Crustal deformation measurement with a high resolution on the order of nano-strains in static to low frequency region is required for geophysical research. Optical fiber sensors are very attractive in this research field due to their unique advantages including high resolution, small size and easy deployment. In this paper, a fiber optic strain sensor with nano-strain-resolution and large measurement range for sensing the earth crustal deformation is reported. With this sensor the tide induced crustal deformation and the seismic wave were successfully recorded in field experiments.
© 2015 Optical Society of America
For geophysical research, e.g., earthquake study, it is required to record the earth crustal deformation field with sensor networks of high-resolution strain sensors deployed at multiple locations . The sensors must be able to provide a strain resolution better than 10 nano-strains (nε), which corresponds to the crustal deformation level induced by oceanic tide. Traditionally, sensors such as extensometers and laser strain-meters installed underground are used to realize such a high resolution [2, 3]. These facilities, however, are difficult to be widely implemented to form a sensor network, due to their size of tens to hundreds of meters in length and their cost of construction and maintenance. Seismometers can provide a high strain resolution for the dynamic deformation of the crustal such as seismic wave, but cannot measure the quasi-static deformation . Global positioning system (GPS) based sensor is suitable for monitoring crustal deformation with high strain resolution over large scale, but the spatial resolution is very limited .
On the other hand, optical fiber sensors are small in size, low-cost in installation, and can easily be multiplexed into sensor networks, making them very attractive for geophysics. Lots of efforts have been done towards this target [5–9]. However, most of the work is for the dynamic strain measurement working as seismic sensors, and the performance of quasi-static strain sensors is not satisfactory. In fact, the widely used fiber optic sensors in engineering area can only provide strain resolutions of 1-10 micro-strains (με) in the frequency region of crustal movement from less than 1 cycle per year to hundreds of hertz. For fiber optic sensors, although even pε resolution has been reported for dynamic strain sensing at kHz region [10–12], the realization of static strain sensing is much more difficult. A dynamic sensing is self-referenced, but a static strain sensor has to be compared with an external standard or reference. Some high resolution static strain sensors use molecular absorption cell as the extra reference, but the measurement range is very limited, e.g., no larger than the bandwidth of the absorption cell [13, 14]. Besides, fiber sensors with molecular absorption cell cannot deal with the disturbance of environmental temperature, which in fact is the main problem for fiber optic sensors in static domain because fiber sensors are sensitive to both strain and temperature. For high-resolution static strain measurement, a common way is to employ a strain-free reference for temperature compensation . The reference is also useful in eliminating other common drift such as the wavelength or intensity variation from the light source.
Towards the strain measurement in geophysical applications, we have developed a series of optical fiber strain sensors with ultra-high resolution [15–18]. At the beginning, we theoretically proved that nε-order strain resolution is achievable with proper sensor configuration by using of fiber Bragg grating (FBG) sensors , and then deployed one set of FBG sensor in field experiment to measure the crustal deformation, obtaining a strain resolution of 10 nε . To achieve even higher strain resolution and quicker measurement, new techniques were proposed and higher frequency resolution corresponding to sub-nε strain resolution was demonstrated in laboratory [16, 17].
In this work, we report the design of an improved high resolution optical fiber strain sensor and the field experimental results. A modified sideband interrogation technique is proposed for the interrogation of the sensor heads, which is composed of a π-phase shifted fiber Bragg grating (π-FBG) for strain sensing and a fiber ring resonator for reference. Compared with our previous work, the newly proposed optical fiber sensor has larger measurement range, better robustness and easier implementation. During the field experiments, the crustal deformation induced by oceanic tide is clearly observed, and the data are compared with that from a nearby 38-meter extensometer, showing that the fiber sensor has a strain resolution on the order of nε. Meanwhile, seismic wave is also recorded thanks to the quick measurement speed of the fiber sensor, proving the potential of covering the whole frequency region for geophysical research.
2. Sensor configuration
An FBG is fabricated by creating periodic variations in the refractive index of the core of an optical fiber . When light propagates through the grating, at a particular wavelength called the Bragg wavelength, the light reflected by the varying zones of refractive indices will be in phase and amplified. The Bragg wavelength λB is given as :12, 20]. In our work, the π-FBG on polarization maintaining fiber (fabricated by Fujikura) is employed for strain sensing. The spectrum is shown in Fig. 1. The bandwidth of the dip is 0.23 pm.
When strain or a temperature change is applied to the FBG, the spectrum will shift accordingly. The relative change of Bragg wavelength is expressed as :Equation (2) shows that the Bragg wavelength is sensitive to both strain and temperature linearly. It should be pointed out that FFPI, which is employed as the strain sensing element in ref , has even narrower dip in spectrum and the same strain / temperature sensitivity as π-FBG. But the FFPI has many resonance frequencies, not compatible with the sideband interrogation technique if large strain measurement range is required.
To distinguish the Bragg wavelength shift caused by strain from that by temperature variation, a strain-isolated reference is necessary to compensate the temperature sensitivity of the FBG. One possible way is to use another π-FBG as the reference. This way, however, limits the measureable strain range of the sensor, because the difference of the resonant frequencies between the strained sensing π-FBG and the free reference π-FBG has to be smaller than the region of radio-frequency (RF) modulation, which will be described later in this paper.
In the sensor proposed in this paper, we designed a fiber ring resonator working as the reference element, as shwon in Fig. 2(a). The fiber ring resonator is composed of a 2x2 polarization maintaining fiber coupler by connecting two of its pigtails. A circulator (CIR) is used to lead the input and output lightwave in a single line structure. The transmission of the fiber ring is :Fig. 2(b). The interval between the resonances is named as free spectrum range (FSR). The FSR of the fiber ring employed in our sensor is measured to be 142.86 MHz, agreeing with its length of about 1.4 m. The fiber ring has the same temperature sensitivity as that of the π-FBG. Any resonance frequency points of the fiber ring can be used as the reference to compensate the temperature sensitivity of the π-FBG. There is always a resonance frequency of the ring close to the resonance of the π-FBG, regardless of the applied strain to the π-FBG.
The interrogation system of the sensor is shown in Fig. 3. For the interrogation of the fiber ring resonator, a so-called Pound-Drever-Hall (PDH) technique is used . As shown in Fig. 3, the lightwave from the laser source is phase-modulated with a phase modulator (PM) driven by a sinusoidal wave from function generator (FG), and sidebands are generated as well as the carrier. A branch of such lightwave is injected to the fiber ring via the coupler (CP) and circulators (CIR), and the output lightwave is detected by the photo detector (PD). The sidebands and carrier have different transmission when pass through the fiber ring due to their different frequencies, resulting in an intensity modulation in the optical power on the PD. The detected signal is then demodulated to produce the PDH signal, as the black line in Fig. 4 (b). Compared with the direct measurement on the transmission of fiber ring, the PDH signal is immune to the intensity fluctuation of the laser and the residual reflection from fiber components along the light path.
An improved sideband interrogation technique is proposed for the interrogation of the π-FBG and to measure the resonance frequency difference between the π-FBG and the fiber ring. As shown in Fig. 3, the other branch of the lightwave after phase modulation is intensity-modulated by an intensity modulator (IM), which is driven at a radio frequency Ω. The intensity modulation generates two sidebands from the carrier, and both sidebands have the same pattern of phase modulation as the carrier, but with a frequency shift of Ω. Either of the sidebands can be used for the interrogation of the π-FBG, just as the interrogation of the fiber ring. Compared with our previous work in ref , this new configuration is more compact and only one radio frequency signal generator (RFSG) is required.
Figure 4(a) illustrates the working principle of the sensor. First, the frequency of the narrow linewidth tunable laser source is tuned close to one resonance of the fiber ring, as the reference lightwave shown in Fig. 4(a). Meanwhile, one of the sidebands is set close to the resonance frequency of the π-FBG by adjusting Ω, as the sensing lightwave in the figure. Next, the frequency of the narrow linewidth laser source is swept around the resonance of the fiber ring. At the same time, one sideband sweeps around the π-FBG. Both the fiber ring resonator and the FBG will produce a PDH signal respectively, as shown in Fig. 4(b). It should be pointed out that the carrier and other sidebands has no contribution in interrogation of the π-FBG, because the corresponding PDH signal approach zero as long as they are far away from the resonance frequency of the π-FBG. A cross-correlation algorithm is employed to calculate the frequency difference of the demodulated signals with high resolution, which has good capability to suppress random noise . The extracted frequency difference plus Ω is the actual resonance difference between the fiber ring and FBG, and this frequency is then used to adjust Ω for the next laser sweep.
With the above feedback control, the center frequency of laser is locked to one resonance of the fiber ring, and one sideband is locked to the resonance frequency of the π-FBG. The resonance difference between the fiber ring and the π-FBG is exactly Ω. If a large strain is applied to the π-FBG, the center frequency of the laser can be locked to a different resonance frequency of the fiber ring, which is close to the resonance frequency of π-FBG, so that the Ω is tuning within the available region of the RFSG. Since the fiber ring has constant resonance frequency interval of FSR, the real strain-induced resonance difference will be Ω + N·FSR, where N is the number of FSR corresponding to the reference resonance frequency change during the measurement. The measurable strain range of the proposed sensor is up to 3000 με without degradation of resolution, only limited by the tunable range of the laser.
To evaluate the parameters of the π-FBG sensor, a nano-positioning stage (PI, P-620.1CD) with resolution of 0.2 nm is employed to apply a variable strain to the π-FBG. The frequency difference (between the π-FBG and reference element) vs. applied strain is shown in Fig. 5. The strain sensitivity of the π-FBG is measured to be 114.0 kHz/nε. Due to the limited strain resolution of the test stage, this test is not suitable to evaluate the strain resolution of the π-FBG sensor.
3. Field experimental results and discussion
The field experiment was carried out in a vault on the coast of Aburatsubo Bay, Kanagawa, Japan. As shown in Fig. 6, a vault is built on the coastline and situated under a cliff about 10-m high. As the oceanic tide level varies, the pressure of the water on the sea bed changes accordingly, resulting in a deformation of the rock mass. This strain is regular with amplitude of με, providing an ideal reference for the assessment of sensor. Besides, there are 3 sets of extensometers with 38m-baseline mounted next to the π-FBG sensor (to the left of the FBG sensor in Fig. 6).
During the in situ demonstration, two piers with distance of 1 m are inserted into the rock bed 30-cm deep and fixed. The π-FBG is mounted between the piers with pre-strain. A strain-isolated fiber ring is placed close to the π-FBG. The vault is enclosed with very stable temperature and the strain measurement is unattended. The interrogation system is the same as illustrated in Fig. 3. A distributed feedback (DFB) diode laser is used as the laser source with frequency tuned via current. The frequency tuning range of the laser is about 1 GHz (8 pm), covering several FSR of the fiber ring. The phase modulator is driven by a function generator (NI, 5412) with a frequency of 10 MHz, while the intensity modulator is driven by a radio frequency signal generator (NI, 5651). The reflected lightwaves are detected by high speed photo detectors (New Focus, 3503). The demodulation is achieved with a dual channel I/Q demodulator. Both I and Q channels are sampled by a high speed analog-to-digital convertor, and then the two channels combine to produce the PDH signal. The sensing speed is about 30 samples per second, and recently it is upgraded to 100 S/s.
Figure 7(a) shows the measured strain by π-FBG and the oceanic tide level over one week during September 1 - 7, 2014. The oceanic tide level is sampled every 30 seconds. The strain of π-FBG is obtained by averaging the raw data to 1 sample per 10 seconds, and the offset is adjusted for easier observation (The π-FBG is tensioned with a large pre-strain for installation, and only the change of measured strain relates to the actual crustal deformation). The very similar shapes of the two curves show that the oceanic tide induced crustal deformation is clearly measured. Figure 7(b) is the comparison of the measured strain by the π-FBG and one nearby extensometer (Ext) with 38-m baseline. The two curves have different amplitude, which is caused by the different position and baseline length (the baseline of installed π-FBG sensor is 1 meter). The extensometer can only provide the averaged strain over its length of baseline, while the π-FBG sensor provides the average strain over a distance of only 1 meter.
The length of baseline determines the spatial resolution of the strain sensor, which plays an important role in geophysical research. For example, as shown in Fig. 7(a), the measured strain by the π-FBG sensor has a phase shift compared with the tide level, while the two curves in Fig. 7(b) are almost in phase. The phase difference is relates with the propagation of crustal deformation in rock, which is an important issue in geophysical researches. The FBG strain sensor provides meter-order spatial resolution on the measurement of deformation distribution, which is almost impossible for traditional extensometers.
To evaluate the strain resolution of the π-FBG sensor, a section of the measured data is analyzed. As shown in Fig. 7(c), due to the topography of Aburatubo Bay and the influence of wind, the tide level sometimes exhibits ripple with amplitude of tens of millimeters, as so-called seiche. The ripple on the tide level results in a corresponding ripple in crustal deformation with amplitude of several nε, which was also observed by the π-FBG as shown in Fig. 7(d). This result proves that the strain resolution of the π-FBG sensor is on the order of nε.
Seismic waves were also recorded thanks to the fast measurement speed of the sensor. Figure 8 shows the raw data of our strain sensor around an earthquake (M3.9, at 23:48, March 17, 2015, JST) in Chiba, Japan. Traditional seismometers are based on acceleration measurement and can only record dynamic signals like seismic wave, while the π-FBG sensor records both dynamic (seismic wave) and quasi-static (oceanic tide induced deformation) strain deformation. Here, the π-FBG sensor shows the potential of covering the whole frequency region involved in geophysical researches.
In summary, we have developed an optical fiber strain sensor for geophysical research with nε-order strain resolution, 1-m spatial resolution, large measurement range and broad frequency region. The sensor head consists of a phase-shifted FBG for sensing and a fiber ring for reference, and a newly proposed complex phase-intensity modulation scheme is used for the interrogation. With this sensor, crustal deformation and seismic wave were successfully recorded in field experiment with a strain resolution on the order of nε. As shown by our work, the optical fiber strain sensor has great potential in providing a high performance, low cost and easy implementation sensor for geophysical applications.
This work was supported by the National Natural Science Foundation of China under Grant 61327812, 61307106, and 61411140038.
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