Research ArticleNeural Network-Based Laser Interferometer Compensation forSeismic Signal Detection

Kyunghyun Lee, Hyungkwan Kwon, and Kwanho You

Department of Electrical Engineering, Sungkyunkwan University, Suwon, Republic of Korea

Correspondence should be addressed to Kwanho You; khyou@skku.edu

Received 19 July 2017; Revised 18 September 2017; Accepted 4 October 2017; Published 22 February 2018

Academic Editor: Jesus Corres

Copyright © 2018 Kyunghyun Lee et al. This is an open access article distributed under the Creative Commons Attribution License,which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

We propose a seismic wave detection method in the frequency domain using a heterodyne laser interferometer, which is used inultraprecision fields as a displacement measurement device. In seismology, it is important to accurately measure seismic waves.To overcome the limited frequency range and low resolution of accelerometers and velocimeters and to enhance the precision ofseismic data analysis, we use the heterodyne laser interferometer as a seismic detection apparatus. We apply the data fusionalgorithm with the adaptive standard deviation ratio (ς) derived from the neural network to improve the laser interferometer’smeasurement precision. Moreover, by using the interferometric characteristics, we analyze the seismic data in the frequencydomain. To determine the location of the epicenter from the body wave propagation analysis, we apply the STA/LTA algorithmto the measurement data. The effectiveness of the proposed laser interferometric seismometer is shown through experiments tolocate the precise epicenter.

1. Introduction

An earthquake is a devastating but common natural disasteraround the world. To reduce and predict the damage causedby earthquakes, it is necessary to precisely measure and ana-lyze the seismic signal. Hence, the study of earthquakes hasbeen performed through various seismic analyses and predic-tions. Methods to analyze earthquakes include spectrumanalysis, magnitude measurement, intensity interpretation,and epicenter decision. The short-time average/long-timeaverage (STA/LTA) trigger algorithm is commonly appliedin microseismic monitoring systems and has gained signifi-cant increased interest. In the STA/LTA algorithm, the mostimportant factor for seismic wave analysis is to identify aseismic event that includes an external disturbance. Widelyused seismic measurement devices include seismic velocime-ters and accelerometers. These apparatuses detect seismicwaves based on force and pressure sensors. They can be clas-sified according to their measurable frequency range asshort-period, long-period, and broadband seismographs.

These apparatuses have defects such as limited frequencyrange and low resolution. Therefore, errors exist when calcu-lating the exact P- and S-wave arrival time.

To improve seismic analyses, Colak et al. [1] proposed anew P- and S-wave arrival time decision method. The dis-crete wavelet transform was used to analyze the change offrequency and energy in high frequency bands. As a result,P- and S-wave arrival time can be measured using a seriesof data windows. Hloupis and Vallianatos [2] suggested anearthquake early warning system, based on a redundantwavelet transform as a processing tool to rapidly estimateearthquake magnitude. The suggested algorithm strengthensthe ability to distinguish body waves from noise. Panagiota-kis et al. [3] proposed an automatic identification methodof P-phase arrival based on energy and frequency character-istics of the local maxima distribution. Moreover, the methodperforms a robust detection against the background noise ofseismograms. Baziw [4] proposed a robust seismic eventidentification algorithm by obtaining the optimal estimateof a possible seismic event based on the Rao-Blackwellized

HindawiJournal of SensorsVolume 2018, Article ID 6490861, 7 pageshttps://doi.org/10.1155/2018/6490861

particle filter and hidden Markov model. This enablesobtaining the real-time phase estimate and the quantified fre-quency content of seismic data.

In this paper, we propose an interferometric seismometerthat is based on a heterodyne laser interferometer and ana-lyze seismic data in the frequency range to estimate epicenterlocation. Using the orthogonal characteristic of two beamsfrom a laser head, the seismic signals are expressed as a formof intensity signal, which is represented as a trigonometricalfunction. Hence, the seismic signal can be detected usingthe laser interferometer. Each observatory has a differentexperimental environment since the observatory needs tobe located in various regions for the seismic signal measure-ment. The nonuniformity of measurement environment suchas temperature and humidity causes the measurement inac-curacy. To compensate for the environmental error thatresides in seismic measurement data using a data fusionmethod, we measure the displacement with two independentlaser heads set separately in opposite directions. Using theneural network, the standard deviation of errors is updatedadaptively according to the experiment temperature change.With the measured data sets, the environmental error isreduced by projecting the measured data onto the points onthe constraint set based on the ideal relationship betweenthe two interferometers [5, 6]. The compensated data areconverted into a signal in the frequency domain to extractthe P- and S-wave arrival times, which are used to calculatethe STA/LTA ratio. The difference between the two arrivaltimes leads to the determination of the epicenter location.

2. A Heterodyne LaserInterferometric Seismometer

To measure displacement, a heterodyne laser interferometeruses the phase difference caused by the Doppler effect. Theheterodyne laser interferometer system consists of a He-Nelaser head, a beam splitter, a polarization beam splitter, pho-todetectors, a moving mirror, and a fixed mirror. Figure 1shows the heterodyne laser interferometer seismic system.The electric fields are measured by detector X. Likewise, the

electric fields reflected by the fixed mirror and the movingmirror are measured by detector Y. The intensities obtainedby detectors X and Y are expressed as follows.

Ir ∝12

A2 + B2 + AB cos Δωt + ϕB − ϕA ,

Im ∝12

A2 + B2 + AB cos Δωt + ϕB − ϕA + Δϕ1

In (1), A and B are the magnitudes of the electric fieldsand ϕA ϕB are the initial phases of laser sources. The signalIr measured by detector X is the reference intensity, and thesignal Im obtained by detector Y is the measurement inten-sity. Δω is the difference between the frequencies of the twoorthogonal beams ω1 and ω2, and Δϕ is the phase differencecaused by the Doppler effect. We use a high-pass filter toeliminate DC components of the intensity signal Im. Theinitial phase values ϕA and ϕB are ignored to obtain phaseinformation. We obtain the AC signal of Im as follows.

Im,AC ∝ AB cos Δωt + Δϕ 2

To obtain the phase value, we use a lock-in amplifier. Thephase value is derived by applying the Ir and Im,AC signalsinto a power divider, multiplier, and low pass filter, sequen-tially. As a result, two orthogonal intensity signals of Ix ∝Im,AC ⋅ Ir and Iy ∝ Im,AC ⋅ Irejπ/2 can be represented as a trig-onometric function.

Ix ∝AB2

cos Δϕ ,

Iy ∝AB2

sin Δϕ3

By using an inverse trigonometric function, the phaseinformation Δϕ related to the displacement is obtained. Wecalculate the displacement change using Δϕ = 4πρΔL/λ. ρ isthe refractive index, λ is the average wavelength, and ΔL isthe difference in optical path length between the fixed mirrorand the moving mirror.

Fixedmirror

Polarizationbeam splitter Moving

mirror

Seismic wavedetectionBeam

splitterLaser head

Detector X Detector Y

Figure 1: Seismic measurement system based on heterodyne laser interferometer.

2 Journal of Sensors

3. Data Fusion-Based Error Compensation

The environmental error causes a significant problem of ameasurement accuracy in case of the nanoscale instrument[7]. In order to improve measurement precision, we use adata fusion method to reduce the error that exists in the mea-surement data. Data fusion uses two measurement data sets,which in this study are obtained by two laser systemsinstalled separately in opposite directions. To utilize thismeasured data as a seismic signal, we compensate the errorto improve the interferometer’s accuracy [8].

We use two independent laser heads, which have thesame performance characteristics, for the data fusionmethod. The two separate laser interferometers measurethe same moving mirror with a displacement of d1 and d2,respectively. In the ideal case, the displacement d1 andd2 should satisfy the following constraint, because the twolaser interferometers measure the identical moving mirrorin the opposite direction. When we measure the displace-ment, the data includes environmental errors since envi-ronmental conditions are not uniform. Therefore, themeasurement values (d1, d2) do not satisfy the ideal con-straint of d1 k + d2 k = 0.

We can represent the relationship between d1 and d2 inthe Cartesian coordinate, where d1 and d2 are distributedaround the constraint of d1 k + d2 k = 0. These patternsshow that the measured displacement data contains environ-mental errors. We project the measured points in the Carte-sian coordinate onto the points on the ideal constraint line tocompensate for the environmental errors. An objective errorfunction is utilized to minimize the environmental error.

Je =12〠N

k=1Ix k − I∗x k 2 + Iy k − I∗y k

24

Here, Ix and Iy are measurement signals that containenvironmental error, while I∗x and I∗y are reference signalswithout environmental error.

Even though the standard deviation is calculated for eachmeasurement step, a compensation parameter (ς) representsone of the values derived under the fixed environment. Toimprove measurement accuracy, it is necessary to adaptivelymodify ς by considering temperature change, which is one ofthe primary environmental error factors. To estimate theadaptive standard deviations, a multilayer neural networkis used. The network is composed of one input layer, twohidden layers, and one output layer. The neurons in the hid-den layers and the output layer follow the hyperbolictangent-sigmoid function f1 x and the log-sigmoid functionf2 x as an activation function, respectively. The activationfunctions enable the neural network to obtain a complexnonlinear model.

f1 x =ex − e−x

ex + e−x,

f2 x =1

1 + e−x

5

The backpropagation algorithm is applied to train andupdate weights in the network. The steepest gradient descentmethod is used during the training period. As a target vector,we obtain the error between the reference signals and themeasurement signals.

VT =Ix − I∗x

Iy − I∗y Itp k =τ6

Here, Itp k = τ is the temperature value during themeasurement process. The intensities from (3) are usedas the inputs of the neural network during the trainingperiod. We define VI = Ix, Iy, Itp

T as an input vector and

VO = eIx , eIyT as an output vector. The objective function

uses the errors between the output from the neural networkand the target vector, VT:

E =12〠N

k=1VT k −VO k 2, 7

where m is the amount of sampled data. Weight values arecalculated with a steepest gradient descent method andupdated until minimizing the objective function.

wk+1j =wk

j − η∂E∂w

8

Here, η is a learning rate and −∂E/∂w is calculated usingthe chain rule. To guarantee a reliable performance, the errorbound of the objective function is set as 10−9. The maximumnumber of the training iterations is limited to 10,000 timesfor computational efficiency. Finally, we get the neural net-work modeled in Figure 2.

The estimated error vector eNN = eIx , eIyT associated

with temperature is obtained from the neural network byapplying measurement signals (Ix, Iy) and temperature (Itp)as an input vector.

eIx , eIyT= NN Ix, Iy, Itp 9

The adaptive standard deviations σ∗1 , σ∗2 are calculated

for each measurement step with the neural network output,eIx , eIy . The loci of the ellipsoidal equation with a centroid,

d1 k , d2 k , and the contact points between xm2 + xm1 = 0and each ellipse can be represented as follows:

xm1 − d1 k2

σ∗1 k 2 +xm2 − d2 k

2

σ∗2 k 2 = 1,

d∗1 k = ±ζ2kd1 k − d2 k

1 + ζ2k,

d∗2 k = ∓ζ2kd1 k − d2 k

1 + ζ2k10

3Journal of Sensors

Here, ζk is the adaptive standard deviation ratio,ζk = σ∗

2 k /σ∗1 k . Finally, the environmental error is com-

pensated by using the adaptive data fusion based on anartificial intelligence projection method.

4. Seismic Data Analysis and STA/LTA Algorithm

To detect the seismic wave, we use the heterodyne laser inter-ferometer system. Using the above equations, we eliminatethe environmental error by the data fusion method, enablingmore precise measurement of the seismic wave. With theseismic data, we obtain P-S wave arrival time (P-S time),which is an important factor for calculating the epicenterlocation. The methods that measure P-S time generally ana-lyze seismic data in the time domain. However, if the ampli-tude of a seismic wave does not change enough during themeasurement interval, it is difficult to distinguish betweenP-wave and S-wave arrival [9]. Hence, we suggest a P-S timemeasurement method in the frequency domain to moreaccurately identify the arrival times of P-wave and S-waves.

When we detect the seismic wave with a laser interferom-eter, the seismic signal can be expressed in terms of the inten-sity of the laser signal in a trigonometric function. Theequation can be represented as follows:

Ix ∝AB2

cos Δϕ ,

Iy ∝AB2

sin Δϕ11

In (11), Ix and Iy are the intensity signals after applyingthe data fusion method to Ix and Iy in (3). As the refractiveindex n and wavelength λ are constants, the change in seis-mic wave movement, ΔL, is proportional to the phasechange, Δϕ. Therefore, the frequency data of the phase signalΔϕ is obtained by the polarity change of the seismic signal,

and the Ix and Iy signals are both suitable for frequency anal-ysis. However, the Iy signal is used to analyze the seismicwave as a sinusoidal wave to avoid a latent effect of nonline-arity [10]. The signals are measured in a discrete form. Thefrequency can be calculated from the signal’s polarity changewith the following equation.

sgn Iy k ⋅ sgn Iy k + 1 < 0 12

Here, sgn ⋅ is the signum function. The final frequencyvalue is represented as f c k =Nc k /2. f c k is the frequencyof the incoming intensity signal, and Nc k is the number ofIy k sign changes in one second. Using this method, we canmeasure the seismic signal in the frequency domain.

An earthquake’s epicenter can be determined using thefrequency variation of Iy k measured by the heterodynelaser interferometer. We analyze this data with the STA/LTA ratio to calculate P-S time. With a threshold triggeralgorithm, we can enhance the analyzing accuracy of seismicdata. The STA/LTA algorithm parameters, such as short-time window size, long-time window size, and thresholdvalue, are determined by the seismic system environment.The STA/LTA algorithm analyzes the data using the differ-ence between STA and LTA characteristics. Finally, we com-pare the measured STA/LTA ratio with the threshold value.The accuracy of the analysis data depends on the STA andLTA window sizes and threshold value. The STA and LTAare represented as follows [11–13].

Sv n =1τs

〠n

k=n−τs

f c k ,

Lv n =1τl

〠n

k=n−τl

f c k

13

Here, τs and τl are the size of the short- and long-timewindows, respectively. We measure the time when the

S1 I1 S1

Sn

Ix

eIx

eIy

Iy

Itp

Yn Sn Zn

Y1 S1 Z1

S1 O1

S2 O2

S2 I2

S3 I3 S5 Y5 S15 Z15

Input layer Hidden layer Output layer

p11 q11

r11

r12

rn1

rn2

r151

r152

q115

q51q5nq515

p15

p21

p25

p35

p31

p1n q1n

qnn

qn1

qn15

p2n

p3n

Figure 2: Neural network model to compensate for the environmental error.

4 Journal of Sensors

STA/LTA ratio becomes greater than the threshold value.The distance between a seismological observatory and anepicenter is calculated using measured P-S time by thefollowing equation.

D =VPVSVP − VS

Tps 14

Here, D is the epicentral distance, VP is the P-wavevelocity, VS is the S-wave velocity, and Tps is the P-S time.

5. Performance Evaluation

In this section, we show the performance of the proposedseismic detection system based on a heterodyne laserinterferometer. To prove the performance and effectivenessof the interferometric seismometer, we use measured seis-mic data detected by the laser interferometric seismometerand the accelerometer, respectively. We use the He-Nelaser head with an intermode beat of 632.9912 nm (Wave-tronics: WT307B). The laser head emits two-frequencybeams of λ1 =632.9912576nm for vertical polarization andλ2 =632.9912604 nm for horizontal polarization, respec-tively. The linear stage (PI: M531.5IM) is used as a vibra-tional source to generate a seismic signal. An accelerometer

(Mitutoyo: JEP-8A3) is used as a reference. Figure 3 showsthe seismic wave measurement system.

First, we prove the environmental error compensationby data fusion method for the measurement precisionenhancement in a laser interferometer. In our simulation,we set the wavelength λ as 632.9912 nm and the refractiveindex as 1.00000026653516. Figure 4 shows the compen-sated data by the data fusion algorithm. The thick lineand thin line represent the compensated seismic data andthe measurement seismic data, respectively. To verify theaccuracy of compensated seismic data using the data fusionin Figure 4, we compare the root-mean-square (RMS) ofthe compensated measurement error with the uncompen-sated one. The RMS error comparison results appear inFigure 5. The environmental errors that occurred in theseismic signal detection are compensated by data fusion.Figure 6 shows the seismic data measured by the laserinterferometric seismometer and the accelerometer, respec-tively. Figure 7 denotes the difference between the trueamplitude and the measurement value at each samplingtime. The thick solid line represents the RMS error of the

Laser headPBSAccelerometer

Stage

Photodetector

Figure 3: Laser interferometric seismometer.

0 5 10 15Times (sec)

20 25

2

1.5

1

0.5

0

−0.5

−1

−1.5

−2

Am

plitu

de (m

m/s

2 )

MeasurementCompensation

Figure 4: Seismic data compensation with data fusion.

0 5 10 15 20 25Time (sec)

RMS

erro

r (m

m/s

2 )

0.07

0.06

0.05

0.04

0.03

0.02

0.01

0

MeasurementCompensation

Figure 5: RMS of displacement error.

AccelerometerLaser interferometer

5 10 15 20 250Time (sec)

−1.5

−1

−0.5

0

0.5

1

1.5A

mpl

itude

(m/s

2 )

Figure 6: Seismic data detection by interferometric seismometerand accelerometer.

5Journal of Sensors

compensated interferometric seismometer amplitude data.The thin dotted line means the RMS error measured froman accelerometer. As shown in this figure, the proposedneural network-based compensated seismic wave is moreprecise than the measurement of accelerometer.

Figure 8 shows the intensity signal Iy k of the seismicwave and the signal in a time-frequency plane measured bythe interferometric seismometer. We obtain the intensity sig-nal (Iy) to minimize the nonlinearity error. The displacementchange of the seismic wave is measured from the phase differ-ence between Ir and Im of the heterodyne interferometer. Toanalyze the seismic data, we represent the seismic signal in atime-frequency plane and observe sudden frequency changesaround 6 and 12 seconds, which are generated by P-wave andS-wave, respectively.

We use the STA/LTA algorithm to measure P-S time forcalculating the epicenter location. First, we determine theSTA and LTA window size. The LTA window size is setas 14 times the STA. Next, the threshold value used for theP-wave and S-wave arrival time is set as 1.3 times the averageof the STA/LTA ratio. The STA/LTA ratio and the thresholdvalue are shown in Figure 9.

From the STA/LTA ratio in Figure 8, we measure P-waveand S-wave arrival time as 5.66 and 12.71 seconds, respec-tively. With the P-wave velocity and the S-wave velocity as8 km/s and 4 km/s, respectively, we calculate the epicentraldistance as 24.20 km using (14). Figure 10 shows the epicen-ter location. ne means the maximum absolute value of theenvironmental noises. We suppose the parameter ne as0.05m/s2 in Figure 10. The distance from the observatoryto the epicenter is measured by the STA/LTA algorithm.

With three distinct sets of observatory data, we canestimate the epicenter location in the overlapping region.Table 1 shows the RMS error comparison of epicenter local-ization method based on the laser interferometric seismome-ter and accelerometer. Although the localization accuracy is

5 6 8 10 12 14 16 18 20 22 24 26Time (sec)

AccelerometerLaser interferometer

00.10.20.30.40.50.60.70.8

RMS

erro

r (m

/s2 )

Figure 7: RMS error comparison between a laser interferometerand accelerometer.

0 5 10 15 20 25Time (sec)

0 5 10 15 20 25Time (sec)

0

5

10

15

20

25

30

35

Freq

uenc

y

−1

−0.5

0

0.5

1

Inte

nsity

of l

y

Figure 8: Intensity and frequency variation of the seismic signal.

STA/LTA

5 10 15 20 250Time (sec)

012345678

STA

/LTA

Figure 9: STA/LTA ratio.

Observatory 1Observatory 2

Observatory 3Epicenter

100 150 200 250 30050Distance (km)

0

50

100

150

200

Dist

ance

(km

)

Figure 10: Epicenter location.

6 Journal of Sensors

decreased as the parameter ne increases, we can confirm thatthe localization result based on the laser interferometric seis-mometer shows better performance than accelerometer.

6. Conclusion

In this paper, we proposed a seismic signal detection methodusing a heterodyne laser interferometer in the frequencydomain. We applied the data fusion algorithm to minimizethe objective error function. To prove the performance ofthe interferometric seismometer, we compared seismic datameasured by a laser interferometric seismometer with datadetected by an accelerometer. Moreover, we measured theseismic signal data in the frequency range with the laserinterferometer. Using the STA/LTA algorithm, the P-S timewas derived. The epicentral distance was calculated usingthe measured P-S time. We confirmed the effectiveness ofthe laser interferometer-based seismometer through simula-tion and experiment.

Conflicts of Interest

The authors declare that they have no conflicts of interestregarding the publication of this paper.

Acknowledgments

This work was supported by the National Research Founda-tion of Korea (NRF) grant funded by the Korea government(MSIP) (NRF-2016R1A2B4011369).

References

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[2] G. Hloupis and F. Vallianatos, “Wavelet-based rapid estima-tion of earthquake magnitude oriented to early warning,” IEEEGeoscience and Remote Sensing Letters, vol. 10, no. 1, pp. 43–47, 2013.

[3] C. Panagiotakis, E. Kokinou, F. Vallianatos, and P. Automatic,“Automatic P-phase picking based on local-maxima distribu-tion,” IEEE Transactions on Geoscience and Remote Sensing,vol. 46, no. 8, pp. 2280–2287, 2008.

[4] E. Baziw, “Real-time seismic signal enhancement utilizing ahybrid Rao-Blackwellized particle filter and hidden Markovmodel filter,” IEEE Geoscience and Remote Sensing Letters,vol. 2, no. 4, pp. 418–422, 2005.

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[7] S. G. Gevorgyan, V. S. Gevorgyan, H. G. Shirinyan, G. H.Karapetyan, and A. G. Sarkisyan, “A radically new principleof operation seismic detector of nano-scale vibrations,” IEEETransactions on Applied Superconductivity, vol. 17, no. 2,pp. 629–632, 2007.

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Table 1: RMS error comparison for various environmental errors (ne).

MeasurementRMS error (km)

ne = 0 05 ne = 0 07 ne = 0 1 ne = 0 15 ne = 0 2Laser interferometric seismometer 2.54 2.81 4.27 5.83 7.19

Accelerometer 4.18 5.22 7.19 9.45 13.21

7Journal of Sensors

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