Monitoring ocean currents during the passage of Typhoon Muifa using optical-fiber distributed acoustic sensing

Domain: earth_science
Published: 2024-02-06
Editorial outcome: major_revision

Abstract
In situ observations under typhoon conditions are sparse and limited. Distributed acoustic sensing (DAS) is an emerging technology that uses submarine optical-fiber (OF) cables to monitor the sea state. Here, we present DAS-based ocean current observations when a super typhoon passed overhead. The microseismic noise induced by ocean surface gravity waves (OSGWs) during Typhoon Muifa (2022) is observed in the ~0.08–0.38 Hz frequency band, with high-frequency (>0.3 Hz) component being tidally modulated. The OSGW propagation along the entire cable is successfully revealed via frequency–wavenumber analysis. Further, a method based on the current-induced Doppler shifts of DAS-recorded OSGW dispersions is proposed to calculate both speeds and directions of horizontal ocean currents. The measured current is consistent with the tidally induced sea-level fluctuations and sea-surface winds observed at a nearby ocean buoy. These observations demonstrate the feasibility of monitoring the ocean current under typhoon conditions using DAS-instrumented cables.

Introduction
Cyclones systems, especially the well-known tropical cyclones (TCs), are devastating events that often have tremendous economic and societal impacts. However, accurately determining TC development, particularly TC intensity, is still a challenge due to the lack of sufficient in situ observations1. While the Dvorak technique2,3, which is empirically based on cloud patterns and the infrared cloud-top temperature, is widely considered the best available tool to determine TC intensity from satellite imagery, its accuracy is unavoidably contaminated by rainfalls, clouds, breaking waves, and spray4. In situ measurements, such as aircraft reconnaissance and ocean buoys, are effective in reducing TC intensity and position uncertainties5. For example, Wang et al.6 recently used drifter current measurements to estimate the sea-surface wind speed, and identified a positive trend of 1.8 ms−1 per decade globally in the weak TC intensity during the 1991–2020 period. However, such in situ hydrological observations remain sparse and limited due to the extreme sea state under TC conditions.

Ocean microseismic noise (typically in ~0.05–0.5 Hz), which is the most energetic component of the seismic noise spectrum mainly originating from ocean surface gravity waves (OSGWs; and hence wind fields) on the sea surface7,8, has been long identified as a potential proxy of the sea state and any associated disturbances, including the tracking and monitoring of TCs over the oceans, thereby providing complementary observations to traditional atmospheric, oceanographic, and satellite observations9–13. Gutenberg14 suggested that microseisms could be used in weather forecasting, and Grevemeyer et al.15 reconstructed the wave climate in the northeast Atlantic Ocean using a 40-year record of wintertime microseisms at Hamburg, Germany. TCs over the oceans have been remotely located and tracked via microseism-based techniques, such as array beamforming16–20. However, most of the relevant studies have been limited to far-field observations at terrestrial broadband seismic stations due to the sparsity of ocean-bottom instrumentation. Davy et al.9 analyzed the microseismic noise from a network of 57 broadband ocean bottom seismometers (OBSs) to infer the evolution of TC Dumile (2013) over the southwestern Indian Ocean, and demonstrated that seafloor microseisms can be used for real-time tracking and monitoring of major storms. However, accurate tracking and detailed near-field investigations of the TC are mainly limited by the complex excitation process and propagation of TC-induced microseisms, as well as the finite number and density of OBSs (average distance of 200 km between OBSs).

Distributed acoustic sensing (DAS) is an emerging technology that can provide strain measurements and effectively turn optical-fiber (OF) cables into dense seismo-acoustic arrays21, thereby motivating many recent advances in microseism research22,23 and ocean observations24–30. Lindsey et al.24 mapped a number of unknown seafloor faults in Monterey Bay via seismic-wave propagation from a minor earthquake that was recorded by a submarine DAS-instrumented OF cable. The recorded microseismic noise and hydrodynamic signals were associated with OSGWs, storm-induced sediment transport, infragravity waves, and breaking internal waves, thereby demonstrating the potential of this optical-fiber sensing method for marine geophysics. Taweesintananon et al.29 observed several types of ocean-bottom signals in the infrasound band (0.01–20 Hz) using a DAS-instrumented cable, and theoretically interpreted their generation mechanisms, including OSGW-loading seafloor pressure fluctuations and seismo-acoustic signals. Williams et al.26 presented the potential application of ocean-bottom DAS in physical oceanography by analyzing OSGW propagation at a qualitative level to roughly estimate the current speed along the cable based on the DAS frequency–wavenumber (f–k) spectrum. Subsequently, Williams et al.28 recovered spatiotemporal variations in current speed along the cable via DAS-based surface gravity wave interferometry. More recently, Mata Flores et al.31 measured the deep-sea current speed with DAS-recorded vortex-induced vibration of suspended cable segments. However, these DAS-based measurements are solely geared towards ocean current speeds and have not yet been able to estimate the current directions, and the potential of utilizing DAS measurements as dense arrays remains to be further evaluated.

Here we report the in situ observations of microseismic noise via a pre-existing submarine DAS-instrumented OF cable in a complex geo-environment of an archipelago during the passage of a super typhoon. These observations show that the ocean-bottom DAS-instrumented cable is sensitive to typhoon-induced microseismic noise, even at low frequencies (<0.1 Hz), and effective in deriving information on OSGW along the cable. We further presented a DAS-based measurement method, which is based on two specific cable segments with different orientations, to successfully reveal both speeds and directions of the horizontal ocean-current component at high spatiotemporal resolutions during such an extreme weather event.

Results
Experiment overview
Typhoon Muifa (2022; known as Typhoon Inday in the Philippines) passed directly over a distributed acoustic sensing observatory (DASO), which utilized a pre-existing ocean-bottom OF cable in the Zhoushan Archipelago, off the northeastern coast of Zhejiang Province, eastern China (Fig. 1). The cable was installed in 2014 and is operated by China Mobile Communications Group. It is about 20 km long, connecting Daishan and Zhoushan islands along a relatively straight route. The detailed survey of the exact cable layout was not authorized due to security considerations. As an alternative, the water depth along the cable was derived from a single-channel seismic profile that was acquired using a 2000-J Squid 2000 Sparker source (Applied Acoustic Engineering; United Kingdom) onboard a boat traveling at about 5.0 knots.

The DAS system, which was developed by the University of Science and Technology of China, was configured to probe phase changes of Rayleigh backscattering with 500-Hz sampling rate and 2-m gauge length. The used cable was spatially sample data 2-m channel interval along the cable, creating 9780 simultaneously recording sensors. However, the first 1125 channels are subaerial on the Daishan island, leaving 8655 channels (corresponding to 17.3 km of the cable; solid blue line in Fig. 1b) distributed beneath the sea surface. The raw DAS-recorded phase change data (with a unit of rad s−1) was further processed into 2 Hz strain rate data with a unit of ε s−1 (See detailed processing steps in Methods). A nearby ocean buoy (with minimum distance of ~1587 m to the cable; Supplementary Fig. 1) provided a continuous and accurate record of the sea-surface winds. These in situ observations during the passage of an ocean storm provided the unique opportunity to investigate the potential of utilizing DAS along pre-existing seafloor cables to monitor the sea state during such extreme weather conditions.

Microseismic noise from ocean surface gravity waves
The microseismic noise recorded by the DASO is first revealed in a distance–frequency spectrogram (Fig. 2a). The spectrogram consists of the upper-quartile spectral power at successive individual channels along the entire cable from 4:10 UTC on September 13 to 12:00 UTC on September 15. The dominant spectral energy is at ~0.2 Hz for most of the channels, with both the amplitude and bandwidth of the spectra being inversely proportional to the water depth along the cable. Notable high-frequency (>0.3 Hz) microseismic noise (HFMN) is distinct where the water depth is shallower than ~15 m. This is consistent with the linear theory of OSGWs, where the seafloor pressure perturbation ΔP induced by an OSGW of height ζ decreases exponentially with water depth h (Supplementary Fig. 2), i.e., ΔP(h,ζ) = ρgζ / cosh(kh), where ρ is the water density and g is gravitational acceleration25. It is worth mentioning that the spectral amplitudes along the first ~3 km of the cable are exceptionally weak as a result of poor coupling between the cable and seafloor due to the rolling topography.

Mean time–frequency spectrograms are calculated at each set of four successive channels along the entire cable to further investigate the temporal evolution of the microseismic noise. The most prominent feature in the relatively shallow-water zone (e.g., channels 1253–1256 and 4068–4071) is that the HFMN is only observed during low tide (Fig. 2b, d). A similar phenomenon has been observed by Williams et al.28 and Taweesintananon et al.29 This can basically be interpreted as tidal modulation of the OSGW seafloor pressure. Crawford et al.32 indicated that the theoretical maximum frequency fmax of the OSGW seafloor pressure, fmax = g/(2πh), can be calculated as fmax = g/(2πh), where n = 1 = kh ≈ 1. By replacing h with the tidally induced change in water depth htide(t), the temporal variations in the theoretical maximum frequency fmax(t) at channels 1253–1256 and 4068–4071 (dashed black line in Fig. 2b, d) agree well with the observed spectral peaks of the HFMN. Conversely, the HFMN and tidal modulation become almost invisible along relatively deep sections of the cable, such as channels 2316–2319 and 5649–5652 (Fig. 2c, e), where the fmax(t) at h ≥ 20 m would fluctuate below 0.3 Hz (Supplementary Fig. 3) and the cable burial depths are likely deeper due to the topographic depressions (Fig. 2a). However, the passage of Typhoon Muifa is clearly visible on the time–frequency spectrograms of these deep channels. The dominant microseismic noise evolves consistently with the observed wind speed (with correlation coefficient reaching about 0.89 around 0.20 Hz; Supplementary Fig. 4) and typhoon track. The typhoon passage over the DASO can be identified with a “quiet” strip on the spectrogram around 14:00 UTC on September 14, 2022 (bounded by the two dashed white lines in Fig. 2c, d).

It is noticeable that although the high-frequency (>0.3 Hz) component seems to lie within the frequency band (~0.1–0.5 Hz) of secondary microseismic noise (SMN), the observed microseismic noise is directly generated by the OSGW seafloor pressure, namely primary microseismic noise (PMN). Traditional observations of microseismic noise on terrestrial seismic networks or OBSs constitute diffuse seismic energy radiated into the far field, whereas the observation is conducted just beneath the water when a typhoon passed overhead in this study. Because the dominant frequency band of typhoon-generated ocean waves in shallow waters can often span over ~0.1–0.35 Hz33,34, the corresponding near-field PMN can extend beyond 0.3 Hz. In addition, the microseismic noise is observed tidally modulated and sensitive to water depth. This is contradictory to the generation mechanism of SMN7, whereby the nonlinear interaction between opposing ocean waves induces a depth-independent pressure fluctuations on the seafloor.

Measurements of ocean wave propagation
Figure 3a–d shows the f–k spectra of the 30-min-long datasets for all 8655 channels at four different stages of Typhoon Muifa. The dominant microseismic energy is detected within the ~0.08–0.38 Hz frequency band and −0.065–0.065 m−1 wavenumber range. The corresponding phase velocity (c = f/k) is the apparent phase velocity of the OSGWs propagating across the OF cable24,25. The spectral energy in the right quadrant of each f–k spectrum with a positive wavenumber, which possesses a positive phase velocity, mainly originates from OSGWs propagating with a northeast component across the cable toward the coast of Daishan Island (landward); conversely, the spectral energy in the left quadrant, which possesses a negative phase velocity, is generated by OSGWs propagating with a southwest component (seaward). The dominant propagation direction of the OSGWs reverses as Typhoon Muifa passes over the DASO (Fig. 3b, c), mainly because the winds rotate counter-clockwise around the typhoon center in the Northern Hemisphere, resulting in predominantly northeast winds and southwest winds blowing over the water when Typhoon Muifa is approaching and departing the DASO, respectively.

Figure 3e–h shows the derived apparent phase velocities and corresponding spectral energies along the entire cable during the passage of Typhoon Muifa, which were calculated via a sliding-window f–k analysis of the entire DASO dataset (see “Methods” for details). Seaward OSGWs with apparent phase velocities of ~8–12 ms−1 in the 0.12–0.28 Hz frequency band are prominent along most of the cable before 14:00 UTC on September 14 (Fig. 3e, f); landward OSGWs with similar apparent phase velocities in the same frequency band become prominent after the passage of Typhoon Muifa (Fig. 3g, h). This reversal of the dominant OSGW propagation direction is consistent with the observed changes in sea-surface wind direction at the nearby ocean buoy (Fig. 1b).

Previous studies25,26,28 have indicated that the most prominent feature of the DAS f–k spectrum is that the lower edges of the spectral energy packets mainly fit the linear OSGW dispersion curve35: f^2 = g/(2π) k tanh(2πkh) (1). Given that the DAS-observed OSGW propagations are apparent, these lower edges are typically thought to be caused by OSGWs propagating axially or paraxially along the cable. However, the fit between the lower edge of the spectral energy packet and the linear OSGW dispersion curve could be affected by several factors, including (1) the directional wave spectrum, (2) the varying bathymetry along the cable, and (3) the ocean current fields above the cable. Considering directional wave spectra with little energy propagating axially or paraxially down the cable, all OSGWs propagate obliquely across the cable and produce apparent phase velocities faster than those predicted by the linear OSGW dispersion relation. On the other hand, the non-flat cable layout would distort the observed apparent OSGW wavenumbers and therefore the apparent phase velocities. It may also lead to multiple dispersive spectral energy packets with lower edges corresponding with OSGW dispersion curves of diverse water depths, as exemplified in Fig. 3a–d. And OSGWs shoaling-up over a slope bathymetry would become higher and steeper, resulting in nonlinear amplitude dispersion effects on the wave phase speeds36,37. Additionally, the underlying ocean currents would induce Doppler effects into the OSGW dispersion relationship38–41, which would manifest as non-reciprocal frequency shifts of the spectral energy packets in the DAS f–k spectrum26 (Fig. 4b, c). Nevertheless, the Doppler effect can also be used to measure the ocean current.

Ocean current measurements, based on Doppler shifts of OSGW fields, have been successfully conducted using radar and optical systems39,40,42–44. These measurements can characterize the spatial variations of currents, yet they are reliant on the weather. The DAS-based observations of the current-induced Doppler-shifts, on the other hand, have been recently proven effective for measuring current speed28. These methods, which use the OSGW-generated pressure disturbances at the seafloor, can function effectively even in harsh weather conditions. It is anticipated to offer a more cost-effective means of measuring submesoscale currents than ocean acoustic tomography45,46 and conventional oceanographic instrumentation, such as moored current meters and acoustic Doppler current profilers. In the following section, an approach utilizing the DAS f–k spectra to characterize ocean currents is proposed. More importantly, even during typhoon conditions, this method can estimate current direction in addition to measuring current speed.

Ocean-current measurements
In this study, the horizontal ocean current flowing over the DAS-instrumented cable is successfully measured using a proposed method (see Methods for details). For example, Fig. 4b, c show the measurement results of the mean ocean current during the period 16:40–16:50 UTC on September 13, 2022, using two adjacent segments (channels 3875–4075 and 4225–4425; red line segments in Figs. 1b, 4a). The OSGW dispersion curves for both cable segments are obviously affected by the current-induced non-reciprocal Doppler shift, which is apparent as a clockwise rotation of the dominant spectral energy packets with respect to the linear OSGW dispersion curves (cyan curves, calculated via Eq. (1)). Asynchronous fit of the Doppler-shifted OSGW dispersion curves (black curves, calculated via Eq. (3) in “Methods”) to the lower edges of the dominant spectral energy packets along both segments yields respective mean ocean-current speed and direction of ~0.7 ms−1 and ~240°.

Figure 4d shows the ocean current flowing over the two selected cable segments during the passage of Typhoon Muifa at a 10-min resolution. A video of the stepwise OSGW dispersion curve fit and corresponding ocean-current measurements is provided (Supplementary Movie). The temporal variations in the measured ocean current are mainly consistent with the tidally induced sea-level fluctuations, with the changes in speed and direction dominated by the tidal current. Similarly, the M2 tidal current has been measured using a DAS-instrumented OF cable28. However, the measured ocean current reverses and strengthens irregularly during the passage of Typhoon Muifa (~11:00 to 19:00 UTC on September 14). This is consistent with the observed sea-surface wind fluctuations at the nearby ocean buoy (Fig. 4e). The correlation coefficient between the measured ocean current directions and observed wind directions is 0.902 (Supplementary Fig. 5). Overall, the above results demonstrate the feasibility of estimating ocean currents (speed and direction) in a shallow water under typhoon conditions via our proposed DAS-based method.

We note that there are potential improvements to our DAS-based ocean-current measurement method. Firstly, despite the endeavors undertaken to sharpen the lower edges of dominant energy packets in f–k spectra for more accurate fitting (see details in Methods), it should be acknowledged that human visual perception in the manual fitting process is intrinsically prone to bias, particularly when dealing with dispersion curves with slight Doppler shifts in a smeared f–k spectrum image. Therefore, an algorithm-based automated fitting process, such as one based on digital image processing or machine learning for edge detection and extraction, is crucial to improve the efficiency and accuracy in follow-up work. Secondly, the nonlinearity of OSGWs would bias the ocean current measurements based on this linear-theory-based method. For example, the nonlinear amplitude dispersion effects of OSGWs with high wave steepness (kζ) over varying shallow bathymetry would lead to higher OSGW phase speeds than those predicted by the linear dispersion relation37,47. So adoption of a proper nonlinear OSGW dispersion relation (e.g., nonlinear Boussinesq theory48) and simultaneous deployment of wave height sensors and tide gauges are expected to alleviate the nonlinear effects. Lastly, it is recommended to install cables that are specifically designed for the purpose of observing ocean currents (e.g., Supplementary Fig. 6a, b), instead of employing pre-existing undersea cables that are rigidly regulated and predetermined in their layout. For example, horizontal arrangement of the cable segments as shown in Supplementary Fig. 6a can effectively mitigate the impact of varying bathymetries discussed in the previous section. Schemes of cable layouts shown in Supplementary Fig. 6b are designed to improve the spatial coverage and resolution of ocean current measurements.

It is important to emphasize that, despite its intrinsic limitations, this approach is expected to have potential implications for oceanography. Given the fact that OSGW-induced seafloor pressure perturbations decay exponentially with water depth, the practical implementation depth H of this method is theoretically capped at one-half of the OSGW wavelength, i.e., H ≤ πk−1. The H is also related to the normalized horizontal compliance ηx of the DAS system, which is the conversion coefficient between the ΔP and horizontal strain rate and affected by various factors28 (e.g., cable-seafloor coupling and cable construction). The H would be deeper for unburied high-sensitivity OF cables than those for telecommunications and power cables used in related studies (e.g., H ≈ 100 and 150 m reported by Sladen et al.25 and Williams at al.28, respectively). Therefore, this approach could be potentially used to monitor tidal currents and issue prior warning for extreme tide events (e.g., storm surges) in coastal areas. In addition, this method measures the depth-averaged horizontal current from ocean surface to the seafloor or the unburied cable. Therefore, measurement of non-uniform 3D currents by this method would be prone to bias (e.g., the biased measurement of linear shear currents exemplified in Supplementary Fig. 7). Yet, this method may have potential for observations of ocean motions with significant vertical components (e.g., submesoscale eddies, internal waves) by utilizing specially planned OF cables. For example, a scheme of multi-layer cable layout as shown in Supplementary Fig. 6c allows for estimation of vertical variations of ocean currents by synchronously measuring the depth-averaged horizontal currents at different layers. It is anticipated that the DAS-based techniques would further facilitate observations of oceanographic phenomena, including tide and internal waves30, and upwellings/downwellings essential for the marine ranching.

Methods
Data processing
The raw DAS dataset DATAraw with the unit of phase change rate (rad s−1) is first converted to dataset DATAstrainrate with the unit of strain rate (ε s−1) as follows:
DATAstrainrate = λ / (4πnGξ) * DATAraw, (2)
where λ = 1.550 × 10−6 m is the laser wavelength of the DAS system, n = 1.467 is refraction index of the OF, G = 2 m is the gauge length and ξ = 0.78 is the photoelastic scaling factor for longitudinal strain. The DATAstrainrate is then processed using the Python package Obspy, including: (1) demeaning and detrending; (2) decimating to 2 point per second and 1-Hz low-pass filtering. Noted that the DAS data used in f–k analysis is further decimated to 1 point per second for calculation efficiency.

Sliding-window f–k analysis
A sliding-window f–k analysis is applied to the whole DASO-recorded dataset to derive the apparent phase velocity along the entire cable during the passage of Typhoon Muifa. The sliding-window is dimensional, and the window lengths are set to 1 h and 400 m in the time and space dimensions, respectively, both with 50% overlap. Each windowed dataset is then transformed to a f–k spectrum via a 2D Fourier transform. The dominant apparent phase velocity of each f–k spectrum is further calculated by averaging the apparent phase velocities at the f–k bins where the spectral energy is greater than 60% of the maximum spectral energy of each f–k spectrum. The spatio-temporal variation of the apparent phase velocity is finally derived on the basis of all of the dominant apparent phase velocities.

Ocean-current measurements from DAS-instrumented cable observations
Figure 4a provides a schematic illustration of the proposed ocean-current measurement method. Assuming that a uniform horizontal ocean current flows over two adjacent segments with different orientations, the current speed U and direction θ can be estimated by synchronously fitting the Doppler-shifted OSGW dispersion curves to the lower edges of dominant spectral energy packets in the f–k spectra of both cable segments. The Doppler-shifted OSGW dispersion curves are expressed as follows26:
(f1 + cos(θ − Φ1)k1)^2 = g/(2π) k1 tanh(2πk1h1), Φ1 ≠ Φ2 (3)
(f2 + cos(θ − Φ2)k2)^2 = g/(2π) k2 tanh(2πk2h2)
where Φ1,2 and h1,2 represent the azimuth angles and water depths of the two selected cable segments, respectively, and f1,2 and k1,2 are the frequencies and apparent wavenumbers of the two corresponding f–k spectra, respectively. U cos(θ − Φ1,2)k1,2 is the Doppler shift term induced by the ocean current. The cable segment selection criterion is that the two adjacent segments should orient differently but within the prevailing wave direction range under stable sea states.

The specific calculation details for this study are described as follows. The cable channels 3875–4075 and 4225–4425 (at 5.5–5.9 km and 6.2–6.6 km respectively; red line segments in Figs. 1b, 4a) are selected according to the above selection criterion and their relatively higher signal-to-noise ratios (Fig. 2a, d). Both selected cable segments consist of 200 channels and possess respective azimuths Φ1 = 249.7° and Φ2 = 214.3° (Fig. 4a). The DAS observations along each cable segment are transformed into a series of consecutive f–k spectra with both the sliding-window length and step equal to 10 min. The f–k spectra for both cable segments at each time window are then paired for the fitting process. We have developed a dedicated graphical user interface (GUI; Supplementary Fig. 8) based on the Python packages Numpy and Matplotlib for manual fitting process. In the case of given Φ1,2, h1,2, f1,2 and k1,2, this GUI allows for the manual adjustment of the “Current speed” and “Current direction” Sliders to conduct synchronous fitting between the corresponding Doppler-shifted OSGW dispersion curves and the lower edges of the dominant spectral energy packets in the f–k spectra of both cable segments. The water depths h1,2 in Eq. (3) are replaced by the tide-modulated water depths h01,2(t) (Fig. 4d), which are estimated as follows:
h01,2(t) = D1,2 + T(t), (4)
where T(t) is the tide level variation of the DASO region, with temporal resolution of 10 min after linear interpolation. Due to the lack of exact information of cable layout and burial, the characteristic water depths of the two selected cable segments D1,2 are estimated using a specialized GUI (Supplementary Fig. 9). Based on the f–k spectra with inconspicuous Doppler shifts of cable segment x (x = 1 or 2) and known T(t), this GUI allows for manual adjustment of the “Dx” Slider to control the variation of h0x(t) to optimize the fit between the corresponding linear OSGW dispersion curves and the lower edges of dominant spectral energy packets. In both GUIs, the dominant spectral energy packets in all of the f–k spectra are highlighted by uniformly rendering with a diverging colormap and filtering out the spectral energy below −115 dB.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "Key results:\n• Ocean current speeds and azimuth are derived from a method based on relafive current-induced\nDoppler shifts on shallow, configuous segments of a DAS cable having different orientafions\n• The measured ocean currents are consistent with fidally induced sea-level fluctuafions, typhoon-\ninduced currents and sea-surface winds observed at a regional ocean buoy\n• The novel detecfion and visualizafion of the wind-generated current structure of a major cyclone by a\nDAS system underneath\nValidity: The methodology proposed is valid and useful in various contexts. However, some clarificafions\nof its implementafion are required, while a detailed discussion of the results is considerably lacking. A\nfew conceptual shorffalls/gaps are present that have to be addressed, but these do not affect the validity\nof the results in general.\nOriginality and significance: The work is original and of immediate interest for the community, notably\nphysical oceanography, ocean engineering, and other ocean-related fields, geophysics and fiber-opfic\nsensing in general.\nData & methodology: The theorefical framework of the approach is valid. The data has enough quality to\nidenfify the physical signals of interest. However, the method is poorly explained and there appears to\nexist some degree of ambiguity in the workflow that might compromise the reproducfion of the results.\nNotably, the presentafion of requirements, validity ranges and limitafions of the method is unclear or\ninsufficient. Although some of the assumpfions of the method are menfioned, these could be stressed\nsome more while others are missing. Some literature is missing or was not acknowledged properly. For\nspecifics, I’ve listed the major comments below.\nAppropriate use of stafisfics and treatment of uncertainfies: Yes, up to some missing descripfions of the\ncorrelafion methodology implemented.\nConclusions: The conclusions and data interpretafion are mostly valid, although perhaps not sufficiently\nbacked-up by more detailed descripfions and discussions, which would in turn facilitate an\nassessment of the robustness and reliability of the method.\nMajor comments:\n1. The key fact that only the horizontal component of the currents is retrieved (i.e. horizontal\ncurrents are assumed) is not menfioned anywhere in the text and should be emphasized in the abstract and in and in at\nleast a couple secfions more. On the other hand, a discussion on the detecfion potenfial of the method\nfor ocean circulafion structures with important verfical components (such as eddies, internal waves or\ndown-/upwelling) is missing. For example, could this method discern between deep/surface currents? or\nbetween currents and other (sub)mesoscale anomalies?\n2. Details on the manual picking and fifting process of the doppler-shifted linear dispersion curves\nimplemented and its limitafion are lacking. This is quite relevant, as the parameterizafion of the f-k\ntransformafion (from which the dispersion metrics are obtained) plays a major role on its SNR and its\nfime-space resolufion trade-off. As the method strongly relies on some assumpfions, namely that:\nbackground currents are horizontal; locally steady and uniform; and that the segment layouts are flat\n(i.e. constant depths), the authors are requested to thoroughly discuss potenfial biasing induced by non-\nuniform 3D currents and sloping/complex bathymetry. Addifionally, as the exact cable layout at the\nseafloor is often unknown, the recommendafion for proper georeferencing/surveying of the segments\nshould be stressed. Also, some comments on potenfial effects related to the spafial stability/variability of\nthe direcfional wave spectrum between the segments would make sense.\n3. A key point stressed by the authors is that the analysed signals correspond to microseisms. As the\nfrequency band of the most energefic signals considered is between 0.1-0.3 Hz, which is well-known to\nlie within the secondary microseismic (double-frequency) band, does this imply that all the phenomena\nobserved are caused by non-linear wave-wave interacfions? On the other hand, this same frequency\nband corresponds to the dominant surface gravity wave peak in shallow areas and, as the authors\nmenfion, the esfimated phase speeds are between 8~12 m/s, which are way too slow for microseisms\nwhile are at the same fime consistent with typical phase speeds of ocean surface gravity waves. It\ntherefore seems more plausible that all the signals analysed by the authors are being induced directly\nupon the cable by gravity waves.\n4. L 191-6: Although the slowest apparent component is more likely to correspond to the true wavefield\nspeed, this is not always necessarily the case. As an example, what if several swells with different speeds\nare superposed in a way that those that arrive (nearly) axially are even faster than those at an angle?\nThis is parficularly relevant for cyclones, as their direcfional wave spectrum can be complex and\nasymmetric among its four quadrants (see e.g. Hu & Chen, 2011-Direcfional spectra of hurricane-generated waves in the Gulf of Mexico). The fact that previous studies have fifted linear gravity wave\ndispersion curves to their f-k spectra does not imply that the observed waves propagated parallel to the\ncable, as f-k dispersion branches could sfill be apparent. Assuming true propagafion along a line is\ngenerally incorrect and may generally lead to errors, as only non-axial components might occur.\nHowever, the fact that all observed wavelengths are apparent does not appear to affect the results, but\nthe fact should be clarified, specially for the non-specialist readers.\n5. L 255-7 The authors menfion that the picking and fifting is done manually. Although the\nsupplementary video showing the several picked f-k spectra are helpful to visualize this, further details\non the workflow and criteria used to perform this picking and fifting are necessary. Also, do the authors\nenvision a potenfial way to effecfively and accurately automafize the procedure?\n6. L 258-60 The selecfion criteria of the three channel ranges shown in Fig 2 was not enfirely clear to me\nunfil I read these lines. The fact that these kind of specific cable segments are required for the method to\nwork should be menfioned somewhere in the introducfion, at least. Furthermore, it is somewhat\nconfusing that none of the data segments highlighted in Figs. 1 and 4 is studied in Fig. 2. It would make\nsense to at least highlight the segments in Fig. 2.\n7. It is known that the detecfion of surface gravity waves with seafloor DAS is not possible at all depths,\nas these can aftenuate significantly over deep waters, as implied by the eq. referenced in L 138. This\nposes a major, addifional limitafion to the method, as it could only be implemented over secfions that\nare not too deep. As far as I see, this limitafion is not menfioned and should be clearly stated. For\ninstance, how does the reliability of the method vanishes as a funcfion of\ndepth/wavelength/waveheight? and what are the useful cable depth ranges for the method to work?\n8. L 305 – Some parts of the methods are not explained in much detail, such that several quesfions are\nleft open. For instance, What is the selecfion criteria of the segments? Also, how exactly is the fifting\nprocess performed to solve for the system of equafions (2)? If, as stated in L324-5, energy below 17dB is\nfiltered for every window, does this imply that the minimum speed dispersion curve envelopes may not\nbe picked or are not being sought at all? If picking is done manually, doesn’t the colormap scale affect\nthe interpreter’s choice? Addifionally, details about the uncertainty of the method are missing. This may\ninclude a discussion on error propagafion during the fifting process, which is prone to ambiguity for\nnoisy/smeared fk images.\n9. L 313 – The length of each of the selected cable segments is about 400 m (according to the channel\nspacing reported of 2m), but a constant depth is assigned to each. Is the bathymetry truly flat for these\nsegments? If not (as it appears from the boftom profile), how are these constant depth values defined?\nand how exactly does the assumpfion of flat bathymetry under a sloping segment affect the results? This\ncould be e.g. quanfified/shown in a figure.\n10. A data processing secfion is missing. Any preprocessing of the data (e.g. unit conversion, filtering,\ndecimafion, detrending, etc.) prior to the implementafion of the method (or the lack of any processing\nstep) must be reported accordingly.\nSuggested improvements:\n• As the study deals specifically with the esfimafion of the magnitude (speed) and azimuth of ocean\ncurrents, the proposed fitle might be a bit too broad and ambiguous. My suggesfion would be to change\nit to “Direcfional (or azimuthal) monitoring of ocean currents during the passage of Typhoon Muifa\n(2022) using opfical-fiber distributed acousfic sensing” or something similar that emphasizes ocean\ncurrents. As there is a recent study on deep sea current detecfion with DAS using a different approach\n(hanging cable secfions) by Mata Flores et al. (2023), the suggested fitle would emphasize the fact that\nyour method addifionally retrieves current azimuth, as opposed to the former study, that only retrieve\nmagnitudes. Also, including a brief comparison of your method with that of the former study seems\nappropriate.\n• It would encourage the authors to discuss potenfial hydrodynamic effects on the measurements. For\ninstance, how is the method expected to be affected by the potenfially non-linear (high kζ) wave regime\nof large storms (such as a typhoons) where linear theory no longer applies and waves can break and\ninteract?\n• In Fig 1b, the spafial extent and wind direcfion of the cyclone would be useful to understand the\nexpected wave direcfional distribufion during the typhoon during closest approach (e.g. contours\nindicafing the extent of the maximum wind speeds/ROCI/isobars/…). Are there any models of wave/wind\nstress direcfion available for the region, such as hindcasts?\n• In Fig 2 the authors could use different colors (not repeafing them) for each of the curves overlain to\nimprove clarity of the figure. Also, reporfing the depths of the shown channel ranges in the figure would\nhelp the reader. Including a fourth spectrogram panel for some of the shallow channels around ~5km\nalong the cable (e.g. those used in Fig. 4) might be interesfing, as the spectral power seems quite high\nhere.\n• In general, it would be interesfing to see some more discussion on the physical oceanographic\nimplicafions and applicafions of the method, at least in a general way. This could opfionally focus on the\nregional oceanographic sefting (e.g. well-known surface/deepsea circulafions in the region) where the\nexperiment was carried out. For instance, is it possible to link the esfimated current speed and azimuth\nvalues to previous observafions in the region or observafions for other cyclones? It is remarkable that\nfidal modulafions and fidal currents can be observed so clearly in the data. As the typhoon-induced\ncurrents seem to be canceled or even reversed by the fides, could this mean that some currents might\nbe overshadowed by the local fides if not fast enough? The method could also potenfially be used to\nretrieve fidal components under steady condifions, a fact that is worth highlighfing.\n• This and other DAS methods have a potenfially high impact for oceanography, so that cable dedicated\ndeployments might be planned in the future. What would the author’s suggesfions be for future studies\nplanning to lay cables targefing ocean currents? For example, in terms of geometry, locafion, etc? The\nauthors could also highlight that the simultaneous use of mulfiple cables or addifional sensors (e.g.\ncurrent-meters, buoys, moorings, sensor arrays) might provide a complementary view of the\noceanographic regime.\nReferences:\n• L53-65 – Although some references were included, in my opinion, it would be fair to add a few more\non cyclone-related microseisms, considering the vast amount of literature available, including review\npapers and books.\n• L60-5 – The cited reference of Davy et al., 2014 is very relevant for the current work as it dealt with the\ndetecfion of a cyclone passing overhead an array of broadband OBSs and hydrophones in the ocean, in\nanalogy with the presented case of typhoon Muifa with DAS. However the way that this work is\nreferenced and discussed in the text does not seem make jusfice to this fact (which is not highlighted at\nall) nor to its findings in general. For instance, in L64 I find “limited” far more accurate than “prohibited”\n(see Sec. 6 in Davy et al, 2014). At the same fime, I disagree that it was is only the sparsity of stafions in\nthat work what limited the storm tracking (which in fact I consider quite remarkable given the variable\ngeometry, areal extent and the complexity of the gravity wave and bathymetry-dependent seismic noise\nradiafion pafterns of a cyclone, specially in the near-field) and I also disagree that this “...prohibited… a\ndetailed near-field invesfigafions of the TC”, as the authors of that work showed in detail and with good\ndata quality the wave polarizafion and amplitude aftenuafion funcfions induced by the cyclone passing\noverhead, amongst others.\n• L66-84. A few references could be added that are relevant for surface gravity wave analyses with DAS:\nGuerin et al., 2022 and Sladen et al., 2019. For ocean microseism studies with DAS: Xiao et al, 2022 and\nTonegawa et al., 2022. On the other hand, are there any previous studies addressing surface gravity\nwaves and their relafionship with ocean currents from theorefical perspecfives or proposed\nexperimental methods not related to DAS, such as acousfic/remote sensing/oceanography? This would\nbe worthy to be menfioned and discussed for general context.\n• L 212-14 – this is a quite well-known fact within the oceanographic community, thus adding a few older\nreferences would be very perfinent e.g. Leckler, 2015 - Analysis and Interpretafion of Frequency–\nWavenumber Spectra of Young Wind Waves\nClarity and context:\n• L20 - “...current-induced Doppler shifts”: the authors could indicate what parficular physical signal\nexperiences this effect\n• L33 - “Tropical cyclones (TCs)”: Perhaps this study could be safely generalized for Cyclones?(this would\nimplicitly also include subtropical and extratropical)\n• L49 - “Microseismic noise (~0.05–0.5 Hz)...”: Ocean microseismic noise (as e.g. lakes can generate\nmicroseisms at up to 2 Hz)\n• L73 – small typo: “opfical-fiber”\n• L87-9 - “...These observafions show that the ocean-boftom DAS-instrumented cable is sensifive to\ntyphoon-induced microseismic noise, even at ultra-low frequencies (<0.1 Hz), and effecfive in deriving\ninformafion on OSGW.”. How do the authors tell apart secondary microseisms from SGWs in the\nfrequency range of interest?\n• L 108: is the buoy really collocated with the studied cable segments? If not (as it seems), what is the\ninter-distance for each case?\n• L 165: in Fig 2a was the data lowpassed at 0.4Hz? The decrease above this bound seems abnormally\nsudden\n• L 146. The same phenomenon was reported and studied in detail in ref #22.\n• L 147-49. Since kh~1 seems to be a constrain of the cited equafion, is it then only valid for deep waves?\nFig 2b is convincing but the authors could also include the same frequency limits for Figs 2c,d\n• L 158: The authors could comment somewhere on the specific correlafion method used to obtain the\ncoefficient. The same applies to figures S1 and S2.\n• L 183. “with a northeast component” would be more accurate. A similar comment applies to L185\n• L 186-190: As the typhoon approaches from the south, westward winds occur just before its arrival,\nwhile eastward winds dominate afterwards, which is contrary to what is wriften in the text. This can be\nconfirmed by the dominant seaward energy in Fig 3b and the opposite in 3c.\n• L198-200: I fail to understand the exact connecfion of this sentence to the previous ones: the fact DAS\ncan provide measurements of surface gravity waves has already been demonstrated.\n• L211 – what other factors?\n• L 252-3 – what are the specific requirements for the method to work on the alluded environments?\n• In Figure 3, between ~4-6 km along the cable there is a shallow cable secfion of high wave energy\nwhich also increases as the storm approaches, both seawards and landwards. However, the wave speeds\nappear to increase a bit more in the seaward component relafive to the background level than they do\nafter the storm leaves in the landward component. What could cause this?\n• L 312 The wavelengths retrieved from a DAS segment are always apparent, meaning that the\nwavenumbers (k1, k2) are apparent too. This should be emphasized, as the method would eventually not\nallow for the recovery of the propagafion angle of the waves. Some addifional tests or discussion on the\nexpected performance of the method within the parameter domain would help in its validafion, i.e. as a\nfuncfion of the amplitude and angle of incidence of the waves relafive to the cable, the relafive angle\nbetween the segments, the water depth, the strength and azimuth of the current, etc.\n• L 319 – How are this fide-modulated depths obtained? Is a reference fide gauge required for the\nmethod to work? If so, this should be clearly stated.\n• The seismic profile/bathymetry data shown in Fig 1c does not seem to be menfioned in the Data\navailability statement.\n• The gauge length, fime sampling rate and unit measured by the DAS system (strain/strain rate?) are\nmissing and should be reported.\nInflammatory material: None\nReviewer #2 (Remarks to the Author):\nThis is a review of the manuscript \"Monitoring the sea state during the passage 1 of Typhoon\nMuifa (2022) using opfical-fiber distributed acousfic sensing\". This manuscript presents a very nice observafion\nof the effect on Distributed Acousfic Sensing of a typhoon propagafion over a fiber opfic cable. This is an\nexcepfional sefting to study the seismic signals generated by strong oceanic events. I do not have many\ncomments and I found this study very interesfing but I believe a few things should be considered.\nWhile I understand the paper is observafional, I think the authors should discuss at least a liftle the\nwaves that are observed on the signals. There is no real discussion of this while I feel necessary since\nphase velocifies are discussed. One disadvantage of DAS data is that observafions are only made over\none dimension. Consequently, a discussion of wave propagafion and types cannot be avoided in my\nopinion. The authors show very nice observafions but the impact could be discussed more.\nI had to go back and forth a lot to use the figures and I think a few changes could be made to help. In\nFigure 2 b,c,d the locafions are defined as channels but in 2 a and Figure 1 the distance is represented in\nkm. Moreover, the water depth is an important feature so I would make that more directly clear for the\ndifferent cases.\nIt would be interesfing to represent the locafion of the parficular focus zones showed on Figure 2 also in\nFigure 1. Moreover, the authors show how the fidal signals dominate in shallow water on one side of the\nfiber. This was quite surprising and interesfing for me. I believe it would be useful to show the\nobservafions on the other side of the fiber. Indeed, as the slope is very different, a comparison would be\nvery informafive.\nMinor comments:\n- Line 17: I am not sure I would use the term “hydrological” in the first sentence since it suggests that is\nwhat DAS data obtains. I am not sure it is there yet.\n- Line 33-36: The authors menfion the damage on land and need for intensity esfimafion at the\nbeginning of the paper. To me this implied that there was esfimafion in the manuscript of intensity on\nland which I realized later was not the case.\n- Line 89 : Frequencies inferior to 0.1 Hz are not “ultra low” in seismology. I would suppress the ultra.\n- Figure 2: It could help to add the colored triangles from a) in b,c,d to make the reading of the figure\neasier\n- Line 229-230 : I understand that the authors detail the methodology in the method part but something\nshould sfill be said about it apart from the fact that it is “novel”.", "reviewer_2": "This is a review of the manuscript \"Monitoring the sea state during the passage 1 of Typhoon\nMuifa (2022) using opfical-fiber distributed acousfic sensing\". This manuscript presents a very nice observafion\nof the effect on Distributed Acousfic Sensing of a typhoon propagafion over a fiber opfic cable. This is an\nexcepfional sefting to study the seismic signals generated by strong oceanic events. I do not have many\ncomments and I found this study very interesfing but I believe a few things should be considered.\nWhile I understand the paper is observafional, I think the authors should discuss at least a liftle the\nwaves that are observed on the signals. There is no real discussion of this while I feel necessary since\nphase velocifies are discussed. One disadvantage of DAS data is that observafions are only made over\none dimension. Consequently, a discussion of wave propagafion and types cannot be avoided in my\nopinion. The authors show very nice observafions but the impact could be discussed more.\nI had to go back and forth a lot to use the figures and I think a few changes could be made to help. In\nFigure 2 b,c,d the locafions are defined as channels but in 2 a and Figure 1 the distance is represented in\nkm. Moreover, the water depth is an important feature so I would make that more directly clear for the\ndifferent cases.\nIt would be interesfing to represent the locafion of the parficular focus zones showed on Figure 2 also in\nFigure 1. Moreover, the authors show how the fidal signals dominate in shallow water on one side of the\nfiber. This was quite surprising and interesfing for me. I believe it would be useful to show the\nobservafions on the other side of the fiber. Indeed, as the slope is very different, a comparison would be\nvery informafive.\nMinor comments:\n- Line 17: I am not sure I would use the term “hydrological” in the first sentence since it suggests that is\nwhat DAS data obtains. I am not sure it is there yet.\n- Line 33-36: The authors menfion the damage on land and need for intensity esfimafion at the\nbeginning of the paper. To me this implied that there was esfimafion in the manuscript of intensity on\nland which I realized later was not the case.\n- Line 89 : Frequencies inferior to 0.1 Hz are not “ultra low” in seismology. I would suppress the ultra.\n- Figure 2: It could help to add the colored triangles from a) in b,c,d to make the reading of the figure\neasier\n- Line 229-230 : I understand that the authors detail the methodology in the method part but something\nshould sfill be said about it apart from the fact that it is “novel”."}, "author_response": "Point-by-Point Response to Comments\nby the Editor and Reviewers\nNOTE: Line numbers indicated in this file correspond to the revision-\ntracked manuscript (PDF version) with the changes noted.\nReviewer #1\nKey results:\n“Ocean current speeds and azimuth are derived from a method based on relative current-\ninduced Doppler shifts on shallow, contiguous segments of a DAS cable having different\norientations”\n“The measured ocean currents are consistent with tidally induced sea-level fluctuations,\ntyphoon-induced currents and sea-surface winds observed at a regional ocean buoy”\n“The novel detection and visualization of the wind-generated current structure of a major\ncyclone by a DAS system underneath”\nValidity:\n“The methodology proposed is valid and useful in various contexts. However, some\nclarifications of its implementation are required, while a detailed discussion of the results is\nconsiderably lacking. A few conceptual shortfalls/gaps are present that have to be addressed,\nbut these do not affect the validity of the results in general.”\nOriginality and significance:\n“The work is original and of immediate interest for the community, notably physical\noceanography, ocean engineering, and other ocean-related fields, geophysics and fiber-optic\nsensing in general.”\nData & methodology:\n“The theoretical framework of the approach is valid. The data has enough quality to\nidentify the physical signals of interest. However, the method is poorly explained and there appears to\nexist some degree of ambiguity in the workflow that might compromise the reproduction of the\nresults. Notably, the presentation of requirements, validity ranges and limitations of the method\nis unclear or insufficient. Although some of the assumptions of the method are mentioned,\nthese could be stressed some more while others are missing. Some literature is missing or was\nnot acknowledged properly. For specifics, I’ve listed the major comments below.”\nAppropriate use of statistics and treatment of uncertainties:\n“Yes, up to some missing descriptions of the correlation methodology implemented.”\nConclusions:\n“The conclusions and data interpretation are mostly valid, although perhaps not sufficiently\nbacked-up by more detailed descriptions and discussions, which would in turn facilitate an\nassessment of the robustness and reliability of the method.”\nTHANK YOU. We appreciate very much for the meticulous review. We have incorporated\nall the comments by Reviewer 1.\nMajor comments:\n1. “The key fact that only the horizontal component of the currents is retrieved (i.e. horizontal\ncurrents are assumed) is not mentioned anywhere in the text and should be emphasized in the\nabstract and in at least a couple sections more. On the other hand, a discussion on the detection\npotential of the method for ocean circulation structures with important vertical components\n(such as eddies, internal waves or down-/upwelling) is missing. For example, could this method\ndiscern between deep/surface currents? or between currents and other (sub)mesoscale\nanomalies?”\nDONE. Yes. Only the horizontal component of the ocean currents is measured. Following\nthe reviewer’s suggestion, we have revised the manuscript as follows:\nLines 26-28 (in the Abstract)\nModified\n“The ocean current is also derived via a novel method, based on measurements\nof the current-induced Doppler shifts.”\nto\n“Further, a novel method based on the current-induced Doppler shifts of DAS-\nrecorded OSGW dispersions is used to calculate both speeds and directions of\nhorizontal ocean currents.”\nLines 123-143\nModified\n“These observations show that the ocean-bottom DAS-instrumented cable is\nsensitive to typhoon-induced microseismic noise, even at ultra-low frequencies (<0.1\nHz), and effective in deriving information on OSGW and ocean-current propagation\nat high spatiotemporal resolutions during such an extreme weather event.”\nto\n“These observations show that the ocean-bottom DAS-instrumented cable is\nsensitive to typhoon-induced microseismic noise, even at ultra-low frequencies (<0.1\nHz), and effective in deriving information on OSGW along the cable. We further\npresented a novel measurement method, which is based on two specific cable\nsegments with different orientations, to successfully reveal both speeds and\ndirections of the horizontal ocean-current component at high spatiotemporal\nresolutions during such an extreme weather event.”\nLine 182 (in the caption of Figure 1)\nModified “current measurements” to “horizontal current measurements”\nLines 382, 470, 496, 530\nModified “ocean current” to “horizontal ocean current”.\nWe acknowledge that this method cannot discern between deep/surface currents with a\nsingle submarine cable, since the method measures the depth-averaged horizontal current\nfrom ocean surface to the seafloor or the unburied/suspended cable. However, it is expected\nto measure the differences between depth-averaged currents at different depth using a\ndedicated vertical multi-layer cable (e.g., Figure S5c) and further estimate the vertical\nvariations of ocean currents. Accordingly, in the revised manuscript we have added\ncorresponding discussions (Lines 446-465), as follows:\n“In addition, this method measures the depth-averaged horizontal current from ocean\nsurface to the seafloor or the unburied cable. Therefore, measurement of non-uniform\n3D currents by this method would be prone to bias (e.g., the biased measurement of\nlinear shear currents exemplified in Figure S7). Yet, this method may have potential\nfor observations of ocean motions with significant vertical components (e.g.,\nsubmesoscale eddies, internal waves) by utilizing specially planned OF cables. For\nexample, a scheme of multi-layer cable layout as shown in Figure S6c allows for\nestimation of vertical variations of ocean currents by synchronously measuring the\ndepth-averaged horizontal currents at different layers. It is anticipated that the DAS-\nbased techniques would further facilitate observations of oceanographic phenomena,\nincluding tide and internal waves30, and upwellings/downwellings essential for the\nmarine ranch.”\nFigure S6c. Schemes of cable layouts designed to retrieve the vertical variations of\nhorizontal ocean currents.\n2. “Details on the manual picking and fitting process of the doppler-shifted linear dispersion\ncurves implemented and its limitation are lacking. This is quite relevant, as the parameterization\nof the f-k transformation (from which the dispersion metrics are obtained) plays a major role on\nits SNR and its time-space resolution trade-off. As the method strongly relies on some\nassumptions, namely that: background currents are horizontal; locally steady and uniform; and\nthat the segment layouts are flat (i.e. constant depths), the authors are requested to thoroughly\ndiscuss potential biasing induced by non-uniform 3D currents and sloping/complex bathymetry.\nAdditionally, as the exact cable layout at the seafloor is often unknown, the recommendation\nfor proper georeferencing/surveying of the segments should be stressed. Also, some comments\non potential effects related to the spatial stability/variability of the directional wave spectrum\nbetween the segments would make sense.”\nDONE. Thanks for the suggestion. In the revised manuscript, we have provided a more\ndetailed description of the manual picking and fitting process of the doppler-shifted\ndispersion curves in the Methods section (Lines 542-572), as follows:\n“The specific calculation details for this study are described as follows. The cable\nchannels 3875–4075 and 4225–4425 (at 5.5–5.9 km and 6.2–6.6 km respectively;\nred line segments in Figures 1b and 4a) are selected according to the above\nselection criterion and their relatively higher signal-to-noise ratios (Figures 2a\nand d). Both selected cable segments consist of 200 channels and possess\nrespective azimuths 𝛷 = 249.7° and 𝛷 = 214.3° (Figure 4a). The DAS\n! \"\nobservations along each cable segment are transformed into a series of\nconsecutive 𝑓–𝑘 spectra with both the sliding-window length and step equal to\n10 min. The 𝑓–𝑘 spectra for both cable segments at each time window are then\npaired for the fitting process. We have developed a dedicated graphical user\ninterface (GUI; Figure S8) based on the Python packages Numpy and Matplotlib\nfor manual fitting process. In the case of given 𝛷 , ℎ , 𝑓 and 𝑘 , this\n!,\" !,\" !,\" !,"}]

Decision letter