Introduction

Probing length changes of deployed telecommunication fibers as a way to access ground motion has attracted growing interest from Earth scientists1,2,3,4,5,6,7,8 and network operators9,10,11, that foresee the possibility of implementing distributed, spatial-aliasing-free sensor grids exploiting the infrastructure already in place for global telecommunications in a scalable and sustainable way. While other Distributed Acoustic Sensing (DAS) techniques12 have a short range and cannot be applied to fibers carrying the internet traffic, novel approaches based on the interferometry of continuous-wave coherent lasers13,14 and state-of-polarization analysis9 enabled earthquake detection on operational telecommunication links both on land15,16,17 and over transoceanic distances9,14,18, disclosing opportunities for pervasive and global monitoring of our planet.

Laser interferometry measures the variation of the optical path length experienced by a coherent laser radiation as it travels a fiber subjected to strain13,14,15,17, with higher sensitivity and broader linear range compared to polarization-based sensing18. Its implementation on land-based fibers generally allows a more insightful interpretation of the fiber response than with sub-sea cables, thanks to a larger number of traditional sensors available in cable surroundings15,17,19. However, laser interferometry on land cables is also attractive per se, as a tool for monitoring densely-populated areas: here, the fiber pervasiveness compensates for the poor coverage by traditional seismic networks, which privilege sensor installation in quieter regions, and enables applications such as people flows and vehicle traffic monitoring.

We describe the realization of a seismic observatory based on laser interferometry, operational for two years on a wavelength-multiplexed telecommunication link in Italy, and present the first results of continuous acquisition over a long period, in which we systematically compared fiber data to those from nearby stations of the Italian permanent seismic network (IV network) managed by Istituto Nazionale di Geofisica e Vulcanologia-INGV (see Methods). We found recurrent behavior and underlying scaling rules, which enabled us to make quantitative considerations on the cable response to different classes of events and the possibility of using laser interferometry both as a research and a survey tool in different contexts.

The fiber is 39 km long, mostly housed inside conduits along a road infrastructure, except for ~100 m in aerial cable. It crosses few bridges and terminates in medium-sized towns, thus suffering from diverse and time-varying noise processes. Its average azimuthal direction is 155° (see Supplementary Fig. 1). Figure 1a shows the cable layout and the location of the nearest sensors of the IV network. Specifically, IV.ASCOL was installed at one cable end for this experiment and was used, together with IV.TERO, for comparison throughout the analysis (see Methods). The fiber is part of a regional ring architecture, owned and managed by a commercial provider and used for data transmission at 100 Gb s−1 with quadrature phase-shift keying (QPSK) modulation. A single wavelength channel is dedicated to our experiment, while the rest of the bandwidth is used for data traffic. The sensing light signal is produced by a compact narrow-linewidth laser, wavelength-multiplexed to the internet traffic and launched into the network. Two measurement schemes were tested in different periods of the time frame we report on. They differ only in technical details, overall being conceptually similar. In the first scheme (Fig. 1b), we measure the interference between the signal traveling the round-trip and a local reference beam. Here, a single laser interrogator enables to derive the fiber deformation from a measurement of the phase accumulated by the optical carrier in a round-trip. In the second scheme (Fig. 1c), we use a pair of laser sources, launched in opposite directions into the cable and interfered at the opposite end with the local radiation. In this scheme, the information is extracted by combining measurements collected at the two cable ends (see Methods)20.

Fig. 1: Experimental layout.
figure 1

a Map43 of the deployed observatory and its geographical location. Triangles indicate the location of nearby seismometric stations, the closest of which, IV.ASCOL and IV.TERO (orange), were used for comparison throughout the analysis. IV.ASCOL was installed at the fiber end in the town of Ascoli, IV.TERO is about 9 km west to the fiber. Stars indicate epicenters of specific events shown in this study. b Sketch of the optical scheme. In Ascoli, the laser radiation is split into two parts: one serves as a reference beam, the other passes through a frequency shifter, is spectrally combined with telecom data (TX/RX) using optical Add/Drop multiplexers, amplified and launched towards the remote end in Teramo. Here, it is reflected back along an adjacent fiber in combination with telecom data and, once back in Ascoli, it is recombined to the reference beam to extract an interference signal. c Modified optical scheme, in which two separate lasers, hosted at opposite cable ends, are launched in opposite directions and interfered with the local laser. Frequency deviations introduced by the fibers deformation are retrieved by combining synchronous recordings gathered at the two cable ends. The frequency shifter is here used to add a periodical modulation pattern to the carrier frequency for synchronizing remote acquisitions (see Methods).

Full size image

Results

On a standard seismometer, the probability P to detect an event depends on its magnitude M and hypocenter distance to the fiber d. Assuming P is related to the recorded peak value of a physical quantity (e.g. ground acceleration or velocity), the following relation holds21:

$$P={A}_{2}\frac{1{0}^{{A}_{1}M}}{d}$$
(1)

where A1 depends on the type of physical measure and A2 is a generic scaling coefficient. For interferometry-based earthquake detection, no scaling law was reported so far. We performed this analysis, generating an earthquake catalog22 that included over 600 events with magnitude between 1 and 8 and epicenter distances up to 2000 km, spanning a time frame of 1.5 years. We included all earthquakes located by INGV monitoring system in the considered period and looked for signature of the events on fiber recordings (see Methods). The distribution of detected, unsure and non-detected events as a function of their magnitude and distance to the closest point on the fiber (Fig. 2a) well agrees with Eq. (1).

Fig. 2: Sensitivity of the fiber as an earthquake detector.
figure 2

a Map of events considered in the 1.5-year-long catalog as a function of their magnitude and distance to the closest point of the fiber. Color indicates if the event was detected (green), unsure (light-green) or non-detected (empty) by the fiber. The line shows the estimated sensitivity threshold for our sensor. Labels (I), (II) and (III) indicate specific events which are described in this study. The inset zooms on events in a range of 20 km to 100 km and magnitude 2 to 3.5. b Same events as the inset, mapped as a function of their angular distribution and distance to the fiber. Circles dimensions indicate magnitude class; the dashed line indicates the average direction of the cable.

Full size image

The sensitivity threshold line (blue curve in Fig. 2a) is found iteratively by minimizing the cumulative number of detected events below the line and non-detected events above the line and corresponds to A1 = 0.403 ± 0.001 and A2 = (3280 ± 10) m (see Methods). Although the fiber suffers from a higher level of integrated noise as compared to a seismometer, A1 is of the same order of magnitude for the fiber and IV.ASCOL (see Supplementary Fig. 2) and comparable to the values published in the literature for scaling peak ground accelerations or velocities. This estimation could be refined with the better statistics enabled by ongoing data collection. The weakest event we were able to observe had Ml = 1.4, epicenter 2.4 km away from the closest point of the fiber, 17.5 km depth, and was recorded in the night, when the noise was lower.

In fact, the background noise recorded by the fiber changes by 10 dB between day and night, related to the intensity of human activities, and shows the signature of randomly distributed, non-stationary events that affect the detection of weakest earthquakes on daily hours. In addition, the two aerial segments of the cable introduce noise in the spectral region around 1 Hz, which is relevant to seismic detection (see Supplementary Figs. 3 and 4). Our results indicate that the detection of weak events is possible even in such an unfavorable environment. Even if impairments cannot generally be predicted or avoided on telecom-integrated sensing systems, also due to a lack of precise knowledge of the fiber’s housing conditions, we foresee their impact could be reduced in more complex architectures where a single laser interrogator simultaneously probes separated cables.

We also analyzed the detection probability of average-size earthquakes in local areas as a function of their angular distribution (Fig. 2b) and observed a larger fraction of successful detection in the transverse direction. This suggests that wavefront curvature and angle of incidence with respect to local portions of the cable19 may have a role in building the cable response and highlights the importance of increasing the catalog size to allow for more conclusive claims.

For a direct comparison of fiber and conventional seismometer measurements, an appropriate conversion metrics between quantities had to be considered, as recordings substantially differ from two points of view: first, fiber sensors measure an optical phase, while seismometric sensors measure ground velocities or accelerations; second, fiber sensor measurements are related to the integral of a distributed deformation, while seismometric sensors measure local quantities. Operationally, we record the time derivative of the phase φ(t) accumulated in a round-trip, i.e. the instantaneous frequency deviations of the incoming optical signal with respect to the injected one \(\Delta \nu (t)=\dot{\varphi }(t)/2\pi\). As other authors16, we found similarities in the time evolution and spectral composition of this quantity with the ground velocity v(t) recorded by nearby seismometers.

Even if a precise analytical model is beyond the scope of our work, we understand these similarities to be consistent with expectations from a functional point of view (see Methods), although the signal recorded by the fiber results from the combination of local deformations induced along the three directions and at different portions of the cable. As an example, Fig. 3 compares Δv(t) (orange, uppermost panel) with v(t) measured by seismometers along the vertical, North-South and East-West axes (blue, panels 2 to 4) for the three events marked in Fig. 2. For each event, zoom on the P- and S-wave arrivals is shown in the right panel, and arrivals of the two are indicated as P and S (for clarity on a single panel only). As expected, recorded ground velocities may differ significantly for the three axes of a seismometer. This depends on many factors, among which the distance to the hypocenter and the magnitude of the earthquake, the history of the earthquake rupture, the propagation media and local effects. Traces were deconvolved from the seismograph response.

Fig. 3: Time traces of relevant case studies.
figure 3

a Recordings of the Turkey Mwp= 7.9 event occurred on Feb. 6th, 2023, with the fiber (panel 1, orange) and IV.ASCOL (panels 2 to 4, blue). On the right, a zoom on the P- and S-waves arrivals. b Recordings of the Ml=2 event occurred in Civitella del Tronto on Feb. 19th, 2022 with the fiber (orange) and IV.ASCOL (blue). c) Recordings of the Ml=3.4 event occurred in Accumoli on Feb. 27th, 2022 with the fiber (orange) and IV.TERO (blue). Wave arrival is indicated by P and S. Data from both the fiber and the seismometer have been band-pass filtered with a 6th order, bidirectional Butterworth filter to maximize signal/noise ratio on the fiber recording. The pass-band was 0.005 Hz to 0.5 Hz for the Turkey event, and 1.3 Hz to 20 Hz for the Civitella and Accumoli events. Seismometers data were deconvolved from the sensor’s response.

Full size image

Figure 3a shows traces of the event that occurred in Turkey on Feb. 6th, 2023 (moment magnitude23Mwp = 7.9, distance to the fiber 2000 km), labeled (I) in Fig. 2. The high signal/noise ratio on the fiber recording allows a sharp picking of the P-wave arrival time, with similar quality as obtained from seismometer data, and a clear identification of the S-wave arrival. We note that the scaling between the amplitude of the perturbation on the fiber and the vertical and North-South velocity components of IV.ASCOL is about 106 Hz m−1 s. The same scaling is confirmed for another far-field event, where a correlation is also found between the time evolution of fiber and IV.TERO recordings (see Supplementary Fig. 5).

Figure 3b shows traces of an event that occurred in Civitella del Tronto on Feb. 19th, 2022 (Ml = 2, epicenter depth 18 km and hypocenter distance 5 km from the closest point of the fiber), labeled (II) in Fig. 2. Because of the epicenter location, the seismic phases arrive earlier at the fiber location than at IV.ASCOL. However, the short distance to the fiber may entangle the identification of phase arrival times, preventing from precise picking. The scaling coefficient between recordings on the fiber and seismometer is about 2 × 107 Hz m−1 s, a factor ~20 higher than for the Turkey event (this factor is consistent with other observations on a regional scale). This supports the indication of Fig. 2b, that the wavefront curvature and angle of incidence with respect to local portions of the cable19 may have a non-trivial impact in determining the overall cable response and amplification. This condition is opposite to the previous case (far-field event), in which the seismic components reaching the cable had a wavelength comparable to the cable length, thus washing out local effects and giving rise to a response which is more similar to that of a point-like sensor. More quantitative considerations would require integration of local strain derived from a priori knowledge of the wave propagation dynamics17 which was not available for this event.

Figure 3c shows the recordings of an event that occurred in Accumoli (Ml = 3.4, epicenter at 32 km from the closest point of the fiber and 27 km from IV.TERO), labeled (III) in Fig. 2. The scaling factor between fiber and seismometer measurements is similar to the previous case. The arrival time of the P- and S- waves is evident: in particular, the P-wave is detected on the fiber with a lag of 0.9 s with respect to IV.TERO. This is consistent with expectations within the uncertainty of the available propagation model, assuming a velocity of 6 km s−1 for the P-wave and considering that IV.TERO is 5 km closer to the epicenter.

These results confirm that interferometric fiber recordings can be used for earthquake localization based on the picking of phase arrival times on a set of cables13 or in combination with seismometers, provided that standard localization algorithms are adapted to take into account the distributed nature of the sensor.

Spectral analysis discloses additional information about earthquakes dynamics. In seismometers, Fourier amplitude spectra of accelerations (\(\dot{v}\)) are predicted to follow a standard Brune’s model24 and increase proportionally to f 2, with f the Fourier frequency, up to a corner frequency fc, above which they flatten. The model also predicts a relation between fc, the source physical parameters and the event magnitude (see Methods).

We analyzed the spectral composition of all events detected by both the fiber and IV.ASCOL in a range of 100 km from our observatory, and extrapolated the respective corner frequencies. Farther events are excluded, as their spectrum is expected to be significantly affected by propagation. As an example, the spectra of three events with increasing magnitude are shown in Fig. 4a (spectra of all events are shown in Supplementary Fig. 6).

Fig. 4: Spectral analysis and magnitude determination.
figure 4

a Spectral composition of the accelerations recorded by IV.ASCOL East-West component (blue, right panel) and fiber differentiated frequency data (orange, left) for three events, two with epicenters in Civitella (1st and 2nd row) and one in Accumoli (3rd row) and Ml = 2.0, 3.0 and 3.9. The spectral response of the fiber well reproduces that of the seismometer. Black dashed lines indicate fits on the low and high end of the detection band, their crossing corresponding to fc (for clarity, this point is indicated by an arrow in the first subplot only). The shaded area indicates the background noise recorded by the sensor 1 minute before the event. b fc as retrieved from IV.ASCOL (right, blue) and fiber (left, orange) are plotted as a function of magnitude, evidencing a linear relation between the two quantities. Dashed and dotted lines indicate lower and upper limits obtained for typical source parameters; in particular, we let the stress-drop Δσ to vary between 0.1 MPa and 3 MPa (see Methods). c) Dispersion plot of the corner frequency as extrapolated from the fiber and IV.ASCOL, with color scale representing magnitude. Correlation between the response of the two sensors is found (r = 0.81), suggesting that spectral analysis of fiber recordings enables one to infer event magnitudes similarly to seismometers. The dashed line is a linear fit to the data.

Full size image

The spectral content of fiber recordings reproduces that obtained by IV.ASCOL, highlighting the broadband response of the cable as a sensor and corroborating our decision to compare recordings of Δν with v, or the corresponding time derivatives. Also, we note that in all spectra the scaling between the cable and seismometer is consistent with that observed for the Civitella and Accumoli events (Fig. 3b, c), and generally higher than observed for the Turkey (Fig. 3a) event. Figure 4b shows the corner frequency values extrapolated from the fiber (orange, left) and IV.ASCOL (blue, right) as a function of magnitude, highlighting in both cases a decreasing trend consistent with the expected one. Pearson’s correlation coefficient between magnitude and fc is r = − 0.60 and r = − 0.59, respectively, indicating that the reason for statistical dispersion is not related to the data quality. Instead, we ascribe it to differences in the physical source parameters between various events, as indicated by the predicted limits when typical numbers are plugged into the model (dotted and dashed lines, see Methods). Pearson’s test between the corner frequencies retrieved by the two sensors (Fig. 4c) returns r = 0.81, confirming a good correlation between the two. However, values extrapolated by the fiber appear to be systematically higher than for IV.ASCOL. This is confirmed by a linear fit to the data in Fig. 4c, which returns a slope of (0.9 ± 0.1) Hz Hz−1 and intercept of (2.0 ± 0.7) Hz. Further inspection from a larger event catalog will help finding an explanation (see also Methods).

This analysis reveals a crucial aspect of fiber-based earthquake detection, i.e. that spectral analysis of fiber deformations can indeed support magnitude estimation for small and mid-size seismic events, even in the impossibility to calibrate the absolute cable response to ground motion due, e.g., to unknown fiber-to-ground coupling parameters or integration effects.

Discussion

With 1.5 years of uninterrupted data collection on a land-based fiber shared with data traffic, we were able to characterize laser interferometry as a tool for earthquake detection, also taking advantage of the presence of co-located seismometers with well-known responses. Within the same period, no degradation in data traffic quality metrics was reported, which is a prerequisite for the application of the technique to the existing fiber infrastructure.

We showed that events with Ml = 2 or larger can be reliably detected at local distances. For the Italian earthquake catalog25, Ml = 2 represents the average magnitude for completeness and in the surveillance system the alert-threshold to the Civil Protection Department is Ml = 2.526: smaller events are not felt unless they have very superficial hypocenters or happen in the quietest moments of the day. Detection of such events with a fiber hosted in a road infrastructure extending to city centers and including aerial segments reveals the concrete potential of laser interferometry for supporting traditional monitoring in highly-populated areas. It also highlights the capability to bring data from weak earthquakes that might not be traced unless seismometers are present in a range of few tens of kilometers from the epicenter. Such dense coverage is in general only available in high-risk areas and is uncommon on the broadest extent of the planet. Considering the current increase in fiber cable deployment to meet the growing capacity needs for next-era communications, we believe the interesting target for network-integrated sensing to be weak yet close events, rather than teleseismic signals for which the existing network is already adequate. In the perspective of integrating laser interferometry into telecommunication grids, the scaling law we found for the event detection probability can be exploited to draw territorial maps of covered regions by following the hosting infrastructures path and validate small-event detections in combination with spectral analysis, even lacking information on detailed cable routes and mechanical coupling to the ground.

From another perspective, the analysis of background noise confirms that this technology is suitable for monitoring a large variety of phenomena besides earthquakes, such as vehicle traffic and infrastructure mechanical resonances. In this respect, the availability of large catalogs from land-based observatories, validated by comparison with seismometer data, is crucial in developing advanced signal analysis and training machine learning routines27.

While commercial DAS systems are a powerful tool for high-resolution mapping of localized portions of the territory and support ambitious tasks such as the imaging of the generation and waves propagation of seismic events28,29, laser interferometry holds the potential for supporting daily seismic monitoring services, with two advantages over DAS even in spite of a lower space resolution. First, being compatible with data traffic, it leverages the pervasiveness of optical telecommunication grids, enabling a better coverage of broad areas than possible with dedicated cables. Second, commercial DAS systems produce data volumes in excess of 100 GB day−1 at 250 Hz sampling rate, which is presently not sustainable in the perspective of permanent operation. While more efficient data compression and processing methods may improve the exploitability of DAS data for such applications, our laser interferometry system already produces a data throughput as low as 1.2 GB day−1 at a higher sampling rate of 1 kHz (see Methods), easily handled also in time-critical applications. The possibility of picking the arrival time of P and S waves can be used for earthquake localization if combined with the information derived from other cables or other sensors. In this sense, we foresee that complex challenges such as global environmental monitoring cannot be addressed using a single technology alone, but require a comprehensive approach that combines information from diverse sensors such as seismometers, DAS, laser interferometry or polarization analysis, upon infrastructure availability and with a weight that depends on the target application.

Size, weight, and power consumption of the laser interrogator, as well as cost, are important concerns when considering large-scale applications and mass production. For our experiment, we made use of a research-grade, sub-Hz linewidth laser, with a few times the size of commercial DAS systems and similar cost. Results indicate, however, that performances can be relaxed in favor of compactness and ease of maintenance. Meanwhile, laser integration technologies are progressing30,31, holding promises for mass-scale production and associated reduction of costs. These lasers could eventually be integrated into coherent transceivers, allowing information to be extracted from the carriers phase of coherent communication signals similarly to what has been demonstrated for their polarization9,10. Although this is not possible with the laser sources in use in telecommunications today, it may represent in the future the most effective route to the integration of sensing capabilities in modern smart multi-service grids in a scalable and sustainable approach.

Methods

Experimental layout

The fiber optical length is sensed using an inteferometric scheme in one of the two following configurations. In the first scheme (Fig. 1b) an ultrastable laser beam is split into two branches, one of which travels the link in a round-trip before being recombined to the other. We collect the self-heterodyne beatnote between the two, oscillating at the shifter frequency, 40 MHz in our work. The instantaneous frequency of the beatnote depends on combined variations of the refractive index and length of the deployed fiber, induced by forces exerted onto it from the surrounding environment. The signal is sampled and demodulated to extract the optical carrier frequency variations at a typical rate of 1 kHz, then stored in a database22. The size of compressed data ranges between 26 MB hour−1 at 1 kHz sampling rate and 270 MB hour−1 at 10 kHz. Collected data are filtered and decimated to a final rate of 100 Hz for analysis. Heterodyne detection is preferred to homodyne detection, as it enables signal processing in the radio-frequency domain instead of the low-frequency band, where detection noise would be degraded by the sampling electronics.

In the second configuration (Fig. 1c), a pair of lasers, each housed in a network node, is launched towards the remote end and interfered with the local laser. In this configuration, the beatnotes recorded at the two ends oscillate at the frequency difference between the two optical carriers, about 1.1 GHz in our experiment. Their instantaneous frequency depends on the instantaneous frequencies of the interfering lasers, as well as on the shifts experienced by the remote laser while traveling through connecting fibers. Each beatnote is independently demodulated, and by synchronously combining the obtained signals with a proper sign, it can be demonstrated20 that the lasers noise is rejected, being common between the two, while the fiber-induced shifts remain. To enable common-mode rejection of the lasers noise, the measurements at the two nodes need to be synchronized to at least 5 μs. We achieve this by applying a frequency step to the frequency shifter. This brings the beatnotes recorded at the two cables end out of the demodulation bandwidth and then in again, triggering the start of acquisition with sufficient synchronization. A full characterization of this process is reported in ref. 20. Acquisitions are referenced to Universal Coordinated Time (UTC) to about 10 ms using Network Time Protocol provided by Internet connection.

In both schemes, we make the assumption that perturbations are symmetrical in the two directions, as the fibers are laid parallel into the same cable.

The instrumentation is housed at the telecom network nodes and installed in compliance with rack standards.

The link implements Dense Wavelength Division Multiplexing (DWDM). All optical carriers, included the one used for this work, are combined through an Optical Add/Drop Multiplexer, equalized and launched into the fiber. An optical preamplifier is installed at the far cable end, before de-multiplexing, to compensate for a 10 dB optical loss. Launching from the opposite direction follows the same scheme. The ultrastable laser has been installed into the DWDM hardware as an alien wavelength with the possibility to equalize and raise alarms in case of faults to the system.

Seismic stations

Data acquired from the optical fiber were compared with seismological data acquired by IV.TERO and IV.ASCOL seismic stations. IV.TERO is the seismic station of the Italian National Seismic Network26,32) closest to the fiber end in Teramo, Italy. The station is located at 670 meters above mean sea level, along the slope of a headland in the piedmont of the Central Apennines. IV.TERO is equipped with velocimetric (Nanometrics TRILLIUM-40s) and accelerometric (Kinemetrics EPISENSOR-FBA) sensors, connected to a 6 channel GAIA-2 seismic digitizer. All instruments are located in an inspection pit approximately 2 m deep from the ground level. The geophysical and geological surveys performed for the site characterization of the station indicate a stiff site characterized by a value of VS30 of 981 m/s.

Station IV.ASCOL was installed in the town of Ascoli, on the ground floor of the network point-of-presence that houses the laser interrogator. The station consists of a velocimetric (Lennartz Le3D-5s) and an accelerometric sensor (Kinemetrics EPISENSOR-FBA) connected to a 6 channel REFTEK-RT130 seismic digitizer. The hardware was lent by the COREMO program of INGV especially for this experiment. Although located in an unfavorable area, characterized by high anthropogenic noise and possible site amplification phenomena (the site is on fluvial deposits), it was decided to install the station in close proximity to the fiber cable, for easier comparison of the recordings. Both IV.TERO and IV.ASCOL stations send, by WIFI and UMTS transmission, respectively, acquired data in near-real-time to INGV’s data collection server, where they can be gathered and distributed via Web Services based on the FDSN specification33.

Selection of events for the sensitivity analysis and validation criteria

From continuous acquisitions, we automatically extracted windows where to look for signatures of seismic events according to the expected arrival times of the seismic wave to fiber, IV.ASCOL and IV.TERO, derived from a priori knowledge of the event source position and propagation parameters. For each earthquake, the used source parameters (origin time, hypocenter coordinates, and magnitude) were extracted from the seismic catalog produced by INGV seismic surveillance center34. The source-fiber distance was computed with respect to the middle of the cable (42.73693°N, 13.674261°E).

We considered in our analysis events with: M ≥ 4 closer than 2000 km, or Ml ≥ 2.5 closer than 300 km, or Ml ≥ 0.4 closer than 30 km, occurred between Jun 19th, 2021 and Sep 26th, 2022. To increase statistics in the high-distance/high-magnitude end of the plot, we added events from the recent sequence that occurred in Turkey, including those with Mwp ≥ 5 that occurred between Feb. 6th and March 23th 2023 closer than 300 km to the epicenter of the first event. Also, we included a seismic sequence that occurred off-shore Ancona, at a distance of about 130 km from the middle of the fiber (coordinates of main earthquake of the sequence, Mw 5.5: 43.9833°N, 13.3237°E) in November 2022, that featured co-localized events in a broad range of magnitudes. To include this sequence, we considered events with Ml ≥ 2 closer than 180 km from the fiber, which occurred between Nov. 9th, 2022 and Nov. 18th, 2022.

Waveforms of earthquakes recorded along the fiber and at seismic stations were selected using the theoretical P arrival times computed using the TauP method35. The travel times were computed in the 1D Earth reference velocity model ak13536, which provides a good fit to a wide variety of seismic phases and improves on the previous IASP9137 Earth model in terms of data and methodologies.

For each considered timeframe, we looked for the signature of the wave detection on the fiber according to typical criteria used in seismic analysis and assigned it a score (0 = event not detected; 100 = event clearly visible; intermediate values reflect the confidence on detection and are plotted in light-green color in Fig. 2 of the main text). To make a decision, we considered both the time trace (i.e. clear onset of a phase from background noise; temporal evolution and duration in consideration of epicenter distance; match of the recording with the expected arrival time of the seismic wave to the closest portion of the cable) and the spectral composition of the signal.

In Fig. 2 of the main text, events marked green are those who featured a score ≥ 60; unsure events are those who featured a score between 5 and 60.

Interpretation of fiber data and comparison to seismometer recordings

The phase accumulated by the optical carrier as it travels a fiber with length L can be related to the integral of local ground strain ϵ along the full cable path, weighted by a coupling coefficient γc and a geometrical scaling coefficient γg. The former quantifies the anchoring of the fiber to the surrounding ground and depends on construction factors such as the kind of conduit where the fiber is placed, the cable armoring4,8 or the presence of gel rather than simple air-filling38.

The geometrical scaling coefficient takes into account the relative orientation of the cable and the local strain direction19,39 and the ratio between the seismic wavelength and the fiber length projected along the wave direction. For instance, because of the integration effect, we would expect null response from a perfectly straight cable hit by a seismic wave incident from the longitudinal direction when the cable ends happen to be in nodal points; instead, response would be higher when the cable ends happen to be perfectly out of phase39. From a practical point of view, this sort of considerations, well-modeled in standard Distributed Acoustic Sensing, cannot be extended to coherent interferometry in a straightforward way, as real cables always feature changing orientation and have dimensions comparable or larger than seismic wavelengths19. Still, attempting at a functional interpretation of fiber recordings, a general relation can be established between the instantaneous frequency deviations of the optical carrier (\(\Delta \nu =\dot{\varphi }/2\pi\)), and the time derivative of integral strain:

$$\Delta \nu =\frac{1}{2\pi }\dot{\varphi }=2\frac{nL}{\lambda }{\int_{L}}{\gamma }_{{{{{{{{\rm{g}}}}}}}}}(s){\gamma }_{{{{{{{{\rm{c}}}}}}}}}(s)\dot{\epsilon }\,{{{{{\rm{d}}}}}}s$$
(2)

where we parametrized γg and γc accounting for the fact that they are local quantities, λ is the optical wavelength (1.5 μm), the factor 2 indicates that the fiber is traveled in a round-trip and we assumed a constant refractive index n throughout the cable.

The relation between strain, or its derivative, and ground motion parameters is, in general, less trivial. Observations with standard Distributed Acoustic Sensing confirm that a linear relation exists between \(\dot{\epsilon }\) and ground velocity components v along the strain direction recorded at the edges of the gauge length g2,39,40, with g of the order of a few meters:

$$\dot{\epsilon }=[v(g/2)-v(-g/2)]/g$$
(3)

However, this relation could be extended to the km-scale only in the case of a perfectly straight fiber under homogeneous strain conditions. On deployed fiber layouts with changing orientation and non-homogeneous deformations, knowledge of velocity components at the cable end are not sufficient to quantitatively predict the cable response and propagation models for the seismic wave need to be computed to enable integration of local deformation through the cable path17.

Still, we expect a linear functional relation between the recorded frequency deviations and the ground velocity to be preserved, which is consistent with the reported measurements for the analyzed cases.

Calculation of spectra and corner frequency extrapolation

For all detected events in a range of 100 km from the fiber we computed the fast Fourier transform (FFT) of the recording over a time interval of 20 s, with Hann window and no averaging to enable sufficient resolution at lowest frequencies. The start time of signal windows was automatically set to be 1 s before the calculated arrival time of the P-wave in the center of the cable, except for two cases where it had to be fixed manually due to incorrect arrival time prediction. A similar procedure was followed to calculate the background noise (shaded area): integration intervals had the same duration, and the start time was either automatically set to 60 s before that of the signal or manually adapted to exclude non-stationary noise arising by chance during the considered period. In this latter case, we shifted the window by up to a few tens of seconds, maintaining the same duration. The modulus of the FFT was normalized by the square-rooth of the channel bandwidth. Results are shown in Supplementary Fig. 6 both for the fiber (orange) and IV.ASCOL East-West component (blue).

To extrapolate the corner frequency, we fitted the above spectra with polynomials of the kind FFT(f ) = b2f 2 and FFT(f ) = b0f 0 in Fourier frequency intervals 1.2–3 Hz and 10–30 Hz, respectively. The interpolation limits have been chosen to exclude spectral regions where the noise on fiber recordings covers the signal, and especially the discrete noise peaks at 0.75 Hz and 0.95 Hz. The corner frequency is calculated as the crossing point between the two fitted lines, i.e. \({f}_{{{{{{{{\rm{c}}}}}}}}}=\sqrt{{b}_{0}/{b}_{2}}\).

Spectra shown in Fig. 4 and Supplementary Fig. 6 were obtained by resampling the frequency axis to a logarithmic scale, to improve the graphical quality at high Fourier frequencies by ensuring a constant logarithmic resolution.

The corner frequency is related to the source physical parameters and seismic moment Mo according to41:

$${f}_{{{{{{{{\rm{c}}}}}}}}}=k{C}_{{{{{{{{\rm{d}}}}}}}}}\beta {\left(\frac{16}{7}\frac{\Delta \sigma }{{M}_{{{{{{{{\rm{o}}}}}}}}}}\right)}^{1/3}$$
(4)

with Δσ the stress-drop, Cd the directionality coefficient ranging between 0.1 and 10, β the rupture velocity and coefficient k = 0.37. Using the relation Mo = 101.5M+9.142, with M the event magnitude, we can derive the relation between fc and M:

$${f}_{{{{{{{{\rm{c}}}}}}}}}=k{C}_{{{{{{{{\rm{d}}}}}}}}}\beta {\left(\frac{16}{7}\frac{\Delta \sigma }{1{0}^{1.5M+9.1}}\right)}^{1/3}$$
(5)

Clearly, all these parameters may change from an event to the other, although the greatest variability is found for Δσ, which may vary on almost two orders of magnitude in the range 0.1–3 MPa.

The dashed and dotted lines shown in Fig. 4b of the main text indicate the corner frequency extrapolated from Eq. (5) using β=3 km s−1, Cd=1 and Δσ= 0.1 MPa or 3 MPa, respectively. A decreasing trend of the corner frequency is observed as the event magnitude increases, with the dispersion of results consistent with inhomogeneities in source parameters.

In our derivation of corner frequencies, we did not take into account propagation effects on the source spectrum, and did not apply any threshold on the event detection quality, based e.g. on signal/noise considerations. These effects may also play a role in explaining the dispersion of experimental results. As highlighted in the Main text, some bias is clearly distinguishable between values derived from the fiber or IV.ASCOL, whose reason deserves further investigation. At this stage, we cannot exclude some bias in the fit of the low-frequency components of spectra with a polynomial of the kind b2f 2 component due to the high noise at 0.75 Hz and 0.95 Hz affecting the cable.

The analysis was repeated with the vertical and North-South components of IV.ASCOL recordings with no substantial differences.

Reporting summary

Further information on research design is available in the Nature Portfolio Reporting Summary linked to this article.