effects, such as temperature variations), the phase of the reflected light varies over time. These phase variations are linearly related to the strain changes parallel to the fiber axis. OFS uses reflections of a continuous wave laser from a Faraday mirror at the far end of the fiber, while DAS relies on backscattered laser pulses that are reflected from inherent imperfections (random or engineered) spatially distributed along the fiber. These backscattered reflections are very weak, so an average is taken over each specific fiber length (gauge length). While OFS returns a continuous uninterrupted signal corresponding to the differential phase from the total length of the sensing arm compared to the reference arm, DAS samples a series of strain measurements from hundreds of short segments distributed along the fiber's length.

Both DAS and OFS systems consist of three primary components: (a) a single-frequency and stable laser, (b) detectors and signal processing electronics, and (c) optical fiber and protective cable. OFS electronics typically offer straightforward responses with relatively low detection bandwidths (<100 kHz). In contrast, DAS electronics require high electronic bandwidths, often employing proprietary designs, present greater complexity, but provide much more information. Fiber and cable responses also have uncertainties due to variations in cable design and coupling of the cable to the ground, which can be particularly challenging for telecom fibers deployed in unknown (direct burial or conduit) or non-observable conditions (such as on a seafloor), and uncertainties due to temperature changes. Another challenge with DAS is understanding the exact relationship between the measurements and the actual ground motion, especially concerning seismic waves. Unlike standard seismometers calibrated on shake tables with known displacements, DAS measures the average transient strain over a gauge length. Accurately converting DAS data into actual ground motion measurements with quantifiable errors is critical for quantitative data analysis and modeling.

To address these challenges, recent studies have compared DAS signals with co-located seismic sensors or arrays (e.g., Ichinose et al., 2022;Jousset et al., 2018;Lellouch et al., 2020;Lindsey et al., 2020;Paitz et al., 2021;Wang et al., 2018), but there has been limited exploration into comparing DAS with strain measurements taken from the same cable simultaneously. Therefore, a field experiment was conducted using the same cable in both onshore and offshore environments, eliminating the effects of location and cable variations. The findings were then analyzed with measurements from a laboratory experiment designed to examine the amplitude response of DAS, revealing insight and constraints on the differences between DAS and OFSs, as well as recordings from a co-located seismometer. The seismic data is essential for this analysis because it allows us to assess the real-world performance and accuracy of DAS and OFSs. By comparing these data sets, we can better understand the limitations and strengths of each method in various conditions, leading to more informed conclusions about their applicability and reliability. This study focuses on the relationship between DAS measurements and ground motion, providing constraints on the actual DAS response and a basis for modeling. Additionally, this knowledge is applied to the signals of unknown sources observed from the underwater cable.

The experiment took place on Whidbey Island in Puget Sound, Washington (Figure 1a). We leased dark fibers in an optical fiber cable that links Whidbey Island and Camano Island across Saratoga Passage, utilizing infrastructure owned by Whidbey Telecom. Our equipment was located on a concrete pad beneath a protective roof at the Greenbank site (labeled SLC in Figure 1a). It was housed in unsealed equipment enclosures but without other environmental controls. An onshore buried optical fiber cable, installed in an underground conduit at a depth of 0.91 m, connects the SLC to the Hidden Beach Vault (HBV). This 6.85 km cable features a gel-filled central tube containing all the fibers and uses a loose-tube construction. At the HBV, it is spliced to a 4.14 km marine cable with a tight-buffer construction. This armored cable lies on the bottom of Saratoga Passage and runs to the Camano Beach Vault (CBV), where it is spliced back to a land cable. The underwater bathymetry, depicted in Figure 1b, reaches depths of ∼90 m.

Figure 2 illustrates the detailed design of OFS. All active components-laser, detectors, signal processors, and recorders-were housed at the SLC. Two Michelson interferometers, illuminated by a stable, narrow-linewidth laser, were formed using 3 × 3 couplers and Faraday mirrors. The 3 × 3 couplers produce quadrature fringe signals that facilitate homodyne resolution of increasing and decreasing optical path length changes (Zumberge et al., 2004). The "land" interferometer extended between the SLC and the HBV. Its 3 × 3 coupler and a short reference arm were both housed within the SLC. The interferometer, terminated with a Faraday mirror installed in the HBV, sensed the length of the dark fiber #4 in Figure 2. The second "ocean" interferometer, configured with a 3 × 3 coupler and short reference arm installed in the HBV, sensed the length of the marine cable (fiber #5 in Figure 2) terminated by a Faraday mirror in the CBV. The length changes in fiber #4 are referred to as "Whd2" in the text and those in fiber #5 as "Whd1." Since the laser illuminating the ocean interferometer was located 6.85 km from the SLC, there was a possibility that variations along that path could modulate the phase of the light arriving at the HBV coupler, adding noise to the ocean interferometer. This noise can be detected and removed by tracking the length of that cable with the land interferometer, but this correction was unnecessary as the environmental noise experienced by the marine cable was significantly higher. The two interferometers operated continuously for 2 years (16 April 2021-12 April 2023), except for a period when power was interrupted and the laser lost lock. Additionally, a DAS interrogator (Sintela Onyx v1.0) was connected to another dark fiber in the same cable (17 March 2022-20 January 2023), with a gauge length of 6.38 m and a channel spacing of 6.38 m (total 1,721 channels). After 16 November 2022, the channel spacing was adjusted to 3.19 m (total 3,439 channels) due to the updated field-programmable gate array (FPGA) driver. An attempt to monitor polarization variations in another dark fiber recorded no significant data. Finally, an STS2 (high-gain) seismometer was placed in an enclosure at the SLC, with data recorded using a Quanterra Q330 logger.

Due to the large optical path imbalance in the two OFS Michelson interferometers (sensing arms of 6.85 and 4.14 km vs. reference arms of a few centimeters), a very stable laser frequency is required to ensure that laser Earth and Space Science 10.1029/2024EA003940 frequency fluctuations do not contaminate the strain measurements. For these experiments, we used a frequencystabilized laser based on a compact Er:fiber laser that is frequency-locked to a highly stable Fabry-Perot cavity using the Pound-Drever-Hall (PDH) method (Black, 2001). The cavity is a hollow cylinder made of Ultra Low Expansion glass (ULE) with optically contacted "super mirrors" that provide a high finesse (545,000) and narrow cavity linewidth (5.5 kHz). It is maintained under high vacuum, thermally isolated, and temperature-controlled at the zero-expansion turning point of the ULE cavity. The laser system (model SLS-INT-1550-200-1) was located on a concrete pad under a fiberglass enclosure and a larger protective roof, but without walls and no additional environmental controls with temperatures ranging from -2°C to 30°C over the duration. This system worked remarkably well, and the laser remained locked to the stable cavity over the two-year period. The only exception was when a major storm interrupted power for several hours, depleting the UPS capacity and requiring the restoration of the high vacuum in the field.

The PDH lock allows the laser frequency to be offset from the cavity resonance by a synthesized RF frequency. Changing the frequency offset allows accurate calibration of the optical lengths of the fibers in the OFS. The net result is a laser at 1,565 nm (191.5 THz) that has a spectral linewidth of ∼1 Hz that is tunable over a small range (± 200 MHz). The fractional frequency instability is <3 × 10 -15 for averaging times up to 10 s, which supports corresponding interferometric strain measurements at that level.

Most data reported here focuses on fiber strain for frequencies between 0.01 and 20 Hz and thus the stable laser instability does not contribute significant uncertainty to the measurements. However, we collected fiber strain and temperature data for 2 years (Figure 3). Typically when ULE cavities are new there is a small linear drift in the resonance frequency, as the cavity ages the drift rate decreases gradually over a few years. Before shipping the laser system to Whidbey, the optical frequency was measured at Stanford relative to atomic frequency references (a) Continuous strain was processed using a low-pass filter and decimated as the method described in (Agnew & Hodgkinson, 2007) for the two-year duration of the experiment. The strain recordings are represented by the red line for buried land fiber and the blue line for ocean-bottom fiber. The gap starting at the beginning of 2022 was caused by the laser losing lock after an extended power failure that depleted the on-site uninterruptible power supply. Since the strain record is relative, an arbitrary offset was applied to the records following the gap. (b) The temperature measurements were taken with a sensor resting on the concrete pad at the SLC. This temperature record was processed using the filter design described in panel (a).

10.1029/2024EA003940 and GPS using a femtosecond optical frequency comb (Ma et al., 2004). At that time, we measured an optical frequency drift rate of ∼ -15 kHz/day. The PDH frequency lock synthesized offset was then used to cancel the linear drift. Observed daily variations in a laboratory environment with the linear drift removed were about 400 Hz excursions. After transportation and installation at the field site, those fluctuations were likely somewhat larger in the uncontrolled outdoor Whidbey field site. Nevertheless, in that environment, we expect that the laser frequency fluctuations were <3 kHz/day (fractionally 1.5 × 10 -11 /day), which is to be compared to the fiber strain/temperature excursions that were typically 10 -6 /day. The interferometric data were sampled at 20,000 samples/s, processed in real-time to yield an unwrapped phase, filtered and decimated to 20 samples/s, and streamed to servers at UCSD. The ambient air temperature and polarization changes of the fiber "e" in Figure 2 were also recorded.

Figure 3 displays the continuous strain records from the two OFSs. The normal optical fiber of telecommunications has a temperature coefficient of the optical path length of 10 -5 °C-1 . The daily air temperature fluctuations, in the range of 5-10°C, attenuated by a factor of 100 at a 0.5 m depth, cause a diurnal strain signal of 10 3 nanostrain (10 -5 °C-1 × 10°C/ 100) . This was consistent with what was observed in the Whd2 (onshore OFS) recording at daily periods. The seafloor temperature, which we did not record, exhibits significantly less variation at daily periods and likely even less at annual periods.

The yearly strain records from the land cable are also expected to follow the annual fluctuations in air temperature. Figure 3 shows temperature excursion from -2°C to 30°C and an average annual seasonal air temperature swing of ∼ 10°C, which should produce an apparent strain of 10 5 nanostrain. This is also observed in the Whd2 recording. The smaller amplitude and delayed temperature peaks in Whd1 (offshore OFS) are attributed to temperature variations whose timing and amplitude are governed by the local oceanography rather than the atmosphere. In addition to confirming the expected temperature coefficient of the optical fibers, the long-term records are mainly useful for checking the sign of the interferometers (positive strain indicates lengthening or heating of the fiber). The focus here is on signals at frequencies higher than 0.01 Hz. Consequently, the temperature correction is omitted in the following.

A comparative analysis involving distributed strain measurements from both DAS and OFS was conducted to calibrate the DAS strain recording. The analysis incorporated data from the Mw 7.6 Michoacan earthquake on 19 September 2022 (the epicenter can be seen in Figure 1a). Summing the DAS recordings shown in Figure 4 gives the total strain. To address the overlap caused by the gauge length and channel spacing, either all or only half of the channel numbers were summed in this study, depending on the channel spacing. The total onshore strain was obtained by summing the strain measurements within channel numbers 0-1,073, while the total offshore strain was acquired by summing channel numbers greater than 1,073, as both gauge length and channel spacing are 6.38 m. The summed DAS recordings are presented in Figure 5.

The strain records were then compared with strain simulations derived from teleseismic data recorded by the STS2 seismometer at the SLC, focusing on the frequency range 0.1-0.01 Hz. The conversion of ground velocity from seismic data to strain was performed utilizing the equation presented below (Hatfield et al., 2022).

here ϵ is strain, A is the amplitude of the disturbance, ω is the angular frequency, t is time, ḋ0 is the ground velocity measured by the seismometer, and v is the apparent velocity. Considering that the seismic velocity is denoted by c, the apparent velocity is calculated as c/cos (θ), where θ is the angle between the strainmeter baseline and the incident seismic ray vector. This equation is applicable only for seismic wavelengths much longer than the strainmeter baseline. For example, within the frequency range of 0.1-0.01 Hz, the corresponding Rayleigh

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wavelengths range 40-400 km. We focus on surface waves, as they dominate the waveforms, albeit with minor contributions from body wave phases.

Before analysis, the STS2 seismometer was calibrated by measuring the conversion factor between counts and velocity. This involved placing the seismometer on a shaking table and using a linear variable differential transformer (LVDT) to induce known displacements with a specific voltage. The horizontal LVDT coefficient is 2.629 (mm/volt). Velocity was then calculated from the displacement across various frequencies, and the conversion factor between counts in the STS2 data logger and the induced velocity was measured. The measurements are shown in Figure 6. An average conversion factor of 1.2 × 10 -10 (velocity (m/s)/count) was used for the horizontal components, which matched the expected value of a high-gain STS combined with a Q300 digitizer.

The horizontal components (E-W and N-S) of the seismometer were then rotated to optimize the correlation coefficient (CC) between seismic recordings and strain measurements obtained from OFS. The angle was determined to calculate the apparent velocity. The final comparison is shown in Figure 7. The recordings from the summed DAS channels and the OFS are consistent, with a CC value higher than 0.95. Compared to the estimated strain derived from the seismometer records, the CC values are 0.482 for offshore calibration and 0.833 for the Earth and Space Science 10.1029/2024EA003940 CHIEN ET AL. Earth and Space Science

10.1029/2024EA003940 onshore one, but amplitudes of strains on fibers are lower than those inferred from seismic data by a factor of ∼4.4.

In this section, a seven-month recording (June-December) of 2022 was utilized. Take December 29th's daily recording as an example. The analysis of these oceanic signals involved using DAS to localize their sources within the 0.1-0.5 Hz frequency range. To quantify the time range of these oceanic signals, the standard deviation (STD) was calculated every 2.5 min. A threshold was set at STD values above the upper quartile to identify signal peaks. We then applied hierarchical clustering (Bar-Joseph et al., 2001;Müllner, 2011) to group these peaks, providing time constraints on these oceanic signals, and compared these signals with NOAA tidal current predictions derived from 37 tidal harmonic constituents observed over multiple years at the west of Camano Island (the location of this station is shown in Figure 1a). These processed results are shown in Figure 9, and the comparison reveals that these oceanic signals are associated with current speeds. These oceanic signals corresponded to the maximum current speeds in a day, and even within a monthly range (Figure 10). The relationship between peak amplitude and current speed was also analyzed. As the average current speed exceeded 10 cm/s, the amplitudes of these oceanic signals were activated (Figure 11).

The origins of these oceanic signals were localized on the cable using both DAS and OFS. The oceanic signal from the 29 December daily recording is considered and indicated in the dashed window in Figure 9. The measurements show that the OFS and the summed DAS strain recording exhibit striking similarity, with the CC value of 0.962 (Figure 12). Since the OFS measures the total strain along the fiber and is highly correlated with the summed DAS strain recordings, we used the summed DAS strain to compute the CC value for each individual channel. This approach helps to localize the source of the signal, as DAS records strain within a specific gauge length. The recorded waveforms across DAS channels and their respective CC values are displayed in Figure 13. Upon comparison with the underwater bathymetry, it indicates that the strain measurements are primarily from the eastern side of underwater (the CBV side), particularly at the pivotal turning point of the slope (Figure 14). Earth and Space Science Earth and Space Science 10.1029/2024EA003940

Given the consistency of summed DAS recording and OFS within the 0.01-0.1 Hz range, calibrating DAS to OFS presents a new opportunity to explore DAS amplitude response in a laboratory setting. DAS records the strain by measuring the backscattered signal phase. Given the incident wavelength, refractive index, Pockels coefficient of the single-mode fiber, and gauge length, the axial strain measurement along the fiber axis at any given time is linearly related to the phase change of the backscattered signal caused by dilation or contraction. For calibration, the experimental setup is shown in Figure 15. Two side-by-side fibers were wrapped around a PZT, with a totallength interferometer formed on one of them using a 1,310 nm laser. We determined the peak-to-peak AC voltage required to create a 2π radians phase change (as indicated by the quadrature fringe Lissajous pattern achieving a complete ellipse). This coefficient of phase change per voltage change, adjusted by the ratio of 0.85 (1,310 nm/ 1,550 nm) due to the DAS unit's laser wavelength, allowed us to establish a known phase change on the second fiber, probed by the DAS, for a given PZT drive voltage. Earth and Space Science

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For the specific PZT (outside diameter 38.1 mm, wall thickness 2 mm, height 25.4 mm, with 13 fiber wraps), a coefficient of 0.74 radians/volt at 1,310 nm and 0.63 radians/volt at 1,550 nm was determined. Driving the PZT with 21 V while scanning the wrapped fiber with the DAS (at 1,550 nm) was expected to produce a phase change of 13.23 radians. As shown in Figure 16, 12.81 radians were observed, differing only by 3% (within the uncertainty of the method). The test was conducted at 0.2 Hz to avoid contamination by background temperature changes. To assess the frequency response of the DAS, the experiment was repeated at frequencies of 0.01, 0.02, 0.2, 2, and 20 Hz. The results are plotted in Figure 17a. Lindsey et al. (2020) observed that the DAS amplitude response remained flat below 0.1 Hz and increased by 3-11 dB in the higher frequency (0.1-1 Hz) when studying teleseismicity. Teleseismic events have dominant Earth and Space Science 10.1029/2024EA003940 frequencies below 0.1 Hz, suggesting earthquake characteristics influence this observation. This could introduce variability in observations at frequencies above 0.1 Hz. To address this, our laboratory experiment uses a PZT to generate strain. By modulating the voltage, the PZT can produce only a few nanostrains at the specific channels with various frequencies. Our results indicate that the DAS measurement is -3.22 dB during a 0.01 Hz deformation, with a measured value of 9.14 radians compared to the expected value of 13.23 radians. This decrease is more pronounced compared to measurements at higher frequencies. To further validate our experimental findings, we compared the magnitudes of the spectrograms between DAS and OFS during the mentioned Mw 7.6 Michoacan earthquake. The magnitude ratios are ∼0 dB between 0.03 and 0.3 Hz, consistent with the experimental measurements (Figure 17b). However, examining laboratory measurements below 0.03 Hz or above 0.3 Hz is challenging due to the lower energy levels of the earthquake.

Comparing the fiber strain measurements with the strain estimated from seismic data reveals a difference between the onshore and offshore segments. The onshore seismometer yields a CC value of 0.833 with the onshore fiber segment signal. In contrast, the CC value between the estimated strain and the offshore fiber drops to 0.482. The Figure 15. Experimental setup.

Earth and Space Science 10.1029/2024EA003940 difference in correlation is likely influenced by several factors, including the distance from the seismometer, the type and coupling of the cable, and the effects of overlying seawater and underlying sediment on the marine cable.

Additionally, a difference in amplitude by a factor of ∼4.4 is observed with the onshore fiber. The amplitude variation noted here was also observed in a similar calibration by Canitano ( 2024), and could be due to multiple factors. First, as we applied Equation 1 for strain simulation by seismic recording, the uncertainties of θ and v should be considered. θ is decided by the orientation of the fiber and the backazimuth of the earthquake. Unlike the straight fiber orientation in the field experiment of Hatfield et al. (2022), the fiber was deployed along the coastal road and underwater (see Figure 1a). This deployment could result in uncertainties related to fiber orientation that are difficult to remove. The backazimuth was calculated from the locations of the epicenter and the STS2 at the SLC, with the uncertainty generally less than a few degrees. v has some uncertainties because Rayleigh waves have dispersion characteristics with higher speeds at longer periods. Paitz et al. (2021) indicated that assuming a constant phase velocity led to variations in DAS amplitudes during the conversion to a strain field. However, the focused frequency range in this study is 0.1-0.01 Hz, which is broadband, and there is only a trivial change as we shift v in the reasonable range. Earth and Space Science 10.1029/2024EA003940 amplitude due to coupling conditions. In the full-waveform simulation, Celli et al. (2024) observed strong impacts on recorded signals, including amplitude and phase delays, from cable-ground coupling and local site effects. These studies collectively underscore the influence of fiber coupling on DAS recordings. Thus, we attribute the observed amplitude factor in our case primarily to the coupling conditions. Not surprisingly, deployed telecom cables are designed to protect the optical fibers from external disturbances and damage, so they are typically loosely constrained in channels within the protective cable. This leads to reduced coupling between the optical fiber and the outer protective layers of the cable and the ground. In addition, the cables are deployed within buried conduits in many locations. All these factors tend to attenuate the strain signal away from the source, though other factors may also play a role. The amplitude discrepancy observed in our case suggests that DAS or OFS studies, particularly those involving recorded amplitudes, should be calibrated with a nearby, precisely tuned seismometer.

The underwater signals recorded by OFS Whd1 correspond to tidal ebb and flow, with amplitudes increasing as current speeds exceed ∼10 cm/s. This observation indicates a strong connection to oceanic tides and suggests a possible trigger by tidal stress. The hypothesized source of these signals is the increased turbulence generated during peak oceanic tides, resulting in stronger strain variations along the fiber. Though this hypothesis is challenging to further analyze due to the limited additional information, such as underwater pressure measurements, this finding is supported by Burchard and Hetland (2010), which simulated estuarine circulation and suggested tidal straining as a primary mechanism to generate turbidity maxima. Bassett et al. (2013Bassett et al. ( , 2014) ) found strong correlations between acoustic noise at higher frequencies (>1 Hz) and tidal current speeds. Additionally, Podolskiy et al. (2016) provided evidence that microseismicity in Bowdoin Glacier, Greenland, is driven by variations in strain rate, which corresponds to longitudinal stretching of the glacial surface controlled by melt rate of ice and tidal height fluctuations.

The localized results obtained using DAS and the OFS indicate that these underwater signals are concentrated on the eastern side of the oceanic sound, particularly at the turning point of the slope. Lazar et al. (2018) indicated that the topographic slope conducted a strong submesoscale velocity field in their numerical simulation, suggesting a potential for the slope to be impacted by underwater turbulence. This simulation helps explain why the strongest observed signals are localized at the turning point of the slope. The evidence presented links underwater signals recorded by optical fibers to oceanic tides. It demonstrates the ability to localize potential triggering sources along the fibers through the combined use of DAS and OFS.

Utilizing the same cable for DAS and OFS, and the co-located STS2 seismometer on Whidbey Island, Washington, we calibrated the recordings with a teleseismic event. The strain recordings from the summed DAS channels are consistent with those from the OFS. Compared to strain simulations derived from seismic data, the strain measurements showed well-matched phases, but an amplitude reduction factor of ∼4.4 was observed for the optical fibers. This amplitude discrepancy is likely influenced by fiber coupling conditions. Additionally, a laboratory approach for measuring DAS amplitude response is presented, using a PZT to generate strain at specific channels of the fiber. This approach is independent of natural earthquakes, unlike experiential comparisons such as waveform analysis between DAS and a geophone, and it does not require complex simulations.

Our laboratory experiments highlight a notable decrease in recorded amplitude at lower frequencies (0.01 Hz) for DAS compared to higher frequency ranges, underscoring the importance of considering amplitude response in relevant studies. Analysis of underwater signals using DAS and OFS revealed a correlation with tide speed, particularly concentrated around slope turning points on the eastern side of the study region, suggesting an impact of bathymetric conditions.

Earth and Space Science 10.1029/2024EA003940 gov/noaacurrents/predictions?id=PUG1622_3). More details of the comparison between strain recordings and seismic data can be found in Hatfield et al. (2022).