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detection processes RB phase by mixing with itself with a time delay (Masoudi et al., 2013; Wang, Wang, et al., 2015; Wang, Shang, et al., 2015). A coherent heterodyne demodulation DAS system was proposed by Lu et al. (2010). The phase information of heterodyne signal was obtained by mixing the electrical driving signal of acoustic optical modulator (AOM); a spatial resolution of 5 m and a frequency response range of 1 kHz were achieved; and signal‐to‐noise ratio (SNR) was increased to 6.5 dB with 100 averaging times. To overcome polarization‐induced signal fading, an improved polarization‐maintaining scheme was presented (Qin et al., 2011). Further, a kind of double‐pulse approach was proposed by Alekseev et al. (2014b), which used phase‐modulated probe signals with predefined different phase shift sequences of 0, −2/3π, and 2/3π. The system demonstrated a distributed phase monitoring capability over 2 km range with 100 Hz sinusoidal strain from piezoceramic modulator. Another dual‐pulse DAS system with different frequency shifts was investigated by He et al. (2017). Combined with heterodyne demodulation, the strain frequency response was in the range of 50 Hz to 25 kHz, with a 0.9‐73 rad amplitude on a 470 m long optical fiber. There are two kinds of interferometer DAS systems based on 3 × 3 coupler or PGC demodulation algorithm. For the former, a symmetric 3 × 3 coupler is adopted to eliminate slow phase shift of the interferometer (Sheem, 1981); the interference phase formed by self‐delay of RB in a single pulse is recovered by using the feature of coupler with a phase difference of ±120° between output ports. Such an alternative approach was demonstrated by Masoudi et al. (2013); the demonstrated setup has a spatial resolution of 2 m with a frequency range of 500‐5000 Hz along 1 km optical fiber (Masoudi et al., 2013). Because of three detectors and a sampling rate of 300 MSa/s per channel, the total data size would reach around 900 MSa/s, which leads to a huge challenge to realize real‐time data processing. For PGC‐DAS system (Fang et al., 2015), a PGC was introduced to overcome the initial phase shift problem (Dandridge et al., 1982), and an unbalanced MI with Faraday rotator mirrors (FRMs) was implemented to eliminate the influence of polarization fading (Huang et al., 1996). Compared with 3 × 3 demodulation, only one detector is needed, and a relatively low data stream helps to online recover phase information.

      Here, we present a real‐time PGC‐DAS system. Combined with characteristics of large dynamic range and high sensitivity of PGC demodulation algorithm (Wang et al., 2015), the proposed system provides an effective technical solution to distributed fiber acoustic sensing. The sensing distance could reach 10 km with the minimum sample interval of 0.4 m. Corresponding to the average phase noise of 5 × 10^‐4 rad/√Hz, a strain sensitivity of 8.5 pε/√Hz was achieved with a spatial resolution of 10 m, as well as a frequency response range of 2 Hz to 1 kHz over 10 km sensing distance. A field trial of this PGC‐DAS system was performed to compare nodal geophones. Results show that seismic records have a high consistency between them, proving the feasibility of PGC‐DAS system in seismology.

4.2. PRINCIPLE

The principle of PGC‐DAS system is shown in Figure 4.1. A coherent input light pulse passes through a circulator into the sensing optical fiber. RB light enters into an unbalanced MI with FRMs at the ends. There is a phase modulator on one arm of MI and an optical delay L_MI on the other arm. RB signal mixes with itself and is detected by one photoelectric detector (PD).

      Intensity distribution of RB light is a type of Fourier transform of random permittivity fluctuations (Bao et al., 2016). Assume that the sensing fiber is composed of successive slices with a length of ΔL. Each slice contains M scattering centers, and polarization states between each scattering center are consistent. The interference field of backscattered light at distance L_m = mΔL can be expressed by (Park et al., 1998):

      (4.1)

where E₀ is electric field intensity of the incident light; P_m is polarization‐dependent coefficient ranging from 0 to 1; α is optical power attenuation coefficient; r_k and φ_k are scattering coefficient and phase of the kth scattering center, respectively; a_i and φ_i are reflectivity and phase of scattering unit, respectively; and β is propagation constant.

Figure 4.1 Principle of PGC‐DAS system with an unbalanced MI.

      Then, scattering light enters into MI, and RB1 and RB2 separated by L_MI interference due to the same optical path. The interference electrical field E(t) is written as:

      (4.2)

      With simplified coefficients A and B, the interference intensity is given by:

(4.3)

For PGC demodulation algorithm, a sinusoidal signal with a modulation frequency of ω_c is loaded on one arm of MI. Therefore, an additional phase modulation C ⋅ cos (ω_ct) is introduced in

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