Abstract

This study proposes a high-accuracy transient response fiber optic seismic accelerometer based on the resonance suppression mechanism. A shock-absorbing ring is embedded in the accelerometer structure, which acts as a mechanical antiresonator. The experimental results show that the sensitivity at the resonance frequency is suppressed by 21.79 dB, and the 3 dB operating bandwidth is extended without reducing the average sensitivity. Under this condition, the high-accuracy transient response is obtained during the vibration-event test. This study provides a practical seismic acquisition technique solution for vertical seismic profiling monitoring in the smart oilfield.

© 2019 Optical Society of America

Fiber optic accelerometers have received growing interest in the oilfield and in oil well logging [13]. In well logging, the three-component fiber optic accelerometer system is installed in the oil well to detect the vertical seismic profiling data; these data can be used to evaluate the hydraulic fracturing effects, hence realizing the oil/gas reservoir monitoring [46]. Except for the advantages such as high sensitivity, electric insulation, multiplexing ability, etc., the fiber optic accelerometers can operate under the down-well environment with a temperature of 150 deg that is not possible with traditional electric accelerometers. All these advantages make fiber optic accelerometers a promising candidate for smart oilfield applications [7].

The sensitivity and the operating bandwidth are two of the key performance parameters for the fiber optic accelerometers [8,9]. Knudsen et al. reported a fiber optic accelerometer system with the average sensitivity of 40 dB rad/g and the operating bandwidth of 800 Hz for the seismic reservoir monitoring [10]. Theoretically, both the sensitivity and the operating bandwidth are desired to be as large as possible. However, due to the principle mechanism of the fiber optic accelerometer, the operating bandwidth and the sensitivity are inversely proportional; this represents that the maximum operating bandwidth has to decrease if higher sensitivity is needed. For example, Freitas et al. reported a fiber optic accelerometer with a sensitivity of 55 dB rad/g, while the maximum operating bandwidth was only up to 250 Hz [7]. Chen et al. reported a fiber optic accelerometer with a sensitivity of 50 dB rad/g, while its operating bandwidth varied only from 2 to 150 Hz [11]. Therefore, how to increase the operating bandwidth without reducing the sensitivity is of continuous interest to researchers in this field.

The transient response accuracy is another key performance parameter [12], and the damping is the main influential factor. In vertical seismic profiling monitoring applications, the fiber optic accelerometers should be able to retrieve the seismic waveform in order to locate the epicenter orientation [13]; hence, the high-accuracy transient response is desired and a proper damping factor should be well-designed. The traditional methods of adjusting damping include injecting the viscous liquid or high-pressure gas into the device structure. In the previous works [14], the silicone oil was selected to inject, and the stamper damping was optimized due to the large viscosity of the silicone oil. However, this method also has several disadvantages. First, a good sealing performance is needed to avoid the leakage of the silicone oil, which may face challenges in the harsh down-well environment. Second, the vacuum procedure is needed during the liquid injection process to evacuate the air, which increases the procedure’s complexity. In a word, the traditional methods are hard to apply to the actual applications, and the novel designs are desired.

In this Letter, the improvement of the transient response accuracy is mainly discussed. We propose a novel high-accuracy transient response fiber optic seismic accelerometer without injecting the additional viscous liquid, and a shock-absorbing ring is embedded in the accelerometer structure to act as a mechanical antiresonator. The damping factor increases from 0.027 to 0.47, and the sensitivity at the resonance frequency is suppressed by 21.79 dB; hence, the 3 dB operating bandwidth is extended without reducing the average sensitivity. Under this condition, the transient response accuracy is improved effectively in the vibration-event test with a cross-correlation coefficient of 0.94, which is experimentally confirmed by a commercial piezoelectric accelerometer. This study provides a practical seismic acquisition technique solution for vertical seismic profiling monitoring.

Figure 1 represents the cross-section structure of the proposed fiber optic seismic accelerometer. It consists of a metal mass, a bottom base, an elastic enhanced layer, a top plate, and an unbalanced fiber optic interferometer. When the accelerometer suffers from the external vibration, the axial movement of the metal mass compresses the elastic enhanced layer, leading to the length variation of the interference arm and then to the phase variation of the interference light. Therefore, the external vibration can be retrieved by demodulating the phase variation of the interference light. For this type of the fiber optic accelerometer, the stamper damping performs as the main damping factor. Besides, different from the other fiber optic accelerometers, the center of the metal mass is raised, and a shock-absorbing ring is embedded between the top plate and the metal mass; a minor torsional moment is applied on the ring by rotating the screw on the top plate. This shock-absorbing ring is made of the fluorine rubber, and the elastic material provides a buffer between the top plate and the metal mass; therefore, the high-frequency components around the resonance zone can be suppressed effectively. Theoretically, this ring is equivalent to an “additional damping” that is applied to the accelerometer. On the contrary, if the shock-absorbing ring is not considered, the high-frequency components around the resonance zone will be easier to be excited by the wide-spectrum signal source, which forms the interference to the effective signal detection.

 figure: Fig. 1.

Fig. 1. Cross-section structure of the fiber optic seismic accelerometer.

Download Full Size | PPT Slide | PDF

The interference principle is illustrated in Fig. 2. The interferometer mainly consists of a 1×2 optical coupler, and the two ends of output fibers are connected with the Faraday reflective mirrors (FRMs) to form the two beams of the Michelson interferometer. The two beam lengths are designed as 0.5 and 20.5 m, respectively; the 20.5 m length fiber is wrapped around the elastic enhanced layer, and the 0.5 m length fiber is wrapped directly around the metal mass. Assuming a dual-pulse train with spatial separation of 40 m is injected into the 1×2 optical coupler, it returns two pulse trains due to the reflection of the FRMs, and the interference occurs between the pulse-12 and the pulse-21 due to the spatial coincidence.

 figure: Fig. 2.

Fig. 2. Illustration of the interference principle.

Download Full Size | PPT Slide | PDF

Theoretically, the presented accelerometer can be considered as a second-order mass-spring system, as seen in Fig. 1. According to Newton’s second law, the dynamic equation can be expressed as

(c1+c2)dx0(t)dt+kx0(t)=md2xi(t)dt2,
where x0(t) is the relative displacement between the metal mass and the elastic enhanced layer, xi(t) is the displacement of the metal mass, c1 is the stamper damping, c2 is the damping introduced by the shock-absorbing ring, m is the mass of the metal, and k is the stiffness.

If the interferometric phase demodulation is considered, the dynamic phase sensitivity Ø/a of the Eq. (1) can be expressed as [4]

Øa=(Øa)01(1f2f02)2+4ξ2f2f02,
ξ=c1+c22mk,
where Ø/a represents the phase per unit acceleration, namely dynamic phase sensitivity, (Ø/a)0 is the phase sensitivity in the flat bandwidth, f0 is the resonance frequency, and ξ is the damping factor of the accelerometer. When the vibration frequency f is far less than the resonance frequency f0, the phase sensitivity is almost equal to (Ø/a)0. However, when the vibration frequency f is set as the resonance frequency f0, the phase sensitivity is equal to (1/2ξ)·(Ø/a)0, and under this condition, if the damping factor ξ increases, the phase sensitivity will decrease; hence, the resonance phenomenon can be suppressed gradually. From Eq. (2), we conclude that the key point to suppress the resonance phenomenon is to increase the damping factor ξ, and in this Letter, it is realized by introducing the shock-absorbing ring.

In addition, the transient response of the fiber optic accelerometer is also discussed in this study. The transfer function of the transient response in Laplace space H(s) is expressed as

H(s)=Y(s)X(s)=f02(s2+2ξf0s+f02),
where X and Y represent the exciting signal and the corresponding response, s is the Laplace factor, and X(s),Y(s) are, respectively, the exciting signal and the response in the Laplace domain. From Eq. (4), it is observed that the transient response of the accelerometer mainly depends on the resonance frequency f0 and the damping factor ξ.

Next, the fiber optic sensing system is built experimentally to evaluate its transient response performance, and a commercial piezoelectric sensing system is also built up as the references, as seen in Fig. 3. The cross-correlation coefficient between these two accelerometers is compared to evaluate quantitatively the response accuracy of the fiber optic accelerometer. For the fiber optic sensing system, the dual-pulse heterodyne demodulation technique is used [15]. The laser launches the continuous light with the center wavelength of 1554 nm; two acoustic-optic modulators (AOMs) are driven by the AOM driver to generate the dual-pulse train with the pulse width of 140 ns and pulse repetition rate of 200 kHz, and a 40 m long fiber is placed after one AOM so that the two pulses are separated spatially. Then, the dual-pulse train is injected into the fiber optic accelerometer; the return interferometric pulse train is collected by the demodulation module, and the phase variations are finally demodulated based on the heterodyne algorithm. During the transient response test, both the fiber optic accelerometer and the piezoelectric accelerometer are fixed on the ground. The rubber ball falls from a certain height to simulate the perforating shot signal during the vertical seismic profiling monitoring process; once the ball rebounds from the ground, the data acquisition process terminates, and both transient response curves are compared.

 figure: Fig. 3.

Fig. 3. Diagram of the transient response test platform.

Download Full Size | PPT Slide | PDF

The result of the frequency-dependent sensitivity curve is shown in Fig. 4. The upper limit of the test frequency is set at 2000 Hz, which is able to cover the frequency range of the actual seismic wave signals in the smart oilfield. The blue curve represents that the shock-absorbing ring is embedded, corresponding to the newly designed fiber optic accelerometer, and the red curve represents that the shock-absorbing ring is not considered. From the red curve, we observe that the resonance frequency of the accelerometer is around 1600 Hz, and the peak sensitivity value is 65.08 dB rad/g. Besides, the operating bandwidth is found as 800 Hz, and the average sensitivity is 39.80 dB within the operating bandwidth. On the other hand, from the blue curve, it is clear that the peak value of the resonance frequency is largely suppressed; the sensitivity value at 1600 Hz is only 43.29 dB rad/g, which is 21.79 dB lower than the red curve, and the sensitivity fluctuation is only 2.94 dB within an acceptable test frequency range (100 to 2000 Hz). Besides, the numerical fitting value of the damping factor increases from 0.027 to 0.47 based on the optimized solution algorithm, and the specific algorithm principles are presented in our previous study [14]. This result confirms that the damping factor is improved by embedding a shock-absorbing ring into the accelerometer structure, and the resonance phenomenon is suppressed effectively. Moreover, as the resonance phenomenon is suppressed, the 3 dB operating bandwidth is also extended without reducing the average sensitivity.

 figure: Fig. 4.

Fig. 4. Frequency-dependent sensitivity curve of the fiber optic accelerometer (dB=20·log10).

Download Full Size | PPT Slide | PDF

Then, the transient response performance is evaluated. Figures 5(a) and 5(b) represent the transient responses under the condition that the shock-absorbing ring is not/is embedded into the fiber optic accelerometer. For both Figs. 5(a) and 5(b), the vibration event in first 20 ms is focused, and the vibration amplitudes are normalized. In Fig. 5(a), the obvious differences of the transient response are observed between the two accelerometers. Particularly, from 7 to 20 ms, the fiber optic accelerometer retrieves more high-frequency waveforms compared to the piezoelectric accelerometer, signifying that part of the invalid high-frequency components are excited by the fiber optic accelerometer, and the cross-correlation coefficient between these two curves is estimated at only 0.75. However, in Fig. 5(b), the transient response of the fiber optic accelerometer is obviously improved, and the cross-correlation coefficient between the two accelerometers increases to 0.94, which is better than the previous work result of 0.92 obtained by the traditional method [14]. Moreover, the presented novel fiber optic accelerometer avoids the complex vacuum procedure and the strict sealing requirements. This phenomenon signifies that the transient response performance of the presented fiber optic accelerometer is improved effectively after the resonance suppression, and under this condition, it is capable of reflecting the true transient response with high accuracy.

 figure: Fig. 5.

Fig. 5. Comparison of the transient response curves in the time domain (a) without a shock-absorbing ring and (b) with a shock-absorbing ring.

Download Full Size | PPT Slide | PDF

The improvements of the transient response can be observed more clearly in the corresponding time-frequency diagram. In Fig. 6(a), the shock-absorbing ring is not considered; if we focus on the beginning of the vibration process, the fiber optic accelerometer suffers a wide spectrum excitation from about 580 to 1850 Hz, and the vibration amplitudes are obviously larger than that of the piezoelectric accelerometer according to the color map. These amplitude differences signify that the fiber optic accelerometer has not reflected the true transient response. When the damping factor is as low as 0.027, the frequency components that distribute around the resonance zone of 1600 Hz are easier to be excited during the wide spectrum excitation process, and this can explain the amplitude differences in the marked zone in Fig. 6(a). However, when the shock-absorbing ring is considered and the damping factor increases to 0.47, as shown in the marked area of Fig. 6(b), the amplitudes at the beginning of the vibration are greatly weakened, and the amplitude consistency is largely improved between the two accelerometers. This time-frequency result confirms again the improvement of the transient response of the novel fiber optic accelerometer.

 figure: Fig. 6.

Fig. 6. Comparison of the transient response curves in the time-frequency domain (a) without a shock-absorbing ring and (b) with a shock-absorbing ring.

Download Full Size | PPT Slide | PDF

In summary, we demonstrate a high-accuracy transient response fiber optic seismic accelerometer, and a shock-absorbing ring is designed to act as a mechanical antiresonator. The experimental results show that the damping factor of the fiber optic accelerometer increases from 0.027 to 0.47, and the sensitivity at the resonance frequency is suppressed by 21.79 dB. Moreover, the 3 dB operating bandwidth is also extended without reducing the average sensitivity. Under this condition, the accelerometer shows the high-accuracy transient response with a cross-correlation coefficient of 0.94, which is confirmed by the commercial piezoelectric accelerometer. In addition, the different dimensions and the materials of the shock-absorbing ring may affect slightly the resonance suppression performance; thus, a systematical study is necessary. This will lead to further investigations in the future. This work is helpful to improve the measurement accuracy and reduce the error of the seismic event, and it provides a practical technical solution for the seismic acquisition during vertical seismic profiling monitoring.

Funding

Natural Gas Hydrate Exploration and Production Test (DD20160217).

REFERENCES

1. B. N. P. Paulsson, J. Thornburg, and R. He, Energy Procedia 63, 4323 (2014). [CrossRef]  

2. J. Pan, H. You, Y. Pan, D. Wu, L. Yu, X. Wang, X. Qiu, and M. Zhang, Measurement 79, 198 (2016). [CrossRef]  

3. G. Peng, J. He, S. Yang, and W. Zhou, Measurement 58, 130 (2014). [CrossRef]  

4. N. Zeng, C. Z. Shi, M. Zhang, L. W. Wang, Y. B. Liao, and S. R. Lai, Opt. Commun. 234, 153 (2004). [CrossRef]  

5. Y. Weng, X. Qiao, T. Guo, M. Hu, Z. Feng, R. Wang, and J. Zhang, IEEE Sens. J. 12, 800 (2012). [CrossRef]  

6. B. Hornby, F. Bostick, B. Williams, K. Lewis, and P. Garossino, Geophysics 70, E11 (2005). [CrossRef]  

7. J. M. D. Freitas, Meas. Sci. Technol. 22, 052001 (2011). [CrossRef]  

8. N. Basumallick, P. Biswas, K. Dasgupta, and S. Bandyopadhyay, Sens. Actuators A, Phys. 194, 31 (2013). [CrossRef]  

9. J. M. D. Freitas, J. P. F. Wooler, and P. J. Nash, Meas. Sci. Technol. 17, 1819 (2006). [CrossRef]  

10. S. Knudsen, G. B. Havsgard, A. Berg, D. Thingbo, F. Bostick, and M. Eriksrud, in 18th International Conference on Optical Fiber Sensors (2006), paper FB2.

11. J. Chen, T. Chang, Q. Fu, J. Lang, W. Gao, Z. Wang, M. Yu, Y. Zhang, and H.-L. Cui, Sensors 17, 47 (2016). [CrossRef]  

12. G. Liu, M. Han, and W. Hou, Opt. Express 23, 7237 (2015). [CrossRef]  

13. P. Keul, E. Mastin, J. Blanco, M. Maguérez, T. Bostick, and S. Knudsen, Lead. Edge 24, 68 (2005). [CrossRef]  

14. Y. Duo, L. Fei, H. Xiangge, and Z. Min, Opt. Fiber Technol. 45, 58 (2018). [CrossRef]  

15. F. Liu, S. Xie, X. Qiu, X. Wang, S. Cao, M. Qin, X. He, B. Xie, X. Zheng, and M. Zhang, J. Lightwave Technol. 34, 5453 (2016). [CrossRef]  

References

  • View by:

  1. B. N. P. Paulsson, J. Thornburg, and R. He, Energy Procedia 63, 4323 (2014).
    [Crossref]
  2. J. Pan, H. You, Y. Pan, D. Wu, L. Yu, X. Wang, X. Qiu, and M. Zhang, Measurement 79, 198 (2016).
    [Crossref]
  3. G. Peng, J. He, S. Yang, and W. Zhou, Measurement 58, 130 (2014).
    [Crossref]
  4. N. Zeng, C. Z. Shi, M. Zhang, L. W. Wang, Y. B. Liao, and S. R. Lai, Opt. Commun. 234, 153 (2004).
    [Crossref]
  5. Y. Weng, X. Qiao, T. Guo, M. Hu, Z. Feng, R. Wang, and J. Zhang, IEEE Sens. J. 12, 800 (2012).
    [Crossref]
  6. B. Hornby, F. Bostick, B. Williams, K. Lewis, and P. Garossino, Geophysics 70, E11 (2005).
    [Crossref]
  7. J. M. D. Freitas, Meas. Sci. Technol. 22, 052001 (2011).
    [Crossref]
  8. N. Basumallick, P. Biswas, K. Dasgupta, and S. Bandyopadhyay, Sens. Actuators A, Phys. 194, 31 (2013).
    [Crossref]
  9. J. M. D. Freitas, J. P. F. Wooler, and P. J. Nash, Meas. Sci. Technol. 17, 1819 (2006).
    [Crossref]
  10. S. Knudsen, G. B. Havsgard, A. Berg, D. Thingbo, F. Bostick, and M. Eriksrud, in 18th International Conference on Optical Fiber Sensors (2006), paper FB2.
  11. J. Chen, T. Chang, Q. Fu, J. Lang, W. Gao, Z. Wang, M. Yu, Y. Zhang, and H.-L. Cui, Sensors 17, 47 (2016).
    [Crossref]
  12. G. Liu, M. Han, and W. Hou, Opt. Express 23, 7237 (2015).
    [Crossref]
  13. P. Keul, E. Mastin, J. Blanco, M. Maguérez, T. Bostick, and S. Knudsen, Lead. Edge 24, 68 (2005).
    [Crossref]
  14. Y. Duo, L. Fei, H. Xiangge, and Z. Min, Opt. Fiber Technol. 45, 58 (2018).
    [Crossref]
  15. F. Liu, S. Xie, X. Qiu, X. Wang, S. Cao, M. Qin, X. He, B. Xie, X. Zheng, and M. Zhang, J. Lightwave Technol. 34, 5453 (2016).
    [Crossref]

2018 (1)

Y. Duo, L. Fei, H. Xiangge, and Z. Min, Opt. Fiber Technol. 45, 58 (2018).
[Crossref]

2016 (3)

F. Liu, S. Xie, X. Qiu, X. Wang, S. Cao, M. Qin, X. He, B. Xie, X. Zheng, and M. Zhang, J. Lightwave Technol. 34, 5453 (2016).
[Crossref]

J. Chen, T. Chang, Q. Fu, J. Lang, W. Gao, Z. Wang, M. Yu, Y. Zhang, and H.-L. Cui, Sensors 17, 47 (2016).
[Crossref]

J. Pan, H. You, Y. Pan, D. Wu, L. Yu, X. Wang, X. Qiu, and M. Zhang, Measurement 79, 198 (2016).
[Crossref]

2015 (1)

2014 (2)

G. Peng, J. He, S. Yang, and W. Zhou, Measurement 58, 130 (2014).
[Crossref]

B. N. P. Paulsson, J. Thornburg, and R. He, Energy Procedia 63, 4323 (2014).
[Crossref]

2013 (1)

N. Basumallick, P. Biswas, K. Dasgupta, and S. Bandyopadhyay, Sens. Actuators A, Phys. 194, 31 (2013).
[Crossref]

2012 (1)

Y. Weng, X. Qiao, T. Guo, M. Hu, Z. Feng, R. Wang, and J. Zhang, IEEE Sens. J. 12, 800 (2012).
[Crossref]

2011 (1)

J. M. D. Freitas, Meas. Sci. Technol. 22, 052001 (2011).
[Crossref]

2006 (1)

J. M. D. Freitas, J. P. F. Wooler, and P. J. Nash, Meas. Sci. Technol. 17, 1819 (2006).
[Crossref]

2005 (2)

B. Hornby, F. Bostick, B. Williams, K. Lewis, and P. Garossino, Geophysics 70, E11 (2005).
[Crossref]

P. Keul, E. Mastin, J. Blanco, M. Maguérez, T. Bostick, and S. Knudsen, Lead. Edge 24, 68 (2005).
[Crossref]

2004 (1)

N. Zeng, C. Z. Shi, M. Zhang, L. W. Wang, Y. B. Liao, and S. R. Lai, Opt. Commun. 234, 153 (2004).
[Crossref]

Bandyopadhyay, S.

N. Basumallick, P. Biswas, K. Dasgupta, and S. Bandyopadhyay, Sens. Actuators A, Phys. 194, 31 (2013).
[Crossref]

Basumallick, N.

N. Basumallick, P. Biswas, K. Dasgupta, and S. Bandyopadhyay, Sens. Actuators A, Phys. 194, 31 (2013).
[Crossref]

Berg, A.

S. Knudsen, G. B. Havsgard, A. Berg, D. Thingbo, F. Bostick, and M. Eriksrud, in 18th International Conference on Optical Fiber Sensors (2006), paper FB2.

Biswas, P.

N. Basumallick, P. Biswas, K. Dasgupta, and S. Bandyopadhyay, Sens. Actuators A, Phys. 194, 31 (2013).
[Crossref]

Blanco, J.

P. Keul, E. Mastin, J. Blanco, M. Maguérez, T. Bostick, and S. Knudsen, Lead. Edge 24, 68 (2005).
[Crossref]

Bostick, F.

B. Hornby, F. Bostick, B. Williams, K. Lewis, and P. Garossino, Geophysics 70, E11 (2005).
[Crossref]

S. Knudsen, G. B. Havsgard, A. Berg, D. Thingbo, F. Bostick, and M. Eriksrud, in 18th International Conference on Optical Fiber Sensors (2006), paper FB2.

Bostick, T.

P. Keul, E. Mastin, J. Blanco, M. Maguérez, T. Bostick, and S. Knudsen, Lead. Edge 24, 68 (2005).
[Crossref]

Cao, S.

Chang, T.

J. Chen, T. Chang, Q. Fu, J. Lang, W. Gao, Z. Wang, M. Yu, Y. Zhang, and H.-L. Cui, Sensors 17, 47 (2016).
[Crossref]

Chen, J.

J. Chen, T. Chang, Q. Fu, J. Lang, W. Gao, Z. Wang, M. Yu, Y. Zhang, and H.-L. Cui, Sensors 17, 47 (2016).
[Crossref]

Cui, H.-L.

J. Chen, T. Chang, Q. Fu, J. Lang, W. Gao, Z. Wang, M. Yu, Y. Zhang, and H.-L. Cui, Sensors 17, 47 (2016).
[Crossref]

Dasgupta, K.

N. Basumallick, P. Biswas, K. Dasgupta, and S. Bandyopadhyay, Sens. Actuators A, Phys. 194, 31 (2013).
[Crossref]

Duo, Y.

Y. Duo, L. Fei, H. Xiangge, and Z. Min, Opt. Fiber Technol. 45, 58 (2018).
[Crossref]

Eriksrud, M.

S. Knudsen, G. B. Havsgard, A. Berg, D. Thingbo, F. Bostick, and M. Eriksrud, in 18th International Conference on Optical Fiber Sensors (2006), paper FB2.

Fei, L.

Y. Duo, L. Fei, H. Xiangge, and Z. Min, Opt. Fiber Technol. 45, 58 (2018).
[Crossref]

Feng, Z.

Y. Weng, X. Qiao, T. Guo, M. Hu, Z. Feng, R. Wang, and J. Zhang, IEEE Sens. J. 12, 800 (2012).
[Crossref]

Freitas, J. M. D.

J. M. D. Freitas, Meas. Sci. Technol. 22, 052001 (2011).
[Crossref]

J. M. D. Freitas, J. P. F. Wooler, and P. J. Nash, Meas. Sci. Technol. 17, 1819 (2006).
[Crossref]

Fu, Q.

J. Chen, T. Chang, Q. Fu, J. Lang, W. Gao, Z. Wang, M. Yu, Y. Zhang, and H.-L. Cui, Sensors 17, 47 (2016).
[Crossref]

Gao, W.

J. Chen, T. Chang, Q. Fu, J. Lang, W. Gao, Z. Wang, M. Yu, Y. Zhang, and H.-L. Cui, Sensors 17, 47 (2016).
[Crossref]

Garossino, P.

B. Hornby, F. Bostick, B. Williams, K. Lewis, and P. Garossino, Geophysics 70, E11 (2005).
[Crossref]

Guo, T.

Y. Weng, X. Qiao, T. Guo, M. Hu, Z. Feng, R. Wang, and J. Zhang, IEEE Sens. J. 12, 800 (2012).
[Crossref]

Han, M.

Havsgard, G. B.

S. Knudsen, G. B. Havsgard, A. Berg, D. Thingbo, F. Bostick, and M. Eriksrud, in 18th International Conference on Optical Fiber Sensors (2006), paper FB2.

He, J.

G. Peng, J. He, S. Yang, and W. Zhou, Measurement 58, 130 (2014).
[Crossref]

He, R.

B. N. P. Paulsson, J. Thornburg, and R. He, Energy Procedia 63, 4323 (2014).
[Crossref]

He, X.

Hornby, B.

B. Hornby, F. Bostick, B. Williams, K. Lewis, and P. Garossino, Geophysics 70, E11 (2005).
[Crossref]

Hou, W.

Hu, M.

Y. Weng, X. Qiao, T. Guo, M. Hu, Z. Feng, R. Wang, and J. Zhang, IEEE Sens. J. 12, 800 (2012).
[Crossref]

Keul, P.

P. Keul, E. Mastin, J. Blanco, M. Maguérez, T. Bostick, and S. Knudsen, Lead. Edge 24, 68 (2005).
[Crossref]

Knudsen, S.

P. Keul, E. Mastin, J. Blanco, M. Maguérez, T. Bostick, and S. Knudsen, Lead. Edge 24, 68 (2005).
[Crossref]

S. Knudsen, G. B. Havsgard, A. Berg, D. Thingbo, F. Bostick, and M. Eriksrud, in 18th International Conference on Optical Fiber Sensors (2006), paper FB2.

Lai, S. R.

N. Zeng, C. Z. Shi, M. Zhang, L. W. Wang, Y. B. Liao, and S. R. Lai, Opt. Commun. 234, 153 (2004).
[Crossref]

Lang, J.

J. Chen, T. Chang, Q. Fu, J. Lang, W. Gao, Z. Wang, M. Yu, Y. Zhang, and H.-L. Cui, Sensors 17, 47 (2016).
[Crossref]

Lewis, K.

B. Hornby, F. Bostick, B. Williams, K. Lewis, and P. Garossino, Geophysics 70, E11 (2005).
[Crossref]

Liao, Y. B.

N. Zeng, C. Z. Shi, M. Zhang, L. W. Wang, Y. B. Liao, and S. R. Lai, Opt. Commun. 234, 153 (2004).
[Crossref]

Liu, F.

Liu, G.

Maguérez, M.

P. Keul, E. Mastin, J. Blanco, M. Maguérez, T. Bostick, and S. Knudsen, Lead. Edge 24, 68 (2005).
[Crossref]

Mastin, E.

P. Keul, E. Mastin, J. Blanco, M. Maguérez, T. Bostick, and S. Knudsen, Lead. Edge 24, 68 (2005).
[Crossref]

Min, Z.

Y. Duo, L. Fei, H. Xiangge, and Z. Min, Opt. Fiber Technol. 45, 58 (2018).
[Crossref]

Nash, P. J.

J. M. D. Freitas, J. P. F. Wooler, and P. J. Nash, Meas. Sci. Technol. 17, 1819 (2006).
[Crossref]

Pan, J.

J. Pan, H. You, Y. Pan, D. Wu, L. Yu, X. Wang, X. Qiu, and M. Zhang, Measurement 79, 198 (2016).
[Crossref]

Pan, Y.

J. Pan, H. You, Y. Pan, D. Wu, L. Yu, X. Wang, X. Qiu, and M. Zhang, Measurement 79, 198 (2016).
[Crossref]

Paulsson, B. N. P.

B. N. P. Paulsson, J. Thornburg, and R. He, Energy Procedia 63, 4323 (2014).
[Crossref]

Peng, G.

G. Peng, J. He, S. Yang, and W. Zhou, Measurement 58, 130 (2014).
[Crossref]

Qiao, X.

Y. Weng, X. Qiao, T. Guo, M. Hu, Z. Feng, R. Wang, and J. Zhang, IEEE Sens. J. 12, 800 (2012).
[Crossref]

Qin, M.

Qiu, X.

J. Pan, H. You, Y. Pan, D. Wu, L. Yu, X. Wang, X. Qiu, and M. Zhang, Measurement 79, 198 (2016).
[Crossref]

F. Liu, S. Xie, X. Qiu, X. Wang, S. Cao, M. Qin, X. He, B. Xie, X. Zheng, and M. Zhang, J. Lightwave Technol. 34, 5453 (2016).
[Crossref]

Shi, C. Z.

N. Zeng, C. Z. Shi, M. Zhang, L. W. Wang, Y. B. Liao, and S. R. Lai, Opt. Commun. 234, 153 (2004).
[Crossref]

Thingbo, D.

S. Knudsen, G. B. Havsgard, A. Berg, D. Thingbo, F. Bostick, and M. Eriksrud, in 18th International Conference on Optical Fiber Sensors (2006), paper FB2.

Thornburg, J.

B. N. P. Paulsson, J. Thornburg, and R. He, Energy Procedia 63, 4323 (2014).
[Crossref]

Wang, L. W.

N. Zeng, C. Z. Shi, M. Zhang, L. W. Wang, Y. B. Liao, and S. R. Lai, Opt. Commun. 234, 153 (2004).
[Crossref]

Wang, R.

Y. Weng, X. Qiao, T. Guo, M. Hu, Z. Feng, R. Wang, and J. Zhang, IEEE Sens. J. 12, 800 (2012).
[Crossref]

Wang, X.

J. Pan, H. You, Y. Pan, D. Wu, L. Yu, X. Wang, X. Qiu, and M. Zhang, Measurement 79, 198 (2016).
[Crossref]

F. Liu, S. Xie, X. Qiu, X. Wang, S. Cao, M. Qin, X. He, B. Xie, X. Zheng, and M. Zhang, J. Lightwave Technol. 34, 5453 (2016).
[Crossref]

Wang, Z.

J. Chen, T. Chang, Q. Fu, J. Lang, W. Gao, Z. Wang, M. Yu, Y. Zhang, and H.-L. Cui, Sensors 17, 47 (2016).
[Crossref]

Weng, Y.

Y. Weng, X. Qiao, T. Guo, M. Hu, Z. Feng, R. Wang, and J. Zhang, IEEE Sens. J. 12, 800 (2012).
[Crossref]

Williams, B.

B. Hornby, F. Bostick, B. Williams, K. Lewis, and P. Garossino, Geophysics 70, E11 (2005).
[Crossref]

Wooler, J. P. F.

J. M. D. Freitas, J. P. F. Wooler, and P. J. Nash, Meas. Sci. Technol. 17, 1819 (2006).
[Crossref]

Wu, D.

J. Pan, H. You, Y. Pan, D. Wu, L. Yu, X. Wang, X. Qiu, and M. Zhang, Measurement 79, 198 (2016).
[Crossref]

Xiangge, H.

Y. Duo, L. Fei, H. Xiangge, and Z. Min, Opt. Fiber Technol. 45, 58 (2018).
[Crossref]

Xie, B.

Xie, S.

Yang, S.

G. Peng, J. He, S. Yang, and W. Zhou, Measurement 58, 130 (2014).
[Crossref]

You, H.

J. Pan, H. You, Y. Pan, D. Wu, L. Yu, X. Wang, X. Qiu, and M. Zhang, Measurement 79, 198 (2016).
[Crossref]

Yu, L.

J. Pan, H. You, Y. Pan, D. Wu, L. Yu, X. Wang, X. Qiu, and M. Zhang, Measurement 79, 198 (2016).
[Crossref]

Yu, M.

J. Chen, T. Chang, Q. Fu, J. Lang, W. Gao, Z. Wang, M. Yu, Y. Zhang, and H.-L. Cui, Sensors 17, 47 (2016).
[Crossref]

Zeng, N.

N. Zeng, C. Z. Shi, M. Zhang, L. W. Wang, Y. B. Liao, and S. R. Lai, Opt. Commun. 234, 153 (2004).
[Crossref]

Zhang, J.

Y. Weng, X. Qiao, T. Guo, M. Hu, Z. Feng, R. Wang, and J. Zhang, IEEE Sens. J. 12, 800 (2012).
[Crossref]

Zhang, M.

J. Pan, H. You, Y. Pan, D. Wu, L. Yu, X. Wang, X. Qiu, and M. Zhang, Measurement 79, 198 (2016).
[Crossref]

F. Liu, S. Xie, X. Qiu, X. Wang, S. Cao, M. Qin, X. He, B. Xie, X. Zheng, and M. Zhang, J. Lightwave Technol. 34, 5453 (2016).
[Crossref]

N. Zeng, C. Z. Shi, M. Zhang, L. W. Wang, Y. B. Liao, and S. R. Lai, Opt. Commun. 234, 153 (2004).
[Crossref]

Zhang, Y.

J. Chen, T. Chang, Q. Fu, J. Lang, W. Gao, Z. Wang, M. Yu, Y. Zhang, and H.-L. Cui, Sensors 17, 47 (2016).
[Crossref]

Zheng, X.

Zhou, W.

G. Peng, J. He, S. Yang, and W. Zhou, Measurement 58, 130 (2014).
[Crossref]

Energy Procedia (1)

B. N. P. Paulsson, J. Thornburg, and R. He, Energy Procedia 63, 4323 (2014).
[Crossref]

Geophysics (1)

B. Hornby, F. Bostick, B. Williams, K. Lewis, and P. Garossino, Geophysics 70, E11 (2005).
[Crossref]

IEEE Sens. J. (1)

Y. Weng, X. Qiao, T. Guo, M. Hu, Z. Feng, R. Wang, and J. Zhang, IEEE Sens. J. 12, 800 (2012).
[Crossref]

J. Lightwave Technol. (1)

Lead. Edge (1)

P. Keul, E. Mastin, J. Blanco, M. Maguérez, T. Bostick, and S. Knudsen, Lead. Edge 24, 68 (2005).
[Crossref]

Meas. Sci. Technol. (2)

J. M. D. Freitas, Meas. Sci. Technol. 22, 052001 (2011).
[Crossref]

J. M. D. Freitas, J. P. F. Wooler, and P. J. Nash, Meas. Sci. Technol. 17, 1819 (2006).
[Crossref]

Measurement (2)

J. Pan, H. You, Y. Pan, D. Wu, L. Yu, X. Wang, X. Qiu, and M. Zhang, Measurement 79, 198 (2016).
[Crossref]

G. Peng, J. He, S. Yang, and W. Zhou, Measurement 58, 130 (2014).
[Crossref]

Opt. Commun. (1)

N. Zeng, C. Z. Shi, M. Zhang, L. W. Wang, Y. B. Liao, and S. R. Lai, Opt. Commun. 234, 153 (2004).
[Crossref]

Opt. Express (1)

Opt. Fiber Technol. (1)

Y. Duo, L. Fei, H. Xiangge, and Z. Min, Opt. Fiber Technol. 45, 58 (2018).
[Crossref]

Sens. Actuators A, Phys. (1)

N. Basumallick, P. Biswas, K. Dasgupta, and S. Bandyopadhyay, Sens. Actuators A, Phys. 194, 31 (2013).
[Crossref]

Sensors (1)

J. Chen, T. Chang, Q. Fu, J. Lang, W. Gao, Z. Wang, M. Yu, Y. Zhang, and H.-L. Cui, Sensors 17, 47 (2016).
[Crossref]

Other (1)

S. Knudsen, G. B. Havsgard, A. Berg, D. Thingbo, F. Bostick, and M. Eriksrud, in 18th International Conference on Optical Fiber Sensors (2006), paper FB2.

Cited By

Optica participates in Crossref's Cited-By Linking service. Citing articles from Optica Publishing Group journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (6)

Fig. 1.
Fig. 1. Cross-section structure of the fiber optic seismic accelerometer.
Fig. 2.
Fig. 2. Illustration of the interference principle.
Fig. 3.
Fig. 3. Diagram of the transient response test platform.
Fig. 4.
Fig. 4. Frequency-dependent sensitivity curve of the fiber optic accelerometer ( dB = 20 · log 10 ).
Fig. 5.
Fig. 5. Comparison of the transient response curves in the time domain (a) without a shock-absorbing ring and (b) with a shock-absorbing ring.
Fig. 6.
Fig. 6. Comparison of the transient response curves in the time-frequency domain (a) without a shock-absorbing ring and (b) with a shock-absorbing ring.

Equations (4)

Equations on this page are rendered with MathJax. Learn more.

( c 1 + c 2 ) d x 0 ( t ) d t + k x 0 ( t ) = m d 2 x i ( t ) d t 2 ,
Ø a = ( Ø a ) 0 1 ( 1 f 2 f 0 2 ) 2 + 4 ξ 2 f 2 f 0 2 ,
ξ = c 1 + c 2 2 m k ,
H ( s ) = Y ( s ) X ( s ) = f 0 2 ( s 2 + 2 ξ f 0 s + f 0 2 ) ,

Metrics