Distributed Acoustic Sensing in Geophysics. Группа авторов

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Figure 1.28 Ultimate SNR spectral response of DAS with standard and engineered fiber and geophone antenna. Pulse width of DAS is the same as distance between scatter centers along engineered fiber—5 m, and gauge length of DAS is the same as distance between geophones—10 m.

The shot or Poisson noise limit for phase measurement Φ_min is proportional to , where the coefficient depends on the phase‐detection approach. For a classical phase‐locked homodyne, only half of the photons reach the photodetector when the interferometer operates in quadrature, and so the noise is . For both heterodyne and/or homodyne phase detection, the photons number halves again (Kazovsky, 1989), as sine and cosine signal components should be measured independently, and so the noise rises to . Direct photodetection at λ = 1550nm is not sufficiently sensitive, so DAS usually uses an erbium doped fiber amplifier (EDFA) to boost the signal, which introduces additional noise. This noise can be simply represented by a noise figure N_F ≈ 3, which can be reached with appropriate optical filtering as explained in Kirkendall & Dandridge (2004). In this case, the shot noise limit is then given by:

(1.45)

where visibility, V = 0.5, includes all other system imperfections such as polarization mismatch. Equation 1.45 represents the white noise level for 1 second time integration of the DAS signal. For engineered fiber, the number of photons can be up to 100 times larger than for conventional Rayleigh backscattering, so the noise will be 10 times smaller.

      Another advantage of DAS with engineered fiber is a wider dynamic range that is defined as the ratio of the maximum detectable signal to the noise level. The typical geophone bandwidth is ΔF = 100Hz, so the minimum strain level ε_min detectable for DAS for gauge length L₀ = 10m within the same detection bandwidth is:

(1.46)

      where A₀ = 115nm is the elongation corresponding to one radian phase shift (Equation 1.14).

      Experimental measurements with conventional fiber DAS found a value three times higher, at 0.03nanostrain (Miller et al., 2016). In this case, there was some extra flicker noise, as discussed earlier (see Figure 1.11). Here, a spiky noise structure corresponds to algorithm discontinuities that amplify photodetector noise, with a spectrum after DAS signal time integration, which is ∝F⁻¹. The typical low frequency limit when excessive noise starts to dominate over shot noise is between 10 and 100 Hz, depending on the fiber conditions.

For engineered fiber (Farhadiroushan et al., 2021), reflectivity can be engineered to be hundreds of times higher than the normal Rayleigh level, without any significant problems with crosstalk, such that R = 100 · R_BS · τ = − 45dB. As a result, sensitivity is ten times higher, at around 1picostrain, which corresponds to a 100x (20 dB) improvement in acoustic signal sensitivity.

It is important to compare the shot noise level of DAS with the noise level of high‐sensitivity geophones and seismometers. The DAS white noise value should be added to flicker noise with coefficient μ and corrected for spatial filtering (Equation 1.46) as: