# Seismo-Acoustic Analysis for Accurate Clock-Drift Correction of Autonomous Long-Term Hydrophones

Romain Safran, Alexey Sukhovich, Julie Perrot, Pierre-Yves Raumer, Sara

Bazin, Anne Briais, Jean-Yves Royer

► To cite this version:

Romain Safran, Alexey Sukhovich, Julie Perrot, Pierre-Yves Raumer, Sara Bazin, et al. Seismo-Acoustic Analysis for Accurate Clock-Drift Correction of Autonomous Long-Term Hydrophones. OCEANS 2025 Brest, Jun 2025, BREST, France. pp.1-7, 10.1109/OCEANS58557.2025.11104407. hal-05410885

HAL Id: hal-05410885

https://hal.science/hal-05410885v1

Submitted on 11 Dec 2025

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_1.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
Seismo-acoustic analysis for accurate clock-drift
correction of autonomous long-term hydrophones

Romain Safran

Univ Brest/CNRS/Ifremer - Geo-Ocean
F-29280 Plouzané, France
romain.safran@univ-brest.fr

Alexey Sukhovich

Univ Brest/CNRS/Ifremer - Geo-Ocean
F-29280 Plouzané, France
sukhovich@univ-brest.fr

Julie Perrot

Univ Brest/CNRS/Ifremer - Geo-Ocean
F-29280 Plouzané, France
julie.perrot@univ-brest.fr

Pierre-Yves Raumer

Univ Brest/CNRS/Ifremer - Geo-Ocean
F-29280 Plouzané, France
pierre-yves.raumer@univ-brest.fr

Sara Bazin

Univ Brest/CNRS/Ifremer - Geo-Ocean
F-29280 Plouzané, France
sbazin@univ-brest.fr

Anne Briais

Univ Brest/CNRS/Ifremer - Geo-Ocean
F-29280 Plouzané, France
anne.briais@cnrs.fr

Jean-Yves Royer

Univ Brest/CNRS/Ifremer - Geo-Ocean
F-29280 Plouzané, France
ORCID: https://orcid.org/0000-0002-7653-7715

**Abstract**—Accurate timing is crucial for precise seismic event localization from trilateration, particularly in long-term hydrophone monitoring, which assumes that all instruments are synchronized. This study addresses the challenge of estimating clock drift in autonomous underwater hydrophones deployed in the southern Indian Ocean as part of the OHA-SIS-BIO array. When GPS synchronization is impossible upon recovery due to battery failure, alternative methods to estimate clock drift become essential. We apply an approach based on weighted least-squares, which compares arrival-times of teleseismic P-waves recorded on a hydrophone station with arrival-times predicted by a propagation model in the Earth. By leveraging the International Seismological Center's EHB earthquake catalog and selecting events with large magnitude, we were able to infer clock drift with improved precision. This approach is effective, as demonstrated by the good match between calculated and directly measured clock drift, and thus provides reliable drift estimates for hydrophones that cannot be synchronised upon recovery.

**Keywords**—Hydrophone, Clock Drift Correction, Seismo-Acoustic, Teleseismic P-Wave, Underwater Acoustics

I. INTRODUCTION

Seismometers are essential for monitoring ground motion and seismic activity. However, due to the rapid attenuation of seismic waves in solid-Earth, land-based networks are not able to detect low-magnitude events from remote plate boundaries such as seafloor spreading ridges. Hydroacoustic waves generated by earthquakes in the ocean, on the opposite, can propagate in the ocean over thousands of kilometers with little attenuation. This is the reason why, in 2010, a large hydrophone array was deployed to monitor the seismic activity of the seafloor spreading system in the southern Indian ocean (Fig. 1). This hydrophone array, called OHA-SIS-BIO for “Observatory of HydroAcoustics from SISmicity and Biodiversity in the Indian Ocean” [11], was maintained until 2023. This monitoring project stemmed from the hydrophone ability to detect low-magnitude seismic events from acoustic waves generated in the water by seismic P-Primary and S-Secondary waves reaching the seafloor, known as T-Tertiary waves. T-waves can propagate up to thousands of

kilometers within the Sound Fixing and Ranging channel (SOFAR). Their arrival times on an autonomous hydrophone array allow, by trilateration, to determine the origin time and location of their sources.

The OHA-SIS-BIO array was composed of 7 to 12 autonomous hydrophones moored in the SOFAR channel and encompassing the three spreading ridges of the Indian Ocean (Fig. 1). They had an autonomy between 12 and 24 months at a sampling frequency of 240Hz. Sampling was triggered by a high-precision quartz internal clock, with a drift in the order of a few seconds per year of recording. Instruments were all synchronized with GPS time before deployment and upon recovery to measure the time difference between the hydrophone and GPS times (skew). Assuming a linear drift with time, a linear time correction can then be applied to the continuous data. However, when the batteries failed before the hydrophone recovery, the skew can no longer be measured by GPS time synchronization. Since the accuracy of the trilateration of a seismic event is time-sensitive, one needs to find an alternative method to assess the clock-drift so a temporal correction can be applied. Sukhovich et al. [1] developed a method to estimate clock drift using distant seismic events with large enough magnitudes to generate T-waves at the foot of the mooring, recorded by the hydrophones with a sufficient signal/noise ratio. The aim of this study is to adjust and apply this method to some of our hydrophone data.

This study leverages OHA-SIS-BIO data acquired in 2018, a period during which the hydrophones composing the array experienced both known and unknown clock drifts. Out of the nine hydrophones in this array, four ran out of battery and their clock could not be synchronized. The clock drift of the remaining ones was measured at recovery and ranged from -0.79 to 0.03 ppm (Table 1). Here we apply the method of Sukhovich et al. [1] to infer the drift of the 9 hydrophones from a set of large earthquakes recorded by land-based seismological networks (Fig. 1).
## II. DATA & METHODOLOGY

### A. Seismic Event Selection and Catalog Integration

Rather than relying on the NEIC earthquake catalog [6] as in [1], we opted for the more accurate EHB seismic event catalog [7] from the International Seismological Center (ISC). The EHB catalog offers refined estimates of the hypocenter location and origin time on well constrained seismic events using the EHB algorithm [2], making it particularly suitable for our analysis. Events were selected with a minimum magnitude of $Mw \ge 6$, resulting in a dataset of 146 seismic events between January 2018 and February 2019 that aligned with our hydrophone recording period (Fig.2). For each event, the latitude, longitude, depth, and associated error information were stored in our database.

Then, for each event, we computed the angular distance between the earthquake source and each recording station. We then calculated the theoretical arrival times for seismic phases P at each hydrophone using the ak135 1D velocity model [5]. To refine these predictions, we added the travel time of the acoustic wave from the seafloor to each hydrophone, with a sound velocity derived from the In Situ Analysis System temperature and salinity grid (ISAS-T/S fields) [3]. Monthly temperature and salinity values near each hydrophone were extracted, allowing us to estimate local sound velocities via the Thermodynamic Equation of Seawater (TEOS-10). [4]

<figure><img src="image_2.png" /><figcaption>Fig. 1: OHASISBIO array in the southern Indian Ocean in 2018 (red triangles) and set of large earthquakes (black stars) used in this study to infer the hydrophone clock drift.</figcaption></figure>

<figure><img src="image_3.png" /><figcaption>Fig. 2: Hydroacoustic data recorded by the OHASISBIO array in 2018 (blue rectangles) and teleseismic events used in this study (red dots) to independently calibrate their clock drift.</figcaption></figure>
<figure><img src="image_4.png" /><figcaption>Fig. 3: (Top frame) Example of predicted (dash blue) and manually picked (solid red) seismic arrival times in an ELAN audio recording. (Bottom frame) Enlarged section centered on the arrival time, with filtered signal (black) and energy envelope (blue), presented in arbitrary units</figcaption></figure>

## B. Phase Identification & Picking of Arrival times

Timestamps of the hydrophone recordings, initially in GPS time, were converted into UTC time, to conform with the seismic catalog (i.e. corrected for leap seconds). For each of the 146 seismic events, the predicted arrival time was plotted in a 4 minute-long window of hydrophone data to search for the corresponding P-phase arrival at the station (Fig. 3). When a corresponding P-phase arrival was clearly identifiable in the waveform data, the arrival time was manually picked and assigned a quality uncertainty in seconds. Energy plots and band-pass filtered waveforms were used to help the arrival-time picking. Typically, the observed arrival times fell within five seconds of the predicted ones. For each hydrophone, between 5 and 33 arrivals were identified and picked, depending on the signal to noise ratio.

## C. Clock Drift Estimation

To estimate the clock drift of each hydrophone, we compared the observed and predicted arrival times of seismic phases and modeled the drift as a linear function of time. We applied a weighted least-squares (WLS) linear regression to the arrival time residuals.

The relationship between observed (y) and predicted (x) arrival times was modeled as:

$$y_i = a x_i + b$$

where a (unitless) quantifies the clock drift and b (seconds) represents the absolute timing offset.

The drift rate in parts per million (ppm) is derived as:

$$Drift = (a - 1) \times 1e6. (ppm)$$

Parameters a and b were estimated via weighted least squares (WLS), minimizing:

$$J(a,b) = \sum_{i} w_{i} \cdot (y_{i} - a \cdot x_{i} - b)^{2}$$

with weights $w_i = 1/\sigma_i^2$

## D. Uncertainty Propagation and Weighting Scheme

To ensure robust regression, we weighted each arrival time based on its estimated uncertainty. The total uncertainty for each arrival time residual was computed as:

$$\sigma_i = \sqrt{\sigma_{point, i}^2 + \sigma_{cat, i}^2}$$

where:

* $\sigma_{point, i}$ is the uncertainty in manually picking the arrival time from hydrophone waveform,

* $\sigma_{cat, i}$ is the uncertainty in the earthquake origin time and theoretical travel time estimation from the seismic catalog.

Each event was assigned a weight inversely proportional to the squared uncertainty $\sigma_i$, ensuring that events with lower uncertainty contribute more strongly to the regression, while minimizing the impact of poorly constrained arrivals.
### E. Incorporating a Constant Offset

A systematic offset **b** was introduced in the model to account for potential systematic biases in travel time predictions. These biases may arise from:

* Local Seismic Velocity Variations: The ak135 model provides global average velocities, but deviations due to local lithospheric structures can cause systematic arrival time shifts.

* Instrument Positioning Errors: Variations in hydrophone depth and mooring slant could slightly alter the effective travel path of acoustic waves.

* Seismic-to-Acoustic Wave Coupling Delays: Small, unmodeled time lags between seismic-to-acoustic wave conversion and detection at the hydrophone could introduce additional biases.

We chose $t_0$ as the initial hydrophone's date of synchronization. The resulting offset (**b**) is expressed in this reference frame, so that at $t=0$ we expect to have a value close to zero. By explicitly modeling this offset, we mitigate systematic errors and improve the accuracy of drift estimation.

The least square problem can be written in its matrixial form and the solution is :

$$ \begin{bmatrix} a \\ b \end{bmatrix} = (X^T W X)^{-1} X^T W Y, $$

where **X** is the design matrix, **Y** represents the observed data points, **W** is the inverse of the variance/covariance matrix describing the data points $y_i$, which are assumed to be independent normal random variables and defined as **W**=diag(wi). Parameter uncertainties $\sigma_a, \sigma_b$ were derived from the covariance matrix, yielding 95% confidence intervals:

$$ CI(a) = a \pm 1.96 \cdot \sigma_a, $$

and

$$ CI_{Drift} (ppm) = (a - 1) \times 10^6 \pm 1.96 \cdot \sigma_a \times 10^6 $$

## III. RESULTS & DISCUSSION

### A. Clock drift estimations

We applied the WLS linear regression to estimate the clock drift and its associated 95% confidence intervals (CI) for each hydrophone station. In parallel, the reduced Chi-square coefficient was calculated to evaluate the goodness-of-fit for the regression model. The accuracy of the clock-drift estimates strongly depends on the number of observed arrivals. Table 1 summarizes the measured and estimated drift values, offsets, and statistical parameters for all stations.

For stations with robust GPS synchronization (i.e., sufficient battery level at recovery), such as ELAN, SSEIR, SWAMS-bot (with the exception of MADE), the estimated drifts agree with the measured values, as shown for the ELAN station in Fig. 4. During the 5 months of MADE recordings, the number of telesesimic events was limited (Fig. 2, Table 1) and recordings were noisy, leading to only five observed arrivals, hence the large confidence uncertainties, which bracket the actual drift.

In contrast, for hydrophones that had to be restarted after their recovery, due to battery failure, the drift estimates and their CIs deviate from the GPS-based measurements. This is not surprising since (i) the frequency of the internal clock slightly changes whenever the clock is turned off and on, (ii) the elapsed time between synchronizations did not exceed a few hours or a day vs. a year or so for the instruments that were still recording at recovery, and (iii) in this short elapsed time, the clock ran at room temperature. For these stations, we successfully identified a large number of arrivals (Fig. 2, Table 1). The events were well distributed in time, leading to a clock-drift estimate with a 95% confidence interval of less than 0.07 ppm. The drift for station WKER2 is, however, ill-constrained by only 8 arrivals. Fig.5 illustrates the clock-drift estimation at the RTJ station.

<table><caption>Table 1: Summary of measured and estimated clock drift and offset derived from teleseismic arrival-times in the OHASISBIO Hydrophone Stations. Grayed rectangles indicate measured drift outside the 95% confidence intervals (CI) of the estimated drift. When batteries failed, clock drift were measured after restarting the instrument, at room temperature, and for few hours only, and are thus likely to be inaccurate.</caption><thead><tr><th></th><th>Estimated drift (ppm)</th><th>95% CI inf</th><th>95% CI sup</th><th>Offset b (s)</th><th>Reduced chi²</th><th>Measured drift (ppm)</th><th>Battery</th><th>Number of Events</th></tr></thead><tbody><tr><td>ELAN</td><td>-0,020</td><td>-0,099</td><td>0,059</td><td>1,652</td><td>1,66</td><td>-0,0222</td><td>ok</td><td>25</td></tr><tr><td>MADE</td><td>-0,060</td><td>-1,121</td><td>1,001</td><td>0,600</td><td>5,23</td><td>-0,7980</td><td>ok</td><td>5</td></tr><tr><td>MADW</td><td>0,159</td><td>0,086</td><td>0,221</td><td>0,637</td><td>1,33</td><td>0,0020</td><td>exhausted</td><td>20</td></tr><tr><td>NEAMS</td><td>0,119</td><td>0,058</td><td>0,179</td><td>1,482</td><td>1,83</td><td>0,2601</td><td>exhausted</td><td>33</td></tr><tr><td>RTJ</td><td>-0,059</td><td>-0,115</td><td>-0,003</td><td>1,517</td><td>1,23</td><td>0,0300</td><td>exhausted</td><td>32</td></tr><tr><td>SSEIR</td><td>-0,030</td><td>-0,085</td><td>0,026</td><td>1,987</td><td>1,41</td><td>-0,2861</td><td>exhausted</td><td>26</td></tr><tr><td>SSWIR</td><td>0,063</td><td>-0,024</td><td>0,150</td><td>0,984</td><td>1,12</td><td>0,0346</td><td>ok</td><td>18</td></tr><tr><td>SWAMS-bot</td><td>0,019</td><td>-0,048</td><td>0,086</td><td>0,443</td><td>0,45</td><td>0,0048</td><td>ok</td><td>10</td></tr><tr><td>WKER2</td><td>0,139</td><td>-0,076</td><td>0,353</td><td>0,303</td><td>2,27</td><td>-0,0203</td><td>exhausted</td><td>8</td></tr></tbody></table>
<figure><img src="image_5.png" /><figcaption>Fig. 4: Time drift estimate for the ELAN station, whose drift has been measured at recovery. (Top) Blue circles represent the time discrepancy between predicted and picked P-phase arrival-times with its associated uncertainty; the horizontal axis is the elapsed time since the initial hydrophone synchronization. The red line shows the linear regression curve, with its 95% confidence interval (shaded). (Bottom) Standardized residuals relative to the predicted drift (dashed line), normalized by the uncertainties; positive residuals in blue, negative residuals in red. Dotted gray lines indicate ±2 standard deviation limits.</figcaption></figure>

<figure><img src="image_6.png" /><figcaption>Fig. 5: Time drift estimate for the RTJ station, whose drift is unknown. (Top) Blue circles represent the time discrepancy between predicted and picked P-phase arrival-times with its associated uncertainty; the horizontal axis is the elapsed time since the initial hydrophone synchronization. The red line shows the linear regression curve, with its 95% confidence interval (shaded). (Bottom) Standardized residuals relative to the predicted drift (dashed line), normalized by the uncertainties; positive residuals in blue, negative residuals in red. Dotted gray lines indicate ±2 standard deviation limits.</figcaption></figure>

## B. Comparative analysis of EHB and NEIC clock drift

We were able to find and associate homologous seismic events from the EHB and NEIC catalogs. Using the estimated arrival times for the NEIC catalog, we reestimated the clock drift for the ELAN, SSWIR, and SWAMS-bot stations, for which we had a large number of events and a known skew. Fig. 6 compares the measured and estimated clock drifts with their 95% confidence intervals (CI) from the EHB and NEIC catalogs.

We observe that the NEIC catalog produced slightly different results for the ELAN station, deviating further from the measured drift, whereas the resulting clock drifts were nearly identical for SSWIR and SWAMS-bot stations. Most events in these catalogs exhibit minor differences. However, a few events show significant discrepancies, with one or two notable cases observed at the ELAN station.

As the EHB event source location and original time estimates are improved, the resulting standard deviations for this catalog are smaller, leading to narrower confidence intervals compared to the NEIC catalog.
<figure><img src="image_7.png" /><figcaption>Fig. 6: Comparisons of estimated drift and 95% CI using EHB (blue) or NEIC (red) seismic catalog and compared with actual measured clock drifts (green diamond).</figcaption></figure>

### C. Uncertainty Analysis and Limitations

The precision of the clock-drift estimation is closely linked to the number of usable arrival observations. For stations such as MADE, WKER2, and SWAMS-bot, a limited number of observations—primarily due to high ambient noise and challenges in accurately picking arrival times—resulted in larger uncertainties. The reduced Chi-square values, mostly ranging between 1 and 2, suggest a slight underestimation of the uncertainties. This discrepancy could indicate either that the uncertainty estimates are too optimistic or that the regression model does not fully capture all sources of variability in the data.

Potential factors contributing to these limitations include:

* Ambient noise: High noise levels complicate the precise picking of arrival times.

* Local anomalies: Variations in the local sub-seafloor structure and bathymetry can affect the travel times of teleseismic waves.

* Model simplifications: The assumption of a purely linear drift during the entire deployment may lead to residual errors.

### D. Potential Improvements

To address these limitations, several refinements could be considered:

* Enhanced arrival time picking: Further processing of the raw hydrophone data, possibly following approaches such as that proposed by Simon et al. [8] could improve the accuracy of arrival time determination.

* Incorporation of Additional Seismic Phases: Including extra seismic phases from the same earthquake, such as pP, PcP, PKIKP phases, may increase the number of observations, thereby refining the drift estimates and reducing the confidence intervals. With the caveat that the predicted arrival times of these phases will be more prone to uncertainties in the Earth velocity model.

* Refined Uncertainty Estimation: Improving the estimation of uncertainties by refining error propagation techniques and incorporating a more detailed statistical model to derive more accurate CI.

* Local Velocity Model Adjustments: Incorporating detailed local velocity structure and bathymetric corrections could further improve travel time predictions.

In summary, while the estimated clock drifts are generally consistent with expected values, the method's accuracy is influenced by several factors including the local noise environment. Continued refinement of both the arrival picking process and the uncertainty modeling is expected to further improve the precision of the clock-drift correction.

## IV. CONCLUSION & FUTURE WORK

This study confirmed the methodology of leveraging seismic phase arrivals to successfully correct clock drift in autonomous long-term hydrophones. By using a weighted least-squares regression model, we estimated both a linear clock drift factor (a) and a systematic offset (b), effectively compensating for time discrepancies caused by clock drift and environmental uncertainties. The adoption of the ISC-EHB catalog enhanced the precision of seismic event arrival times compared to the NEIC catalog, reducing outliers and improving confidence intervals. For stations synchronized upon recovery, the estimated clock drifts are consistent with the actual measured values. This good agreement suggests that, when the drift cannot be measured without restarting the instruments at recovery, the new estimates are likely more accurate than the measured ones and should be used instead.

The main limitation of this approach remains the difficulty in observing and picking arrivals in noisy environment and/or the possible lack of teleseismic events during short-term monitoring, as observed for station MADE or WKER2.

An accurate clock synchronization is critical for the precise localization of seismic events by trilateration and the long-term analysis of hydroacoustic databases. In future work, we will explore an alternative approach based, in a similar way, on T-wave arrival times from acoustic events determined from the hydrophones with known clock drifts. The comparison of predicted and observed arrival times at hydrophones with unknown clock drifts will provide an independent way for checking and perhaps improving drift estimates based on teleseismic events.

## ACKNOWLEDGMENTS

The authors wish to thank the Captains and crews of R/V Marion Dufresne for the successful deployment and recovery of the OHASISBIO hydrophones during multiple cruises. Ship time was funded by the French Oceanographic Fleet. The instruments were funded by the *Contrats de Projet Etat-Région Bretagne* ODO and O3DO. The French Polar Institute (IPEV) and the French Oceanographic Fleet funded the ship time for the deployment and recovery of the OHASISBIO network [9][10] (Doi 10.17600/18000653 and 10.17600/18000974). R. Safran was funded by a doctoral fellowship from the *Région Bretagne* and ANR MUSIC (grant ANR-23-EDIR-0002).
REFERENCES

[1] A. Sukhovich, J. Perrot, and J.-Y. Royer, "Using Teleseismic P-Wave Arrivals to Calibrate the Clock Drift of Autonomous Underwater Hydrophones," Bulletin of the Seismological Society of America, vol. 111, no. 1, pp. 21-35, Feb. 2021, doi: 10.1785/0120200217

[2] E. R. Engdahl, R. Van Der Hilst, and R. Buland, "Global teleseismic earthquake relocation with improved travel times and procedures for depth determination," Bulletin of the Seismological Society of America, vol. 88, no. 3, pp. 722-743, Jun. 1998, doi: 10.1785/BSSA0880030722.

[3] N. Kolodziejczyk, A. Prigent-Mazella, and F. Gaillard, "ISAS temperature, salinity, dissolved oxygen gridded fields," 2023, SEANOE. doi: 10.17882/52367.

[4] T. J. McDougall and P. M. Barker, Getting started with TEOS-10 and the Gibbs Seawater (GSW) Oceanographic Toolbox. Battery Point, Tas.: Trevor J McDougall, 2011.

[5] B. L. N. Kennett, E. R. Engdahl, and R. Buland, "Constraints on seismic velocities in the Earth from traveltimes," Geophysical Journal International, vol. 122, no. 1, pp. 108-124, 1995, doi: 10.1111/j.1365-246X.1995.tb03540.x.

[6] "Earthquake Hazards Program | U.S. Geological Survey." Accessed: Mar. 25, 2025. [Online]. Available: https://www.usgs.gov/programs/earthquake-hazards

[7] "ISC-EHB Bulletin," International Seismological Centre. doi: 10.31905/PY08W6S3.

[8] J. D. Simon, F. J. Simons, and G. Nolet, "Multiscale Estimation of Event Arrival Times and Their Uncertainties in Hydroacoustic Records from Autonomous Oceanic Floats," Bulletin of the Seismological Society of America, vol. 110, no. 3, pp. 970-997, Jun. 2020, doi: 10.1785/0120190173.

[9] J. Y. Royer « VT 164 / OHA-SIS-BIO-11 cruise, Marion Dufresne R/V », 2019, Sismer. doi: 10.17600/18000974.

[10] J. Y. Royer, « MD 216 / MOUILLAGE OHA-SIS-BIO cruise, Marion Dufresne R/V », 2018, Sismer. doi: 10.17600/18000653.

[11] J. Y. Royer, "OHA-SIS-BIO - OBSERVATOIRE HYDROACOUSTIQUE," 2009, doi: 10.18142/229.