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Abstract
A broadband optical fiber seismometer based on FBG resonator is proposed for earthquake monitoring. The principle and key technique, high-resolution ultralow-frequency wavelength interrogation by dual-laser swept frequency and beat frequency method, are discussed and analyzed. From the simulation and test results, the seismometer works at broadband range from 0.01 Hz to 10 Hz with a sensitivity of better than 330 pm/g and the wavelength resolution of the interrogation system is better than 0.001 pm/√Hz from 0.1 Hz to 10 Hz. A three-channel correlation method is used to measure the self-noise of the seismometer. It reaches a noise level of 2.7 × 10−7 ms−2/√Hz@0.1 Hz, which is lower than the earth’s background noise (the new high noise model, NHNM). An earthquake monitoring experiment is conducted in a low noise seismic station. The recorded seismic waves are analyzed, which suggests that the proposed seismometer has the ability to record the close microearthquake and distant great earthquake with a high signal-noise ratio (SNR). This is the first time that a FBG-based middle-long period seismometer with lower self-noise than NHNM and large dynamic range (100 dB) is reported.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Seismology method provides most of the information for earthquake monitoring and prediction [1]. However, with the development of urbanization and industrialization of human society, more and more environmental noise decreases the quality of the traditional seismic observation results. In order to eliminate the ground noise, downhole seismic monitoring becomes an alternative of earthquake monitoring in the future [2]. To achieve a high-precision, stable, and continuous observation in the deep well, many new problems, such as resistance to high temperature and high pressure, power supply, data collection and transmission, should be solved [3]. However, conventional seismographs including pendulum seismograph, moving-coil seismograph, and piezoelectric seismograph face a technical challenge in all of these areas [4].
Over the past two decades, fiber Bragg grating (FBG), FBG based Fabry-Perot interferometer (FBG-FP), π-phase-shifted FBG (π-FBG) and fiber laser are widely used for acceleration detection in the field of perimeter security, structural health monitoring and oil exploration, which show many advantages owing to their capability of real-time, in situ, sensitive strain measurement with low cost, small size, fast response and immunity to electromagnetic interference [5, 6]. They are usually designed as a FBG seismic geophone or an acceleration sensor by a certain physical structure model, such as cantilever and quality block-diaphragm, which usually works at the frequency range from 1 Hz to hundreds of Hz [7–10]. It is well-known that the main frequency of the nature earthquake signal is usually from 120 s (about 0.0083 Hz), even lower, to 10 Hz [11]. But because of the terrible low-frequency noise of the interrogation system, it is difficult to realize the high-resolution measurement of low-frequency seismic signal, especially the signals less than 0.1 Hz, for these FBG sensors.
So it is a key technique to promote the ultralow-frequency wavelength measurement resolution for the design of a FBG based broadband seismometer. In fact, a high-resolution low-frequency FBG resonator wavelength measurement system can be realized by using an absolute wavelength calibration device, such as H13C14N standard gas cells and optical frequency comb, and laser frequency-locking interrogation technique [12, 13]. But it is hard to multiplex multi-component sensors for these system. Besides, optical frequency comb is expensive and H13C14N standard gas cells are affected by ambient temperature so that they are not suitable for an on-site multi-components low frequency seismometer. Recently, different high-resolution FBG resonator static wavelength interrogation techniques based on narrow linewidth tunable laser and reference FBG resonator are reported [14, 15]. We also have done a lot of discussions about this system in our previous work [16–18]. But the reference FBG resonator, using for laser low-frequency noise compensation, increases the difficulty of designing the multi-components sensors. In addition, the reference FBG resonator is also sensitive to dynamic earthquake signal and ambient vibration noise and may lead to an error measurement of the seismic waves because of its additional response.
In this paper, we propose a broadband FBG resonator seismometer based on double-diaphragm acceleration model. A novel high-resolution ultralow-frequency wavelength interrogation technique based on a single FBG resonator by dual-laser swept frequency and beat frequency method is proposed. The principle and key technique are discussed and analyzed. The calibration method of the ultralow-frequency sensitivity is introduced. The test of the self noise of the FBG-FP seismometer are also first explored based on three-channel correlation method. An earthquake monitoring experiment was carried out in a low noise seismic station and the recorded seismic waves are analyzed.
2. Principle and key technique
2.1 Principle
The fundamental structure of the FBG resonator seismometer is based on second order spring-mass-damper acceleration model, which is shown in Fig. 1(a). The mass block is the equivalent of an inertial component. The FBG-FP and the component provide stiffness and damper. According to our previous report [19], we know that the dynamic sensitivity of the seismometer can be expressed as
where (Ma)0 is the sensitivity of the seismometer when the response frequency is much smaller than the natural frequency and normally called the static sensitivity (f = 0 Hz), f is the frequency of the acceleration load, f0 is the natural frequency of the seismometer, the damping coefficient , is the damping ratio determined by the damper of the vibration system, k = kb + kf, is the total elastic coefficient of the seismometer, kb is the total elastic coefficient of diaphragm, kf is elastic coefficient of fiber.
Fig. 1 The second order spring-mass-damper acceleration structure model (a), structural sectional view (b) of the FBG resonator seismometer.
From the formula (1), Figs. 1(a) and 1(b), the proposed seismometer consists of a FBG resonator (FBG-FP), a moving mass block, two diaphragms, two fixed end caps, a shell and a fixed support. The two diaphragms (diaphragm A and B), installed on the sensor shell through the fixed end cap, are working as the elastic element. The mass, which is installed between the diaphragms, has been enlarged to make the nature frequency lower to detect the low frequency earthquake signal. The FBG-FP is anchored at the fixed end cap and diaphragm B by fixing glue. When the seismic wave induces vibration of the stainless steel shell, the seismometer will have a center wavelength shift due to the axial strain induced by the inertial force of the mass. Then the seismic waves can be recorded by measuring the wavelength shift of FBG-FP. As a reasonable structure and parameter configuration, the seismometer can maintain a high dynamic sensitivity within a wide frequency band range.
2.2 Key technique
In order to detect the low-frequency earthquake signals using the proposed FBG-FP seismometer, a high resolution ultra-low-frequency wavelength interrogation system comes to be a key technique. In general, a reference FBG-FP resonator is used for compensating laser low-frequency frequency noise and achieving high-resolution low-frequency wavelength measurement [14, 15]. But the reference increases the difficulty of sensor design and may lead to an error measurement of the seismic waves because of its additional response.
Here, we proposed a novel high-resolution ultralow-frequency FBG-FP wavelength interrogation technique without reference FBG-FP by dual-laser swept frequency and beat frequency method. The schematic configuration of the interrogation system and the schematic diagram of wavelength detection process of the FBG-FP are shown in Figs. 2(a) and 2(b). Two narrow linewidth tunable fiber lasers with the same type (NKT E15) are used to interrogate the FBG-FP respectively through a light switch. The linewidth of the fiber lasers is less than 100 Hz. The fiber lasers offer a PM (Polarization Maintaining) output to ensure a fixed orientation of the polarization, which is important to get a high-stability beat frequency signal. A controller is used to control the two lasers and the light switch work synergistically. The principle is that the two fiber lasers are used for wavelength detection alternately. The beat frequency signal between the two fiber lasers are used for their wavelength drift compensation. The working process of the interrogation system can be understood in this way: (1) firstly, the La channel of the light switch is open and Lb channel is closed while the wavelength-scan laser 1 is used to detect the resonant peak of FBG-FP. Then we can get a set of data sequences of the FBG-FP reflectance spectra and the value of the FBG-FP wavelength change. (2) secondly, keep the wavelength of laser 1 return to start location and measure the frequency value of the beat signal between laser 1 and laser 2. (3) thirdly, keep the La channel closed and Lb channel open and use laser 2 to detect the resonant peak of FBG-FP. Then another set of data sequences of the FBG-FP reflectance spectra and another value of the FBG-FP wavelength change are obtained. Then the information of the wavelength change by the ambient temperature and strain can be obtained using the proposed algorithm. Each completion of these three steps is defined as one measurement cycle.
Fig. 2 The schematic configuration of the interrogation system (a) and the schematic diagram of wavelength detection process of the FBG-FP (b). ISO, isolator; CP, coupler; CIR, circulator; PC, polarization controller; PD, photodiode; A/D, analog-to-digital converter.
Here, it is assumed that the wavelength of the two fiber lasers will remain the same when the two fiber lasers complete one full wavelength detection process. Δλε,T represents the wavelength change of the FBG-FP resonance peak synthetically caused by the ambient temperature and strain. Δλ'ε,T represents the wavelength change of the FBG-FP resonance peak in next measurement cycle. The wavelength-scan period is set to 0.02 s (50 Hz) for every laser, the beat frequency measurement period is set to 0.01 s (100 Hz). So the total time to get one point of Δλε,T is 0.05 s, which means the sampling rate of the system is 20 S/s. During continuous measurement, the wavelength shifts (ΔλL1, ΔλL2) of the two lasers are changing because of their own frequency instability. However, we can calculate the values of Δλε,T without the influence of the frequency instability of the lasers through a simple ternary linear equations shown as below. That means ΔλL1 and ΔλL2 have no effect on the results of Δλε,T when the dual-laser swept frequency and beat frequency method is proposed to interrogation the FBG-FP.
where λ1 is the value of the FBG-FP wavelength measured by laser 1, λ2 is the value of the FBG-FP wavelength measured by laser 2, λB is the frequency value of the beat signal between laser 1 and laser 2. a, b, c is initial value of λ1, λ2, λB.In the proposed interrogation system, the proposed FBG-FP is formed by two identical high-reflectivity FBGs. The parameters of the FBG-FP are: nominal center wavelength 1550.000 nm, cavity length 14 mm, the 3 dB bandwidth and peak reflectivity of the FBGs are 0.6 nm and 99.3%. The free spectral range (FSR) and the bandwidth of the FBG-FP resonance peaks are 60 pm and 22.5 MHz (0.18 pm) respectively. Figure 3 is the picture and reflectance spectra of the FBG-FP by triangular wave frequency scanning method.
Fig. 3 The picture (a) and reflectance spectra (b), (c) of the FBG-FP. There are two reflection peak in (b) during a full triangular wave scanning period. (c) is a partial enlargement of (b).
We place the FBG-FP in a vacuum of vibration and sound isolation to measure the low frequency wavelength resolution of the proposed system. In this constant environment, we can ignore the effect of temperature in the short measurement period (10 minute). λB is acquired by Fig. 4(a) which is the beat frequency signals between laser 1 and laser 2 and measured using a high speed oscilloscope card (NI 5771). The FFT algorithm is carried out in a FPGA chip (NI 7972R). The sample rate of the beat frequency signals is set to 800 MHz and the size of the single FFT algorithm calculation is limited to 65536 in the NI 7972R with LabVIEW software, the ultima size of the single FFT calculation is set to 65536 to make the system have a highest frequency measurement resolution of 400 MHz / 65536 = 6.1 kHz (4.88 × 10−5 pm). Such a higher beat frequency measurement resolution is no longer main limit factor of system measurement resolution. Actually, the system measurement resolution is mainly limited by the wavelength resolution using the narrow linewidth tunable fiber lasers to detect the resonant peak of FBG-FP. Figure 4(b) represents the final time-domain noise level of the system within 5 minutes, which is calculated based on formula (2). Figure 4(c) is the power spectral density of Fig. 4(b). Because of the narrow bandwidth of FBG-FP resonance peaks, the dual-laser swept frequency and beat frequency measurement method, we can find that the proposed FBG-FP wavelength interrogation system reaches a very low noise level of −53.15 dB pm/√Hz@0.01 Hz and −60.35 dB@0.1 Hz from Fig. 4(c). According the definition (0 dB corresponding to 1 pm/√Hz), the noise levels of the interrogation system at 0.01 Hz and 0.1 Hz can be expressed as 0.0022 pm/√Hz and 0.00096 pm/√Hz. Because the noise level greater than 1 Hz is obviously lower than the one at 0.1 Hz, so the authors come to a conclusion that the noise level less than 0.001 pm/√Hz from 0.1 Hz to 10 Hz. The maximum detectable wavelength is 60 pm determined by the fast wavelength tuning range of the lasers. This suggests that the proposed system has a large dynamic range of 100 dB.
Fig. 4 The measurement results of the interrogation system: (a) the beat frequency signals between laser 1 and laser 2, (b) the final time-domain noise level of the system, (c) the power spectral density of (b).
3. Design, simulation and calibration of the FBG-FP seismometer
The diaphragm of the proposed seismometer is designed an equicohesive cantilever beam, shown in Figs. 5(a) and 5(b), whose length, width, thickness and Young modulus are defined as l, b, h, E respectively. Then we can get the elastic coefficient kb of the cantilever beam. Similarly, the elastic coefficient of the fiber can be calculated by the length L, cross-sectional area A and Young modulus Ef of the fiber. Then we can get the static sensitivity and the resonant frequency of the seismometer through the follow formula.
where Δx and a represent the displacement and acceleration of the moving mass block, λB is the original central wavelength of the FBG-FP, pe is elasto-optical coefficient.Fig. 5 The simulation analysis (a) and (b), the material properties and geometric parameter of the seismometer (c).
Equation (3) provides a guidance direction for the design and improvement of the FBG-FP seismometer. It can be found that ratio of the radius of the diaphragm and the contact radius of the mass and the diaphragm have significant influence on the sensitivity of the seismometer as well as the thickness of the diaphragm. The material properties and geometric parameters of the seismometer are shown in Fig. 5(c). The designed sensitivity of the FBG-FP seismometer is calculated to be about 330 pm/g. According to the wavelength noise level of with lower 0.001 pm, the FBG-FP seismometer reaches a noise level of better than 3.03 μg/√Hz (about 3.03 × 10−5 ms−2/√Hz) from DC – 10 Hz.
The calibration of the FBG resonator based seismometer was carried out according to DB/T 22-2007 (Calibration Standard of the Earthquake Seismograph in the People’s Republic of China). Shown in Fig. 6(a), a velocity-type vibrostand is used for applying incentive and an electronic velocity-type seismograph is used as a standard for comparative measurement. The test frequency range of the imposed velocity signal is from 0.001 Hz to 10 Hz whose upper limit is decided by the updata rate of the FBG-FP wavelength interrogation system. From the test results, Figs. 6(b) and 6(c), we can find that the seismometer has a sensitivity of 342 pm/g and a resonant frequency of 23 Hz. By the design of the reasonable structure and parameter configuration, the sensitivity of the proposed seismometer is about an order of magnitude higher than previous report [19].
Fig. 6 The calibration of the FBG-FP seismometer: (a) the actual picture of comparative measurement, (b) the measurement results of the frequency response and (c) the measured sinusoidal acceleration signal at 1 Hz, 0.1 Hz and 0.002 Hz from the vibrostand.
4. Self noise test and seismic response analysis
4.1 Self noise test
As one of the most important performance parameter, the self-noise of seismograph is usually measured at a quiet seismic station and calculated by a particular algorithm [20]. To get the actual instrument self-noise, the environmental disturbances and earth’s self-oscillation should be eliminated by signal processing. In the past, self noise is tested by two identical seismographs which have the same transfer function (according to DB/T 22-2007). But the transfer function of the FBG-FP seismometer system is difficult to obtain. Three-channel correlation analysis method can be used for measuring the self noise of the seismometer if we get its time-domain noise signal but don’t know its transfer function. The self noise autopower spectrum of the FBG-FP seismometer can be written [20]:
where i, j, k = 1, 2, 3 and i ≠ j ≠ k, Pii is the autospectra of the FBG-FP seismometer numbered as i, Pji, Pik, Pjk are the cross-spectra between the different two FBG-FP seismometers.The test of the self noise of FBG-FP seismometers is carried out at Bai Jiatuan National Seismostation of China which has a superior low noise level. Three identical FBG-FP seismometers connect to the same wavelength interrogation system which is more than 100 meters away from them to reduce the interference. The data update rate of the interrogation system is set to 20 Hz. Figure 7(a) is the on-site picture where three identical FBG-FP seismometer is installed together and keep the same direction. Figure 7(b) shows the comparison between the self noise autopower spectrum of the FBG-FP seismometer and the New High Noise Model (NHNM). We can see that the FBG-FP seismometer reaches a noise level of better than 3.0 × 10−7 ms−2/√Hz from 0.1 Hz – 10 Hz (2.7 × 10−7 ms−2/√Hz@0.1 Hz) which is lower than NHNM [21]. So the proposed seismometer can be used for actual earthquake monitoring.
Fig. 7 Self noise test: (a) on-site picture, (b) self noise autopower spectrum of the FBG-FP seismometer, noise level comparison between the proposed seismometer and the earth’s background noise.
According the reference [21], the noise level, below 0.05 Hz, increases exponentially caused by the noise characteristics of the earth itself. The low-frequency self noise level of a seismic instrument will be affected by the earth background noise and the ambient temperature simultaneously [22]. In the manuscript, the self noise of the proposed FBG-FP resonator seismometer is tested using three-channel correlation analysis method [20]. The earth background noise can be partly eliminated by the signal processing method. However, the effect of the earth background can’t fully eliminated in the test results of the self noise of the FBG-FP seismometer because of the limitations of the consistency of the sensors and the algorithm. In addition, the ambient temperature disturbance will lead to wavelength drift of the FBG-FP seismometer in low frequency band. So the self noise of the FBG-FP seismometer below 0.05 Hz is influenced by the noise characteristics of the earth itself and the ambient temperature instability.
4.2 Earthquake monitoring and seismic response analysis
The earthquake monitoring experiment was carried out in Laodian seismostation in Zhaotong city, Yunnan province, China. The scheme and installation photo is shown in Fig. 8. The sensor head is installed in the bedrock and are connected to the interrogation system by a 150 m long armored optical cable. In our experiment configuration, a GPS receiver is connected to a GPS timing and positioning equipment (NI 6683H) for acquiring the exact time when the seismic waves arrive. An electrical seismograph installed in the same seismic station was used for comparison.
Fig. 8 The scheme and installation site photo of the earthquake monitoring experiment by the proposed FBG-FP seismometer
Figure 9(a) shows recorded close nature microearthquake signals, whose magnitude is ML 1.2, from Ludian county of Yunnan province, China. The distance from the earthquake to the seismic station is within 35 kilometers. Because the noise level of the FBG-FP seismometer is lower than NHNM from 0.1 Hz – 10 Hz, we can find that the proposed seismometer has the ability to record the close high-frequency microearthquake with high SNR. The coefficient of correlation between the FBG-FP seismometer and the electrical seismograph reaches 0.997. In comparison to microearthquake detection, distant ultra-low-frequency great earthquake measurement not only need high enough sensitivity but also need wide enough working frequency band and low self noise in the whole band. The recorded distant great earthquake signals of two different sensors are shown in Fig. 9(b). Primary wave, shake wave, and surface wave are both clear to judge time difference for determining the distance of the earthquake. But the electrical seismograph shows higher SNR. Their coefficient of correlation is only 0.826 because of the rising self noise of the FBG-FP seismometer below 0.1 Hz. The SNR of the recorded close high-frequency ML 1.2 microearthquake signal is higher than the one of the recorded distant ultra-low-frequency ML 6.7 great earthquake signal. The reasons can be explained in this way. The main frequency of the close high-frequency microearthquake is high and the acceleration energy to the seismometer is large. In the meantime, the proposed seismometer has a low noise level at high frequency band. So the SNR of the recorded close high-frequency ML 1.2 microearthquake signal is high. On the contrary, the main frequency of distant great earthquake signal is very low and the acceleration energy to the seismometer is greatly weakened. And the proposed seismometer has a high noise level at low frequency band. So he SNR of the recorded distant ultra-low-frequency ML 6.7 great earthquake signal is obviously lower than the one of the ML 1.2 earthquake signal. In order to solve this problem, the low-frequency noise level should be further reduced in the future work.
Fig. 9 The recorded close microearthquake signals and distant great earthquake signals: (a) Ludian Country magnitude ML1.2 earthquake within 35 kilometers, (b) Aketao Country magnitude ML 6.7 earthquake over 3000 kilometers from the Laodian seismic station, Zhaotong City, Yunnan Province, China.
An higher wavelength interrogation technique and more stable temperature environment will be helpful to improve the performance of the FBG-FP seismometer. Actually, the measurement resolution of the FBG-FP seismometer system can be improved by reducing the wavelength scan range of laser, which means sacrificing dynamic range of the system. In the future, we can also use the dual-laser lock frequency and beat frequency technique to improve the measurement resolution.
5. Conclusion
This paper reports a FBG-FP seismometer for earthquake monitoring. A novel high-resolution large-dynamic ultralow-frequency FBG-FP wavelength interrogation technique without reference is proposed. Not only can the proposed method solve the problem of the terrible low-frequency noise of the lasers, but also it can eliminate the influence of the additional response of the reference. The principle, design, simulation of the proposed seismometer is introduced and analyzed detailedly. According the results of theoretical calculation and calibration, the seismometer works at the frequency band from 0.01 Hz to 10 Hz and reaches a sensitivity of better than 330 pm/g and a noise level of 2.7 × 10−7 ms−2/√Hz@0.1 Hz (2.7 μg/√Hz@0.1 Hz) which meets NHNM. An earthquake monitoring experiment is conducted in a low noise seismic station. From the analysis results of the recorded seismic waves, the proposed seismometer has the ability to record the close microearthquake and distant great earthquake with high SNR, which suggests that the proposed FBG-FP seismometer has a good potential ability of earthquake monitoring.
Funding
National Key R&D Program of China (2017YFB0405503); National Natural Science Foundation of China (NSFC) (61605196); Youth Innovation Promotion Association of CAS (2016106).
Acknowledgments
This work was partially carried out at Bai Jiatuan seismostation of China Earthquake Administration. The authors acknowledge supports from Seismological Bureau of Zhaotong, Yunnan province.
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