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Abstract
A micro ultrasonic sensor based on an advanced suspended-core fiber is proposed and employed for in-lab seismic physical modeling. A free suspended core is obtained by acid corrosion and two cascaded uniform fiber Bragg gratings (FBGs) are imprinted in the suspended-core fiber. The sensor response and stability are largely improved due to the using of dual-FBG reflectors instead of weak-reflection fiber mirrors for constructing an in-fiber interferometer. The characteristics of reflection spectra and ultrasonic response of the sensor are analyzed and demonstrated experimentally. Comparative measurements are also carried out to prove the sensor superiority over the conventional weak-reflection one. Moreover, the sensor is used for seismic physical modeling to show its ability of practicable usage. Both the crosswell seismic and surface seismic in seismic exploration are modeled respectively based on reservoir and fault models. Various reservoir velocities are measured and each is consistent with the reported results. The fault features are also well reconstructed in the form of a cross-section model image. The improved sensor approach greatly promotes the application of the suspended-core fiber for weak acoustic detection in seismic physical modeling.
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1. Introduction
Seismic physical modeling is expected to promote the exploitation of oil and gas resources with lower cost and better controllability in laboratory [1]. Ultrasonics are employed to simulate the field seismic exploration usually in the frequency range of hundreds of Hertz [2–4]. The fiber-optic Fabry-Perot interferometers (FPIs) are always the most commonly used in ultrasonic detection because of their advantageous characteristics, such as flexible structure, easy fabrication, considerable sensitivity, and wide-frequency response [5–7]. Diaphragm-based fiber-optic FPIs have attracted more interest and most of them behave well in recovering the structural features of seismic physical models [8–10]. Inevitably, some of the ultrathin diaphragms are easily to be damaged and show poor chemical stability and heat resistance. Additional protective or waterproof packaging also give rise to unwanted effects both in response amplitude and detection resolution. Since there is no need of multilayer fabrication and diaphragm transferring, fiber Bragg gratings (FBGs) offer a valuable alternative to FPIs in acousto-ultrasonic detection [11]. In order to obtain an approximate uniform strain along the entire length, the grating length should be comparable to or smaller than the ultrasonic wavelength [12,13]. A sufficiently short FBG is required to detect the high-frequency ultrasonic waves, but it also comes with the side-effects of gentle slope and reduced reflectivity. Some post-processing technologies are employed to enhance the grating sensitivity, such as chemical etching, mechanical grinding, cone-shaped focusing and low elastic-modulus coating [8,14–16], which conversely degrade the optical stability and detection resolution.
The in-fiber FPI with FBG reflectors (FBG-FPI) possesses the advantages of both FPI and FBG, and thus attracts much attention in elastic wave detection [17–19]. Compared with the dissipative Fabry-Perot cavity, the FBG-FPI has the obvious merits of high quality factor, high structure stability, and ease of manufacturing and tuning. Therefore, it is a strong candidate to yield improvement in the sensing of weak ultrasonic signal. Wang et al. fabricated a microfiber FBG-FPI sensor to measure the underwater acoustic field [20]. The tapered microscaled FBG-FPI limits its application due to the lack of sufficient mechanical strength and stability. Rong et al. proposed an FBG-FPI probe for ultrasonic imaging of seismic physical models [21]. The process of long chemical etching causes the spectral distortion and degradation of FBG-FPI. Previously, we have presented a micro suspended-core FPI sensor [5]. The suspended-core fiber enables the dual benefits of spatial resolution and detection sensitivity by simply etching the suspended-core diameter to few microns. However, the fiber splicing and corrosion result in a weak-reflection FPI. The sensing spectrum varies with surroundings due to evanescent field effect, which brings inconvenience to the wavelength locking of edge filtering demodulation. Therefore, it is much necessary to further improve the acoustic performance of the suspended-core fiber through FBG-FPI for high-fidelity seismic physical modeling.
In this paper, a micro suspended-core fiber sensor based on FBG-FPI is proposed for ultrasonic detection in seismic physical modeling. Two cascaded uniform FBGs are imprinted in the suspended-core fiber, which is achieved by acid corrosion of a microstructured fiber. Compared with the previous suspended-core FPI sensor [5], the sensor response and stability are largely improved due to the using of dual-FBG reflectors instead of weak-reflection fiber mirrors, although both sensors have similar design of self-shielding cladding surrounding the free suspended core. The reflection spectra and ultrasonic response of the sensor are characterized theoretically and experimentally. Comparative measurements are also carried out to prove the sensor superiority over the previous one. Meanwhile, two specific physical models are constructed to simulate the crosswell seismic and surface seismic in seismic exploration. Reservoir velocities are measured correctly and fault features are well reconstructed by processing the transmission and reflection data collected via the sensor.
2. Fabrication and mechanism
2.1 Sensor design
Figure 1(a) shows the schematic diagram of the proposed suspended-core fiber sensor. The sensor fabrication consists of acid corrosion, fiber splicing and FBG inscription. One end of the grapefruit photonic crystal fiber (PCF) is acid etched to obtain a free suspended core. The other end of the etched PCF is then arc-fusion spliced to a standard single-mode fiber (SMF). Then two cascaded uniform FBGs are separately inscribed into the suspended core (FBG1) and the followed unetched core area (FBG2) of the PCF, as shown in Fig. 1(a). The light from the lead-in SMF travels forward along the PCF to reach the two FBG reflectors, thus forming a well-defined FBG-FPI probe. When applied on the suspended core, the underwater acoustic signal causes the slight wavelength mismatch of the two FBGs and results in the shift of the FBG-FPI reflection spectrum for edge filtering detection. Compared with the previous suspended-core FPI sensor [5], the proposed one has a similar design of self-shielding cladding surrounding and protecting the suspended core from collision, and also a comparable spatial resolution because of the corrosion-induced small-diameter suspended core. Furthermore, the sensor response and stability are largely improved due to the using of dual-FBG reflectors instead of weak-reflection fiber mirrors in Ref. [5]. Compared to the mentioned FBG-FPI sensors in normal fiber [18,19] and diameter-reduced fiber [20,21], the advanced suspended-core sensor has the distinct advantages in sensor fabrication and acoustic performance.
Fig. 1. (a) Schematic diagram of the suspended-core fiber sensor based on FBG-FPI. (b) Microscope image of the SMF-PCF fusion splicing. (c) Cross-sectional image of the unetched PCF. (d) Cross-sectional image of the etched PCF. (e) Microscope image of the suspended core inscribed with FBG1 (the yellow dashed frame indicates the suspended core).
The microscope image of the fusion-spliced SMF-PCF is shown in Fig. 1(b). The fiber splice is conducted via the core self-alignment process of an arc fusion splicer (Fujikura 80C) at a splicing condition of −60 bit discharge power and 300 ms discharge time. There is no obvious microstructure collapse at the fusion interface. Figure 1(c) shows the cross-sectional image of the unetched PCF. The highlighting fiber core is germanium-doped silica with a diameter of 14 µm. The inner cladding wrapping the core has a diameter of 28 µm. Six air holes with a major axis length of 16.3 µm are arranged symmetrically around the core within the fiber cladding. The outmost layer sealing the air holes is a 32-µm-thick cladding. Besides, the wall thickness between two adjacent air holes is about 6 µm. Compared to the thin-walled PCF with a 3-µm-diameter core in Ref. [5], the larger-core PCF in Fig. 1(c) is more suitable for the batch fabrication of uniform FBGs using a laser direct writing system [22].
The first and foremost is to etch one end of the PCF, thus removing the periodic air-hole cladding and finally leaving a single suspended core. Herein 49% hydrofluoric acid is used and the acid corrosion is processed at room temperature. The acid solution is sucked into the air-hole cladding by capillary force. A series of suspended-core fibers with different corrosion time are fabricated through repeated experiments. The attitude and length of the free suspended core are further confirmed by microscopic observation both in cross-section and lateral views. The etching rate of the suspended-core length is achieved to be around 52 µm/min. Thus, the corrosion process is controlled to fabricate the suspended core with a specific length. For uniform FBGs, as the grating length increases, so does the resultant reflectivity. When the corrosion time exceeds 7 minutes, the obtained suspended core tends to be located off-center. Eventually, the time period is set to 6 minutes and a suspended-core length of ∼300 µm is achieved accordingly. Figures 1(d) and 1(e) show the cross-section and lateral views of the suspended-core fiber, respectively. The whole periodic structure of the air holes shows a faster corrosion and finally disappears in Fig. 1(d). A suspended-core structure with a diameter of 23 µm, consisting of the core and the partial inner cladding, stands straight in the center. Furthermore, the microscope image in Fig. 1(e) clearly illustrates the separated suspended core marked in the yellow dashed frame, which confirms the optimization of the acid corrosion and the uniformity of the suspended core.
A femtosecond Ti:sapphire laser (Libra-USP-HE, Coherent Inc.) is employed for FBG inscription [23]. The laser energy is stabilized at about 200 nJ per pulse. The type-II FBG1 at the suspended-core area has a grating period of 1.6 µm, a central wavelength of approximate 1560 nm, and a peak reflectivity of ∼10%. Afterwards, another identical FBG, i.e., FBG2, is imprinted with a grating length of 300 µm at the unetched core area following FBG1. The separation distance between the two FBGs can be adjusted, thus forming the different effective lengths of the resultant Fabry-Perot cavity. An optical sensing interrogator (SM 125, Micron Optics) with a wavelength accuracy of 1 pm is employed to record the reflected intensity spectrum. Figure 2 shows the reflection spectra of the FBG-FPI sensors with separation distances of 500 µm, 1000 µm, 3000 µm, and 5000 µm, respectively. The processed in-line FBGs present a typical dual-FBG Fabry-Perot interference, which features narrow spectral notches within the FBG reflection range [18,19]. The measured free spectral ranges (FSRs) are 1059 pm, 650 pm, 247 pm, and 156 pm, corresponding to the FBG spacings of 500 µm, 1000 µm, 3000 µm, and 5000 µm, respectively. Considering the effective cavity length is a sum of the effective lengths of the FBGs and the separation distance between them [24], the estimated FSRs are respectively 1033 pm, 635 pm, 250 pm, and 156 pm, which agree well with the measured values. The cavity characteristics can be modified as needed by changing the FBG inscription and their physical gap. Eventually, the FBG spacing is fixed at 3000 µm to obtain a relative low intensity loss and narrow reflection bandwidth.
Fig. 2. The reflection spectra of the proposed sensor with different grating spacings: (a) 500 µm, (b) 1000 µm, (c) 3000 µm, and (d) 5000 µm.
Compared with the previous suspended-core FPI sensor [5], the proposed sensor has the advanced improvement in spectral stability and response amplitude. As shown in Fig. 3(a), the reflection spectrum of the FBG-FPI sensor after 6 months almost coincides with the initial one. The inset of Fig. 3(a) around 1561 nm confirms the long-term stability with wavelength shift of less than 20 pm and intensity change of below 0.4 dB. Considering the fact that the ultrasonic detection is carried out in water, the spectral variation of the FBG-FPI sensor from air to water is shown in Fig. 3(b). The corresponding inset exhibits wavelength shift of ∼90 pm and intensity change of ∼0.3 dB. In contrast, the FPI sensor in Ref. [5] presents significant changes both in spectral profile and intensity loss when entering water. Figure 3(c) shows the spectra comparison of the two suspended-core sensors in water. Apparently the FPI sensor presents a lager intensity loss of about −29.41 dBm. Besides, the proposed sensor has a steeper spectral slope of 56.91 dB/nm (slope A) than 7.85 dB/nm (slope B) of the previous one. Thus, the response amplitude of the FBG-FPI sensor is obviously improved by edge filtering demodulation. Furthermore, the spatial frequency spectra of the two suspended-core sensors are displayed in Fig. 3(d). More cladding modes in higher order are excited in the FPI sensor and thus more sensitive to external environmental disturbances. The dual-FBG reflectors in FBG-FPI confines most of the excited modes into the core area and provides a largely improved spectral quality.
Fig. 3. (a) The long-term stability of the FBG-FPI sensor. (b) Spectral variation of the FBG-FPI sensor in air and water. (c) Spectra comparison of the FBG-FPI and FPI sensors. (d) Spatial frequency spectra of the two suspended-core fibers.
2.2 Sensing principle
The response mechanism can be well demonstrated by the suspended-core model in the inset of Fig. 4(a), i.e., a single degree of freedom mass-spring vibration system. The PZT mainly emits longitudinal wave as the ultrasonic source. Considering that the ultrasonic wavelength (typically in the level of millimeter in water) is larger than the suspended-core diameter, the ultrasonic waves applied on the sensor can be idealized as plane waves. Correspondingly, the suspended core periodically deforms in the form of axial tension or compression. Given the applied ultrasonic pressure $\Delta P$, the axial length of the suspended core is modulated as follows [5]:
where L, $\Delta L$, E, and D are respectively the original length in Z-direction, the length change, the Young’s modulus, and the diameter of the suspended core. The FBG1 imprinted in the suspended core is modulated accordingly under the ultrasonic pressure, which finally leads to the spectrum change of the FBG-FPI sensor. Based on the coupled-mode theory and beam propagation method, the FBG-FPI reflectance of low reflection gratings can be expressed as [24]: where ${r_g}$ is the grating reflectance, ${n_{eff}}$ is the effective refractive index of the suspended core, ${L_{FPI}}$ is the effective cavity length, and $\lambda$ is the operating wavelength. It indicates that the FBG-FPI reflectance consists of the FPI cosine modulation within the FBG bandwidth range. The modulated FBG1 causes the wavelength mismatch between FBG1 and FBG2:Fig. 4. (a) Numerical simulation of the natural frequency of the suspended core versus its length (inset: schematic diagram of the interaction between the suspended core and ultrasonic waves). (b) Numerical simulation of the amplitude-frequency curve of the suspended core when its length is fixed at 300 µm.
In view of the freedom mass-spring vibration model, the proposed suspended core has the similar frequency feature to the previous one [5]. According to the Hooke’s law, the natural frequency of the suspended core can be expressed as:
3. Experiment results and discussion
3.1 Sensor characterization
The experimental setup for seismic physical modeling consists of three parts: the ultrasonic source by PZT excitation, the ultrasonic propagation in seismic physical models, and the ultrasonic reception by the sensor. The PZT emits continuous and pulsed waves that vary in frequency and intensity. The seismic physical modeling is performed on customized scaled models made of synthetic materials. The transmission and reflection waves of seismic physical models immersed in a water tank are captured by the suspended-core sensor, which is then demodulated based on edge filtering technique. Refer to Ref. [5] for more details on setting the detection system.
The PZT respectively emits 500 kHz, 1 MHz, and 4 MHz continuous/pulsed waves with driving voltage of 100 V. The output wavelength of the tunable laser source is located at 1560.97 nm for optimal edge filtering. Under the operating signal amplification (×10) and bandpass filtering of a photodetector, the time-domain results of sensor response are shown in Fig. 5. Due to the using of different types of PZT and the varied axial spacing between the sensor and PZT, the signal voltages are all normalized to show the smooth wideband frequency response of the suspended-core sensor below 5 MHz. The real-time response in Fig. 5(a) are uniform quasi-sinusoidal curves with little distortion. The pulsed signals in Fig. 5(b) exhibit some weak resonant components following the main peak, which may result from the multiple resonances of the PZT source or the trapped waves after ambient reflections.
Fig. 5. Time-domain response to (a) 500 kHz, 1 MHz, and 4 MHz continuous waves and (b) 500 kHz, 1 MHz, and 4 MHz pulsed waves.
The sensor response to the changes in driving voltage and axial spacing are respectively shown in Fig. 6, so as to characterize the sensor linearity. When the driving voltage of pulsed waves increases from 100 V to 400 V in steps of 50 V while other conditions keep constant, the suspended-core sensor has a good linearity in Fig. 6(a) with a response increment of 7 mV per pulse voltage. In addition, the separation distance between the sensor and PZT is changed independently from 3 cm to 12 cm with an interval of 1 cm. As can be seen in Fig. 6(b), the sensor linearity is quite well with a response attenuation of 50 mV/cm. Thus, the sensor response is linearly proportional to the applied ultrasonic strain field. The proposed sensor is capable of providing high-fidelity ultrasonic reconstruction in seismic physical modeling.
Fig. 6. Sensor linearity: (a) signal voltage versus pulse voltage; (b) signal voltage versus separation distance.
In order to characterize the sensor resistance to low-frequency surrounding noises, the weak vibration excitation with vibration acceleration of 0.5 m/s2 and frequency range from 10 Hz to 200 Hz is applied into the radial and axial directions of the suspended-core fiber respectively, as shown in the insets of Fig. 7(a). The output voltages at different frequencies indicate that the sensor has a good resistance to vibration noises. By comparison, the FPI sensor using an ultrathin gold film in Ref. [8] has a higher acoustic sensitivity within a wider frequency band, which enables the ultrasonic wave to be detected in air. Therefore, it easily suffers from the disturbance of environmental vibrations. The temperature response of the suspended-core fiber is shown in Fig. 7(b). It is seen that the temperature variation shifts the central wavelength of FBG-FPI to be 10 pm/°C, which is consistent with the temperature drift of interreference fringe in Ref. [17]. Considering that the experiment is carried out in water at an air-conditioned room temperature, the temperature effect can be excluded. Alternatively, a feedback interrogation scheme can be developed to keep the sensor maintained at the optimum bias point [25]. Moreover, the sensor response is continuously monitored for hours and the signal fluctuation is less than 0.1 V in Fig. 7(b), which further verifies the long-term stability.
Fig. 7. Sensor stability: (a) resistance to radial and axial vibration noises; (b) central wavelength shift with ambient temperature and signal monitoring in hours.
Comparative measurements are carried out in Fig. 8 by using the two suspended-core sensors based on FBG-FPI and FPI in Fig. 3(c). Both of them are exposed to 1 MHz pulsed waves under the same condition. As shown in Fig. 8(a), the two suspended-core sensors present a similar well-defined response curve. The FBG-FPI-based suspended core has a peak-to-peak voltage of 2.35 V and the FPI-based one presents a peak-to-peak voltage of 0.07 V. The time-domain signals are converted into their counterparts in frequency domain by using a fast Fourier transform. As shown in Fig. 8(b), the dominant frequencies of the two sensors are both around 1 MHz, corresponding well with the pulsed source. The other frequency components around the main peak may result from the multifrequency excitation of PZT. In addition, the FBG-FPI sensor presents an amplitude increment of more than 30 dB over the FPI sensor. Thus, the proposed sensor shows a greater response so as to extract the weak ultrasonic echoes in seismic physical modeling.
Fig. 8. Comparative measurements of the two suspended-core sensors based on FBG-FPI and FPI in (a) time domain and (b) frequency domain.
3.2 Seismic physical modeling
The proposed sensor is used for seismic physical modeling, including crosswell seismic and surface seismic. For crosswell seismic modeling, the ultrasonic transmission technique is used to acquire the velocity variance of ultrasonic waves passing through the model. For surface seismic modeling, the ultrasonic pulse-echo method is utilized to capture the echo data reflected from each layer and the model features are reconstructed by time-of-flight.
Figures 9(a) and 9(b) show the in-lab seismic physical model for crosswell seismic modeling. The model is designed to simulate the multilayer and multiphase geological region on site, which contains several structural layers and water/oil contents. The layer 1 originates from the mixture preparation of silica powder, epoxy resin and curing agent according to a certain proportion. The middle layer, i.e., layer 2, is made of terra alba, epoxy resin and curing agent in proportion. The layer 3 as the capping layer consists of paraffin refined wax. The thicknesses of the layers 1, 2, and 3 are 1 cm, 1.5 cm, and 1.2 cm, respectively. The model dimension is about 23 cm×13 cm×3.7 cm. Especially, the middle layer is molded as the reservoir stratum, which is composed of the intact area (a), water area (b), water/oil mixing area (c), and oil area (d) from left to right in Fig. 9(a) and 9(b).
Fig. 9. Crosswell seismic modeling: (a) the vertical view of the reservoir stratum before capping (the markers of a, b, c, and d represent the intact area, water area, water/oil mixing area, and oil area, respectively); (b) the photograph of the multilayer and multiphase physical model; (c) the transmission signals of areas a, b, c, and d received by the suspended-core sensor in colored curves and the corresponding reference signal in black curve.
The PZT and the fiber sensor are located on the opposite sides of the model. Both ends of the two components are flattened against the model surface and their centers are also kept in a line perpendicular to the model surface. Four single-shot acoustic waveforms are respectively measured at the defined areas (a, b, c, and d). Since different materials and water/oil contents are adopted for model fabrication, the ultrasonic waves have different propagation velocities when passing through each layer. The material velocities (travel times) of layers 1, 2, and 3 are pre-measured by transmission experiment to be 2220 m/s (4.5 µs), 2112 m/s (7.1 µs), and 1428 m/s (8.4 µs), respectively. Figure 9(c) shows the transmission signals of areas a, b, c, and d received by the suspended-core sensor. Meanwhile, the reference signal is drawn to indicate the reference time of ultrasonic transmission. For clarity, the black arrows mark the reference time and the first peak of each transmission. It is obvious that the travel time strongly depends on the model areas for the different arrivals of the first peak. As for the intact area (a), the total travel time of ∼20 µs agrees well with the pre-measured layers. In addition, the travel times of areas b, d, and c are extracted as 23.04 µs, 27 µs, and 24.84 µs, respectively. Thus, the ultrasonic velocities of water, oil, and water/oil mixture can be respectively calculated as 1480 m/s, 1064 m/s, and 1256 m/s, which are consistent with the reported values [26,27].
Another step-type physical model is shown in Fig. 10(a) to simulate the geological structure of faults, such as graben and horst. As for the surface seismic modeling, the reflection experiment is carried out to reconstruct the model image by time-of-flight. As shown in Fig. 10(a), the model consists of two parts along the x axis: the upper translucent PMMA and the bottom white mixture of silicon rubber, epoxy resin, and curing agent. The ultrasonic velocities of the two parts are about 2360 m/s (the upper) and 1250 m/s (the bottom). Several acoustic reflection surfaces are defined along the y axis: R0 represents the outside surface and R1, R2, and R3 are the material interfaces between PMMA and the mixture. The three interfaces have the same length of 5 cm in the y direction. The heights between R0 and the interfaces along the x direction are 4 cm (R0R1), 3 cm (R0R2), and 5 cm (R0R3). The final integrally-formed model in Fig. 10(a) has a dimension of 15 cm×10 cm×6.5 cm.
Fig. 10. Surface seismic modeling: (a) the photograph of a step-type cuboid model (the x direction represents the variation of model components and the y direction indicates the change in step heights); (b) the typical time-domain echoes at each step; (c) the cross-section image reconstructed by the approach of time-of-flight.
The PZT and the fiber sensor are located on the same side of the model, and fixed on a motorized stage over the model to perform a point-to-point line scanning. Both ends of the two components are immersed in water and separated from the model by approximate 3 cm. Series of ultrasonic pulse-echoes are acquired by scanning detection along the y axis. When travelling through the step-type model, ultrasonic waves are partly reflected as echoes due to the difference of acoustic impedance and propagation velocity at R0, R1, R2, and R3. Figure 10(b) shows the resultant time-domain echoes at each step. The voltage peaks clearly demonstrate the acoustic reflection surfaces. The echoes by R0 present a significantly higher amplitude around 40 µs and the undersurface of the cuboid model is hardly recognizable due to large acoustic attenuation. The time-of-flights of R0R1, R0R2, and R0R3 are respectively calculated as 33.9 µs, 25.42 µs, and 42.37 µs, which match well with the echo curves in Fig. 10(b). Moreover, a cross-section model image is reconstructed in Fig. 10(c). Additional data filtering and amplification are used to emphasize the three interfaces of R1, R2, and R3. The step-type feature is distinctly displayed, corresponding well to the actual model in Fig. 10(a). Some distortions, such as the blurred ends of R1, R2, and R3 and the fake layers presented in multiple parallel lines around the interfaces, may result from the acoustic propagation behaviors, such as scattering and reverberation [8,28].
4. Conclusion
In conclusion, an advanced suspended-core fiber sensor is demonstrated and used for in-lab seismic physical modeling. Comparative experiments are carried out to prove the sensor superiority on spectral stability and ultrasonic response over the previous suspended-core sensor. The key of achieving improvement is due to the using of dual-FBG reflectors instead of weak-reflection fiber mirrors for constructing a suspended-core interferometer. As expected, the proposed sensor performs well both in modeling of crosswell seismic and surface seismic. Besides the similarities with the reported one, such as compact structure and micro size, the new suspended-core fiber provides crucial improved capabilities to seismic physical modeling methods.
Funding
National Natural Science Foundation of China (61735014, 61927812, 62005214).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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