light generated by the ith backscattering enhanced point can be expressed as:
(3.1)
While the electric field intensity of the local oscillator can be described as:
(3.2)
Therefore, the signal received by the BPD can be represented as:
(3.3)
Where asi and aL are the amplitudes of the pulse signal from the ith microstructure and the local oscillator, respectively, S is the responsibility of the BPD, Δf = fS − fL = 200 MHz is the frequency shift of the probe pulse, and φi = φsi − φL is the phase difference between the signal light from the ith microstructure and the local oscillator. The frequency shift of 200 MHz could move the sensing signal to a high‐frequency band, which is beneficial in eliminating the low‐frequency noise. As shown in Figure 3.6b, a band‐pass filter (BPF) with center frequency at 200 MHz is used for signal denoising. After band‐pass filtering, the relatively pure beat frequency signal Data(i) can be obtained. In addition, a reference function is developed for phase extraction, as well as its orthogonal function that is generated by the Hilbert transform, which can be expressed as:
(3.4)
(3.5)
Multiply Iri(t) by Iref1 and Iref2, respectively, and then a pair of the orthogonal functions about φi can be obtained after the low‐pass filter (LPF). Furthermore, the differential cross‐multiplying algorithm is employed to calculate the φi, and the following result is obtained:
(3.6)
Then, the phase change of the sensing fiber between ith and (i+1)th backscattering enhanced point can be described as:
(3.7)
Consequently, the amplitude, frequency, and phase of the acoustic wave are represented by the optical phase change Δφi. Notably, here the spatial resolution is decided by the spatial interval of the backscattering enhanced scatters in the DMOF, and Δφi is directly served as the output of each channel without additional moving average algorithm.
3.2.5. Performance of the DMOF‐DAS
Based on the preceding key techniques, we developed the DMOF‐DAS system as presented in Figure 3.7a, and the DMOF with a microstructure spatial interval of 5 m and a length of 1.44 km was deployed as the sensing fiber for the field test. Intrinsically speaking, the acoustic signal acted as the dynamic strain change on the sensing fiber. To test the acoustic sensitivity and linearity of the DMOF‐DAS system response, a section of 1‐m‐long sensing fiber was wrapped on a cylindrical piezoelectric transducer (PZT), and a strain change with the step of 19.23 nε was applied on the fiber through the PZT. As illustrated in Figure 3.7b, the system exhibited high sensitivities of 0.0153 rad/nε for strain increasing and 0.0152 rad/nε for strain decreasing, as well as an ultrahigh linearity of 1. The slight phase difference between the two curves was only 0.0286 rad, which demonstrated an extremely low hysteresis error. It should be noted that the actual sensitivity of the DMOF‐DAS system with 5 m spatial resolution will be five times that of the tested 1‐m‐long fiber, reaching 0.076 rad/nε. Figure 3.7c shows the power spectral density (PSD) of 1 Hz acoustic signal and the noise floor in static condition for estimating the strain measurement accuracy. It can be deduced that the minimum detectable strain change could be 4 nε/√Hz at 0.01 Hz and 3.4 pε/√Hz at 10 Hz, corresponding to the noise floor of 0.3 rad/√Hz and 2.7 × 10−4 rad/ √ Hz, respectively. These test results demonstrate the ultrahigh sensitivity, especially at the low‐frequency band. Moreover, obvious peak locating at 1440 m, 60 kHz in Figure 3.7d, indicates that the maximum frequency of the acoustic signal can reach up to 60 kHz.
Figure 3.7 Sensing performance of the DMOF‐DAS system: (a) Photograph of the equipment; (b) strain sensitivities and hysteresis for the strain increasing and decreasing processes; (c) noise PSD of phase change on two sections of the fiber with 1 Hz dynamic strain change and static strain change, respectively; and (d) frequency spectrum along the 1.44‐km‐long fiber when the dynamic strain change at a frequency of 60 kHz is applied on the fiber.
3.3. BOREHOLE SEISMIC SURVEY TESTS AND RESULTS
3.3.1. Zero‐Offset VSP Survey in Fushan Oil Field
A field test using the DMOF‐based fiber optic DAS system was conducted in the Fushan oil field of China National Petroleum Corporation (CNPC) in China. A zero‐offset VSP survey was performed; its schematic is depicted in Figure 3.8a. A water‐filled source pit for the electrical spark seismic source was used to generate seismic energy on the surface near the wellhead. A 524‐m‐long sensing DMOF optical fiber cable with a tight buffer, strength member, and outer jacket was deployed into a cased borehole with a weight bar at the bottom to pull the fiber cable down in the borehole. The fiber cable was freely floated in the water‐injection‐filled borehole without any clamping, and the coupling between the fiber cable and the wellbore was realized by water.
Figure 3.8 Field test in the Fushan oil field: (a) Schematic of the zero‐offset VSP; (b) the DMOF‐based fiber optic DAS system recorded borehole seismic data (inset: amplitude spectra of the seismic data); and (c) Frequency‐wavenumber (F‐K) domain spectra of the