Abstract

Detection of earthquakes and tidal variations via measurement of strain in the Earth’s crust requires compact and robust instrumentation with low power usage that can be deployed in the field. Here we demonstrate a stationary-wave integrated Fourier transform spectrometer (SWIFTS) and measure the variations induced by ground strain on an optical fiber Bragg grating sensor using two short (17±2mm) Fabry–Perot (FP) cavities, one for the sensor, and one for temperature compensation. The SWIFTS delivers spatial interferograms that are then Fourier transformed to deduce the deformation from a cross-spectral analysis of the FP spectra. The full system is tested in field conditions to record crustal earth strain signals and successfully detect the earth tide and an earthquake signal. With this low-coherency interferometry technique, this system offers an excellent compromise between the resolution needed and the cost of a fully autonomous field instrument.

© 2015 Optical Society of America

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References

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  1. P. Ferraro, G. De Natale, “On the possible use of optical fiber Bragg gratings as strain sensors for geodynamical monitoring,” Optics Lasers Eng. 37, 115–130 (2002).
    [Crossref]
  2. S. DeWolf, F. Wyatt, M. Zumberge, D. Agnew, “Vertical and horizontal optical fiber strainmeters for measuring earth strain,” in AGU Fall Meeting Abstracts (AGU, 2012), Vol. 1, p. 0918.
  3. S. DeWolf, “Optical fiber sensors for infrasonic noise wind noise reduction and earth strain measurement,” Ph.D. thesis (University of California, San Diego, 2014).
  4. Z. He, Q. Liu, T. Tokunaga, “Ultrahigh resolution fiber-optic quasi-static strain sensors for geophysical research,” Photonic Sens. 3, 295–303 (2013).
    [Crossref]
  5. S. Avino, J. A. Barnes, G. Gagliardi, X. Gu, D. Gutstein, J. R. Mester, C. Nicholaou, H.-P. Loock, “Musical instrument pickup based on a laser locked to an optical fiber resonator,” Opt. Express 19, 25057–25065 (2011).
    [Crossref]
  6. M. A. Zumberge, S. DeWolf, F. K. Wyatt, D. C. Agnew, D. Elliott, W. Hatfield, “Results from a borehole optical fiber interferometer for recording earth strain,” Proc. SPIE 8794, 87940Q (2013).
  7. G. Gagliardi, M. Salza, S. Avino, P. Ferraro, P. De Natale, “Probing the ultimate limit of fiber-optic strain sensing,” Science 330, 1081–1084 (2010).
    [Crossref]
  8. Q. Liu, Z. He, T. Tokunaga, K. Hotate, “An ultra-high-resolution FBG static-strain sensor for geophysics applications,” in Fourth European Workshop on Optical Fibre Sensors (EWOFS) (International Society for Optics and Photonics, 2012), paper 76530W.
  9. E. Le Coarer, S. Blaize, P. Benech, I. Stefanon, A. Morand, G. Lérondel, G. Leblond, P. Kern, J. M. Fedeli, P. Royer, “Wavelength-scale stationary-wave integrated Fourier-transform spectrometry,” Nat. Photonics 1, 473–478 (2007).
    [Crossref]
  10. M. De Mengin, “Etude d’un spectromètre integré swifts pour réaliser des capteurs optiques fibrés pour les sciences de l’observation,” Ph.D. thesis (Université Joseph Fourier, 2014).
  11. K. Matsumoto, T. Sato, T. Takanezawa, M. Ooe, “Gotic2: a program for computation of oceanic tidal loading effect,” J. Geod. Soc. Jpn. 47, 243–248 (2001).
  12. B. Saleh, P. Antoine Blum, “Monitoring of fracture propagation by quartz tiltmeters,” Eng. Geol. 79, 33–42 (2005).
    [Crossref]
  13. S. Takemoto, “Effects of local inhomogeneities on tidal strain measurements,” Bull. Disaster Prev. Res. Inst. 31, 211–237 (1981).
  14. J. Gomberg, D. Agnew, “The accuracy of seismic estimates of dynamic strains: an evaluation using strainmeter and seismometer data from Pinon Flat Observatory, California,” Bull. Seismol. Soc. Am. 86, 212–220 (1996).
  15. R. Hart, M. Gladwin, R. Gwyther, D. Agnew, F. Wyatt, “Tidal calibration of borehole strain meters: removing the effects of small-scale inhomogeneity,” J. Geophys. Res. [Solid Earth] 101, 25553–25571 (1996).
    [Crossref]

2013 (2)

M. A. Zumberge, S. DeWolf, F. K. Wyatt, D. C. Agnew, D. Elliott, W. Hatfield, “Results from a borehole optical fiber interferometer for recording earth strain,” Proc. SPIE 8794, 87940Q (2013).

Z. He, Q. Liu, T. Tokunaga, “Ultrahigh resolution fiber-optic quasi-static strain sensors for geophysical research,” Photonic Sens. 3, 295–303 (2013).
[Crossref]

2011 (1)

2010 (1)

G. Gagliardi, M. Salza, S. Avino, P. Ferraro, P. De Natale, “Probing the ultimate limit of fiber-optic strain sensing,” Science 330, 1081–1084 (2010).
[Crossref]

2007 (1)

E. Le Coarer, S. Blaize, P. Benech, I. Stefanon, A. Morand, G. Lérondel, G. Leblond, P. Kern, J. M. Fedeli, P. Royer, “Wavelength-scale stationary-wave integrated Fourier-transform spectrometry,” Nat. Photonics 1, 473–478 (2007).
[Crossref]

2005 (1)

B. Saleh, P. Antoine Blum, “Monitoring of fracture propagation by quartz tiltmeters,” Eng. Geol. 79, 33–42 (2005).
[Crossref]

2002 (1)

P. Ferraro, G. De Natale, “On the possible use of optical fiber Bragg gratings as strain sensors for geodynamical monitoring,” Optics Lasers Eng. 37, 115–130 (2002).
[Crossref]

2001 (1)

K. Matsumoto, T. Sato, T. Takanezawa, M. Ooe, “Gotic2: a program for computation of oceanic tidal loading effect,” J. Geod. Soc. Jpn. 47, 243–248 (2001).

1996 (2)

J. Gomberg, D. Agnew, “The accuracy of seismic estimates of dynamic strains: an evaluation using strainmeter and seismometer data from Pinon Flat Observatory, California,” Bull. Seismol. Soc. Am. 86, 212–220 (1996).

R. Hart, M. Gladwin, R. Gwyther, D. Agnew, F. Wyatt, “Tidal calibration of borehole strain meters: removing the effects of small-scale inhomogeneity,” J. Geophys. Res. [Solid Earth] 101, 25553–25571 (1996).
[Crossref]

1981 (1)

S. Takemoto, “Effects of local inhomogeneities on tidal strain measurements,” Bull. Disaster Prev. Res. Inst. 31, 211–237 (1981).

Agnew, D.

J. Gomberg, D. Agnew, “The accuracy of seismic estimates of dynamic strains: an evaluation using strainmeter and seismometer data from Pinon Flat Observatory, California,” Bull. Seismol. Soc. Am. 86, 212–220 (1996).

R. Hart, M. Gladwin, R. Gwyther, D. Agnew, F. Wyatt, “Tidal calibration of borehole strain meters: removing the effects of small-scale inhomogeneity,” J. Geophys. Res. [Solid Earth] 101, 25553–25571 (1996).
[Crossref]

S. DeWolf, F. Wyatt, M. Zumberge, D. Agnew, “Vertical and horizontal optical fiber strainmeters for measuring earth strain,” in AGU Fall Meeting Abstracts (AGU, 2012), Vol. 1, p. 0918.

Agnew, D. C.

M. A. Zumberge, S. DeWolf, F. K. Wyatt, D. C. Agnew, D. Elliott, W. Hatfield, “Results from a borehole optical fiber interferometer for recording earth strain,” Proc. SPIE 8794, 87940Q (2013).

Antoine Blum, P.

B. Saleh, P. Antoine Blum, “Monitoring of fracture propagation by quartz tiltmeters,” Eng. Geol. 79, 33–42 (2005).
[Crossref]

Avino, S.

Barnes, J. A.

Benech, P.

E. Le Coarer, S. Blaize, P. Benech, I. Stefanon, A. Morand, G. Lérondel, G. Leblond, P. Kern, J. M. Fedeli, P. Royer, “Wavelength-scale stationary-wave integrated Fourier-transform spectrometry,” Nat. Photonics 1, 473–478 (2007).
[Crossref]

Blaize, S.

E. Le Coarer, S. Blaize, P. Benech, I. Stefanon, A. Morand, G. Lérondel, G. Leblond, P. Kern, J. M. Fedeli, P. Royer, “Wavelength-scale stationary-wave integrated Fourier-transform spectrometry,” Nat. Photonics 1, 473–478 (2007).
[Crossref]

De Mengin, M.

M. De Mengin, “Etude d’un spectromètre integré swifts pour réaliser des capteurs optiques fibrés pour les sciences de l’observation,” Ph.D. thesis (Université Joseph Fourier, 2014).

De Natale, G.

P. Ferraro, G. De Natale, “On the possible use of optical fiber Bragg gratings as strain sensors for geodynamical monitoring,” Optics Lasers Eng. 37, 115–130 (2002).
[Crossref]

De Natale, P.

G. Gagliardi, M. Salza, S. Avino, P. Ferraro, P. De Natale, “Probing the ultimate limit of fiber-optic strain sensing,” Science 330, 1081–1084 (2010).
[Crossref]

DeWolf, S.

M. A. Zumberge, S. DeWolf, F. K. Wyatt, D. C. Agnew, D. Elliott, W. Hatfield, “Results from a borehole optical fiber interferometer for recording earth strain,” Proc. SPIE 8794, 87940Q (2013).

S. DeWolf, F. Wyatt, M. Zumberge, D. Agnew, “Vertical and horizontal optical fiber strainmeters for measuring earth strain,” in AGU Fall Meeting Abstracts (AGU, 2012), Vol. 1, p. 0918.

S. DeWolf, “Optical fiber sensors for infrasonic noise wind noise reduction and earth strain measurement,” Ph.D. thesis (University of California, San Diego, 2014).

Elliott, D.

M. A. Zumberge, S. DeWolf, F. K. Wyatt, D. C. Agnew, D. Elliott, W. Hatfield, “Results from a borehole optical fiber interferometer for recording earth strain,” Proc. SPIE 8794, 87940Q (2013).

Fedeli, J. M.

E. Le Coarer, S. Blaize, P. Benech, I. Stefanon, A. Morand, G. Lérondel, G. Leblond, P. Kern, J. M. Fedeli, P. Royer, “Wavelength-scale stationary-wave integrated Fourier-transform spectrometry,” Nat. Photonics 1, 473–478 (2007).
[Crossref]

Ferraro, P.

G. Gagliardi, M. Salza, S. Avino, P. Ferraro, P. De Natale, “Probing the ultimate limit of fiber-optic strain sensing,” Science 330, 1081–1084 (2010).
[Crossref]

P. Ferraro, G. De Natale, “On the possible use of optical fiber Bragg gratings as strain sensors for geodynamical monitoring,” Optics Lasers Eng. 37, 115–130 (2002).
[Crossref]

Gagliardi, G.

Gladwin, M.

R. Hart, M. Gladwin, R. Gwyther, D. Agnew, F. Wyatt, “Tidal calibration of borehole strain meters: removing the effects of small-scale inhomogeneity,” J. Geophys. Res. [Solid Earth] 101, 25553–25571 (1996).
[Crossref]

Gomberg, J.

J. Gomberg, D. Agnew, “The accuracy of seismic estimates of dynamic strains: an evaluation using strainmeter and seismometer data from Pinon Flat Observatory, California,” Bull. Seismol. Soc. Am. 86, 212–220 (1996).

Gu, X.

Gutstein, D.

Gwyther, R.

R. Hart, M. Gladwin, R. Gwyther, D. Agnew, F. Wyatt, “Tidal calibration of borehole strain meters: removing the effects of small-scale inhomogeneity,” J. Geophys. Res. [Solid Earth] 101, 25553–25571 (1996).
[Crossref]

Hart, R.

R. Hart, M. Gladwin, R. Gwyther, D. Agnew, F. Wyatt, “Tidal calibration of borehole strain meters: removing the effects of small-scale inhomogeneity,” J. Geophys. Res. [Solid Earth] 101, 25553–25571 (1996).
[Crossref]

Hatfield, W.

M. A. Zumberge, S. DeWolf, F. K. Wyatt, D. C. Agnew, D. Elliott, W. Hatfield, “Results from a borehole optical fiber interferometer for recording earth strain,” Proc. SPIE 8794, 87940Q (2013).

He, Z.

Z. He, Q. Liu, T. Tokunaga, “Ultrahigh resolution fiber-optic quasi-static strain sensors for geophysical research,” Photonic Sens. 3, 295–303 (2013).
[Crossref]

Q. Liu, Z. He, T. Tokunaga, K. Hotate, “An ultra-high-resolution FBG static-strain sensor for geophysics applications,” in Fourth European Workshop on Optical Fibre Sensors (EWOFS) (International Society for Optics and Photonics, 2012), paper 76530W.

Hotate, K.

Q. Liu, Z. He, T. Tokunaga, K. Hotate, “An ultra-high-resolution FBG static-strain sensor for geophysics applications,” in Fourth European Workshop on Optical Fibre Sensors (EWOFS) (International Society for Optics and Photonics, 2012), paper 76530W.

Kern, P.

E. Le Coarer, S. Blaize, P. Benech, I. Stefanon, A. Morand, G. Lérondel, G. Leblond, P. Kern, J. M. Fedeli, P. Royer, “Wavelength-scale stationary-wave integrated Fourier-transform spectrometry,” Nat. Photonics 1, 473–478 (2007).
[Crossref]

Le Coarer, E.

E. Le Coarer, S. Blaize, P. Benech, I. Stefanon, A. Morand, G. Lérondel, G. Leblond, P. Kern, J. M. Fedeli, P. Royer, “Wavelength-scale stationary-wave integrated Fourier-transform spectrometry,” Nat. Photonics 1, 473–478 (2007).
[Crossref]

Leblond, G.

E. Le Coarer, S. Blaize, P. Benech, I. Stefanon, A. Morand, G. Lérondel, G. Leblond, P. Kern, J. M. Fedeli, P. Royer, “Wavelength-scale stationary-wave integrated Fourier-transform spectrometry,” Nat. Photonics 1, 473–478 (2007).
[Crossref]

Lérondel, G.

E. Le Coarer, S. Blaize, P. Benech, I. Stefanon, A. Morand, G. Lérondel, G. Leblond, P. Kern, J. M. Fedeli, P. Royer, “Wavelength-scale stationary-wave integrated Fourier-transform spectrometry,” Nat. Photonics 1, 473–478 (2007).
[Crossref]

Liu, Q.

Z. He, Q. Liu, T. Tokunaga, “Ultrahigh resolution fiber-optic quasi-static strain sensors for geophysical research,” Photonic Sens. 3, 295–303 (2013).
[Crossref]

Q. Liu, Z. He, T. Tokunaga, K. Hotate, “An ultra-high-resolution FBG static-strain sensor for geophysics applications,” in Fourth European Workshop on Optical Fibre Sensors (EWOFS) (International Society for Optics and Photonics, 2012), paper 76530W.

Loock, H.-P.

Matsumoto, K.

K. Matsumoto, T. Sato, T. Takanezawa, M. Ooe, “Gotic2: a program for computation of oceanic tidal loading effect,” J. Geod. Soc. Jpn. 47, 243–248 (2001).

Mester, J. R.

Morand, A.

E. Le Coarer, S. Blaize, P. Benech, I. Stefanon, A. Morand, G. Lérondel, G. Leblond, P. Kern, J. M. Fedeli, P. Royer, “Wavelength-scale stationary-wave integrated Fourier-transform spectrometry,” Nat. Photonics 1, 473–478 (2007).
[Crossref]

Nicholaou, C.

Ooe, M.

K. Matsumoto, T. Sato, T. Takanezawa, M. Ooe, “Gotic2: a program for computation of oceanic tidal loading effect,” J. Geod. Soc. Jpn. 47, 243–248 (2001).

Royer, P.

E. Le Coarer, S. Blaize, P. Benech, I. Stefanon, A. Morand, G. Lérondel, G. Leblond, P. Kern, J. M. Fedeli, P. Royer, “Wavelength-scale stationary-wave integrated Fourier-transform spectrometry,” Nat. Photonics 1, 473–478 (2007).
[Crossref]

Saleh, B.

B. Saleh, P. Antoine Blum, “Monitoring of fracture propagation by quartz tiltmeters,” Eng. Geol. 79, 33–42 (2005).
[Crossref]

Salza, M.

G. Gagliardi, M. Salza, S. Avino, P. Ferraro, P. De Natale, “Probing the ultimate limit of fiber-optic strain sensing,” Science 330, 1081–1084 (2010).
[Crossref]

Sato, T.

K. Matsumoto, T. Sato, T. Takanezawa, M. Ooe, “Gotic2: a program for computation of oceanic tidal loading effect,” J. Geod. Soc. Jpn. 47, 243–248 (2001).

Stefanon, I.

E. Le Coarer, S. Blaize, P. Benech, I. Stefanon, A. Morand, G. Lérondel, G. Leblond, P. Kern, J. M. Fedeli, P. Royer, “Wavelength-scale stationary-wave integrated Fourier-transform spectrometry,” Nat. Photonics 1, 473–478 (2007).
[Crossref]

Takanezawa, T.

K. Matsumoto, T. Sato, T. Takanezawa, M. Ooe, “Gotic2: a program for computation of oceanic tidal loading effect,” J. Geod. Soc. Jpn. 47, 243–248 (2001).

Takemoto, S.

S. Takemoto, “Effects of local inhomogeneities on tidal strain measurements,” Bull. Disaster Prev. Res. Inst. 31, 211–237 (1981).

Tokunaga, T.

Z. He, Q. Liu, T. Tokunaga, “Ultrahigh resolution fiber-optic quasi-static strain sensors for geophysical research,” Photonic Sens. 3, 295–303 (2013).
[Crossref]

Q. Liu, Z. He, T. Tokunaga, K. Hotate, “An ultra-high-resolution FBG static-strain sensor for geophysics applications,” in Fourth European Workshop on Optical Fibre Sensors (EWOFS) (International Society for Optics and Photonics, 2012), paper 76530W.

Wyatt, F.

R. Hart, M. Gladwin, R. Gwyther, D. Agnew, F. Wyatt, “Tidal calibration of borehole strain meters: removing the effects of small-scale inhomogeneity,” J. Geophys. Res. [Solid Earth] 101, 25553–25571 (1996).
[Crossref]

S. DeWolf, F. Wyatt, M. Zumberge, D. Agnew, “Vertical and horizontal optical fiber strainmeters for measuring earth strain,” in AGU Fall Meeting Abstracts (AGU, 2012), Vol. 1, p. 0918.

Wyatt, F. K.

M. A. Zumberge, S. DeWolf, F. K. Wyatt, D. C. Agnew, D. Elliott, W. Hatfield, “Results from a borehole optical fiber interferometer for recording earth strain,” Proc. SPIE 8794, 87940Q (2013).

Zumberge, M.

S. DeWolf, F. Wyatt, M. Zumberge, D. Agnew, “Vertical and horizontal optical fiber strainmeters for measuring earth strain,” in AGU Fall Meeting Abstracts (AGU, 2012), Vol. 1, p. 0918.

Zumberge, M. A.

M. A. Zumberge, S. DeWolf, F. K. Wyatt, D. C. Agnew, D. Elliott, W. Hatfield, “Results from a borehole optical fiber interferometer for recording earth strain,” Proc. SPIE 8794, 87940Q (2013).

Bull. Disaster Prev. Res. Inst. (1)

S. Takemoto, “Effects of local inhomogeneities on tidal strain measurements,” Bull. Disaster Prev. Res. Inst. 31, 211–237 (1981).

Bull. Seismol. Soc. Am. (1)

J. Gomberg, D. Agnew, “The accuracy of seismic estimates of dynamic strains: an evaluation using strainmeter and seismometer data from Pinon Flat Observatory, California,” Bull. Seismol. Soc. Am. 86, 212–220 (1996).

Eng. Geol. (1)

B. Saleh, P. Antoine Blum, “Monitoring of fracture propagation by quartz tiltmeters,” Eng. Geol. 79, 33–42 (2005).
[Crossref]

J. Geod. Soc. Jpn. (1)

K. Matsumoto, T. Sato, T. Takanezawa, M. Ooe, “Gotic2: a program for computation of oceanic tidal loading effect,” J. Geod. Soc. Jpn. 47, 243–248 (2001).

J. Geophys. Res. [Solid Earth] (1)

R. Hart, M. Gladwin, R. Gwyther, D. Agnew, F. Wyatt, “Tidal calibration of borehole strain meters: removing the effects of small-scale inhomogeneity,” J. Geophys. Res. [Solid Earth] 101, 25553–25571 (1996).
[Crossref]

Nat. Photonics (1)

E. Le Coarer, S. Blaize, P. Benech, I. Stefanon, A. Morand, G. Lérondel, G. Leblond, P. Kern, J. M. Fedeli, P. Royer, “Wavelength-scale stationary-wave integrated Fourier-transform spectrometry,” Nat. Photonics 1, 473–478 (2007).
[Crossref]

Opt. Express (1)

Optics Lasers Eng. (1)

P. Ferraro, G. De Natale, “On the possible use of optical fiber Bragg gratings as strain sensors for geodynamical monitoring,” Optics Lasers Eng. 37, 115–130 (2002).
[Crossref]

Photonic Sens. (1)

Z. He, Q. Liu, T. Tokunaga, “Ultrahigh resolution fiber-optic quasi-static strain sensors for geophysical research,” Photonic Sens. 3, 295–303 (2013).
[Crossref]

Proc. SPIE (1)

M. A. Zumberge, S. DeWolf, F. K. Wyatt, D. C. Agnew, D. Elliott, W. Hatfield, “Results from a borehole optical fiber interferometer for recording earth strain,” Proc. SPIE 8794, 87940Q (2013).

Science (1)

G. Gagliardi, M. Salza, S. Avino, P. Ferraro, P. De Natale, “Probing the ultimate limit of fiber-optic strain sensing,” Science 330, 1081–1084 (2010).
[Crossref]

Other (4)

Q. Liu, Z. He, T. Tokunaga, K. Hotate, “An ultra-high-resolution FBG static-strain sensor for geophysics applications,” in Fourth European Workshop on Optical Fibre Sensors (EWOFS) (International Society for Optics and Photonics, 2012), paper 76530W.

M. De Mengin, “Etude d’un spectromètre integré swifts pour réaliser des capteurs optiques fibrés pour les sciences de l’observation,” Ph.D. thesis (Université Joseph Fourier, 2014).

S. DeWolf, F. Wyatt, M. Zumberge, D. Agnew, “Vertical and horizontal optical fiber strainmeters for measuring earth strain,” in AGU Fall Meeting Abstracts (AGU, 2012), Vol. 1, p. 0918.

S. DeWolf, “Optical fiber sensors for infrasonic noise wind noise reduction and earth strain measurement,” Ph.D. thesis (University of California, San Diego, 2014).

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Figures (5)

Fig. 1.
Fig. 1.

Principle of operation for the sensor. A SLED source emits toward the two FP cavities. A circulator grabs the reflected light through a polarizer (P) toward the SWIFTS, whose acquisition is triggered by the PPS signal sent from a distant GPS receiver. The interferograms digitized by the SWIFTS are sent to a PC.

Fig. 2.
Fig. 2.

Example of interferograms and Fourier transform modulus for the FP sens (red) and FP ref (blue) cavities. (a) Superposition of two interferograms measured separately. (b) Discrete Fourier transforms computed on the I 2 pulses and displayed as a function of wavelength. The nominal central wavelengths are 850 and 851 nm. The shift of the blue peak is 0.1 nm and corresponds to a Δ T of 14°C. The shift of the red peak is 0.4 nm and includes the effect of the same Δ T plus a pretension strain of 0.035%.

Fig. 3.
Fig. 3.

Earth-tide record. Upper plot: raw signal (gray) superposed with the signal filtered in the M2, S2, and K1 tide bands. Lower plot: theoretical signal obtained from Gotic2 software.

Fig. 4.
Fig. 4.

Magnitude 8.1 Chilean earthquake record. Upper plot: strain signal derivated from seismic records. Lower plot: strain signal from SWIFTS sensor. The average noise level ( 25 n ϵ ) in the band of filtering is shown by a dashed line.

Fig. 5.
Fig. 5.

Comparison of power spectral density for different types of optical fiber strain sensors. (1) Vertical strain records obtained at Piñon Flat with 250 m long Michelson designs [3]: different temperature corrections, (blue and orange, [3]) and an estimate of the sensors’ pure noise level (green [3]). (2) Our sensor (black). (3) Noise level obtained in the [1; 1. e 2 ] Hz band [7] in a laboratory experiment with an insulated 13 cm long FP resonator (red, dashed).

Tables (1)

Tables Icon

Table 1. Shape Functions for Quadratic Line Elements

Equations (4)

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

I ( x ) > I ( x + d x ) = I ( x + x · ϵ ) .
Φ ( k , t ) = arg { I I ( k , t ) } = k Δ ( t ) .
Δ sens Δ ref = ( ϵ + α T 1 + β T 2 ) sens ( α T 1 + β T 2 ) ref .
Δ sens = a · Δ ref 2 + b · Δ ref + ϵ ,

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