# Correction of OBS clock errors using Scholte waves retrieved from cross-correlating hydrophone recordings

Correction of OBS clock errors using Scholte waves retrieved from cross-correlating hydrophone... Abstract One of long-standing problems in underwater seismic studies is the inaccurate timing due to the fact the internal clock of Ocean Bottom Seismograph (OBS) is unable to synchronize with GPS. Here we present correcting large OBS clock errors and temporal drifts in a passive-source OBS array experiment in South China Sea by cross-correlating hydrophone recordings of OBS pairs. We show that, in this experiment, the noise cross-correlation function (NCCF) from hydrophone signals can retrieve higher signal-to-noise ratio (SNR) Scholte waves than the NCCF from seismometer. Because the hydrophone is positioned in the water above the seafloor, their NCCFs are thus less contaminated by more complicated solid-mode phases at the sediment-covered seafloor, leading to higher SNR for hydrophone's NCCFs. The relatively high SNR of Scholte waves enables us to use the daily NCCF (or stacked NCCFs of a few days) to constrain the temporal variations of the clock errors. A two-step approach is employed in this study to tackle large OBS clock errors: using predicted traveltimes of P phases from earthquakes to roughly correct the time, and then using the time asymmetry of two Scholte waves on NCCF to fine-tune the clock drifts. The uncertainty analysis indicates that the average error of our corrections is less than 0.2 s, suggesting the clock-corrected OBS data are valuable for seismic studies using surface waves and S waves. Time-series analysis, Interface waves, Seismic instruments, Seismic noise 1 INTRODUCTION The high precision timing at a station is crucial in most seismic studies such as earthquake location and tomography. The internal clock of a seismograph operates based on high quality quartz crystals, which inevitably has drifts over time (Gardner & Collins 2012). To correct the drift, seismographs have to synchronize their clocks with the Global Positioning System (GPS) at regular bases to achieve an accuracy up to ∼0.1 ms (Dana & Penrod 1990). However, underwater instrumentation like Ocean Bottom Seismograph (OBS) is unable to communicate with satellites. The time base of these instruments at seafloor, therefore, totally relies on their own clocks, often leading to a less than ideal accuracy in timing. In some cases, glitches with the clocks or data loggers could generate very large errors due to the temperature and pressure changes at the seafloor (e.g. Hannemann et al. 2014; Liu et al. 2014; Takeo et al. 2014). A widely used method correcting the timing is to synchronize the internal clock with GPS before and after recovery, and allocate the drift evenly to recordings at different times based on the assumption that the drift is linear (e.g. Geissler et al. 2010; Gouedard et al. 2014), which is obviously not true. For long-term passive-source deployment, some instruments may lose power for clocks upon recovery if they use one power system for both the data logger and the clock (e.g. Hannemann et al. 2014; Liu et al. 2014; Stähler et al. 2016), leading to the failure of this correction. Recent underwater instruments started to use more accurate atomic clocks (e.g. Gardner & Collins 2012), which of course reduce the drift significantly. However, much higher power consumption than the conventional quartz clock, beside the high cost, prevents its wide applications in large, long-term array experiments. Therefore, the timing issue is still one of the long-standing challenges in marine seismic investigations. Recently, seismologists have used coherent signals extracted from noise cross-correlation function (NCCF) to tackle the timing issue for land stations (e.g. Stehly et al. 2007; Sens-Schönfelder 2008; Xia et al. 2015) as well as OBSs (e.g. Gouedard et al. 2014; Hannemann et al. 2014; Takeo et al. 2014). By carefully analysing the traveltime evolutions of casual and anticasual coherent signals on NCCFs, seismologists are able to distinguish the effect of clock error from other factors causing traveltime fluctuation such as temporal velocity changes in the medium and the inhomogeneous noise source distribution (e.g. Stehly et al. 2007; Sens-Schönfelder 2008; Gouedard et al. 2014). In those studies, the seismometer recordings are used to extract the coherent signals, mostly Rayleigh waves. However, the signal-to-noise (SNR) of Rayleigh waves retrieved from vertical components is not always high enough in OBS investigations due to the poor coupling of the free-fall OBS and large station intervals. For instance, Stähler et al. (2016) showed that, when interstation distances larger than 150 km, the usage of NCCF of the vertical seismometer components was not able to retrieve clock drifts. Therefore, it is sometimes difficult to use Rayleigh waves with low SNR to correct the clock of OBSs. In these cases, the Scholte wave, another type of interface wave often observed at seafloor with higher frequencies (e.g. Yao et al. 2011; Ruan et al. 2014), may be used for this purpose. Here we show that the hydrophone signals collected in a passive-source OBS array experiment in South China Sea (SCS) can be cross-correlated to pick up the coherent Scholte waves, and use them to correct very large clock errors of OBSs and their drifts over time in the experiment. 2 THE EXPERIMENT, DATA SET AND THE CLOCK ERRORS A passive-source OBS array experiment was carried out in 2012 at the central sub-basin of SCS (Liu et al. 2014). The main objective of the experiment is to study the lithospheric structure beneath the fossil ridge and its post-spreading magmatism. The SCS opened as an ocean basin at about 32 Ma, and closed at ∼15.5 Ma (Li et al. 2015). The age of the area where the OBS array was located, however, ranges from ∼23 to 16 Ma. As a result, the seafloor is covered by thick sediments, and its average water depth is ∼3900 m. This experiment deployed 18 OBSs near the fossil ridge and the seamount chain (Fig. 1) in April 2012. One year after the deployment, 11 stations were successfully recovered, which included 8 Guralp 40T OBSs and 3 I-4C OBSs. Among them, there are only 7 40Ts and 2 I-4Cs that recorded valid data. Due to the limited lifespan of the battery, the duration of the data is only 7 months, instead of the whole year. The instruments had long stopped recording data when they were recovered in April 2013. Unlike more recent and advanced instruments, this type of OBS has one power system for both clock and the data logger. When the battery runs out, the clock stops working as well. Therefore, synchronization with GPS upon recovery was not possible, leading to even more severe timing issue in this experiment. In this study, the data set is the 7 month continuous records of seven Guralp 40T OBSs, recorded at three-component seismometers and hydrophones. Figure 1. View largeDownload slide The OBS array deployed in the central sub-basin of South China Sea along the fossil ridge from 2012 to 2013. Black triangles are OBSs failed to recover. Yellow ones indicate those recovered but not used due to various data problems or different hydrophone. Red triangles are OBSs retrieved valid data and are used in this study. SZP is a land station at Luzon island. Figure 1. View largeDownload slide The OBS array deployed in the central sub-basin of South China Sea along the fossil ridge from 2012 to 2013. Black triangles are OBSs failed to recover. Yellow ones indicate those recovered but not used due to various data problems or different hydrophone. Red triangles are OBSs retrieved valid data and are used in this study. SZP is a land station at Luzon island. To understand the severity of the clock issue in this OBS array, we first estimated the errors using earthquake signals. We hand-picked the first arrival P phases on seismograms of 52 local and regional earthquakes with clear onsets, and compared them with the predicted arrivals based on the standard earth model IASP91 (Kennett & Engdahl 1991). As shown in Figs 2 and 3, the arrival times of P waves at most of OBSs have significant differences from their predications. While a few second arrival time differences can be attributed to heterogeneities in the Earth's structure and the errors of source parameters in the catalogue, such large shifts as shown in Fig. 3 can only be explained by the clock errors. The differences at OBSs HY02 and HY10 even reach as large as hundreds of seconds (their means are 87 and 193 s, respectively). Furthermore, HY10 changed its time base sharply about one month after deployment (Figs 3b and c). Previous study using the same type of instrument also reported similar clock errors (Hannemann et al. 2014). Shifts at HY13, HY17 and HY18 are also significant, but appear to be static based on their small standard deviations. The clock at OBS HY15 appears to be accurate because it has very small mean and standard variation. Figure 2. View largeDownload slide The hydrophone recordings from an earthquake occurred at Okhotsk Sea at 2:59 on 2012 August 14. The traces are aligned with the predicted P-wave arrival times based on the IASP91 model (red vertical lines), which have significant differences with onsets of P phases for most of OBSs in the array. HY08 is not included in this study because it has a different type of hydrophone. Figure 2. View largeDownload slide The hydrophone recordings from an earthquake occurred at Okhotsk Sea at 2:59 on 2012 August 14. The traces are aligned with the predicted P-wave arrival times based on the IASP91 model (red vertical lines), which have significant differences with onsets of P phases for most of OBSs in the array. HY08 is not included in this study because it has a different type of hydrophone. Figure 3. View largeDownload slide (a,b) Clock errors at OBSs, estimated from predicted P phases of 52 earthquakes, as a function of the earthquake origin time in Julian day of 2012. The vertical axis is the difference between picked arrival time of P phase (Tpick) and predicted arrival time (Tpred) based on IASP91. Note that, unlike other OBSs having relatively static shifts varying only slightly, HY10 sharply changed its time base: the error jumped from about 9 s to about 192 s on day 151. (c) The amplitude images of the daily NCCFs in the frequency band 0.1–0.2 Hz of the OBS pairs HY02-HY10 and HY10-HY13. Note that the coherent Scholte waves sharply jumped on day 151, with the same pattern as in the arrival time analysis of earthquakes shown in (b). Figure 3. View largeDownload slide (a,b) Clock errors at OBSs, estimated from predicted P phases of 52 earthquakes, as a function of the earthquake origin time in Julian day of 2012. The vertical axis is the difference between picked arrival time of P phase (Tpick) and predicted arrival time (Tpred) based on IASP91. Note that, unlike other OBSs having relatively static shifts varying only slightly, HY10 sharply changed its time base: the error jumped from about 9 s to about 192 s on day 151. (c) The amplitude images of the daily NCCFs in the frequency band 0.1–0.2 Hz of the OBS pairs HY02-HY10 and HY10-HY13. Note that the coherent Scholte waves sharply jumped on day 151, with the same pattern as in the arrival time analysis of earthquakes shown in (b). We note that the large static components in several clock drifts (e.g. HY17 and HY18) occurred at early stages in their deployments, and were nearly flat through the records. These errors were obviously not linear. If the clocks had been synchronized upon recovery using conventional correction approach (e.g. Geissler et al. 2010), the static drifts might have been blindly linearly interpolated over the entire records. 3 CLOCK ERRORS DETERMINED BY NCCF 3.1 SNR of OBS NCCFs and the Scholte wave It has been well established that the ambient NCCF between pair of stations can reveal the Green's function between them (e.g. Shapiro & Campillo 2004). There are many studies using OBS data to pick up the empirical Green's function (e.g. Harmon et al. 2007; Yao et al. 2011; Harmon et al. 2012; Takeo et al. 2014; Zha et al. 2014). Compared to NCCFs obtained through seismic stations on land, the OBS NCCF generally has lower signal-to-noise ratio (SNR; e.g. Lin et al. 2006). There are several factors contributing to this. For example, tilt noise due to currents and infragravity waves lead to bad quality data (Webb 1998). The properties of media could also play a part. Unlike a free surface where Rayleigh waves are generally observed, the seafloor is a complex interface at which physical properties change gradually from seawater, unconsolidated sediment to hard rock. The energy trapped along this interface is not just fundamental Rayleigh wave. Higher mode Rayleigh wave, Stoneley wave and others (e.g. Yao et al. 2011; Takeo et al. 2014) may coexist. The amplitude of each individual phase could be higher because of presumably more diffuse noise in the ocean, but when many waves with different velocities are overlapped, the phase of interest are contaminated by other waves, leading to lower SNR (Fig. 4). Figure 4. View largeDownload slide The noise cross-correlation functions (NCCFs) of one OBS pair (HY15-HY16) from (a) hydrophone recordings and (b) vertical components of seismometer recordings. Top images show the amplitude of daily NCCFs in the frequency band of 0.1–0.2 Hz. The bottom traces are the waveforms of cross-correlation stacked over all days at the pair of stations. While the signal-to-noise ratio (SNR) of the Scholte phases in (a) is 20.43, that of (b) is only 11.07. The SNR is calculated by the average absolute amplitude within the shaded window divided by the average amplitude in the noise window, which is defined as a 400 s window following the shaded signal. Figure 4. View largeDownload slide The noise cross-correlation functions (NCCFs) of one OBS pair (HY15-HY16) from (a) hydrophone recordings and (b) vertical components of seismometer recordings. Top images show the amplitude of daily NCCFs in the frequency band of 0.1–0.2 Hz. The bottom traces are the waveforms of cross-correlation stacked over all days at the pair of stations. While the signal-to-noise ratio (SNR) of the Scholte phases in (a) is 20.43, that of (b) is only 11.07. The SNR is calculated by the average absolute amplitude within the shaded window divided by the average amplitude in the noise window, which is defined as a 400 s window following the shaded signal. In contrast with a Rayleigh wave that propagates near the air–solid interface or a Stoneley wave that propagates near a solid–solid interface, the Scholte wave is another type of interface wave commonly observed at a fluid–solid boundary like seafloor (e.g. Scholte 1947; Rauch 1980; Yao et al. 2011; Flores-Mendez et al. 2012; Ruan et al. 2014). The attenuation of Scholte wave is much faster in the solid than in the fluid. Therefore, most of Scholte wave energy is localized on the fluid side (Gusev et al. 1996; Zhu et al. 2004). In order to achieve a better coupling with the seafloor, the seismometer of OBS is often buried in the sediment after sitting at seafloor for a while. Thus, the NCCF through seismometer recordings is capable of picking up many phases along the seafloor (Takeo et al. 2014), particularly, those propagating in the solid part of this interface. On the other hand, the hydrophone of an OBS is to record the pressure changes of seawater, must be positioned in the seawater, often a little bit above the seabed. For example, the hydrophone of 40T OBS is attached on the main frame of the instrument, which is about 1.0 m higher than the seafloor. As a result, the NCCFs of hydrophone recordings mainly retrieve waves that can only propagate in the fluid, not severely contaminated by solid-mode Rayleigh waves and other phases. Therefore, it has higher SNR than NCCF of seismometers. Fig. 4 clearly illustrates the SNR difference of those two type of NCCFs. Like Rayleigh waves, Scholte waves are dispersive (Rauch 1980; Bohlen et al. 2004; Potty et al. 2012). The frequency-dependent velocities depend on the water depth, the physical properties of sediment and seawater (Harmon et al. 2007; Yao et al. 2011). Numerical modelling shows that (Flores-Mendez et al. 2012), under the condition of general seafloor, the group velocity of Scholte wave is close to 1.0 km s−1. Fig. 5 shows the NCCF traces obtained from our OBS hydrophone pairs (after correcting their timings). The strong coherent signals between two red lines have a speed of ∼1.0 km s−1, consistent with the speed of Scholte waves at seafloor constrained by numerical modelling. Figure 5. View largeDownload slide The NCCFs of nine OBS pairs versus their station intervals. Note that the NCCFs have been corrected by using the initial time correction estimated from earthquakes. Figure 5. View largeDownload slide The NCCFs of nine OBS pairs versus their station intervals. Note that the NCCFs have been corrected by using the initial time correction estimated from earthquakes. 3.2 Determine the clock errors using Scholte waves on NCCF The time asymmetry of Rayleigh waves on NCCF has been used to correct clock errors for both land seismic stations and OBSs (e.g. Stehly et al. 2007; Sens-Schönfelder 2008; Gouedard et al. 2014; Hannemann et al. 2014; Takeo et al. 2014). This method is based on the assumption that, in an ideal scenario, the waveforms in the casual and anti casual parts on NCCF should be in perfect symmetry, and stay static over time. For real NCCFs, however, the symmetry could be broken because of the clock errors of two receivers, uneven noise sources and medium velocity changes over time. For most study regions without short-term tectonic activities, the effect of temporal velocity structure changes can be reasonably neglected. The other two factors can be distinguished by examining the temporal evolution pattern of the asymmetry. Because clock shifts affect casual and anti casual traveltimes exactly in an opposite manner, their traveltime difference therefore will remain constant over time. On the other hand, the noise from opposite direction will evolve exactly in the same way, and the traveltime difference will not stay constant (Stehly et al. 2007; Sens-Schönfelder 2008; Gouedard et al. 2014). We will use this method to show that the clock shifts, instead of the uneven noise distribution, are responsible for most of the asymmetry on NCCFs in our data. We use coherent Scholte waves on NCCFs by cross-correlating hydrophone recordings, instead of Rayleigh waves from seismometer signals, to correct the clocks. Our method of calculating NCCF was given by Bensen et al. (2007) and Yao et al. (2011). The daily hydrophone recordings from each OBS are first down-sampled, and band-filtered by 0.1–0.2 Hz. To remove the effects of earthquake signals, we apply one bit normalization and whitening to the data. Daily recordings are divided into 2 hr windows which are then used to calculate the daily NCCFs at frequency band of 0.1–0.2 Hz. We note that we focus on the frequency band of 0.1–0.2 Hz because the Scholte wave is supposed to have strong amplitude in this band given properties of seafloor sediment and the water depth. Experiments show that (Park et al. 2005; Flores-Mendez et al. 2012; Potty et al. 2012) the largest Scholte wave amplitude is expected when the parameter, λ/H, the wavelength and water depth ratio, falls in the range of 1.0–4.0. Assuming the shear velocity of the soft sediment at seafloor of the SCS is 1.0 km s−1, and water depth is 4000 m, the frequency range of 0.1–0.2 Hz will lead to the λ/H in the range of 1.25–2.5. Figs 4 and 6 give examples of our daily NCCFs. Their temporal evolution shows that, while asymmetries of two Scholte waves in casual and anti casual parts are always significant over time, their time distance only fluctuate slightly. This indicates most of the asymmetries can be attributed to the clock errors. Therefore, we will first assume the asymmetry is solely caused by relative clock shifts to calculate them, and then assess how big the effects of the noise source distribution are. Figure 6. View largeDownload slide The amplitude of daily NCCFs at the pair of stations HY02–HY15 in the frequency band of 0.1–0.2 Hz. The bottom is the stacked NCCFs over all days. The black solid line indicates the average time difference between the two coherent Scholte waves. It locates in the middle of two peaks between the negative and positive sides. The dash rectangles mark the time symmetrical windows of causal and anti causal NCCFs, which are cross-correlated to calculate the daily time difference. Figure 6. View largeDownload slide The amplitude of daily NCCFs at the pair of stations HY02–HY15 in the frequency band of 0.1–0.2 Hz. The bottom is the stacked NCCFs over all days. The black solid line indicates the average time difference between the two coherent Scholte waves. It locates in the middle of two peaks between the negative and positive sides. The dash rectangles mark the time symmetrical windows of causal and anti causal NCCFs, which are cross-correlated to calculate the daily time difference. With the above assumption, the relative clock error between two stations is equal to the offset of the central point of two coherent Scholte waves from time 0. We determine it through cross-correlating causal and anti causal parts of NCCF. Because waveforms of two Scholte waves are not identical, a simple, direct cross-correlation could result in false corrections, especially in our case where errors reach hundreds of seconds for some OBSs. To avoid this situation, we employ a two-step approach. We first apply an initial correction (dt1) to the NCCFs. There are two ways to determine dt1. It can be the mean difference shown in Fig. 3 for each OBS pair; the other way is to stack all daily NCCFs of each OBS pair altogether to form a stacked NCCF, through which dt1 is determined by waveform cross-correlation (Fig. 6). We found that the two methods yield slightly different initial corrections. But they will not affect our final correction because an initial correction is just to ensure the symmetric point is close to time 0 and, in the next step, the time windows for cross-correlation contain the right Scholte waveforms. Supporting Information Table S1 gives the initial corrections of nine OBS pairs using the stacked NCCF. In the next step, after initial correction for all daily NCCFs, we select two time symmetric windows containing Scholte waves, and cross-correlate them to further determine their traveltime difference, dt2 (Fig. 6). Thus the final clock correction for each station pair would be dt = dt1 + dt2. This method can be applied to a stacked NCCF, and a static relative correction for an OBS pair can be calculated. However, it is more often that the clock error drifts over time during a long period of deployment (e.g. Sens-Schönfelder 2008; Gouedard et al. 2014; Hannemann et al. 2014). As shown in Fig. 4, Scholte waves derived from hydrophones have relatively high SNR. Instead of stacking all daily NCCFs, we can calculate the temporal variation of the clock error by using daily NCCFs directly, or more practically, stacked NCCFs of a short period, say a few days (Supporting Information Fig. S1). Because the short-term, localized noise sources also contribute to the time asymmetry of coherent phases, using stacked NCCFs of many days could reduce this effect. In this study, the relative correction of each OBS pair (Fig. 7) is computed by using stacked NCCFs of the nearest 11 d (before and after 5 d of a given day). Figure 7. View largeDownload slide Left: temporal variation of relative clock errors for three OBS pairs (black solid curve) derived from time asymmetry of Scholte waves on the causal and anticausal sides of NCCFs. Right: temporal variation of Scholte wave's traveltime between each OBS pair, which is half of the time distance between two Scholte waves in causal and anticausal sides (determined by waveform cross-correlation). The black circle is the daily (11 d stacked) average traveltime. Red line is the average of traveltime of all day. The average and the maximum of error are given in the figures. In the ideal case of evenly distribution of noise sources, the traveltime is a constant over time. Figure 7. View largeDownload slide Left: temporal variation of relative clock errors for three OBS pairs (black solid curve) derived from time asymmetry of Scholte waves on the causal and anticausal sides of NCCFs. Right: temporal variation of Scholte wave's traveltime between each OBS pair, which is half of the time distance between two Scholte waves in causal and anticausal sides (determined by waveform cross-correlation). The black circle is the daily (11 d stacked) average traveltime. Red line is the average of traveltime of all day. The average and the maximum of error are given in the figures. In the ideal case of evenly distribution of noise sources, the traveltime is a constant over time. In order to assess how severely the noise source distribution affects the traveltimes of coherent Scholte waves, we examine the temporal variation of the traveltime by calculating the time distance between the Scholte waves on NCCF. The time distance is also obtained by waveform cross-correlation. Their variations over the deployments are shown in right panels of Fig. 7 and Supporting Information Fig. S2. It is worth noting that the values of several OBS pairs show regular monthly fluctuating pattern, which is very likely caused by tidal variations in SCS. After removing the means, the standard deviations of the time distances are less than 0.3 s, which only account for negligible portion of the corrections we calculated (less than 0.5 per cent for most of the OBS pairs except for HY15-HY16). This suggests the noise distribution did cause a little fluctuation of the asymmetry, but its effect is insignificant compared to the clock errors. The amplitude of fluctuation is consistent with previous works (e.g. Yao & Van de Hilst 2009; Froment et al. 2010), which all found the traveltime bias caused by undiffused noises is generally less than 1 per cent. It is challenging to objectively determine uncertainties associated with our relative clock corrections. Because the fluctuation of time distance of two Scholte waves on NCCFs gives the other mechanism, beside the clock error, to account for the asymmetry, it is natural to take these values as the uncertainties of relative clock errors. They will be used to determine the uncertainties of the final absolute clock errors. 3.3 Results of OBS clock errors There are seven OBSs in this array. Ideally, we would have 21 OBS pairs, and the same number of relative errors. However, the fossil ridge, the Huangyan-Zhenbei seamount chain, sits between the southern and northern portions of our array (Fig. 1). The topography high certainly will block the propagations of Scholte waves. As a result, for OBS pairs across the fossil ridge, the SNRs of Scholte waves in NCCFs are relatively low. To obtain reliable corrections, we set an SNR threshold (5.0) and select nine pairs from all available OBSs (Fig. 7 and Supporting Information Fig. S2). The selected nine relative clock errors form a system of equations as   $$\Delta {\tau _i} - \Delta {\tau _j} = d{t_{ij}}$$ (1) where, Δτi, Δτj are the absolute time errors at OBSs i and j, respectively; dtij is the relative error between OBSs i and j. This is a classic underdetermined inverse problem whose solutions cannot be uniquely determined because equations are linearly dependent. To solve this equation, we must identify a reference OBS, assuming its clock is accurate, and other OBSs in the array will synchronize to it. Here we specified HY15 as the reference station (detailed in Section 4), and solve the equation system for the absolute corrections for all OBSs (Fig. 8). Figure 8. View largeDownload slide The temporally varied absolute clock corrections of six OBSs (black lines) based on the assumption that HY15 has an accurate clock. The grey shaded areas are the standard deviation of the corrections. The average and maximum of standard deviations are given in figures. Figure 8. View largeDownload slide The temporally varied absolute clock corrections of six OBSs (black lines) based on the assumption that HY15 has an accurate clock. The grey shaded areas are the standard deviation of the corrections. The average and maximum of standard deviations are given in figures. To determine the uncertainty of clock correction, we employ a bootstrapping analysis (Gouedard et al. 2014). In this process, each relative correction is added a random error, which is uniformly distributed in the range of fluctuating amplitude of time distance for each OBS pair (right panels in Fig. 7 and Supporting Information Fig. S2). With these new data containing error, we solve the equations for absolute corrections. We repeat the process 200 times, and therefore have 200 corrections for each station on each day. The final corrections are the means of these 200 estimations, and their standard deviations are taken as uncertainties of our corrections. As shown in Fig. 8, the average uncertainties of our absolute clock corrections are less than 0.2 s. 4 DISCUSSION 4.1 Effects of undiffused noise sources The accuracy of our corrections depends on how well the NCCF can reconstruct the Green's functions for each OBS pair, which in turn depends on whether the distribution of noise sources is evenly distributed and the wavefield is truly diffuse. Many authors (e.g. Yao & Van de Hilst 2009; Froment et al. 2010; Harmon et al. 2010) have shown that, even if the noise sources are unevenly distributed, traveltimes of the surface waves on NCCFs generally have small bias (<1 per cent) when they are used to invert for the phase velocity. Our analysis of the temporal variation of average traveltimes also indicates their fluctuation over time is less than 1 per cent (Fig. 7 and Supporting Information Fig. S2). In addition, the azimuthal variation of the noise strength also suggests our noise sources do not show strong preferential directions (Supporting Information Fig. S3). Nevertheless, it is interesting to note that, as shown in Fig. 8, on the gradually varied drifts for several OBSs, there exist bumps around day 200. It turns out that, in that period, there were over six typhoons and severe tropical storms overlapped one another, which either directly impacted or were very close to the SCS region (Supporting Information Fig. S4). Therefore, it is clear that the localized noise source does cause slight bias on the clock corrections, whose strength is within the estimated uncertainty. 4.2 Effects of deep-sea currents As mentioned above, the changes of medium velocity could also contribute to the asymmetry of the coherent waveforms over time. One possibility is the deep currents at seafloor could lead to temporal velocity change and anisotropy, generating another source of bias to the correction. We cannot completely rule this out, but the effect should be negligible. First, the deep currents in SCS are much slower (<1 cm s−1; Wang et al. 2011) than the speed of Scholte waves (∼1000 m s−1); second, the directions of the currents would not be exactly parallel to the line linking two stations to generate strong anisotropy; Third, the directions of the currents could change in short period of time, and our corrections are based on the stacked NCCFs of eleven days, which would reduce this effect. 4.3 Reference station for the absolute clock errors The final absolute clock error of each individual OBS depends on the accuracy of the clock of the reference OBS we select. Ideally, a land station with GPS synchronized timing would be the best choice for reference station. There is one station on Luzon Island (SZP) close to our array. We calculate the NCCFs between SZP and our OBSs in two frequency bands. While the SNR of stacked NCCFs at period band 10–20 s are relatively higher, the daily NCCFs, or stacked NCCFs of 11 d, for both frequency bands are too low for the temporally changing clock correction (Supporting Information Fig. S5). Our selection of OBS HY15 as the reference station because it has minimum deviation from the predicted traveltimes, which is an independent constraint other than the NCCF method. On the other hand, the choice of reference station is not a significant issue for some seismic studies, for example, the teleseismic tomography (VanDecar & Crosson 1990) and two-plane wave surface wave tomography (Forsyth & Li 2005) because the relative traveltimes among stations in the array, instead of the absolute traveltimes, are used in these studies. 4.4 Applications of the clock-corrected OBS data The accuracy of OBS clock correction is crucial to estimate of velocity anomaly. Our uncertainty analysis indicates that the average uncertainty of the correction is less than 0.2 s. The typical station interval in this experiment is about 150 km. To be able to detect 1 per cent of velocity anomaly, the traveltime accuracy has to reach about 0.37 s for a medium with 4.0 km s−1 average velocity. Therefore, considering the up limit of the uncertainty, our clock-corrected OBS data can at least be used to surface wave and S wave studies, but can hardly be useful for P wave tomography. 5 CONCLUSIONS The hydrophones of OBSs have the advantage over seismometers at seafloor to retrieve high SNR coherent Scholte waves through noise cross-correlation because hydrophones are positioned in the water above the seafloor, and Scholte phase propagating along the seafloor attenuates much less in the liquid than in the solid. The NCCFs of seismometers at the sediment-covered seafloor are, on the other hand, contaminated by other solid-mode phases from the complex seafloor. Taking advantage of this feature of hydrophone recordings, we calculate the NCCFs of an OBS array deployed in the central sub-basin of the SCS, and use Scholte waves on the NCCFs to correct their clock errors, some of which are very large. Because of the relative high SNR of Scholte waves, the temporal variation of the clock drifts can be determined through the time asymmetry of Scholte waves on NCCFs. The accuracy of the clock correction achieved is valuable for the long period surface wave and S wave studies. Acknowledgements The authors would like to thank the First Institute of Oceanography, State Oceanic Administration, China for providing us the instruments or helps needed on the sea. This project was supported by National Natural Science Foundation of China (41676033 and 91128209), the National Program on Global Changing and Air-Sea Interaction (GASI-GEOGE-05) and Shenzhen Sci. and Tech. Innovation Commission (2017-131, 2017-173). TY and YJC are also funded by faculty startup funds from SUSTech. We thank Dr Harmon, Dr Hannemann and an anonymous reviewer for thoughtful and constructive comments that improved the manuscript a lot. 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Synchronizing intercontinental seismic networks using the 26 s persistent localized microseismic source, Bull. seism. Soc. Am. , 105( 4), 2101– 2108. https://doi.org/10.1785/0120140252 Google Scholar CrossRef Search ADS   Yao H., van der Hilst R.D., 2009. Analysis of ambient noise energy distribution and phase velocity bias in ambient noise tomography, with application to SE Tibet, Geophys. J. Int. , 179( 2), 1113– 1132. https://doi.org/10.1111/j.1365-246X.2009.04329.x Google Scholar CrossRef Search ADS   Yao H., Gouedard P., Collins J.A., Mcguire J.J., van der Hilst R.D., 2011. Structure of young East Pacific Rise lithosphere from ambient noise correlation analysis of fundamental- and higher-mode Scholte-Rayleigh waves, C. R. Geosci. , 343( 8), 571– 583. https://doi.org/10.1016/j.crte.2011.04.004 Google Scholar CrossRef Search ADS   Zha Y., Webb S.C., Wei S.S., Wiens D.A., Blackman D.K., Menke W., Dunn R.A., Conder J.A., 2014. Seismological imaging of ridge–arc interaction beneath the Eastern Lau Spreading Center from OBS ambient noise tomography, Earth planet. Sci. Lett. , 408, 194– 206. https://doi.org/10.1016/j.epsl.2014.10.019 Google Scholar CrossRef Search ADS   Zhu J., Popovics J.S., Schubert F., 2004. Leaky Rayleigh and Scholte waves at the fluid–solid interface subjected to transient point loading, J. acoust. Soc. Am. , 116( 4), 2101– 2110. https://doi.org/10.1121/1.1791718 Google Scholar CrossRef Search ADS   SUPPORTING INFORMATION Supplementary data are available at GJI online. Figure S1. Temporal variation of relative clock error for the OBS pair of HY02-HY15 derived from daily NCCFs (circles) and stacked NCCFs of 11 d (red line). Figure S2. Temporal variations of relative clock errors of other OBS pairs (left) and half of time distance of the two Scholte waves on each NCCF (same as Fig. 7) (right). Because the time base jumped for HY10 on day 151, the vertical axes of two pairs with HY10 after day 151 are on the right side of figures on the left panels (see the caption of Fig. 3 for details). Figure S3. Variation of the normalized amplitude of the NCCFs as the function of the OBS pair's azimuth (in period bands 5–10 s) for all NCCFs with SNR > 3.0. The dots closer to the centre have relatively lower amplitudes. The station intervals are indicated by different colours. Figure S4. Summary of 2012 Pacific typhoon season: timing and intensity (https://en.wikipedia.org/wiki/2012_Pacific_typhoon_season). Please note, from 2012 July 15 to August 20 (197–233 in Julian day), there were over six typhoons and severe tropical storms, which either directly impacted or were very close to the South China Sea region. Figure S5. The NCCFs of seismometer vertical components between OBS HY15 and SZP, the land station at Luzon island in two period bands (left: 5–10 s, right: 10–20 s). Top images give the amplitude of NCCFs for each day. The bottom traces are the waveforms of cross-correlation stacked over all days at the pair of stations. From the stacked NCCFs at 10–20 s, the relative error between SZP and HY15 was estimated, −0.5 s. Table S1. The initial time corrections for each OBS pair derived from the stacked NCCFs over all days. Note that two pairs with HY10 have two initial time corrections separated on day 151 (see the caption of Fig. 3 for details). Please note: Oxford University Press is not responsible for the content or functionality of any supporting materials supplied by the authors. Any queries (other than missing material) should be directed to the corresponding author for the paper. © The Authors 2017. Published by Oxford University Press on behalf of The Royal Astronomical Society. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Geophysical Journal International Oxford University Press

# Correction of OBS clock errors using Scholte waves retrieved from cross-correlating hydrophone recordings

, Volume 212 (2) – Feb 1, 2018
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### Abstract

Abstract One of long-standing problems in underwater seismic studies is the inaccurate timing due to the fact the internal clock of Ocean Bottom Seismograph (OBS) is unable to synchronize with GPS. Here we present correcting large OBS clock errors and temporal drifts in a passive-source OBS array experiment in South China Sea by cross-correlating hydrophone recordings of OBS pairs. We show that, in this experiment, the noise cross-correlation function (NCCF) from hydrophone signals can retrieve higher signal-to-noise ratio (SNR) Scholte waves than the NCCF from seismometer. Because the hydrophone is positioned in the water above the seafloor, their NCCFs are thus less contaminated by more complicated solid-mode phases at the sediment-covered seafloor, leading to higher SNR for hydrophone's NCCFs. The relatively high SNR of Scholte waves enables us to use the daily NCCF (or stacked NCCFs of a few days) to constrain the temporal variations of the clock errors. A two-step approach is employed in this study to tackle large OBS clock errors: using predicted traveltimes of P phases from earthquakes to roughly correct the time, and then using the time asymmetry of two Scholte waves on NCCF to fine-tune the clock drifts. The uncertainty analysis indicates that the average error of our corrections is less than 0.2 s, suggesting the clock-corrected OBS data are valuable for seismic studies using surface waves and S waves. Time-series analysis, Interface waves, Seismic instruments, Seismic noise 1 INTRODUCTION The high precision timing at a station is crucial in most seismic studies such as earthquake location and tomography. The internal clock of a seismograph operates based on high quality quartz crystals, which inevitably has drifts over time (Gardner & Collins 2012). To correct the drift, seismographs have to synchronize their clocks with the Global Positioning System (GPS) at regular bases to achieve an accuracy up to ∼0.1 ms (Dana & Penrod 1990). However, underwater instrumentation like Ocean Bottom Seismograph (OBS) is unable to communicate with satellites. The time base of these instruments at seafloor, therefore, totally relies on their own clocks, often leading to a less than ideal accuracy in timing. In some cases, glitches with the clocks or data loggers could generate very large errors due to the temperature and pressure changes at the seafloor (e.g. Hannemann et al. 2014; Liu et al. 2014; Takeo et al. 2014). A widely used method correcting the timing is to synchronize the internal clock with GPS before and after recovery, and allocate the drift evenly to recordings at different times based on the assumption that the drift is linear (e.g. Geissler et al. 2010; Gouedard et al. 2014), which is obviously not true. For long-term passive-source deployment, some instruments may lose power for clocks upon recovery if they use one power system for both the data logger and the clock (e.g. Hannemann et al. 2014; Liu et al. 2014; Stähler et al. 2016), leading to the failure of this correction. Recent underwater instruments started to use more accurate atomic clocks (e.g. Gardner & Collins 2012), which of course reduce the drift significantly. However, much higher power consumption than the conventional quartz clock, beside the high cost, prevents its wide applications in large, long-term array experiments. Therefore, the timing issue is still one of the long-standing challenges in marine seismic investigations. Recently, seismologists have used coherent signals extracted from noise cross-correlation function (NCCF) to tackle the timing issue for land stations (e.g. Stehly et al. 2007; Sens-Schönfelder 2008; Xia et al. 2015) as well as OBSs (e.g. Gouedard et al. 2014; Hannemann et al. 2014; Takeo et al. 2014). By carefully analysing the traveltime evolutions of casual and anticasual coherent signals on NCCFs, seismologists are able to distinguish the effect of clock error from other factors causing traveltime fluctuation such as temporal velocity changes in the medium and the inhomogeneous noise source distribution (e.g. Stehly et al. 2007; Sens-Schönfelder 2008; Gouedard et al. 2014). In those studies, the seismometer recordings are used to extract the coherent signals, mostly Rayleigh waves. However, the signal-to-noise (SNR) of Rayleigh waves retrieved from vertical components is not always high enough in OBS investigations due to the poor coupling of the free-fall OBS and large station intervals. For instance, Stähler et al. (2016) showed that, when interstation distances larger than 150 km, the usage of NCCF of the vertical seismometer components was not able to retrieve clock drifts. Therefore, it is sometimes difficult to use Rayleigh waves with low SNR to correct the clock of OBSs. In these cases, the Scholte wave, another type of interface wave often observed at seafloor with higher frequencies (e.g. Yao et al. 2011; Ruan et al. 2014), may be used for this purpose. Here we show that the hydrophone signals collected in a passive-source OBS array experiment in South China Sea (SCS) can be cross-correlated to pick up the coherent Scholte waves, and use them to correct very large clock errors of OBSs and their drifts over time in the experiment. 2 THE EXPERIMENT, DATA SET AND THE CLOCK ERRORS A passive-source OBS array experiment was carried out in 2012 at the central sub-basin of SCS (Liu et al. 2014). The main objective of the experiment is to study the lithospheric structure beneath the fossil ridge and its post-spreading magmatism. The SCS opened as an ocean basin at about 32 Ma, and closed at ∼15.5 Ma (Li et al. 2015). The age of the area where the OBS array was located, however, ranges from ∼23 to 16 Ma. As a result, the seafloor is covered by thick sediments, and its average water depth is ∼3900 m. This experiment deployed 18 OBSs near the fossil ridge and the seamount chain (Fig. 1) in April 2012. One year after the deployment, 11 stations were successfully recovered, which included 8 Guralp 40T OBSs and 3 I-4C OBSs. Among them, there are only 7 40Ts and 2 I-4Cs that recorded valid data. Due to the limited lifespan of the battery, the duration of the data is only 7 months, instead of the whole year. The instruments had long stopped recording data when they were recovered in April 2013. Unlike more recent and advanced instruments, this type of OBS has one power system for both clock and the data logger. When the battery runs out, the clock stops working as well. Therefore, synchronization with GPS upon recovery was not possible, leading to even more severe timing issue in this experiment. In this study, the data set is the 7 month continuous records of seven Guralp 40T OBSs, recorded at three-component seismometers and hydrophones. Figure 1. View largeDownload slide The OBS array deployed in the central sub-basin of South China Sea along the fossil ridge from 2012 to 2013. Black triangles are OBSs failed to recover. Yellow ones indicate those recovered but not used due to various data problems or different hydrophone. Red triangles are OBSs retrieved valid data and are used in this study. SZP is a land station at Luzon island. Figure 1. View largeDownload slide The OBS array deployed in the central sub-basin of South China Sea along the fossil ridge from 2012 to 2013. Black triangles are OBSs failed to recover. Yellow ones indicate those recovered but not used due to various data problems or different hydrophone. Red triangles are OBSs retrieved valid data and are used in this study. SZP is a land station at Luzon island. To understand the severity of the clock issue in this OBS array, we first estimated the errors using earthquake signals. We hand-picked the first arrival P phases on seismograms of 52 local and regional earthquakes with clear onsets, and compared them with the predicted arrivals based on the standard earth model IASP91 (Kennett & Engdahl 1991). As shown in Figs 2 and 3, the arrival times of P waves at most of OBSs have significant differences from their predications. While a few second arrival time differences can be attributed to heterogeneities in the Earth's structure and the errors of source parameters in the catalogue, such large shifts as shown in Fig. 3 can only be explained by the clock errors. The differences at OBSs HY02 and HY10 even reach as large as hundreds of seconds (their means are 87 and 193 s, respectively). Furthermore, HY10 changed its time base sharply about one month after deployment (Figs 3b and c). Previous study using the same type of instrument also reported similar clock errors (Hannemann et al. 2014). Shifts at HY13, HY17 and HY18 are also significant, but appear to be static based on their small standard deviations. The clock at OBS HY15 appears to be accurate because it has very small mean and standard variation. Figure 2. View largeDownload slide The hydrophone recordings from an earthquake occurred at Okhotsk Sea at 2:59 on 2012 August 14. The traces are aligned with the predicted P-wave arrival times based on the IASP91 model (red vertical lines), which have significant differences with onsets of P phases for most of OBSs in the array. HY08 is not included in this study because it has a different type of hydrophone. Figure 2. View largeDownload slide The hydrophone recordings from an earthquake occurred at Okhotsk Sea at 2:59 on 2012 August 14. The traces are aligned with the predicted P-wave arrival times based on the IASP91 model (red vertical lines), which have significant differences with onsets of P phases for most of OBSs in the array. HY08 is not included in this study because it has a different type of hydrophone. Figure 3. View largeDownload slide (a,b) Clock errors at OBSs, estimated from predicted P phases of 52 earthquakes, as a function of the earthquake origin time in Julian day of 2012. The vertical axis is the difference between picked arrival time of P phase (Tpick) and predicted arrival time (Tpred) based on IASP91. Note that, unlike other OBSs having relatively static shifts varying only slightly, HY10 sharply changed its time base: the error jumped from about 9 s to about 192 s on day 151. (c) The amplitude images of the daily NCCFs in the frequency band 0.1–0.2 Hz of the OBS pairs HY02-HY10 and HY10-HY13. Note that the coherent Scholte waves sharply jumped on day 151, with the same pattern as in the arrival time analysis of earthquakes shown in (b). Figure 3. View largeDownload slide (a,b) Clock errors at OBSs, estimated from predicted P phases of 52 earthquakes, as a function of the earthquake origin time in Julian day of 2012. The vertical axis is the difference between picked arrival time of P phase (Tpick) and predicted arrival time (Tpred) based on IASP91. Note that, unlike other OBSs having relatively static shifts varying only slightly, HY10 sharply changed its time base: the error jumped from about 9 s to about 192 s on day 151. (c) The amplitude images of the daily NCCFs in the frequency band 0.1–0.2 Hz of the OBS pairs HY02-HY10 and HY10-HY13. Note that the coherent Scholte waves sharply jumped on day 151, with the same pattern as in the arrival time analysis of earthquakes shown in (b). We note that the large static components in several clock drifts (e.g. HY17 and HY18) occurred at early stages in their deployments, and were nearly flat through the records. These errors were obviously not linear. If the clocks had been synchronized upon recovery using conventional correction approach (e.g. Geissler et al. 2010), the static drifts might have been blindly linearly interpolated over the entire records. 3 CLOCK ERRORS DETERMINED BY NCCF 3.1 SNR of OBS NCCFs and the Scholte wave It has been well established that the ambient NCCF between pair of stations can reveal the Green's function between them (e.g. Shapiro & Campillo 2004). There are many studies using OBS data to pick up the empirical Green's function (e.g. Harmon et al. 2007; Yao et al. 2011; Harmon et al. 2012; Takeo et al. 2014; Zha et al. 2014). Compared to NCCFs obtained through seismic stations on land, the OBS NCCF generally has lower signal-to-noise ratio (SNR; e.g. Lin et al. 2006). There are several factors contributing to this. For example, tilt noise due to currents and infragravity waves lead to bad quality data (Webb 1998). The properties of media could also play a part. Unlike a free surface where Rayleigh waves are generally observed, the seafloor is a complex interface at which physical properties change gradually from seawater, unconsolidated sediment to hard rock. The energy trapped along this interface is not just fundamental Rayleigh wave. Higher mode Rayleigh wave, Stoneley wave and others (e.g. Yao et al. 2011; Takeo et al. 2014) may coexist. The amplitude of each individual phase could be higher because of presumably more diffuse noise in the ocean, but when many waves with different velocities are overlapped, the phase of interest are contaminated by other waves, leading to lower SNR (Fig. 4). Figure 4. View largeDownload slide The noise cross-correlation functions (NCCFs) of one OBS pair (HY15-HY16) from (a) hydrophone recordings and (b) vertical components of seismometer recordings. Top images show the amplitude of daily NCCFs in the frequency band of 0.1–0.2 Hz. The bottom traces are the waveforms of cross-correlation stacked over all days at the pair of stations. While the signal-to-noise ratio (SNR) of the Scholte phases in (a) is 20.43, that of (b) is only 11.07. The SNR is calculated by the average absolute amplitude within the shaded window divided by the average amplitude in the noise window, which is defined as a 400 s window following the shaded signal. Figure 4. View largeDownload slide The noise cross-correlation functions (NCCFs) of one OBS pair (HY15-HY16) from (a) hydrophone recordings and (b) vertical components of seismometer recordings. Top images show the amplitude of daily NCCFs in the frequency band of 0.1–0.2 Hz. The bottom traces are the waveforms of cross-correlation stacked over all days at the pair of stations. While the signal-to-noise ratio (SNR) of the Scholte phases in (a) is 20.43, that of (b) is only 11.07. The SNR is calculated by the average absolute amplitude within the shaded window divided by the average amplitude in the noise window, which is defined as a 400 s window following the shaded signal. In contrast with a Rayleigh wave that propagates near the air–solid interface or a Stoneley wave that propagates near a solid–solid interface, the Scholte wave is another type of interface wave commonly observed at a fluid–solid boundary like seafloor (e.g. Scholte 1947; Rauch 1980; Yao et al. 2011; Flores-Mendez et al. 2012; Ruan et al. 2014). The attenuation of Scholte wave is much faster in the solid than in the fluid. Therefore, most of Scholte wave energy is localized on the fluid side (Gusev et al. 1996; Zhu et al. 2004). In order to achieve a better coupling with the seafloor, the seismometer of OBS is often buried in the sediment after sitting at seafloor for a while. Thus, the NCCF through seismometer recordings is capable of picking up many phases along the seafloor (Takeo et al. 2014), particularly, those propagating in the solid part of this interface. On the other hand, the hydrophone of an OBS is to record the pressure changes of seawater, must be positioned in the seawater, often a little bit above the seabed. For example, the hydrophone of 40T OBS is attached on the main frame of the instrument, which is about 1.0 m higher than the seafloor. As a result, the NCCFs of hydrophone recordings mainly retrieve waves that can only propagate in the fluid, not severely contaminated by solid-mode Rayleigh waves and other phases. Therefore, it has higher SNR than NCCF of seismometers. Fig. 4 clearly illustrates the SNR difference of those two type of NCCFs. Like Rayleigh waves, Scholte waves are dispersive (Rauch 1980; Bohlen et al. 2004; Potty et al. 2012). The frequency-dependent velocities depend on the water depth, the physical properties of sediment and seawater (Harmon et al. 2007; Yao et al. 2011). Numerical modelling shows that (Flores-Mendez et al. 2012), under the condition of general seafloor, the group velocity of Scholte wave is close to 1.0 km s−1. Fig. 5 shows the NCCF traces obtained from our OBS hydrophone pairs (after correcting their timings). The strong coherent signals between two red lines have a speed of ∼1.0 km s−1, consistent with the speed of Scholte waves at seafloor constrained by numerical modelling. Figure 5. View largeDownload slide The NCCFs of nine OBS pairs versus their station intervals. Note that the NCCFs have been corrected by using the initial time correction estimated from earthquakes. Figure 5. View largeDownload slide The NCCFs of nine OBS pairs versus their station intervals. Note that the NCCFs have been corrected by using the initial time correction estimated from earthquakes. 3.2 Determine the clock errors using Scholte waves on NCCF The time asymmetry of Rayleigh waves on NCCF has been used to correct clock errors for both land seismic stations and OBSs (e.g. Stehly et al. 2007; Sens-Schönfelder 2008; Gouedard et al. 2014; Hannemann et al. 2014; Takeo et al. 2014). This method is based on the assumption that, in an ideal scenario, the waveforms in the casual and anti casual parts on NCCF should be in perfect symmetry, and stay static over time. For real NCCFs, however, the symmetry could be broken because of the clock errors of two receivers, uneven noise sources and medium velocity changes over time. For most study regions without short-term tectonic activities, the effect of temporal velocity structure changes can be reasonably neglected. The other two factors can be distinguished by examining the temporal evolution pattern of the asymmetry. Because clock shifts affect casual and anti casual traveltimes exactly in an opposite manner, their traveltime difference therefore will remain constant over time. On the other hand, the noise from opposite direction will evolve exactly in the same way, and the traveltime difference will not stay constant (Stehly et al. 2007; Sens-Schönfelder 2008; Gouedard et al. 2014). We will use this method to show that the clock shifts, instead of the uneven noise distribution, are responsible for most of the asymmetry on NCCFs in our data. We use coherent Scholte waves on NCCFs by cross-correlating hydrophone recordings, instead of Rayleigh waves from seismometer signals, to correct the clocks. Our method of calculating NCCF was given by Bensen et al. (2007) and Yao et al. (2011). The daily hydrophone recordings from each OBS are first down-sampled, and band-filtered by 0.1–0.2 Hz. To remove the effects of earthquake signals, we apply one bit normalization and whitening to the data. Daily recordings are divided into 2 hr windows which are then used to calculate the daily NCCFs at frequency band of 0.1–0.2 Hz. We note that we focus on the frequency band of 0.1–0.2 Hz because the Scholte wave is supposed to have strong amplitude in this band given properties of seafloor sediment and the water depth. Experiments show that (Park et al. 2005; Flores-Mendez et al. 2012; Potty et al. 2012) the largest Scholte wave amplitude is expected when the parameter, λ/H, the wavelength and water depth ratio, falls in the range of 1.0–4.0. Assuming the shear velocity of the soft sediment at seafloor of the SCS is 1.0 km s−1, and water depth is 4000 m, the frequency range of 0.1–0.2 Hz will lead to the λ/H in the range of 1.25–2.5. Figs 4 and 6 give examples of our daily NCCFs. Their temporal evolution shows that, while asymmetries of two Scholte waves in casual and anti casual parts are always significant over time, their time distance only fluctuate slightly. This indicates most of the asymmetries can be attributed to the clock errors. Therefore, we will first assume the asymmetry is solely caused by relative clock shifts to calculate them, and then assess how big the effects of the noise source distribution are. Figure 6. View largeDownload slide The amplitude of daily NCCFs at the pair of stations HY02–HY15 in the frequency band of 0.1–0.2 Hz. The bottom is the stacked NCCFs over all days. The black solid line indicates the average time difference between the two coherent Scholte waves. It locates in the middle of two peaks between the negative and positive sides. The dash rectangles mark the time symmetrical windows of causal and anti causal NCCFs, which are cross-correlated to calculate the daily time difference. Figure 6. View largeDownload slide The amplitude of daily NCCFs at the pair of stations HY02–HY15 in the frequency band of 0.1–0.2 Hz. The bottom is the stacked NCCFs over all days. The black solid line indicates the average time difference between the two coherent Scholte waves. It locates in the middle of two peaks between the negative and positive sides. The dash rectangles mark the time symmetrical windows of causal and anti causal NCCFs, which are cross-correlated to calculate the daily time difference. With the above assumption, the relative clock error between two stations is equal to the offset of the central point of two coherent Scholte waves from time 0. We determine it through cross-correlating causal and anti causal parts of NCCF. Because waveforms of two Scholte waves are not identical, a simple, direct cross-correlation could result in false corrections, especially in our case where errors reach hundreds of seconds for some OBSs. To avoid this situation, we employ a two-step approach. We first apply an initial correction (dt1) to the NCCFs. There are two ways to determine dt1. It can be the mean difference shown in Fig. 3 for each OBS pair; the other way is to stack all daily NCCFs of each OBS pair altogether to form a stacked NCCF, through which dt1 is determined by waveform cross-correlation (Fig. 6). We found that the two methods yield slightly different initial corrections. But they will not affect our final correction because an initial correction is just to ensure the symmetric point is close to time 0 and, in the next step, the time windows for cross-correlation contain the right Scholte waveforms. Supporting Information Table S1 gives the initial corrections of nine OBS pairs using the stacked NCCF. In the next step, after initial correction for all daily NCCFs, we select two time symmetric windows containing Scholte waves, and cross-correlate them to further determine their traveltime difference, dt2 (Fig. 6). Thus the final clock correction for each station pair would be dt = dt1 + dt2. This method can be applied to a stacked NCCF, and a static relative correction for an OBS pair can be calculated. However, it is more often that the clock error drifts over time during a long period of deployment (e.g. Sens-Schönfelder 2008; Gouedard et al. 2014; Hannemann et al. 2014). As shown in Fig. 4, Scholte waves derived from hydrophones have relatively high SNR. Instead of stacking all daily NCCFs, we can calculate the temporal variation of the clock error by using daily NCCFs directly, or more practically, stacked NCCFs of a short period, say a few days (Supporting Information Fig. S1). Because the short-term, localized noise sources also contribute to the time asymmetry of coherent phases, using stacked NCCFs of many days could reduce this effect. In this study, the relative correction of each OBS pair (Fig. 7) is computed by using stacked NCCFs of the nearest 11 d (before and after 5 d of a given day). Figure 7. View largeDownload slide Left: temporal variation of relative clock errors for three OBS pairs (black solid curve) derived from time asymmetry of Scholte waves on the causal and anticausal sides of NCCFs. Right: temporal variation of Scholte wave's traveltime between each OBS pair, which is half of the time distance between two Scholte waves in causal and anticausal sides (determined by waveform cross-correlation). The black circle is the daily (11 d stacked) average traveltime. Red line is the average of traveltime of all day. The average and the maximum of error are given in the figures. In the ideal case of evenly distribution of noise sources, the traveltime is a constant over time. Figure 7. View largeDownload slide Left: temporal variation of relative clock errors for three OBS pairs (black solid curve) derived from time asymmetry of Scholte waves on the causal and anticausal sides of NCCFs. Right: temporal variation of Scholte wave's traveltime between each OBS pair, which is half of the time distance between two Scholte waves in causal and anticausal sides (determined by waveform cross-correlation). The black circle is the daily (11 d stacked) average traveltime. Red line is the average of traveltime of all day. The average and the maximum of error are given in the figures. In the ideal case of evenly distribution of noise sources, the traveltime is a constant over time. In order to assess how severely the noise source distribution affects the traveltimes of coherent Scholte waves, we examine the temporal variation of the traveltime by calculating the time distance between the Scholte waves on NCCF. The time distance is also obtained by waveform cross-correlation. Their variations over the deployments are shown in right panels of Fig. 7 and Supporting Information Fig. S2. It is worth noting that the values of several OBS pairs show regular monthly fluctuating pattern, which is very likely caused by tidal variations in SCS. After removing the means, the standard deviations of the time distances are less than 0.3 s, which only account for negligible portion of the corrections we calculated (less than 0.5 per cent for most of the OBS pairs except for HY15-HY16). This suggests the noise distribution did cause a little fluctuation of the asymmetry, but its effect is insignificant compared to the clock errors. The amplitude of fluctuation is consistent with previous works (e.g. Yao & Van de Hilst 2009; Froment et al. 2010), which all found the traveltime bias caused by undiffused noises is generally less than 1 per cent. It is challenging to objectively determine uncertainties associated with our relative clock corrections. Because the fluctuation of time distance of two Scholte waves on NCCFs gives the other mechanism, beside the clock error, to account for the asymmetry, it is natural to take these values as the uncertainties of relative clock errors. They will be used to determine the uncertainties of the final absolute clock errors. 3.3 Results of OBS clock errors There are seven OBSs in this array. Ideally, we would have 21 OBS pairs, and the same number of relative errors. However, the fossil ridge, the Huangyan-Zhenbei seamount chain, sits between the southern and northern portions of our array (Fig. 1). The topography high certainly will block the propagations of Scholte waves. As a result, for OBS pairs across the fossil ridge, the SNRs of Scholte waves in NCCFs are relatively low. To obtain reliable corrections, we set an SNR threshold (5.0) and select nine pairs from all available OBSs (Fig. 7 and Supporting Information Fig. S2). The selected nine relative clock errors form a system of equations as   $$\Delta {\tau _i} - \Delta {\tau _j} = d{t_{ij}}$$ (1) where, Δτi, Δτj are the absolute time errors at OBSs i and j, respectively; dtij is the relative error between OBSs i and j. This is a classic underdetermined inverse problem whose solutions cannot be uniquely determined because equations are linearly dependent. To solve this equation, we must identify a reference OBS, assuming its clock is accurate, and other OBSs in the array will synchronize to it. Here we specified HY15 as the reference station (detailed in Section 4), and solve the equation system for the absolute corrections for all OBSs (Fig. 8). Figure 8. View largeDownload slide The temporally varied absolute clock corrections of six OBSs (black lines) based on the assumption that HY15 has an accurate clock. The grey shaded areas are the standard deviation of the corrections. The average and maximum of standard deviations are given in figures. Figure 8. View largeDownload slide The temporally varied absolute clock corrections of six OBSs (black lines) based on the assumption that HY15 has an accurate clock. The grey shaded areas are the standard deviation of the corrections. The average and maximum of standard deviations are given in figures. To determine the uncertainty of clock correction, we employ a bootstrapping analysis (Gouedard et al. 2014). In this process, each relative correction is added a random error, which is uniformly distributed in the range of fluctuating amplitude of time distance for each OBS pair (right panels in Fig. 7 and Supporting Information Fig. S2). With these new data containing error, we solve the equations for absolute corrections. We repeat the process 200 times, and therefore have 200 corrections for each station on each day. The final corrections are the means of these 200 estimations, and their standard deviations are taken as uncertainties of our corrections. As shown in Fig. 8, the average uncertainties of our absolute clock corrections are less than 0.2 s. 4 DISCUSSION 4.1 Effects of undiffused noise sources The accuracy of our corrections depends on how well the NCCF can reconstruct the Green's functions for each OBS pair, which in turn depends on whether the distribution of noise sources is evenly distributed and the wavefield is truly diffuse. Many authors (e.g. Yao & Van de Hilst 2009; Froment et al. 2010; Harmon et al. 2010) have shown that, even if the noise sources are unevenly distributed, traveltimes of the surface waves on NCCFs generally have small bias (<1 per cent) when they are used to invert for the phase velocity. Our analysis of the temporal variation of average traveltimes also indicates their fluctuation over time is less than 1 per cent (Fig. 7 and Supporting Information Fig. S2). In addition, the azimuthal variation of the noise strength also suggests our noise sources do not show strong preferential directions (Supporting Information Fig. S3). Nevertheless, it is interesting to note that, as shown in Fig. 8, on the gradually varied drifts for several OBSs, there exist bumps around day 200. It turns out that, in that period, there were over six typhoons and severe tropical storms overlapped one another, which either directly impacted or were very close to the SCS region (Supporting Information Fig. S4). Therefore, it is clear that the localized noise source does cause slight bias on the clock corrections, whose strength is within the estimated uncertainty. 4.2 Effects of deep-sea currents As mentioned above, the changes of medium velocity could also contribute to the asymmetry of the coherent waveforms over time. One possibility is the deep currents at seafloor could lead to temporal velocity change and anisotropy, generating another source of bias to the correction. We cannot completely rule this out, but the effect should be negligible. First, the deep currents in SCS are much slower (<1 cm s−1; Wang et al. 2011) than the speed of Scholte waves (∼1000 m s−1); second, the directions of the currents would not be exactly parallel to the line linking two stations to generate strong anisotropy; Third, the directions of the currents could change in short period of time, and our corrections are based on the stacked NCCFs of eleven days, which would reduce this effect. 4.3 Reference station for the absolute clock errors The final absolute clock error of each individual OBS depends on the accuracy of the clock of the reference OBS we select. Ideally, a land station with GPS synchronized timing would be the best choice for reference station. There is one station on Luzon Island (SZP) close to our array. We calculate the NCCFs between SZP and our OBSs in two frequency bands. While the SNR of stacked NCCFs at period band 10–20 s are relatively higher, the daily NCCFs, or stacked NCCFs of 11 d, for both frequency bands are too low for the temporally changing clock correction (Supporting Information Fig. S5). Our selection of OBS HY15 as the reference station because it has minimum deviation from the predicted traveltimes, which is an independent constraint other than the NCCF method. On the other hand, the choice of reference station is not a significant issue for some seismic studies, for example, the teleseismic tomography (VanDecar & Crosson 1990) and two-plane wave surface wave tomography (Forsyth & Li 2005) because the relative traveltimes among stations in the array, instead of the absolute traveltimes, are used in these studies. 4.4 Applications of the clock-corrected OBS data The accuracy of OBS clock correction is crucial to estimate of velocity anomaly. Our uncertainty analysis indicates that the average uncertainty of the correction is less than 0.2 s. The typical station interval in this experiment is about 150 km. To be able to detect 1 per cent of velocity anomaly, the traveltime accuracy has to reach about 0.37 s for a medium with 4.0 km s−1 average velocity. Therefore, considering the up limit of the uncertainty, our clock-corrected OBS data can at least be used to surface wave and S wave studies, but can hardly be useful for P wave tomography. 5 CONCLUSIONS The hydrophones of OBSs have the advantage over seismometers at seafloor to retrieve high SNR coherent Scholte waves through noise cross-correlation because hydrophones are positioned in the water above the seafloor, and Scholte phase propagating along the seafloor attenuates much less in the liquid than in the solid. The NCCFs of seismometers at the sediment-covered seafloor are, on the other hand, contaminated by other solid-mode phases from the complex seafloor. Taking advantage of this feature of hydrophone recordings, we calculate the NCCFs of an OBS array deployed in the central sub-basin of the SCS, and use Scholte waves on the NCCFs to correct their clock errors, some of which are very large. Because of the relative high SNR of Scholte waves, the temporal variation of the clock drifts can be determined through the time asymmetry of Scholte waves on NCCFs. The accuracy of the clock correction achieved is valuable for the long period surface wave and S wave studies. Acknowledgements The authors would like to thank the First Institute of Oceanography, State Oceanic Administration, China for providing us the instruments or helps needed on the sea. This project was supported by National Natural Science Foundation of China (41676033 and 91128209), the National Program on Global Changing and Air-Sea Interaction (GASI-GEOGE-05) and Shenzhen Sci. and Tech. Innovation Commission (2017-131, 2017-173). TY and YJC are also funded by faculty startup funds from SUSTech. We thank Dr Harmon, Dr Hannemann and an anonymous reviewer for thoughtful and constructive comments that improved the manuscript a lot. 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Synchronizing intercontinental seismic networks using the 26 s persistent localized microseismic source, Bull. seism. Soc. Am. , 105( 4), 2101– 2108. https://doi.org/10.1785/0120140252 Google Scholar CrossRef Search ADS   Yao H., van der Hilst R.D., 2009. Analysis of ambient noise energy distribution and phase velocity bias in ambient noise tomography, with application to SE Tibet, Geophys. J. Int. , 179( 2), 1113– 1132. https://doi.org/10.1111/j.1365-246X.2009.04329.x Google Scholar CrossRef Search ADS   Yao H., Gouedard P., Collins J.A., Mcguire J.J., van der Hilst R.D., 2011. Structure of young East Pacific Rise lithosphere from ambient noise correlation analysis of fundamental- and higher-mode Scholte-Rayleigh waves, C. R. Geosci. , 343( 8), 571– 583. https://doi.org/10.1016/j.crte.2011.04.004 Google Scholar CrossRef Search ADS   Zha Y., Webb S.C., Wei S.S., Wiens D.A., Blackman D.K., Menke W., Dunn R.A., Conder J.A., 2014. Seismological imaging of ridge–arc interaction beneath the Eastern Lau Spreading Center from OBS ambient noise tomography, Earth planet. Sci. Lett. , 408, 194– 206. https://doi.org/10.1016/j.epsl.2014.10.019 Google Scholar CrossRef Search ADS   Zhu J., Popovics J.S., Schubert F., 2004. Leaky Rayleigh and Scholte waves at the fluid–solid interface subjected to transient point loading, J. acoust. Soc. Am. , 116( 4), 2101– 2110. https://doi.org/10.1121/1.1791718 Google Scholar CrossRef Search ADS   SUPPORTING INFORMATION Supplementary data are available at GJI online. Figure S1. Temporal variation of relative clock error for the OBS pair of HY02-HY15 derived from daily NCCFs (circles) and stacked NCCFs of 11 d (red line). Figure S2. Temporal variations of relative clock errors of other OBS pairs (left) and half of time distance of the two Scholte waves on each NCCF (same as Fig. 7) (right). Because the time base jumped for HY10 on day 151, the vertical axes of two pairs with HY10 after day 151 are on the right side of figures on the left panels (see the caption of Fig. 3 for details). Figure S3. Variation of the normalized amplitude of the NCCFs as the function of the OBS pair's azimuth (in period bands 5–10 s) for all NCCFs with SNR > 3.0. The dots closer to the centre have relatively lower amplitudes. The station intervals are indicated by different colours. Figure S4. Summary of 2012 Pacific typhoon season: timing and intensity (https://en.wikipedia.org/wiki/2012_Pacific_typhoon_season). Please note, from 2012 July 15 to August 20 (197–233 in Julian day), there were over six typhoons and severe tropical storms, which either directly impacted or were very close to the South China Sea region. Figure S5. The NCCFs of seismometer vertical components between OBS HY15 and SZP, the land station at Luzon island in two period bands (left: 5–10 s, right: 10–20 s). Top images give the amplitude of NCCFs for each day. The bottom traces are the waveforms of cross-correlation stacked over all days at the pair of stations. From the stacked NCCFs at 10–20 s, the relative error between SZP and HY15 was estimated, −0.5 s. Table S1. The initial time corrections for each OBS pair derived from the stacked NCCFs over all days. Note that two pairs with HY10 have two initial time corrections separated on day 151 (see the caption of Fig. 3 for details). Please note: Oxford University Press is not responsible for the content or functionality of any supporting materials supplied by the authors. Any queries (other than missing material) should be directed to the corresponding author for the paper. © The Authors 2017. Published by Oxford University Press on behalf of The Royal Astronomical Society.

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Geophysical Journal InternationalOxford University Press

Published: Feb 1, 2018

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