Distributed Acoustic Sensing in Geophysics

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Distributed Acoustic Sensing in Geophysics
Distributed Acoustic Sensing in Geophysics Methods and Applications Distributed Acoustic Sensing (DAS) is a technology that records sound and vibration signals along a fiber optic cable. Its advantages of high resolution, continuous, and real-time measurements mean that DAS systems have been rapidly adopted for a range of applications, including hazard mitigation, energy industries, geohydrology, environmental monitoring, and civil engineering.
presents experiences from both industry and academia on using DAS in a range of geophysical applications. Volume highlights include: The American Geophysical Union promotes discovery in Earth and space science for the benefit of humanity. Its publications disseminate scientific knowledge and provide resources for researchers, students, and professionals.

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TABLE OF VARIABLES

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
( K , F ) Fourier transforms of seismic signal
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
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

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