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:

xuqiang_68@126.com

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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