## Abstract

Detection of earthquakes and tidal variations via measurement of strain in the Earth’s crust requires compact and robust instrumentation with low power usage that can be deployed in the field. Here we demonstrate a stationary-wave integrated Fourier transform spectrometer (SWIFTS) and measure the variations induced by ground strain on an optical fiber Bragg grating sensor using two short ($17\pm 2\text{\hspace{0.17em}}\text{\hspace{0.17em}}\mathrm{mm}$) Fabry–Perot (FP) cavities, one for the sensor, and one for temperature compensation. The SWIFTS delivers spatial interferograms that are then Fourier transformed to deduce the deformation from a cross-spectral analysis of the FP spectra. The full system is tested in field conditions to record crustal earth strain signals and successfully detect the earth tide and an earthquake signal. With this low-coherency interferometry technique, this system offers an excellent compromise between the resolution needed and the cost of a fully autonomous field instrument.

© 2015 Optical Society of America

## 1. INTRODUCTION

Since the promising and enthusiastic paper by Ferraro and De Natale, in 2002 [1], relatively few attempts have succeeded in providing real deformation signals related to earth crustal processes with fiber Bragg grating (FBG) sensors [2 –4]. This task remains a challenge in earth science to help answer the questions related to long or short transient deformation processes with durations of several hours up to several weeks. On the one hand, the problem of detecting fast deformation (10 Hz to 1 kHz) is solved by very interesting low-noise solutions [5]. On the other hand, low- and very-low-frequency strain sensors (down to less than 10–3 mHz) are subject to drift as well as thermal and pressure noise contaminations on the fiber itself or on the interrogator system. These perturbations make strain sensor realization much more complex. Recently, [2,3,6] used long base optical fibers of Michelson-type design to record earth-tide and earthquake signals at depth (boreholes) and at the surface. In field conditions, using long base sensors, they reached resolutions close to the limits obtained by [7] in lab conditions with a short base (13 cm) Fabry–Perot (FP) design: [10–2; 1 Hz band]. References [4] and [8] demonstrate the capabilities of a narrow linewidth tunable laser to reach resolution of $10n\u03f5$ at low frequencies ($<=1.\mathrm{e}-2\text{\hspace{0.17em}}\text{\hspace{0.17em}}\mathrm{mHz}$) with a short base (3 cm) Bragg grating design in field conditions. In our approach we test a short base sensor design (1.7 cm long FP) with equipment that is perfectly suited for field deployment, i.e., compact, embeddable, low power, and immune to power shutdown since it does not alter the continuity of the long-term signal. In Section 2, we explain the methodology used for the sensor itself and for the processing. In Section 3, we show examples of crustal strain signals recorded in field conditions to quantify the instrument noise level, test the temperature correction procedure, and demonstrate the viability of the instrument in field conditions.

## 2. METHODOLOGY

#### A. Fiber Sensor and Stationary-Wave Integrated Fourier Transform Spectrometer

The strain sensor principle is depicted in Fig. 1. A 100 nm wide light source [superluminescent diode (SLED), centered at 855 nm] emits toward two successive Bragg grating resonators: two FP cavities with respective lengths of 15 and 19 mm, made of FBGs with an average full width at half-maximum (FWHM) of 0.13 nm. One of the FPs serves as a reference; the other is mechanically coupled to the wall of the tunnel. The two FP cavities are distant by a few millimeters and subject to the same environmental variations. The light reflected by the two FPs is sent to the stationary-wave integrated Fourier transform spectrometer (SWIFTS) (commercial model “Zoom Spectra” built by Resolution Spectra SAS, a spin-off company from Grenoble University), which delivers a digitized interferogram every second (see below). The data timing is of crucial importance in geophysical data recordings. This is achieved by triggering the sampling by means of the so-called “pulse per second” (PPS) electric signal delivered by a GPS receiver located 1 km away, outside the gallery, and transmitted through an optical link. Finally, the digitized spectrograms are sent over a gigabyte Ethernet link to a low-power rugged PC running linux. The SWIFTS [9] is a truly static (no moving parts, no frequency scanning), low-coherency spectrometer. It builds a stationary wave generated by the superposition of direct and backward guided optic waves. The backward wave is obtained here by reflection on a mirror. A high-resolution spatial domain interferogram is then obtained along a 2.8 cm waveguide. It is spatially sampled by means of gold nanodot diffractors, periodically distributing every 14 μm in the evanescent field along the surface of the waveguide. This 14 μm physical sampling is equivalent to a 42 μm optical sampling when one considers the optical path and the refraction index of the guide. The light diffracted by these nanodots is then pictured by a high-speed (20 kHz) CCD camera. In our application, the interferogram intensity is averaged by stacking 5000 images every second. Figure 1 shows that all the optical parts of the sensor surrounded by dotted lines are embeddable. In the present experiment, the SLED was left in independent storage. The overall power consumption of the full system is of the order of 10 W, which allows us to set the system in a fully standalone installation powered by solar panels.

#### B. Processing

The interferogram intensity $I(x,t)$ ($x$, distance along waveguide; $t$, time) associated with a FP resonator is composed of several pulses periodically distributed every $L$ mm, where $L$ is the FP cavity length [10], and the pulsewidth is linked to the bandwidth of the FBGs. The first pulse ${I}_{1}(x,t)$ is located at $x=0$ on the mirror, the second ${I}_{2}(x,t)$ at $x=L$, and so on. These pulses are furthermore modulated by the wavelength of the light sent back by the FBGs [Fig. 2(a)]. When the FP cavity is subject to a deformation $\u03f5=\frac{dL}{L}$, the interferogram is stretched according to

The deformations of ${I}_{2}(x)$ and the FP cavity are then identical. In practice, ${I}_{2}(x)$ deformation can be approximated by a simple translation since the spatial extent of the packet is small compared to the distance to the mirror; measuring the cavity deformation is then just a matter of measuring the translation $\mathrm{\Delta}$ of the packet ${I}_{2}(x)$. We tested this approximation by performing both the exact and the approximate processing. No significant improvement could be obtained, while the exact processing is much more time consuming. It is important to mention that for the two cavities having distinct lengths $L$, 15 and 19 mm, respectively, the interferograms do not fully overlap. By applying an appropriate window, one can thus easily extract their respective second packet ${I}_{2}(x)$ to measure their deformations simultaneously (Fig. 2).We now introduce the time dependency. In order to compute the partial interferogram ${I}_{2}(x,t)$ spatial shift at each time $t$, two strategies are possible: spatial or Fourier domain processing. We must point out that the interferograms digitized at 42 μm (optical units) are undersampled and that Fourier domain processing is the easiest solution to overcome this limitation. This is possible because the spatial sampling is not perfectly regular and a simple discrete Fourier transform (DFT) allows retrieving the almost correct spectrum in the correct bandwidth (848–853 nm). The processing is then as follows: at each time $t$, for each cavity, compute the spatial DFT of the interferogram’s second packets ${I}_{2}(k,t)$. Compute the cross spectrum with respect to a reference time $t0\text{:}II(k,t)={I}_{2}(k,t)\xb7{I}_{2}^{*}(k,t0)$. From the cross spectrum, estimate the spatial shift $\mathrm{\Delta}(t)$ from the spectral phase by means of a weighted linear regression:

Alternatively, we can eliminate the need for a reference time by building a cross-spectra matrix for all the times $\{{t}_{i}\}$ in a moving window and by inverting for the relative translations $\mathrm{\Delta}({t}_{i})-\mathrm{\Delta}({t}_{j})$. The FP cavity deformation that is deduced from this processing includes mechanical ($\u03f5$) and linear thermal ($\alpha {T}_{1}$) effects. The SWIFTS waveguide by itself is also subject to thermal perturbations including the dilatation/contraction of the waveguide and the modification of the refraction index. These first-order linear effects are grouped into a single linear thermal response: ($\beta {T}_{2}$). To discriminate thermal and deformation effects, we use the two FP cavities, ${\mathrm{FP}}_{\text{sens}}$ and ${\mathrm{FP}}_{\text{ref}}$, recalling that only ${\mathrm{FP}}_{\text{sens}}$ is coupled to the wall. The relative displacement ${\mathrm{\Delta}}_{\text{sens}}-{\mathrm{\Delta}}_{\text{ref}}$ is directly proportional to the strain deformation, assuming that the thermal effects are identical for the two cavities:## 3. FIELD TESTS

In order to validate the sensor in field conditions and precisely evaluate the resolution in a quiet environment, we installed the strain sensor in a gallery of the Low Noise Underground Laboratory (LSBB) operated by the CNRS at Rustrel, South of France. This laboratory is located in a limestone stable massif, 70 km away from the Mediterranean Sea. It provides a complete infrastructure with minimum thermal and pressure perturbations. The sensor was installed at the end of a gallery, 1000 m away from the entrance and 300 m below the surface. The objective was to record the earth tide, which in this area has no significant contribution from ocean tide. The LSBB facility has no strainmeter for direct comparison with our sensor. We use a comparison with theoretical data for earth tide, and a comparison with an array of seismic sensors. For earth tide, the expected excitation is of the order of $\pm 10n\u03f5$ and was computed using the Gotic2 software [11].

We tested both normal and polarization-maintained (PM) fibers for both the transport fiber (20 m) and the grated fiber to reduce polarization effects. The ${\mathrm{FP}}_{\text{sens}}$ was vertically coupled to the wall using horizontal silica cones, a method that is typical for optical silica tiltmeter installation [12]. Two silica cones, distant by 12 cm with a 100 μm wide and 2 cm long cutting, pinch the optical fiber containing the ${\mathrm{FP}}_{\text{sens}}$. This ${\mathrm{FP}}_{\text{sens}}$ is loosely tied between the cones, while the ${\mathrm{FP}}_{\text{ref}}$ follows the same path but is not tied. We first show the result of a 50-day recording period with standard fibers (i.e., not PM) where the earth-tide signal is compared to the theoretical model obtained by the Gotic2 modeling. Figure 3 shows that we successfully detect the vertical component of the deformation associated with the earth tide (component M2, lunar semidiurnal; S2, solar semidiurnal; K1, lunar diurnal) despite very small amplitudes ($\pm 10n\u03f5$). Indeed, in this test, we reach the limit of the sensor resolution that is of the order of $25n\u03f5$ (signal peak level) in the frequency band [5.e-6 Hz–5.e-4 Hz] (i.e., period from 0.5 to 48 h). The phase differences that we observe between the measured and the theoretical signals can be due to (1) the weak signal–noise ratio, (2) an effect of local geological heterogeneities close to the sensor, (3) perturbations due to atmospheric or hydrologic effects (this effect can be strong for small sensors), or (4) a real discrepancy between observed and modeled tide [13].

In a second example, we show (Fig. 4) the signal recorded during the mag. 8.1 Chilean earthquake of 1 April 2014 (23h46), at the time when seismic waves arrive at Rustrel, 40 min after the earthquake. This example is interesting because the frequency range is quite different from the earth tide and dominated by a 0.05 Hz excitation (crustal Rayleigh surface waves). We compare the signal recorded by the strainmeter with an estimation derived from the seismic records obtained by five close ($<500\text{\hspace{0.17em}}\text{\hspace{0.17em}}\mathrm{m}$) seismic sensors that record the displacement (Ux, Uy, Uz) (Fig. 4). We use an approximation to derivate the vertical strain dUz/dz from the finite difference estimation of the derivatives dUx/dx and dUy/dy [14]. We observe that we correctly detect the arrival of the deformation associated with the earthquake, with the correct amplitude level. The discrepancies between the two waveforms may be again attributed to the noise level, local geological heterogeneities, or the approximation used to estimate the true deformation. This last sequence was recorded with PM optical fibers, where the PM fibers are used everywhere except in the SWIFTS waveguide. The comparison between PM and standard fibers shows no differences in the short-term noise level. We notice, however, a noticeable difference in the long-term quality of the signals ($>3$ months, not shown) with a much more stable response of PM fibers with respect to transient perturbations associated with pressure and temperature (e.g., visits to the gallery).

## 4. DISCUSSION

We discuss our results with respect to those obtained by three other studies [3,7,8], and focus the discussion on (1) sensitivity at high frequencies, (2) thermal correction, (3) polarization perturbation, and (4) adequacy to field instrumentation. We first point out that we use the 850 nm wavelength instead of the more conventional 1500 nm in [3,7,8]. The reason is that the SWIFTS uses an optical detector (CCD camera) in the visible range. This mandatory choice has a disadvantage in terms of Bragg grating costs that are more expensive at 850 nm than at 1500 nm.

In terms of sensitivity, we focus here on short period ($<24\text{\hspace{0.17em}}\text{\hspace{0.17em}}\mathrm{h}$) signals where the SWIFTS inherent noise is mostly apparent (i.e., for $\text{frequency}>1.\mathrm{e}-5\text{\hspace{0.17em}}\text{\hspace{0.17em}}\mathrm{Hz}$). For longer periods, many external sources can contribute to the noise (i.e., nonstrain signal), and our duration of recording (three months) does not allow us to draw any conclusions. Figure 5 shows the power spectral density for the long base (250 m) BOFS vertical strainmeters [3], our 17 mm long sensor, and the noise level obtained by [7] on their short base (13 cm) sensor in the band [0.01 Hz; 1 Hz]. An interesting noise level is obtained by [3] (Fig. 5, green curve) by subtracting the signal recorded by the two adjacent vertical borehole BOFS sensors. The rms noise level in comparable frequency bands gives another comparison. The authors in [8] measured a noise level of $9.8n\u03f5$ for their 3 mm long Bragg grating sensor in the frequency band [1.e-5 Hz, 0.08 Hz] using the earth-tide signal. The authors in [3] measured a noise level of $1.2n\u03f5$ on their BOFS for a seismic event in a similar band. We measure on our SWIFTS sensor a $90n\u03f5$ rms signal level in the same band that we interpret as the spectrometer noise level.

For first-order comparisons, we consider that the sensitivity is inversely proportional to the effective sensor length and summarize the result in Table 1. This table shows what the effective sensor length should be to reach the sensitivity of [3] borehole sensors ($1.2n\u03f5$). The sensor of [7] cannot be directly compared to others, but considering the theoretical noise curve shown in Fig. 5, its sensitivity should be close to [3]. The SWIFTS sensor needs to reduce its noise level by 37 db to reach the level of that in [3]. It is worth noting, however, that the real noise level in [3] is still 30 db lower (Fig. 5, green curve), which implies to use an effective sensor length of about 10 m for the SWIFTS. If we consider that the noise level obtained by [3] is close to what a strainmeter noise level should display to record crustal strain, we see that the optical fiber strain sensor technology is definitely sensitive enough to provide accurate sensors at size as small as 3 cm [8]. SWIFTS technology does not reach the best sensitivity as compared to [7,8]. There are two ways to improve this sensitivity: increase the effective sensor length, or measure simultaneously on an array of short base strainmeters. The next SWIFTS generation will allow us to measure 16 more sensors in parallel. It must be noted that for geoscience applications, the smaller sensor size may not be the best solution. Several authors (e.g., [15]) point out that localized deformation measurements can be strongly affected by local geological heterogeneities. This is a well-known issue for borehole sensors with a typical measurement length of several meters.

In terms of thermal correction, and more generally, for long-term disturbances including pressure, Ref. [3] is the only study that provides long enough records to draw some conclusion. Reference [8] and SWIFTS use the same principle of a reference and sensor Bragg gratings to remove the thermal effects. The Michelson design in [3] provides the same possibility to apply a thermal correction by subtracting the signal of the two arms. The results shown by [3] seem to prove that this principle is good enough to keep thermal disturbance at a sufficiently small level.

The effects of polarization disturbance are only mentioned in [3] and our study. We observe clear effects of polarization disturbance on the quality of the interferograms when the instrument is subject to thermal or mechanical excitations. This was observed on long-term noise levels after moving the fiber or during a temperature drop of 0.01° during winter. We circumvent this problem by using PM fibers, a solution that increases the cost of the fiber sensor. The solution proposed by [3] using a polarizing Faraday mirror is an interesting alternative.

Finally, a point at which the SWIFTS solution clearly encompasses other interrogators is the simplicity of the whole system. This interferometer has no moving parts and no frequency scanning, and performs a fully static measurement. It is compact ($10\text{\hspace{0.17em}}\text{\hspace{0.17em}}\mathrm{cm}\times 10\text{\hspace{0.17em}}\text{\hspace{0.17em}}\mathrm{cm}\times 15\text{\hspace{0.17em}}\text{\hspace{0.17em}}\mathrm{cm}$), and could easily be embedded with the light source. This compactness and low power requirement allows us to deploy a field instrument with a very reasonable cost and infrastructure. Other interesting features are the robustness and the sensor immunity to power failure as it delivers an almost “absolute” measurement of the fiber deformation. Forthcoming tests will investigate the performance of a Michelson-type design and a more extensive analysis of long-term drifts.

## 5. CONCLUSION

We have developed and tested an optical fiber strainmeter using standard FBGs with a new interrogator. The measurement is based on the SWIFTS, a low-power, embeddable system. We have shown different examples of real signals recorded in the LSBB facility in southern France. This demonstrates the capabilities of this instrument and its potential use for earth sciences investigation. The resolution of the SWIFTS does not reach the limits obtained in a laboratory environment with state-of-the-art optical design. However, we observe a resolution of the order perfectly suited to field deployments.

## FUNDING INFORMATION

CNRS (MI Instrumentation aux limites-2014); LABEX OSUG@2020.

## ACKNOWLEDGMENT

The authors thank L. Jenatton for her technical support. We gratefully ackowledge the two anonymous reviewers whose comments helped to improve the manuscript’s clarity. We thank S. Gaffet, A. Cavaillou, and D. Boyer from LSBB for their help and support.

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