18 Garnier, A., & Chanin, M. L. (1992). Description of a Doppler Rayleigh lidar for measuring winds in the middle atmosphere. Applied Physics B, 55(1), 35–40.
19 Ghiglia, D. C., & Pritt, M. D. (1998). Two‐dimensional phase unwrapping. Theory, algorithms, and software. New York, USA: A Wiley‐Interscience Publication.
20 Goodman, J. W. (2005). Introduction to Fourier optics (Chap. 2, 6). Roberts and Company Publishers. Englewood, Colorado.
21 Handerek, V. (2016). U.S. Patent No. 9,304,017. Washington, DC: U.S. Patent and Trademark Office.
22 Hartog, A. H. (2017). An introduction to distributed optical fibre sensors. CRC press. Boca Raton, Florida.
23 Hartog, A. H., Kotov, O. I., & Liokumovich, L. B. (2013, July). The optics of distributed vibration sensing. Paper presented in Second EAGE Workshop on Permanent Reservoir Monitoring 2013–Current and Future Trends. doi: 10.3997/2214‐4609.20131301
24 Hartog, A., & Kader, K. (2012). U.S. Patent Application No. 13/221,280.
25 Hornman, K., Kuvshinov, B., Zwartjes, P., & Franzen, A. (2013, June). Field trial of a broadside‐sensitive distributed acoustic sensing cable for surface seismic. Paper presented in 75th EAGE Conference & Exhibition incorporating SPE EUROPEC 2013. doi: 10.3997/2214‐4609.20130383
26 Itoh, K. (1982). Analysis of the phase unwrapping algorithm. Applied Optics, 21(14), 2470–2470. doi: 10.1364/AO.21.002470
27 Jousset, P., Reinsch, T., Ryberg, T., Blanck, H., Clarke, A., Aghayev, R., et al. (2018). Dynamic strain determination using fibre‐optic cables allows imaging of seismological and structural features. Nature Communications, 9(1), 2509. doi: 10.1038/s41467‐018‐04860‐y
28 Juarez, J. C., Maier, E. W., Choi, K. N., & Taylor, H. F. (2005). Distributed fiber‐optic intrusion sensor system. Journal of Lightwave Technology, 23(6), 2081–2087. doi: 10.1109/JLT.2005.849924
29 Juškaitis, R., Mamedov, A. M., Potapov, V. T., & Shatalin, S. V. (1992). Distributed interferometric fiber sensor system. Optics Letters, 17(22), 1623–1625. doi: 10.1364/OL.17.001623
30 Kazovsky, L. G. (1989). Phase‐and polarization‐diversity coherent optical techniques. Journal of Lightwave Technology, 7(2), 279–292. doi: 10.1109/50.17768
31 Kirkendall, C. K., & Dandridge, A. (2004). Overview of high performance fibre‐optic sensing. Journal of Physics D: Applied Physics, 37(18), R197. doi: 10.1088/0022‐3727/37/18/R01
32 Kreger, S. T., Gifford, D. K., Froggatt, M. E., Soller, B. J., & Wolfe, M. S. (2006, October). High resolution distributed strain or temperature measurements in single‐and multi‐mode fiber using swept‐wavelength interferometry. In Optical Fiber Sensors (p. ThE42). Optical Society of America. doi: 10.1364/OFS.2006.ThE42
33 Lewis, M. F. (1985). On Rayleigh waves and related propagating acoustic waves. In Rayleigh‐wave theory and application (pp. 37–58). Springer, Berlin, Heidelberg.
34 Martin, E. R., Lindsey, N., Ajo‐Franklin, J., & Biondi, B. (2018). EarthArXiv, Introduction to interferometry of fiber optic strain measurements (pp. 1–33).
35 Martins, H. F., Martin‐Lopez, S., Corredera, P., Salgado, P., Frazão, O., & González‐Herráez, M. (2013). Modulation instability‐induced fading in phase‐sensitive optical time‐domain reflectometry. Optics Letters, 38(6), 872–874. doi: 10.1364/OL.38.000872
36 Mateeva, A., Lopez, J., Potters, H., Mestayer, J., Cox, B., Kiyashchenko, D., et al. (2014). Distributed acoustic sensing for reservoir monitoring with vertical seismic profiling. Geophysical Prospecting, 62(4), 679–692.
37 Miller, D. E., Daley, T. M., White, D., Freifeld, B. M., Robertson, M., Cocker, J., et al. (2016). Simultaneous acquisition of distributed acoustic sensing VSP with multi‐mode and single‐mode fibre‐optic cables and 3C‐geophones at the Aquistore CO2 storage site. CSEG Recorder, 41(6).
38 Matichard, F., Lantz, B., Mittleman, R., Mason, K., Kissel, J., Abbott, B., et al. (2015). Seismic isolation of Advanced LIGO: Review of strategy, instrumentation and performance. Classical and Quantum Gravity, 32(18), 185003.
39 Parker, T. R., Farhadiroushan, M., Feced, R., Handerek, V. A., & Rogers, A. J. (1998). Simultaneous distributed measurement of strain and temperature from noise‐initiated Brillouin scattering in optical fibers. IEEE Journal of Quantum Electronics, 34(4), 645–659. doi: 10.1109/3.663443
40 Parker, T., Shatalin, S., & Farhadiroushan, M. (2014). Distributed acoustic sensing—a new tool for seismic applications. First Break, 32(2), 61–69. doi: 10.3997/1365‐2397.2013034
41 Peterson, J. R. (1993). Observations and modeling of seismic background noise (No. 93‐322). US Geological Survey.
42 Posey, R., Johnson, G. A., & Vohra, S. T. (2000). Strain sensing based on coherent Rayleigh scattering in an optical fibre. Electronics Letters, 36(20), 1688–1689. doi: 10.1049/el:20001200
43 Rathod, R., Pechstedt, R. D., Jackson, D. A., & Webb, D. J. (1994). Distributed temperature‐change sensor based on Rayleigh backscattering in an optical fiber. Optics Letters, 19(8), 593–595. doi: 10.1364/OL.19.000593
44 Ringler, A. T., & Hutt, C. R. (2010). Self‐noise models of seismic instruments. Seismological Research Letters, 81(6), 972–983.
45 Rea, N. P., Wilson, T., & Juškaitis, R. (1996). Semiconductor laser confocal and interference microscopy. Optics Communications, 125(1–3), 158–167. doi: 10.1016/0030‐4018(95)00701‐6
46 Richter, P., Parker, T., Woerpel, C., Wu, Y., Rufino, R., & Farhadiroushan, M. (2019). Hydraulic fracture monitoring and optimization in unconventional completions using a high resolution engineered fiber optic distributed acoustic sensor. First Break, 37(4), 66–68.
47 Servin, M., Kujawinska, M., & Padilla, J. M. (2017). Modern fringe pattern analysis in interferometry. In Advanced Optical Instruments and Techniques (pp. 101–152). CRC Press.
48 Shatalin, S. V., Treschikov, V. N., & Rogers, A. J. (1998). Interferometric optical time‐domain reflectometry for distributed optical‐fiber sensing. Applied Optics, 37(24), 5600–5604. doi: 10.1364/AO.37.005600
49 Shatalin, S., Mamedov, A., Potapov, V., & Sedykh, D. (1991). Optical frequency domain multiplexing of fiber‐optic sensors. The First International Soviet Fibre Optics Conference, ISFOC ′91 (pp. 307–308).
50 Subsea Fiber Optic Monitoring (SEAFOM) working group (2018). Measuring Sensor Performance—DAS Parameter Definitions and Tests SEAFOM‐MSP‐02. Retrieved from https://seafom.com/published‐documents/
51 Taylor, H. F., & Lee, C. E. (1993). U.S. Patent No. 5,194,847. Washington, DC: U.S. Patent and Trademark Office.
52 Todd, M. (2011, April). Noise propagation in a 3×3 optical demodulation scheme used for fiber Bragg grating interrogation. Paper presented in Smart Sensor Phenomena, Technology, Networks, and Systems 2011 (Vol. 7982, p. 79820A). International Society for Optics and Photonics. doi: 10.1117/12.878694
53 Unser, M. (1999). Splines: A perfect fit for signal and image processing. IEEE Signal Processing Magazine, 16(6), 22–38. doi: 10.1117/12.467162
54 Wielandt, E., & Widmer‐Schnidrig, R. (2002). Seismic sensing and data acquisition in the GRSN. Ten Years of German Regional Seismic Network (GRSN) (pp. 73–83).
55 Westbrook, P. S., Feder, K. S., Ortiz, R. M., Kremp, T., Monberg, E. M., Wu, H., et al. (2017, April). Kilometer length, low loss enhanced back scattering fiber for distributed sensing. Paper presented in 2017 25th Optical Fiber Sensors Conference (OFS) (pp. 1–5). IEEE.
56 Wuestefeld, A., & Wilks, M. (2019). How to twist and turn a fiber: Performance modeling for optimal DAS acquisitions. The Leading Edge, 38(3), 226–231.
a ( z ) |
arbitrary function |
A 0 |
fiber elongation corresponding to 1 rad of phase shift |
A ( z , t ) |
output of DAS |
A 1( z ) |
output of DAS with first order algorithm |
A 2( z ) |
output of DAS with second order algorithm |
b ( z ) |
arbitrary function |
c |
optical speed of light in fiber |
C |
speed of sound |
D |
DAS dynamic range |
e ( t ′) |
optical field of coherent input pulse |
E ( t ′) |
optical field on photodetector |
ℑ ( K , F ) |
Fourier transforms of seismic signal |
ℑ |
Fourier transform symbol |
F |
frequency of sound |
F MAX |
maximum frequency of sound |
F S |
pulse repetition rate or sampling frequency |
G ( z ) |
geophone antenna response |
hυ |
energy quant |
Im Z |
imaginary part of interference output |
I j( z , t ) |
intensity trace for different interferometric output |
I ( z , t ) |
photodetector intensity trace |
j |
integer number |
K |
acoustic angular wavenumber |
K z |
acoustic angular wavenumber along fiber |
K e |
ratio of optical to physical length of fiber |
L |
fiber length |
L P |
integration length |
L 0 |
interferometer length also known as gauge length |
L S |
scattering zones spacing |
M |
number of scattering zones |
n eff |
fiber effective refractive index |
N F |
noise figure of amplifier |
N |
number of photons per second |
p ( z ) |
averaging function |
P 0 |
input peak power |
P |
number of different interferometric ports or pulses |
R BS |
backscattering coefficient of fiber |
r 0( z ) |
distribution of reflection/scattering coefficient along fiber axis |
r ( z ) |
distribution of reflection/scattering coefficient along fiber axis with optical phase shift included |
Re Z |
real part of interference output |
t ′ |
“fast” optical time scale |
t |
“slow” acoustic time scale |
u ( z , t ) |
ground displacement |
u |
parameter of function |
v ( z ) |
fiber local speed along its axis and also ground speed |
V ( z ) |
interference visibility along fiber |
x |
parameter of integration: coordinate along fiber axis |
z |
coordinate along fiber axis |
z 1 |
parameter of function |
z 2 |
parameter of function |
β |
optical wave propagation constant of fiber |
β 0 |
unperturbed optical wave propagation constant of fiber |
ΔΩ( z ) |
distance variation of Doppler shift along fiber |
Δ v |
distance variation of ground speed |
Δ F |
geophone bandwidth |
δ |
the Dirac delta function |
ε 1 |
maximum recoverable strain for first order algorithm |
ε 2 |
maximum recoverable strain for second order algorithm |
ε min |
minimum strain level |
Φ min |
phase noise |
Γ |
incident angle of seismic wave |
λ |
laser wavelength |
Λ |
spacing of geophones |
μ |
flicker noise coefficient |
ω |
circular frequency of light |
Ω( z ) |
Doppler frequency shift of light |
ψ 0 |
phase shift between delayed optical fields in interferometer |
Φ |
shift of backscattered light |
ρ |
backscattering intensity coefficient |
θ ( z ) |
Heaviside step function |
τ ( z ) |
input pulse |
τ |
optical pulsewidth |
2 Important Aspects of Acquiring Distributed Acoustic Sensing (DAS) Data for Geoscientists
Читать дальше