectra shown in Fig. 3b, c.
For example, during the Philippines tsunami, the
most powerful signal is the 5.9-min signal in Yap
Island, whereas either 29- or 12-min signals are the
governing ones in all of the other stations. The 5.9-
min period is possibly one of the resonance modes
Figure 3
Spectra for the sea level records of the El Salvador tsunami of 27 August 2012 (a) and the Philippines tsunami of 31 August 2012 (b,c).
Fourier analysis is performed for both the entire tsunami waveforms (left panels) and for the first 2 h of the tsunami waveforms (right panels).
Asterisks show some of the peak periods in each spectrum. Solid and dashed lines show the spectra of tsunami and background signals,
respectively
Analysis of the El Salvador and Philippines Tsunamis of August 2012
of the harbor/bay, in which the Yap Island tide
gauge is located.
4.4. Temporal Changes of Dominant Periods
Wavelet analyses for the sea level records of the
El Salvador and Philippines tsunamis are shown in
Fig. 4, as is the global wavelet spectrum, which is the
time-averaged spectral energy over all times. It
should be noted that Fourier analysis (Fig. 3) gives
the power of signals with different periods over the
entire tsunami record, whereas wavelet analysis gives
the time evolution of wave energy. Hence, the
Fourier analysis given by global wavelet spectrum
(Fig. 4) is slightly different from that of normal
Fourier analysis performed by Welch algorithm
(Fig. 3). This is why there are differences between
the amount of peak energy given by Fourier (Fig. 3)
and wavelet analyses (Fig. 4) although the peak
periods are almost the same in both.
4.4.1 El Salvador Tsunami
For the El Salvador tsunami recorded at Santa
Cruz, most of the tsunami energy is distributed in
the narrow period band of 11–24 min over the
entire tsunami oscillations. The Acajutla’s f–tplot
shows that the level of wave energy before the
earthquake occurrence is as high as that after the
earthquake for the period band of around 45 min,
indicating that this period band cannot be attributed
to the tsunami. There is almost no energy at the
period bands of around 7–10 and 18–20 min before
the earthquake occurrence, whereas the wave
energy at these period bands is higher after the
earthquake. This indicates that both of the aforesaid
periods may belong to the tsunami. On the other
hand, we may conclude that the peak period of
45 min at the La Libertad station (Fig. 4a) belongs
to non-tsunami sources (e.g., local and regional
bathymetric effects).
4.4.2 Philippines Tsunami
Based on the f–tplots for the Philippines tsunami
(Fig. 4b, c), it can be seen that most of the wave
energy is distributed at three different period bands
of around 10–13, 25–30, and 45 min. However, the
period band of 45 min most probably belongs to
non-tsunami sources, because the level of energy in
this band is high before the arrival of tsunami in
many of the examined stations. This idea is
supported by the tsunami and background spectra
shown in Fig. 3b, c because the levels of energy in
both spectra are almost the same around the period
of 45 min. Distinct wave trains with high energy
contents are clear at Naha. According to the
wavelet plot of the Ishigakijima record (Fig. 4b),
by neglecting the 45-min signal, the governing
period of tsunami is around 10–12 min for the first
few hours after the tsunami arrival; then the
governing period switches to the period of around
20–28 min. On the contrary, the 28-min signal is
the first signal arriving at the Legaspi station
(Fig. 4b). At Wake Island (Fig. 4c), most of the
tsunami energy occurs at the period of around
10–12 min and almost no energy is present at the
period band of 20–28 min. For Mera (Fig. 4c),
Table 5
Governing periods of the El Salvador tsunami of 27 August 2012
based on the spectra of the first 2 h of the tsunami waveforms
(Fig. 3a/right panel)
No. Station Peak periods (min)
1 La Union 9.4
2 Acajutla 19.3, 7.5
3 DART 43413 7.9
4 Baltra 10.8, 4.9
5 Santa Cruz 18.5, 6.2
6 La Libertad 12.2, 5.9
Table 6
Governing periods of the Philippines tsunami of 31 August 2012
based on the spectra of the first 2 h of the tsunami waveforms
(Fig. 3b, c/right panel)
No. Station Peak periods (min)
1 Legaspi 25.6, 12.4, 5.9
2 Yap Island 28.9, 11.8, 7.9, 5.9
3 Ishigakijima 12.5, 8.2
4 Naha 28.9, 10.4, 7.8
5 Chichijima 15.0, 7.5
6 Tosashimizu 13.1, 8.3
7 Kushimoto 18.3, 7.7
8 Mera 13.2
9 Wake Island 11.1
10 DART 52405 10.4
M. Heidarzadeh, K. Satake Pure Appl. Geophys.
tsunami energy is distributed over a wide period
band of 5–25 min. The governing period is around
10–15 min for Chichijima, while it is around
20–25 min for Kushimoto (Fig. 4c).
4.5. Summary of the Sea Level Data Analysis
The analysis of the El Salvador and Philippines
tsunamis of August 2012 using sea level data showed
some unusual observations, such as: (1) for the El
Salvador tsunami, relatively large wave height of
34.4 cm was observed on the lee side of the Galapagos
island system relative to the direction of incidence of
the tsunami; (2) although the Philippines earthquake
(Mw 7.6) was larger than the El Salvador one (Mw 7.3),
the maximum wave height generated by the El
Salvador tsunami was almost two times bigger than
that generated by the Philippines tsunami; (3) the
largest wave heights produced by the Philippines
tsunami were observed in the far-field especially along
the Japan coast; and (4) the largest wave heights of the
El Salvador tsunami occurred in the far-field. We
perform numerical modeling of both tsunamis in order
to shed some light on the above unusual observations.
Figure 4
Wavelet analysis for the sea level records of the El Salvador tsunami of 27 August 2012 (a) and the Philippines tsunami of 31 August 2012
(b,c). Dashed-vertical dark and purple lines represents the earthquake occurrence and tsunami arrival times, respectively. The small plots,at
the right side of each wavelet plot, show the global wavelet spectrum
Analysis of the El Salvador and Philippines Tsunamis of August 2012
5. Numerical Modeling of Tsunami Waves
and Validation
5.1. Method and Validation
The analytical formulas by OKADA (1985) were
employed to calculate the seafloor deformation due to
the parent earthquake using the seismic parameters of
the earthquake. The earthquake fault parameters are
taken from the GLOBAL CMT (2012) and the USGS
centroid moment solution (USGS 2012a,b) summa-
rized in Table 7. Figure 5a shows the result of the
seafloor deformation modeling. The 1-min bathyme-
try grid provided through the GEBCO digital atlas
was used here for numerical modeling of tsunami
(IOC et al.2003). The numerical model used here is
the same as that described in YALCINER et al.(2004),
solving non-linear shallow water equations using a
leap frog scheme on a staggered grid system. A time
step of 3.0 s is applied and tsunami inundation on dry
land is not included.
To validate the results of tsunami modeling, we
compare time histories of the simulated waves with
actual ones observed on DARTs and tide gauges.
Figure 5b presents the results of this comparison, in
which five actual sea level records are compared with
the simulated ones for each tsunami. Although the
grid spacing is 1 min, good agreement can be seen
between the simulated and observed waveforms. The
agreement is highly satisfactory for DART records.
In Legaspi, the discrepancy between the observed and
simulated wave height is relatively large; however,
the arrival times are almost the same. It seems that
the tsunami simulations performed here are accurate
enough for this study, which is aimed at studying the
propagation pattern of the two tsunamis.
5.2. The El Salvador Tsunami
Snapshots of the El Salvador tsunami in Fig. 6a
show that tsunami waves experience two major
reflections from Isla-Del-Coco and the Galapagos
Islands, which occur about 1.5 and 2.5 h after the
earthquake, respectively. It is clear from Fig. 6a that
each reflection acts as a new source for tsunami
waves, introducing new wave trains into the tsunami
wave field. Late wave trains in tsunami waveforms
(Fig. 2) may be attributed to these reflected waves
that arrive some hours after the earthquake genera-
tion. It is long known that a tsunami is a series of long
waves; not a single wave. This is clear from the
snapshot of the El Salvador tsunami at the time of 3 h
(Fig. 6a) where a chain of successive wave crests
(C) and troughs (T) can be seen.
Figure 6c shows the distribution of the maximum
wave height of the El Salvador tsunami. Most of the
tsunami energy is directed towards the Galapagos
Islands. This is due to the directivity of tsunami
waves in the far-field. Proposed by BEN-MENAHEM
and ROSENMAN (1972), directivity of tsunami indi-
cates that most of the tsunami energy travels
Figure 4
continued
M. Heidarzadeh, K. Satake Pure Appl. Geophys.
perpendicular to the source strike in the far-field.
Considering that the strike of the fault responsible for
the El Salvador tsunami is SE–NW (Fig. 5a), the
largest tsunami waves travel in the NE–SW direction
(Fig. 6c). Hence, observation of the maximum wave
height of the El Salvador tsunami at the Baltra station
can be explained by the directivity effect. Snapshots
of the El Salvador tsunami simulation around the
Santa Cruz station (Fig. 6d) reveal that two different
waves arrived almost at the same time from opposite
sides, and are superpositioned into a single wave. One
wave train comes from around the Isabela Island to
the west and another wave train from the east side of
the Santa Cruz Island. This phenomenon may explain
the relatively large wave height of around 35 cm in
Santa Cruz.
5.3. The Philippines Tsunami
Snapshots of the Philippines tsunami in Fig. 6b
reveal that the tsunami wave field is more compli-
cated than that of the El Salvador tsunami; this can be
attributed to the presence of the Izu-Bonin Island
chain and other Pacific Islands around the tsunami
source area. Tsunami waves are reflected from this
island chain and can hardly exit the Philippine Sea
region. This is also supported by Fig. 6c, where the
distribution of the maximum wave height of tsunami
is presented. Figure 6c reveals that most of the
tsunami energy is confined within the Philippine Sea
region and only a small part of the tsunami is able to
exit from the Philippine Sea.
The other fact in Fig. 6c is that a significant part of
the Philippines tsunami energy is directed towards the
Figure 5
Results of numerical modeling of tsunami. aSeafloor deformation due to the El Salvador and Philippines tsunamis. Numbers on axes are in
degrees. Asterisks show the epicenters of the earthquake. bSimulated and observed waveforms for the two tsunamis
Analysis of the El Salvador and Philippines Tsunamis of August 2012
southern coast of Japan (arrow B in Fig. 6c). In fact, the
energy of the Philippines tsunami is partitioned into
two parts: (1) the first part of tsunami energy travels
perpendicular to the source strike (arrow A in Fig. 6c),
which can be explained by the directivity effect; and (2)
the second part travels towards the southern coast of
Japan (arrow B in Fig. 6c), which can be explained by
the effect of bathymetry on far-field propagation of
tsunamis proposed by SATAKE (1988). Arrows in
Fig. 6b show how the Izu-Bonin Island chain funnels
the tsunami waves towards southern Japan. Observa-
tion of relatively large wave heights in Japanese
coastlines due to the Philippines tsunami may be
explained by this effect.
5.4. Comparing the Two Tsunamis
According to Tables 3and 4, among the examined
sea level records, the average wave height produced
by the El Salvador tsunami is about two times larger
than that produced by the Philippines tsunami,
although the former earthquake (Mw 7.3) was smaller
than the latter earthquake (Mw 7.6). The El Salvador
earthquake was more efficient for tsunami generation
than the Philippines one for three reasons. First, the
former earthquake occurred at a shallower depth.
Second, the former earthquake has a larger dip-slip
component, although the dip angle is smaller
(Table 7). Due to these reasons, the maximum
Figure 6
Results of numerical modeling of tsunami. aSnapshots of tsunami simulations for the El Salvador tsunami. Cand Trepresent crest and trough
waves, respectively. bSnapshots of tsunami simulations for the Philippines tsunami. cDistribution of the maximum wave amplitudes of
tsunami for the two tsunamis. dSnapshots of the El Salvador tsunami around the Santa Cruz station. Numbers on axes are in degrees
M. Heidarzadeh, K. Satake Pure Appl. Geophys.
seafloor uplift due to the El Salvador earthquake is
larger than that of the Philippines earthquake
(Fig. 5a). It is evident that the larger the seafloor
uplift is, the stronger the tsunami. Third, based on the
source-time functions of both earthquakes shown in
Fig. 7, the El Salvador earthquake was a slow
earthquake. The source duration of the El Salvador
earthquake was around 70 s; this is comparable to
some other slow-tsunamigenic earthquakes (known as
‘‘tsunami earthquakes’’), like the 1992 Nicaragua
Figure 6
continued
Table 7
Tectonic parameters used for modeling seafloor deformation at the tsunami source according to GLOBAL CMT (2012) and the USGS (2012a,b)
Event name M
0
a
(dyn. cm)
Mw
b
Fault start point Fault end point Length
(km)
Width
(km)
Slip
(m)
Depth
(km)
Dip
(deg)
Rake
(deg)
Strike
(deg)
Lon (°) Lat (°) Lon (°) Lat (°)
El Salvador
(27 Aug 2012)
1.18 910
27
7.3 88.70 (°W) 12.3 (°N) 89.22 (°W) 12.46 (°N) 60 30 2.2 12 15 81 287
Philippines
(31 Aug 2012)
3.34 910
27
7.6 126.80 (°E) 10.20 (°N) 126.63 (°E) 10.90 (°N) 80 40 3.5 46 45 63 345
a
Seismic moment
b
Moment magnitude
Analysis of the El Salvador and Philippines Tsunamis of August 2012
earthquake (KANAMORI and KIKUCHI 1993) and the
2010 Mentawai earthquake (SATAKE et al.2013). Slow
earthquakes have been reported to be more efficient in
tsunami generation than ordinary ones.
6. Discussions
6.1. Insights into the Tsunami Source Dimension
Using Wavelet Analysis
It is already known that the main governing
periods of tsunamis are normally dictated by the
dimensions of the earthquake fault (i.e., length/
width), as schematically shown for the Philippines
tsunami in Fig. 8(HEIDARZADEH and SATAKE 2013a).
The sea level stations located normal to the fault
strike (e.g., Wake Is. in Fig. 8) are mainly influenced
by the tsunami period determined by the source
width. For other stations located at different sides of
the tsunami source (i.e., the lateral stations like
Legaspi in Fig. 8), the tsunami signal controlled by
the source length is usually the first wave to arrive at
these stations. As most of the tsunami energy is
usually concentrated towards normal to the source
strike (i.e., directivity effect), the period of tsunami is
mainly controlled by the width of the source rupture.
Therefore, even for the stations receiving first waves
imposed by the source length, we may expect that the
governing tsunami signal is the one imposed by the
source width. However, any connection between a
certain period and the width/length of the source fault
needs to be made cautiously, because a tsunami
spectrum usually shows multiple peaks due to the
various local/regional/global bathymetric features. In
fact, the periods dictated by the source fault are
mixed with other periods imposed by bathymetric
effects. In addition, the aforesaid connection between
source dimensions and tsunami governing periods is a
general rule and we may not expect it to hold true for
every tsunami waveform, as tsunami source is, in
reality, a heterogeneous one and tsunami waveforms
are affected by several factors.
The Fourier analysis for the Philippines tsunami
showed that the governing periods of this tsunami
are around 12 and 29 min (Table 6). The wavelet
plot of the Ishigakijima record (Fig. 4b) shows that
the first tsunami wave arriving in this station is
dominated by the 11-min signal, followed by the
25-min signal. For this case, the periods of 11 and
25 min can be possibly attributed to the width and
length of the seafloor rupture, respectively (Fig. 8).
In Chichijima (Fig. 4c), located almost normal to
the fault strike, the 15-min signal is the first one to
arrive at this station and is dominating for almost
the entire tsunami lifetime. This 15-min signal
seems to be dictated by the width of the tsunami
source. We note that we do not necessarily expect
exactly the same signal resulting from source width
at different stations. Taking into account the com-
plex wave field generated by a tsunami due to
irregular bathymetry, as well as tsunami source
heterogeneity, the two signals of 11 and 15 min can
be considered close enough to each other as both
originated from the source width. In Naha, located
at an angle of around 45 degrees relative to the
source strike, the first and the dominating signal is
the one at the period of 28 min, which seems to be
dictated by the length of the tsunami source. For the
two middle-class stations of Naha and Ishigakijima,
i.e. neither located pure normal relative to the
source strike nor pure lateral, it can be seen that in
one of them the first signal is at 11 min and in the
other it is at 28 min. In Wake Island, located truly
Figure 7
Source-time functions for the two earthquakes of El Salvador (27
August 2012-Mw 7.3) and Philippines (31 August 2012-Mw 7.6).
The data is from the finite fault model of USGS (2012a,b)
M. Heidarzadeh, K. Satake Pure Appl. Geophys.
normal to the fault strike, the only tsunami signal is
the 11-min signal, meaning that the spectra of the
Wake Island station is mostly influenced by the
width of the tsunami source rupture. For the Legaspi
station, a pure lateral one, a first 26-min tsunami
signal was recorded (Fig. 4b).
6.2. Tsunami Hazards for Southern Japan
from Philippines Tsunamis
Analysis of sea level records of the 31 August
2012 Philippines tsunami revealed that the largest
wave heights of this tsunami were recorded on tide
gauges along the southern coast of Japan. Using
numerical modeling of tsunami, it was shown
above that a part of the waves generated by the
Philippines tsunami was funneled towards southern
Japan due to the bathymetric features in the
Philippine Sea. According to LANDER et al.
(2003), a similar observation was reported follow-
ing the 3 May 1998 tsunami in the Philippine Sea
(Mw 7.5), which was recorded in some Japanese
costal sites such as Naha and Ishigakijima. Based
on these observations, a large subduction earth-
quake offshore the Philippines is likely to generate
damage along the southern coast of Japan, and
hence, possible tsunami hazards for southern Japan
from submarine earthquakes offshore the Philip-
pines need to be considered.
7. Conclusions
The El Salvador tsunami of 27 August 2012 and
the Philippines tsunami of 31 August 2012 were
studied using 25 sea level records of these tsunamis
and numerical modeling of tsunami waves. The main
findings are as follows:
1. Among the analyzed sea level records for the El
Salvador tsunami, the largest wave height was
observed in Baltra (71.1 cm) at a distance of about
1,400 km from the tsunami source. Near-field
stations of La Union and Acajutla recorded wave
heights of 4.5 and 12.5 cm, respectively. Numer-
ical modeling showed that most of the tsunami
energy is directed towards the Galapagos Islands
(including the Baltra sea level station), and
possibly this is the reason for observing the
maximum wave height of this tsunami in Baltra.
Fourier and wavelet analyses revealed that the
main tsunami peak periods are around 9 and
19 min for this tsunami, and the 45-min peak
observed at some stations does not represent the
tsunami source. The 9-min signal seems to be the
main tsunami signal, as it was observed in many
sea level spectra.
2. For the Philippines tsunami, the maximum wave
height was observed at the Kushimoto station
(30.5 cm), a Japanese tide gauge station located
2,700 km away from the source. Legaspi tide
gauge station located in the near-field recorded a
wave height of 4.2 cm. Relatively large wave
heights were observed at tide gauges located along
the coast of Japan. Numerical modeling showed
that tsunami waves were funneled towards the
southern coast of Japan. Numerical modeling also
revealed that most of the Philippines tsunami
energy was confined within the Philippine Sea
Figure 8
Sketch showing an approximation of the source location of the
Philippines tsunami of 31 August 2012 (rectangle), and the first
tsunami signals traveling towards the tide gauges located normal
(e.g., Chichijima and Wake Island) and parallel (e.g., Legaspi) to
the strike of the tsunami source. Wand Lrepresent width and
length of the tsunami source, respectively. kis the tsunami
wavelength. Solid circles show the locations of the tide gauges
Analysis of the El Salvador and Philippines Tsunamis of August 2012
region. The main tsunami peak periods were
estimated at around 8, 12 and 29 min. The
strongest signal was at the period of around
12 min, as it was more common on the examined
sea level spectra.
3. A connection was made between tsunami govern-
ing periods and source dimensions using wavelet
analysis. Results may suggest that the dominant
period of the first wave at stations normal to the
fault strike usually reflects the fault width, while
the period of the first wave at stations in the
direction of fault strike most probably reflects the
fault length.
Acknowledgments
The sea level data used in this study were provided
through the USA National Oceanographic and Atmo-
spheric Administration (NOAA), and UNESCO
Intergovernmental Oceanographic Commission
(IOC). We express our sincere gratitude to our
colleagues from the sea level data centers at both
NOAA and IOC for their invaluable efforts regarding
the preparation, processing and timely supply of sea
level data which has greatly contributed to tsunami
science in the last decade. Figure 1 was drafted using
the GMT software (WESSEL and SMITH 1991). The
wavelet package by TORRENCE and COMPO (1998) was
used in this study. This article benefitted from
detailed and constructive reviews from two anony-
mous reviewers, for which we are sincerely grateful.
We would like to thank Dr. Hermann Fritz (Georgia
Institute of Technology, USA), the guest editor of this
issue, for his assistance during the revision process of
this article. This study was supported by the Alex-
ander von Humboldt Foundation in Germany and the
Japan Society for Promotion of Science (JSPS) in
Japan.
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Analysis of the El Salvador and Philippines Tsunamis of August 2012
