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
|
|
r0(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
|
|
Δv
|
distance variation of ground speed
|
|
ΔF
|
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
|
|
Φmin
|
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
Mark E. Willis1, Andreas Ellmauthaler1, Xiang Wu2, and Michel J. LeBlanc1
1Halliburton, Houston, Texas, USA
2Halliburton Far East Pte. Ltd., Singapore
ABSTRACT
Fiber‐optic
