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Using Hilbert–Huang Transform (HHT) to Extract Infrasound Generated by the 2013 Lushan
Earthquake in China
X. ZHU,1 Q. XU,1 and H. X. LIU1
Abstract—We applied the Hilbert–Huang transform (HHT)
method to extract the infrasound generated by the 2013 Lushan
earthquake and its following aftershocks in China from a nearly
continuous infrasound recode made 130 km from the earthquake
epicenter. An improved STA/LTA algorithm was adopted for
detecting the ambient infrasonic events from the data record. A
powerful processing technique for non-stationary signal, the HHT,
was applied to extract the significant intrinsic mode functions
(IMFs) of the infrasonic signal associated with the earthquakes.
The features of the extracted IMFs, such as the dominant fre-
quency, the maximum amplitude and the spectral entropy, were
investigated using Hilbert spectral analysis. Regression analysis
between the maximum amplitude in the infrasound spectra and the
magnitudes of the earthquakes was carried out to verify the source
of the infrasound events detected. The results demonstrated that the
HHT method could successfully identify the infrasound related to
the earthquakes.
Key words: Earthquake acoustic, STA/LTA, Hilbert–Huang
transform, features extraction.
1. Introduction
Earthquake generates infrasound—inaudible
sound below the ‘‘normal’’ frequency limit of
human hearing of 20 Hz. The low-frequency char-
acteristics allow infrasound to cover long distances
and bypass obstacles with little dissipation of
energy (Zhu et al. 2013b). Infrasound has been
used in detecting snow avalanches (Scott et al.
2007), volcanic explosions (Green 2005; Green and
Neuberg 2005; Johnson 2007), debris flows (Ko-
gelnig et al. 2014) and other geo-hazards.
Earthquake infrasound has been investigated by
numerous authors. Motion along faults generates
seismic waves, which cause sudden strong vertical
ground displacements. The cyclic ground surface
motions make the air pressure vibrate, and so
radiate infrasonic waves (Krasnov et al. 2011; Le
Pichon et al. 2005a). To date, three possible seis-
mic generation mechanisms of infrasound are
suggested (Kim 2004; Le Pichon et al. 2005b;
Mutschlecner and Whitaker 2005a):
(a) local infrasound waves generated at the infra-
sound monitoring station far from the epicenter
by the vertical strong motion of the seismic
waves—these may involve both wave propaga-
tion and pressure vibration associated with
ground motion;
(b) epicentral infrasound waves generated in the
atmosphere by strong ground motion in the
epicentral region (Kim 2004; Mikumo 1968);
and
(c) diffractive infrasound radiated by topography
when seismic surface waves travel through
mountainous regions (Arrowsmith et al. 2012;
Kim 2004).
On April 20, 2013, an earthquake of Ms 7.0 and
a series of aftershocks struck Lushan County in
Sichuan Province, SW China (Wen and Ren 2014;
Zhu et al. 2013a). More than 30 infrasound events
associated with this main shock and aftershocks
were recorded by infrasound monitoring equipment
about 130 km from the epicenter. Fast Fourier
Transform (FFT) methods are often used to study
the dynamic spectra of infrasound (Mutschlecner
and Whitaker 2005b; ShiNan et al. 1977; Zhu et al.
2014). This method is effective when the signal is
1 State Key Laboratory of Geohazard Prevention and
Geoenvironment Protection (Chengdu University of Technology),
Chengdu 610059, Sichuan, People’s Republic of China. E-mail:
Pure Appl. Geophys. 174 (2017), 865–874
� 2016 Springer International Publishing
DOI 10.1007/s00024-016-1438-1 Pure and Applied Geophysics
stationary and has a good signal-to-noise ratio
(SNR). However, for non-stationary infrasonic
signals in which all frequency components need to
be analyzed across all moments in time, the FFT
method is inadequate and cannot meet requirements
for precision (Wang et al. 2009). Until now,
wavelet transform has been a good non-stationary
data analysis method, but it may also prove to be
inadequate because the wavelet transform is
essentially an adjustable window Fourier transform.
The main defect of wavelet transform (WT) cannot
be overcome: low frequencies have good frequency
resolution but bad time resolution; and high fre-
quencies have good time resolution but bad
frequency resolution. Although wavelet methods
are suitable for analyzing non-stationary data with
frequency changes, its non-locally adaptive
approach introduces computational leakage which
spreads the apparent energy content over a wider
frequency range (Lin and Chu 2012).
The Hilbert–Huang transform (HHT) is a time–
frequency analysis technique for nonlinear and non-
stationary signals. It consists of empirical mode
decomposition (EMD) and Hilbert spectral analysis
(HSA) (Huang et al. 1998; Klionski et al. 2008; Shijie
et al. 2011). It is used to filter and de-noise non-
stationary signals through decomposition and recon-
struction based on the empirical mode
decomposition. The time–frequency features of sig-
nals are investigated with high resolution in both
frequency and time using HSA. This spectrum
method is convenient for discovering hidden ampli-
tude and frequency modulations in signals and
finding domains of energy concentration (Klionski
et al. 2008). The HHT method can be more precise
than the Fourier transform and wavelet transform
methods for analysis of time–frequency localization
(Shijie et al. 2011).
The rest of the paper is organized as follows: a
description of the infrasound dataset associated with
the Lushan earthquake and its aftershocks, the auto-
matic infrasonic event detecting approach and the
HHT-based feature extraction method are presented
in Sect. 2; the results and discussion are presented in
Sect. 3 and, finally, our conclusions are presented in
Sect. 4.
2. Infrasonic Monitoring, Dataset and Methods
2.1. Infrasonic Monitoring
The work principle of the infrasonic sensor is that
it measures capacitance changes caused by acoustic
pressure fluctuations rather than the mechanical
shaking recorded by a regular seismometer. The
capacitance variations generate a proportional volt-
age signal which is recorded continuously. The
infrasonic sensor has a flat and wide frequency
response from 0.0001 to 100 Hz, and the output of
the sensor is filtered between 0.01 and 20 Hz, and
digitized at a sampling rate of 100 Hz.
2.2. Dataset
At 00:02:46 UTC on April 20, 2013, a destructive
earthquake (Ms = 7.0) occurred at Lushan County,
Sichuan Province, China, which was the most
powerful earthquake in this province since the 2008
Wenchuan earthquake (Tao 2014). The local infra-
sonic events, associated with the earthquake and its
aftershocks with magnitude Ms C 3.0, were recorded
by a continuous digital infrasonic monitoring system
and were identified via an automatic detecting
method by the morning of April 22, 2013. Electricity
failure caused by the very severe earthquake, how-
ever, led to a continuity break in the recorded
infrasound and the loss of about 52 aftershock-
associated infrasonic events.
2.3. Improved STA/LTA Algorithm for Detecting
Infrasonic Events
Infrasonic signals are recorded continuously,
making manual identification of a large number of
infrasonic pulse events very time-consuming task. A
common method to detect the advent of a given phase
is to compute certain attributes or ‘‘characteristic
functions’’ (CF), which are devised to identify the
occurrence of signal changes, by calculating average
values within two time windows of different sizes: a
short-term average (STA) and a long-term average
(LTA) (Sabbione and Velis 2013). Short-term values
are sensitive to rapid changes in the amplitude of a
866 X. Zhu et al. Pure Appl. Geophys.
time series, and long-term values measure the local
background amplitude.
We adopted an improved STA/LTA algorithm,
proposed by Sabbione (Sabbione and Velis 2013), to
detect the occurrence of infrasonic events. This STA/
LTA method is based on the classical approach of
Allen (1978), where
CFi ¼ y2i þ Ciðyi � yi�1Þ2; ð1Þ
and,
Ci ¼Rik¼1
Rik¼1 yk � yk�1j
; ð2Þ
where yi is the ith sample of the signal. Then, CFi is
averaged within two consecutive moving windows of
length NSTA and NLTA, respectively, with
NLTA[NSTA. Thus, the STA/LTA ratio is obtained
by means of
STAi
LTAi
¼1
NSTARiþNSTA�1
k CFk
1NLTA
RiþNLTA�1
k CFk
; ð3Þ
where NSTA and NLTA are the corresponding lengths
of the non-overlapping windows. To avoid rapid
fluctuations that may lead to wrong picks, the results
are smoothed. As shown in Fig. 1, this improved
STA/LTA method is sensitive to the occurrence of an
infrasonic event. The arrival times of infrasonic
events are picked at the local maxima of the
smoothed STA/LTA curve, as shown in Fig. 1c.
2.4. Feature Extraction Using the Hilbert–Huang
Transform
Figure 2 shows the flowchart of HHT-based
feature extraction of infrasonic signal. Firstly, with
aim to solve the mode mixing problem, a noise-
assisted data analysis method called ensemble empir-
ical mode decomposition (EEMD) (Chen and Wang
2012; Wang et al. 2012) is adopted as the key part of
the improved HHT algorithm to decompose the
original signal into a collection of intrinsic mode
functions (IMFs). The EEMD method is a self-
adaptive and data-driven decomposition algorithm
that uses local characteristics in the time domain of
the data. As a result of this process, the original signal
x (t) can be represented as follows:
xðtÞ ¼ Rni¼1IMFiðtÞ þ rðtÞ; ð4Þ
where n is the number of mode functions and r is the
final residual which can be interpreted as the direct
Figure 1Application of modified STA/LTA method to infrasonic events
auto-detection. a Infrasonic signals; b STA/LTA ratio and window
scheme. c Smoothed STA/LTA ratio curveFigure 2
Flowchart of HHT-based features extraction for infrasonic signal
Vol. 174, (2017) Using HHT to Extract Infrasound Generated 867
current (DC) component of the signal. The energy
proportion of each IMF in the original signal can be
calculated as follows:
Pi ¼Ei
Rni¼1Ei
¼RNk¼1 IMFiðkÞj2
��
Rni¼1R
Nk¼1 IMFj iðkÞj
2; ð5Þ
where i is the order of IMFs, N is the length of each
IMF ðk ¼ 1; 2; 3; . . .NÞ, and n is the total number of
IMFs. And then, the significant IMFs that represent
useful information of the original signal are selected
by comparing the proportion of energy to a prede-
fined threshold (Pth). The Pth can be defined
experimentally according to the objective data and is
usually selected as between 5 and 30% in practice
(Klionski et al. 2008). So, the significant component
of the original signal can be reconstructed by the sum
of IMFs selected. Figure 3 shows one example of the
significant IMFs selection based on the energy
proportion.
Finally, the selected significant IMFs are pro-
cessed using the Hilbert spectral analysis (HSA) to
obtain insight into the dominant time–frequency
features of the signal. Entropy is an effective way
to quantitatively evaluate the disorder of distribution.
The spectral entropy is calculated to investigate the
frequency distribution characteristics as follows (Fu
et al. 2015; He et al. 2013):
pi ¼Ai
RNi¼1Ai
ð6Þ
SEN ¼ �RNi¼1pi ln pi; ð7Þ
where Ai is the amplitude at the ith frequency point
and pi is the proportion of Ai in the summation of all
Ai. SEN is the spectral entropy.
The Hilbert spectrum is very suitable for process-
ing non-stationary signals, because it provides both
time and frequency information for signals (Fig. 4b).
From the time–frequency distribution image, the
characteristic frequency of infrasonic signals associ-
ated with an earthquake can be clearly identified.
Although wavelet analysis generally performs better
than Fourier analysis and can also provide both time
and frequency information of signals (Han et al.
2011), the Hilbert spectrum has higher frequency
resolution and energy concentration when compared
with the results of the Short-time Fourier Transform
(STFT) (Fig. 4c) and the Continuous Wavelet Trans-
form (CWT) (Fig. 4d).
3. Results and Discussion
3.1. Infrasonic Signal Corresponding to the Main
Shock
The Lushan earthquake occurred at 00:02:46 UTC
on April 20th, 2013. Figure 5 shows the EEMD
results of infrasonic signals from 00:00:00 UTC to
00:13:20 UTC generated by the Lushan earthquake
and its first two aftershocks. There were three
infrasonic events during the time range from
00:02:00 to 00:07:00 UTC, which included the main
shock and two aftershocks, according to the official
report of the China Earthquake Administration. As
shown in Fig. 5, three peaks may be distinguished
clearly from the second IMF and the third one after
performing EEMD to the original signal. Event �
indicates the first infrasonic event. The infrasonic
event � in the original signal shown in Fig. 5 is
clipped for about 80 s due to an outage of the digital
recording system because of the huge power of the
main shock. Excessive decomposition levels will
result in the accumulation of boundary errors, even
making EEMD lose its physical meaning. Therefore,
in order to avoid inaccurate decomposition, the
original signals were decomposed to ten IMF com-
ponents through our manual intervention based on theFigure 3
Significant IMFs selection on the basis of energy proportion
868 X. Zhu et al. Pure Appl. Geophys.
results of several trials. Events ` and ´ are also
identified from the decomposition results. The arrival
times of the three infrasonic events indicate that they
are probably local infrasound produced by coupling
of seismic wave and the atmosphere at the location of
the detection system. The event ˆ, however, is
probably the epicentral infrasound produced by the
main shock, because the duration between ˆ and � is
around 400 s, which is in accordance with the travel
time of the epicentral infrasonic wave at an average
velocity of 320 m/s over the detection distance of
130 km. There was no aftershock occurring around
this time according to the official reports.
Figure 6 shows the HHT-based processing and
analysis results of the event � and event ˆ. The top
panel shows the reconstructed signal on the basis of
the energy proportions of IMFs. The middle panel
shows the time–frequency distribution characteristics,
and the left panel shows the marginal spectra with
identification of the dominant frequency and the
maximum amplitude in this spectra. The frequency
spectrum of the local infrasound is clearly different
from the spectrum of the epicentral infrasound. The
energy of the epicentral infrasound is concentrated
around 0.68 Hz. It is noted that clipping may cause
frequency distortion. However, the significant
Figure 4Comparison of results between Hilbert–Huang transform (HHT), short-time Fourier transform (STFT), and continuous wavelet transform
(CWT) approaches. a Infrasonic signals; b Hilbert spectrum; c STFT spectrum; d CWT spectrum
Vol. 174, (2017) Using HHT to Extract Infrasound Generated 869
differences between the local infrasound and the
epicentral infrasound signals based on the EEMD
results can be readily identified qualitatively in this
study.
Furthermore, the differences between the local
infrasound and the epicentral infrasound are reflected
in both the time and the frequency domains. The
clipping problem of local infrasound may be a little
effect on the frequency content analysis of the first
local infrasonic event. But the amplitude and the
frequency of the epicentral infrasonic event are
obviously smaller than those of the local events in
the frequency domain. Additionally, the shape of the
epicentral infrasonic event envelope is different from
the shape of the local one in the time domain.
3.2. Infrasonic Signals Associated with Aftershocks
In total, 27 of the potentially 33 local infrasonic
events generated by the sequence of aftershocks with
magnitude Ms C 3.0 were identified using the STA/
LTA approach, and were analyzed according to the
work flowchart (Fig. 2). The accuracy of the auto
event detecting approach was about 81.8% based on
Figure 5Empirical mode decomposition of infrasonic signals associated with the Lushan main shock (�), two following aftershocks (` and ´) and one
epicentral infrasonic signal (ˆ). Note: the energy proportion of each IMF is calculated and presented on the right panel. Signal is plotted
beginning from April 20, 2013 at 00:00:00 UTC
870 X. Zhu et al. Pure Appl. Geophys.
the ratio of the number of detected events to the total
number of aftershocks in the recording period.
Figure 7 shows the characteristics of the observed
infrasonic signals associated with an aftershock
occurring on April 20, 2013 at 20:53:44 UTC. The
dominant frequency and the maximum amplitude in
the marginal spectrum (Fig. 7a) were 3.51 Hz and
0.7 Pa, respectively. The FFT-based amplitude spec-
trum of the same signal was also calculated. FFT has
a better calculation efficiency than HHT, but it only
provided the information in the frequency domain as
shown in Fig. 7b. Figure 7c, d also shows the wavelet
result and the STFT result for comparison. The
comparison indicates that HHT provides a higher
frequency resolution and better reflects the dominant
frequency components in both the time and the
frequency domains. Accordingly, 27 local infrasonic
events were processed and analyzed using the same
method.
As shown in Fig. 8a, the dominant frequency
distribution was evaluated using the bootstrap method
on the basis of the finite samples (Markus and
Groenen 1998). The bootstrap procedure involved
choosing random samples with replacement from a
data set and analyzing each sample in the same
manner. Sampling with replacement means that each
observation is selected separately at random from the
original dataset. In this study, 200 random selections
and observations were carried out using the MATLAB
function bootstrap(). The results show that the char-
acteristic frequencies of infrasonic signals associated
with aftershocks mainly concentrate in the range from
3.6 to 3.7 Hz, with a peak value of 3.63 Hz.
Because the local infrasonic event is induced by
the vertical component of the ground surface motion
when the seismic wave passes through the sensor, a
relationship between the infrasonic signals and the
corresponding aftershocks can be estimated. It was
anticipated that the energy of the corresponding
infrasound signal, like that from the seismic wave,
was determined by the seismic surface wave magni-
tude (Ms) because the earthquake sound/infrasound is
the coupling of the earth surface with the air. In this
study, to validate that the infrasound signals had been
produced by earthquakes, it was necessary to know
the possible relation between the infrasound signal
and the corresponding quakes. Therefore, the maxi-
mum amplitude in the Hilbert marginal spectrum was
calculated for all observed events. As shown in
Fig. 8b, the logarithmic relationship between Ms and
Ma was well estimated using regression analysis. The
correlation coefficient of 0.899 suggested that the
infrasound signals were highly related to the magni-
tudes of the observed aftershocks. Additionally, the
distribution of the spectral entropy of the local
infrasound signal observed was estimated using the
Figure 6HHT-based analysis results associated with the first/main earthquake: (a) spectral characteristics of the local infrasound; (b) spectral
characteristics of the epicentral infrasound
Vol. 174, (2017) Using HHT to Extract Infrasound Generated 871
bootstrap method and shown in Fig. 9. The dominant
entropy of the local infrasound signals associated
with aftershocks was about 4.62, while the spectral
entropy of the epicentral infrasound observed was
3.81. This may indicate that the marginal spectrum of
local infrasound signals had a broader distribution
than that of the epicentral infrasound signal. But we
will undertake further study of the epicentral infra-
sound based on more data to confirm this result. As
can be seen in Fig. 6, the characteristics of the
epicentral infrasound signal in both time and fre-
quency domains are different from those of the local
infrasound.
4. Conclusion
In this study, the HHT was employed to process
and analyze the measured infrasonic signals associ-
ated with the 2013 Lushan earthquake and its
aftershocks. An improved STA/LTA algorithm was
employed to identify the infrasonic events. It pro-
vided a detecting accuracy of 81.8%. The significant
IMFs representing the information of interest in the
original signal were extracted based on the results of
EEMD. The spectral characteristics were extracted
from the IMFs using Hilbert spectrum analysis. All
infrasonic signals associated with the aftershocks
Figure 7Analysis results of infrasonic event associated with one aftershock (Ms = 5.0). a HHT-based analysis result, and b FFT-based analysis result,
c CWT analysis result, and d STFT analysis result
872 X. Zhu et al. Pure Appl. Geophys.
were analyzed using the same method. Comparison
between the Hilbert marginal spectrum and STFT,
and CWV-based spectra showed that the frequency
bands of the marginal spectrum were narrower and,
therefore, had a better resolution than the FFT-based
spectrum. The relationship between Ms and Ma was
robust, and demonstrated that our sensors were
operating in the expected manner during the pass-
through of the seismic waves. Additionally, the
characteristics of the epicentral infrasound were dif-
ferent from that of the local infrasound. However, this
could be due to the effect of clipping. Future studies
will be conducted to confirm if there was an actual
frequency difference between the local and epicentral
infrasound, but robust conclusions cannot be derived
from the present dataset because of clipping.
Acknowledgements
This research was supported by the National Basic
Research Program (973 Program) (Grant No.
2013CB733200, 2014CB744703), the Young Scien-
tists Fund of the National Natural Science Foundation
of China (Grant No. 41502293), and Project sup-
ported by the Funds for Creative Research Groups of
China (Grant No. 41521002). We would like to
extend special thanks to Prof. Mauri Mcsaveney for
all his valuable suggestions in greatly improving the
quality of this paper.
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