Locating the precise sources of high-frequency microseisms using distributed acoustic sensing

<title>Abstract</title>         <p>Although microseisms have been observed for more than 100 years, the precise locations of their excitation sources in the oceans are still elusive. Underwater Distributed Acoustic Sensing (DAS) brings new opportunities to study microseism generation mechanisms. Using DAS data off the coast of Valencia, Spain, and applying a cross-correlation approach, we show that the sources of high-frequency microseisms (0.5-2 Hz) are confined between 7 and 27 km offshore, where the water depth varies from 25 to 100 m. Over time, we observe that these sources move quickly along narrow areas, sometimes within a few kilometres. Our method with DAS data allows characterizing microseisms with a high spatiotemporal resolution, opening a new chapter in understanding these global and complex seismic phenomena happening in the oceans.</p>

section_content: There is a long history of studying ambient seismic noise, especially the predominant oceangenerated microseisms [1] [2] [3]. It is now well established that there are two main frequency bands that are referred to as the primary (0. 05-0. 07 Hz) and secondary microseisms (0. 13-0. 40 Hz) [2] [3] [4] [5] [6] [7] [8] [9]. But this is a crude classification as new seismic data have shown more details in the structure of seismic noise. For example, there is evidence that the secondary microseisms consist of two separate peaks within their frequency band 10. Other evidence shows the arrivals of teleseismic signals at about 0. 2 Hz that are generated by far-away storms mix with locally generated secondary microseisms 11, 12. Microseisms can excite both surface and body waves 8, 9, 12, 13, which are extensively used to explore and monitor the Earth's interior at all scales through cross-correlations [14] [15] [16] [17] [18]. Thus far, the lack of high-density offshore seismic observations prevented seismologists from fully characterizing the complexity of microseisms. We can now move beyond this limitation using distributed acoustic sensing (DAS) and existing underwater telecommunication infrastructures 19- 22. 

DAS is a new method to measure the Earth's vibrations at an unprecedented resolution. It uses the optical phase changes of Rayleigh backscattered light to turn fibre-optic cables into dense arrays of seismic sensors measuring dynamic longitudinal strain or strain rate. At the end of the fibre, an interrogator unit (IU) sends laser pulses down the cable. The propagation of the laser pulses is affected by heterogeneities in the fibre and some of the energy travels back to the IU. When the fibre is disturbed by external forcing, changes in the phase of the backscattered light are measured by the IU and can be turned into continuous strain measurements along the fibre with a very high spatial resolution 23, 24. For an extensive review of the DAS technology, we refer the reader to Hartog 25. 

In this study, DAS data were recorded along a sea-bottom cable linking Valencia to Palma de Mallorca, Spain (Fig. 1 ). By using short-term cross-correlation methods, we achieved for the first time precise localisation of the sources of microseisms. We report our observations on the variations of microseism source locations for frequencies about 0. 5-2. 0 Hz. To distinguish this high-frequency signal from the well-known microseisms, we use the term "the High-Frequency microseisms (HF microseisms)" in this study. We found that the excitation source locations of HF microseisms are confined to a zone of about 7-27 km from the coast. Furthermore, the spatial extent of the source at a given time is much smaller, only a few kilometres in extent and this source region moves with the wind constantly. It suggests that the wind-generated ocean waves near the coast are exciting HF microseisms through the wave-wave interactions 2, 3. A theoretical analysis by the normal-mode theory supports this scenario.
section_name: Introduction

section_name: Results

section_content: We used a pre-installed telecommunication fibre-optic cable operated by IslaLink that connects the Spanish peninsula to Mallorca Island from Valencia to Palma de Mallorca (Fig. 1 ). From September 1st to September 15th, 2020, a FEBUS Optics A1-R interrogator was connected to the Valencia side of the cable to probe the first 50 kilometres of the cable. The initial 8,555 meters are located on land, and the following 41,445 meters are under the seabed. According to the installation report provided by the cable operator, the cable is buried ~1 m below the seabed for the full length of the measurement. The data were acquired with a sampling frequency of 1000 Hz, a gauge length of 30. 4 m, and a spatial resolution of 16. 8 m, turning the first 50 km of the cable into a seismic array of 2977 channels. We only analyse the data recorded between September 1st and September 7th, which are continuous, and exclusively focus on the underwater portion of the cable.
section_name: DAS experiment

section_content: Each channel exhibits two energy peaks in the frequency domain (Fig. 2a ). The first peak has a frequency band of 0. 05-0. 2 Hz. It is mainly observed in shallow waters, and its power decreases with increasing water depth. The same signal can be observed in the frequency-wave number analysis (Fig. 3a ) and travels with a phase velocity of ~10 m/s. This corresponds to the propagation of ocean surface gravity waves in the shallow waters, where these waves can directly exert pressure on the fibre-optic cable [19] [20] [21] [22]. The second peak is found in the 0. 5-2 Hz frequency band. This signal travels with a phase velocity of 500-1000 m/s (Fig. 3b ) and corresponds to the propagation of the fundamental-mode Scholte waves (Supplementary Figs. 1 2 3 ), whose energy is essentially trapped under the seabed [19] [20] [21] [22] [26] [27] [28]. 

Figure 2b shows 40 seconds of the strain rate data filtered between 0. 5 and 1 Hz. The propagations of the HF microseisms are revealed through oblique stripes travelling either up to the right toward the land (i. e., landward) or propagating seaward down to the right. In addition, Figure 2c shows that ocean waves that propagate in opposite directions mainly occur in the 0. 25-0. 5 Hz frequency range (period 2-4 s in Fig. 2c ), which corresponds to approximately the double-frequency relationship between the microseism signals and the ocean waves. The modal analysis (Supplementary Figs. 1 2 3 4 5 ) supports that the wave-wave interactions of ocean surface waves generate the wavefield at the seabed that dominates the HF microseisms 2.
section_name: Ocean surface gravity waves and Scholte waves

section_content: To better understand the wavefield created by the HF microseisms, we computed cross-correlation functions (CCFs) of DAS data for every 1. 5-km (i. e., 90 channels) interval along the cable. To increase the stability of the CCF signals, we stacked five adjacent channels. Then, we performed a CCF calculation with the following five stacked channels at 1. 5 km away. In the CCFs, we identify acausal (negative) and causal (positive) wave packets propagating landward and seaward, respectively. These are the same propagating waves observed in Figure 2b. The correlation technique allows us to track the propagation directions of the HF microseisms (Figs. 4a and 4b ). 

Due to the strong energy of this signal, we found that stable CCFs are obtained for time series as short as 10 minutes. These 10-minute CCFs match the 6-day-long stacked CCFs (Figs. 4a and 4b ), implying that Scholte waves are propagating parallel to the fibre. Therefore, we used the 10minute-long time series to gain higher temporal resolution in this study. We computed the CCFs between all channel pairs spaced by 1. 5 km for each 10-minute time series. Therefore, for every 10 minutes, it provides us 2374 CCF results for the entire 2468 DAS channels along the seabed. 

We used the signal-to-noise ratio (SNR) to evaluate the existence and significance of HF microseisms. The SNR was computed by taking the maximum amplitudes of the signals, independently for the acausal part and the causal part, and taking their ratio to the noise amplitude, which was estimated from the average amplitude in the trailing CCF coda for a duration of 200 sec (Supplementary Fig. 6 ). Figure 4a is an example of CCF that clearly shows the landward propagation of HF microseism (acausal part in red) with an SNR of 12. 3. The wave propagation of waves toward the deeper sea (causal part in blue) is, however, unclear even though SNR becomes 3. 1. Figure 4b is a case in which there are clear seaward signals but not a hint of landward propagation. In this case, SNR is 9. 8 for seaward propagation and 3. 2 for landward propagation. 

In general, SNR is larger than 4. 0 when we see a recognisable wave packet in the CCF. Figure 4c shows the results for all the CCFs computed for all 10-minute intervals for the entire six days and expressed as a function of their SNR for both landward (red) and seaward propagation (blue). 

Figure 4c illustrates that between 0 and 7 km from the coast, the causal part of the CCFs (i. e., blue lines) exhibit an overall SNR lower than 3, which means that there is no significant seaward propagation. However, the landward propagating signals are much larger. On the other hand, beyond ~27 km from the coastline, seaward propagation becomes dominant. The landward propagating signals show SNR under 4, suggesting that the wavefield beyond 27 km is dominated by HF microseisms propagating toward the deeper sea. Until now, an excitation source of HF microseisms was assumed to emit seismic waves in both the landward and seaward directions from the source 2, 3, 6, 29. However, the patterns in Figure 4c suggest that the source regions of the HF microseism are mostly confined within 7-27 km from the coast and the sources can radiate seismic waves in either landward or seaward direction and/or both.
section_name: The sources of HF microseisms

section_content: To see the temporal fluctuation of the sources, Figures 5a and 5b show the SNR results as a function of time. For every 10-minute interval, the SNR of seaward and landward signals are plotted from left to right for about six days with respect to distance from the coast. This figure shows that patterns in SNR change rapidly in time, meaning that the source locations are constantly moving. Sometimes, the source is all the way out to 25 km from the coast (black circle on Sept. 

2). This indicates that the landward propagation dominates the wavefield. On Sept. 3 (green circle), the wavefield mostly consists of seaward propagation, which means the excitation source is about 10 km from the coast. And most of the time, the source seems to be somewhere between 15 and 20 km from the coast (pink circle). It is important to recognise that the position of the HF microseisms sources is constantly changing, and the extent of the source is relatively small for a given time instance. 

By putting the variations of SNR in Figures 5a and 5b in a single plot, we can constrain the source locations for the frequency band 0. 5-1 Hz (Fig. 6a ). The positions between the two-colour regions (red and blue) must be the source location because away from the source, the SNR of landward (red) should become smaller toward the deeper sea, and the SNR of seaward (blue) should become smaller toward the coast. This range cannot be determined precisely, but in Figure 6b, we show a case where we treat the region of SNR larger than 5 in both landward and seaward propagations as the source region. The orange area shows the source extent, which oscillates in time and space. 

For each time instance, the spatial extent of the source is limited to an area of a few kilometres to 10 km. A similar analysis was applied to HF microseisms for a higher frequency band 1-2 Hz (Supplementary Fig. 7b ) and shows that the timing of changes in source location mostly agrees with those in Fig. 6b. These results depend on the threshold selection of SNR 5, and a different choice would provide broader or narrower estimates. Nonetheless, in most cases, the extent of the source region appears to be limited to a strip of 10 kilometres, most often within a few kilometres. Such a source area is constantly changing within the 7-27 km region from the coast, which is where the bathymetry varies from 25 to 100 m in depth.
section_name: Spatiotemporal variations of HF microseisms sources

section_content: How can we explain such changes in the excitation source of HF microseisms? We believe that the wave-wave interaction of ocean waves, generated by local winds, can explain these behaviours. 

As Figure 2c shows, the dominant period range of opposing winds is 2-4 seconds. Through the frequency doubling process from the collision of opposing ocean waves 2, 3, 6, 30, they can create seismic wavefields in the range 0. 5-1. 0 Hz, which is found in our data. The modal analysis shows that this process preferentially excites the fundamental-mode surface waves, as shown in Supplementary Figure 4. This mode may be called the Scholte wave as the maximum displacements occur at the sea bottom (Supplementary Fig. 3 ) and decay upward and downward from the seabed. Its large horizontal amplitude indicates an efficient excitation of extensional strain, which is the primary signal in DAS data. The constantly changing source locations are most likely related to the ephemeral behaviours of wind and its related ocean waves (black line in Fig. 6a ). Locations of wave-wave interactions should naturally change if the wind were the source of this process. 

The water depth must be an influential parameter as shown in modal analysis, and thus the efficiency of excitation of such modes can change significantly concerning depth. A relatively flat and shallow Mediterranean seabed with a depth range of 25-100 m may have played a prevailing role in our observations. Excitation of the HF microseisms should differ under different bathymetric conditions. 

There is no question, however, that DAS will soon play a significant role in understanding the excitation mechanisms of microseisms worldwide.
section_name: Discussion

section_name: Methods

section_content: We calculated the two-dimensional frequency-wavenumber (F-K) spectrum by applying a F-K beamforming technique to each hour of the data 31. The aperture of the seismic array determines the resolution of the smallest wavenumber 32. Arrays with large apertures can acquire high-speed seismic waves. For ocean waves, which have relatively large wavenumbers, we used DAS data recorded over 1 kilometre (Fig. 2a ). To observe Scholte waves (Fig. 2b ), we used data recorded over 15 kilometres.
section_name: F-K beamforming

section_content: Waves and wind data were obtained from the Spanish Ports Authority database (Puertos del Estado), called SIMAR (SImulación MARina in Spanish). SIMAR comes from WANA and is based on WAM 33 and WaveWatch III 34. The temporal sampling resolution of the wind data is 1 hour.
section_name: Wind and ocean waves data

section_content: The far-field Green's tensor for a spherical Earth 35 can be written as

where, ′, and are the station location, the source location, and the angular frequency ( = 2 where is the frequency), respectively. The summation is conducted for modes in each modal branch (e. g., the fundamental mode branch, the 1 st overtone branch, etc. ). is the phase velocity of a given mode, is the group velocity, I is the normalization for a spheroidal mode defined by 3 = /( + 1), Δ is the angular distance from the source to the station, is the attenuation parameter for a given mode. Note that this equation is for the spherical Earth. 

We consider a modal excitation problem by the wave-wave interaction of ocean surface waves in a flat-layered model. The horizontal displacement in the cylindrical coordinate can be defined as:

in the radial direction (r). The normalization factor I is defined as:

where () and () are the vertical and horizontal eigenfunction of a spheroidal mode (Rayleigh-wave mode) and z is the vertical coordinate (positive upward) where the sea bottom is = 0 and the ocean surface is =. 

The wave-wave interaction of ocean waves near the ocean surface generates pressure 2 and with an introduction of a surface area, it creates a vertical force = -. This force can be multiplied to the above formula to obtain the generation of horizontal displacements at sea floor. 

Since DAS measures strain along the fibre-optic cable, we differentiate the above formula with respect to and derive the following formula for the extensional strain in the radial direction:

where we only kept the term that differentiates the exponential oscillation term. Differentiation with respect to 1/√ should rapidly become small with distance and the differentiation of the attenuation term should also be small. In this formula, is the horizontal wavenumber. We can rewrite this formula as

where l is the excitation coefficient for a mode defined by:

The efficiency of excitation of various mode branches is related to the size of this term and is computed for various models.
section_name: Excitation of modes by the wave-wave interaction of wind ocean waves

section_content: We vary the ocean depth from 25 m to 500 m and examine the effects on modal excitations. Below the sea bottom, all models have a sedimentary layer of a thickness of 1 km (density (): 2000 kg/m 3, Vp: 2. 0 km/s, Vs: 1. 0 km/s), a transition layer with a thickness of 1 km where and seismic velocities increase linearly with depth and finally connect to the parameters from the PREM model (1981). The PREM parameters are assumed from 2 km below the sea bottom. PREM has the upper crustal parameters of : 2600 (kg/m 3 ), Vp: 2. 6 (km/s), Vs: 3. 2 (km/s), and the parameters after transition to lower crust are : 2900 (kg/m 3 ), Vp: 6. 8 (km/s), Vs: 3. 9 (km/s). m in depth, which are relevant to this study. It also shows that ocean depths deeper than 200 m show much less excitation of Scholte modes. This suggests that the excitation efficiency may greatly differ if the ocean depth steeply increases near the coast. Note that our analysis focuses on the 0. 5-2. 0 Hz frequency range. We define the locations of the HF microseism source using a SNR higher than 5 for both seaward and landward propagating Scholte waves.
section_name: Modal analysis

section_name: Acknowledgements

section_content: We thank IslaLink Holding Iberia S. L. for providing access to the BalaLink underwater fibre infrastructure. We are grateful to the Spanish National Geographic Institute and the Spanish Seismic Network for cooperation and data transfer. We thank Gaëtan Calbris from Febus Optics for his swift help on the field.
section_name: Acknowledgements

section_name: Data Availability

section_content: The data necessary to reproduce all results and figures in this article will be uploaded on an open repository after revision of the paper and before its possible acceptance.
section_name: Data Availability

section_content: All codes used to processed the data and produced figures in this paper are written in Generic mapping tool 36 and Matlab and available from the authors upon request.
section_name: Code Availability

section_name: Ethics declarations

section_content: In Supplementary Figure 1, we show an example of the modal analysis performed with a model that has an ocean depth of 100 m. We use a code for spherical modes that incorporates gravity effects. Therefore, for each wavenumber (horizontal wavelength), we first obtain a tsunami mode with a phase velocity of /. Supplementary Figure 1 shows overtone modes up to the 4 th one. 

The fundamental mode is termed as the Scholte mode for the reasons listed below. Supplementary Figure 2 shows the same set of modes. Tsunami modes are confined to the lowfrequency range (e. g., below 0. 2 Hz) and do not appear in the 0. 5-2. 0 Hz frequency range, which is the focus of this work. The phase velocity of Scholte waves for frequencies above 0. 5 Hz (e. g., 0. 8-1. 0 km/s) shows good agreement with Figure 3b. It supports that we mainly observe the effects of Scholte waves. Eigenfunctions of four modes at 1 Hz, indicated by solid circles in Supplementary Figure 2, are shown in Supplementary Figure 3. 

We name the fundamental mode as the Scholte mode in this paper because eigenfunctions have their maximum amplitudes at the seabed (Supplementary Fig. 3 ). The amplitudes tend to decay up and down from the seafloor, although strictly speaking, they deviate from what were originally known as Scholte waves, which were trapped at the fluid-solid interface on the seafloor. 

The excitation coefficients of these modes are shown in Supplementary Figure 4. This figure shows clearly that the wave-wave interactions at the ocean surface preferentially excite Scholte modes. 

The effect of the ocean depth on the excitation coefficients is shown in Supplementary Figure 5. 

This figure shows that the results in Supplementary Figure 4 remain very similar from 25 m to 100 Contributions H. X. conceived and designed the experiment, analyzed data, and wrote the initial manuscript. T. T. did the modal analysis, contributed to writing, and supervised the project. Z. J. S. collected the DAS data, coordinated the project, and provided critical assistance to the analysis. B. G. and S. R. B. helped to record the DAS data. M. P. visualized the results. L. V. independently verified the results. 

All authors contributed to the manuscript.

section_content: The authors declare that they have no competing interests.
section_name: Ethics declarations

section_content: Supplementary Figures 1 to 7
section_name: Supplementary Information

section_name: Supplementary Materials for