Assessing the short-term clock drift of early broadband stations with burst events of the 26 s persistent and localized microseism

Assessing the short-term clock drift of early broadband stations with burst events of the 26 s... Abstract Accurate seismometer clock plays an important role in seismological studies including earthquake location and tomography. However, some seismic stations may have clock drift larger than 1 s (e.g. GSC in 1992), especially in early days of global seismic networks. The 26 s Persistent Localized (PL) microseism event in the Gulf of Guinea sometime excites strong and coherent signals, and can be used as repeating source for assessing stability of seismometer clocks. Taking station GSC, PAS and PFO in the TERRAscope network as an example, the 26 s PL signal can be easily observed in the ambient noise cross-correlation function between these stations and a remote station OBN with interstation distance about 9700 km. The travel-time variation of this 26 s signal in the ambient noise cross-correlation function is used to infer clock error. A drastic clock error is detected during June 1992 for station GSC, but not found for station PAS and PFO. This short-term clock error is confirmed by both teleseismic and local earthquake records with a magnitude of 25 s. Averaged over the three stations, the accuracy of the ambient noise cross-correlation function method with the 26 s source is about 0.3–0.5 s. Using this PL source, the clock can be validated for historical records of sparsely distributed stations, where the usual ambient noise cross-correlation function of short-period (<20 s) ambient noise might be less effective due to its attenuation over long interstation distances. However, this method suffers from cycling problem, and should be verified by teleseismic/local P waves. Further studies are also needed to investigate whether the 26 s source moves spatially and its effects on clock drift detection. Seismic Noise, Seismic Interferometry, Seismic Instruments 1 INTRODUCTION Various studies have demonstrated the value of historical seismograms, despite of limited number of seismic stations in the early stage of sparse global network (Kanamori 1988), for example, IDA (Agnew et al.1976), GEOSCOPE (Romanowicz et al.1984), TERRAscope (Kanamori et al.1991), GSN (Butler et al. 2004). These waveforms have been used in studies of focal mechanism solutions and earthquake rupture processes (Alvarado & Beck 2006; Batlló et al. 2010; Kanamori et al. 2010, 2012; Pino 2011; Shiba & Uetake 2011; Kulikova & Krüger 2015; Baştürk et al. 2016; Kulikova et al. 2016). These records would be also important in tomography studies, for example, Hearn (1999) imaged uppermost mantle velocity and anisotropy of Europe with International Seismological Centre arrival data as early as 1960. Similarly, Lü et al. (2011) performed Pn travel-time tomography beneath Tibetan Plateau and adjacent regions using historical travel-time data. Their studies demonstrated that historical earthquakes in low seismicity area improved the ray-path coverage. Besides, through the comparison between historical and recent seismic waveform data, researchers have succeeded in detecting structure changes, such as super rotation of the inner core and topographical variation of the inner core boundary (Song & Richards 1996; Wen 2006). Even though these seismic stations had external synchronization systems (e.g. GPS or OMEGA), clock error of some stations has been found due to hardware or software failure (e.g. Stehly et al. 2007; Xia et al. 2015). When these records are used in studies of earthquake location and seismic tomography, arrival residuals and clock error are usually pre-screened to discard travel-time residual outliers. (Hearn et al. 1991; Hearn 1999; Phillips et al. 2007; Li et al. 2012). Seismometer clock error can be detected via comparison with external timing signals (such as GPS) or using the seismic waves emitted by repeating seismic sources (Stehly et al. 2007). There are mainly two kinds of stable and continuous seismic sources, that is, seismic ambient noise and the Persistent Localized (PL) microseism events (Shapiro et al. 2006). Using the empirical greens function extracted from cross-correlation of ambient noise, Stehly et al. (2007) detected variation of surface-wave travel-times in the period bands of 5–10 s and 10–20 s between regional stations in southern California, USA (inset in Fig. 1, station distance ∼ 200 km). They found that the clock of station GSC is stable most of the time. However, in some months of 1992 it has a clock error of about 2 s. This method has also been used to detect the clock error of Ocean-Bottom-Seismometer (OBS) networks with a relatively small aperture (Sens-Schönfelder 2008; Gouédard et al.2014; Hannemann et al.2014). In addition, Xia et al. (2015) proposed a method of assessing long-term stability of station clocks using the 26 s PL signals from the Gulf of Guinea. Their method can detect clock error with an accuracy of a few tenths of a second via cross-correlation between inter-continental stations, and is applicable for seismic data in early Global Seismographic Network era, because the 26 s signal is much stronger than ambient noise in ambient Noise Cross-correlation Function (NCF) for very large interstation distances. Both methods use stacked waveforms over long time (usually one month) to enhance Signal-to-Noise Ratio (SNR), thus it is difficult to detect the short-term change (e.g. in 1 d) of the instrumental clock. Figure 1. View largeDownload slide Distribution of the stations (triangles), earthquakes (circles) and the 26 s PL microseismic source of the Gulf of Guinea (diamond). Inset shows zoomed in map of stations in California, USA. The open circles are earthquakes within 30° and 100° from station GSC, with magnitude above 5.5. Red circles indicate two earthquakes with waveforms displayed in Fig. 6. One is a local earthquake in California on 1992 June 24 with magnitude of 3.1, and the other is a teleseismic earthquake in Fiji on 1992 June 9 with magnitude of 5.6. Figure 1. View largeDownload slide Distribution of the stations (triangles), earthquakes (circles) and the 26 s PL microseismic source of the Gulf of Guinea (diamond). Inset shows zoomed in map of stations in California, USA. The open circles are earthquakes within 30° and 100° from station GSC, with magnitude above 5.5. Red circles indicate two earthquakes with waveforms displayed in Fig. 6. One is a local earthquake in California on 1992 June 24 with magnitude of 3.1, and the other is a teleseismic earthquake in Fiji on 1992 June 9 with magnitude of 5.6. In contrast, short-term instrumental clock error can be detected using signals excited by events which occur frequently. And such events should be powerful enough to be recorded on seismic stations at large distances. Anchieta et al. (2011) compared the teleseismic P waves between close stations and corrected clock drifts of OBS. For regular and precise monitoring of clock variations, repeating moderate or strong earthquakes for the same source region are required. Otherwise, events from different regions might cause inaccuracy from the heterogeneity of the Earth structure. Besides the frequent natural earthquakes, the PL microseism sources also generate strong seismic signals (Shapiro et al. 2006; Zeng & Ni 2010). For example, Oliver (1962, 1963) found that the 26 s source was particularly strong on 1961 June 6–8, then it merged into background noise. He named these abrupt increasing in amplitude as “storm” of microseism and we refer to them as burst events. However, later studies indeed demonstrated its persistent nature, with episodic strong amplitude and weak excitation in other time (Xia et al. 2013). They behave more or less like repeating events with variable excitation strength, which could be used to monitor short-term clock variation (Shapiro et al. 2006; Zeng & Ni 2010; Xia et al. 2013). In this study, we use the burst signal of PL 26 s source to detect the short-term clock error of GSC station (Fig. 1) in 1992. We begin with calculating the NCF between GSC and a reference station (OBN, Scripps Institution of Oceanography 1986) to get the PL 26 s signal. Burst events are selected with high SNR. The waveforms of all burst events are stacked to obtain a reference waveform. We then measure the differential time between each burst waveform with the reference to detect the clock error. A drastic clock change in June is found, and verified with teleseismic and regional P waves. In the end, we discuss the limitation of this method and its applicability to OBS clocks. 2 INSTRUMENTAL CLOCK ERROR DETECTION USING 26 S PL SIGNAL A few PL microseism sources have been identified on the Earth, for example, the 26 s PL source in the Gulf of Guinea (Fig. 1; Oliver 1962; Holcomb, 1980, 1998; Shapiro et al. 2006; Xia et al. 2013), the 26 s PL source near Vanuatu Island (Zeng & Ni 2014) and the 7–15 s source on Kyushu Island (Zeng & Ni 2010). Among them, the 26 s PL source in the Gulf of Guinea is the strongest one, which is suitable for clock error detection. When burst events occur, this signal can be detected almost all over the globe, especially in Europe and North America (Oliver 1962; Xia et al. 2013). The excitation mechanism of this PL source is still unknown, which is usually attributed to the volcanic process, though oceanic processes have also been proposed to explain its variability in strength (Shapiro et al. 2006; Xia et al. 2013). To demonstrate characteristics of the 26 s PL source, we display ambient noise spectra of stations GSC in Southern California and OBN (IRIS/IDA) in Russia (Fig. 2). The spectra of these two stations are calculated for the same time span. On 1992 May 5, there is a sharp peak at the frequency of 0.038 Hz (26 s). Frequency band of the signal is very narrow, around 0.001 Hz. It distinguishes itself from the weak background spectrum around period of 30 s in the New Low-Noise Model (Peterson 1993). The amplitude of this signal is not constant, and sometimes it is relatively weak (e.g. on 1992 February 16). And occasionally, it becomes strong and can be observed on raw long period seismograms at a global scale, which implies it could be as strong as a M5 earthquake (Oliver 1962). Recent study shows that the burst excitation mode usually lasts hours (Xia et al. 2013). Figure 2. View largeDownload slide Spectra of noise records for stations GSC and OBN. (a,b) Spectra of GSC on 1992 February 16 and May 5, respectively. (c,d) Spectra of OBN on the same days. The length of the ambient noise records are 3 hr long, beginning at 12:00:00 (UTC). The grey area specifies the narrow frequency span of 0.037–0.039 Hz. Figure 2. View largeDownload slide Spectra of noise records for stations GSC and OBN. (a,b) Spectra of GSC on 1992 February 16 and May 5, respectively. (c,d) Spectra of OBN on the same days. The length of the ambient noise records are 3 hr long, beginning at 12:00:00 (UTC). The grey area specifies the narrow frequency span of 0.037–0.039 Hz. Based on the persistence and localization of this 26 s signal, Xia et al. (2015) demonstrated feasibility of using it to detect the long-term instrumental clock error. One month-long NCFs are calculated between inter-continental stations. They measured the differential time between NCF waveform with a reference NCF which is obtained with yearly stacking. But their method cannot resolve clock problems shorter than one month. Stehly et al. (2007) found there are gradual clock drift of GSC station in April, May and June of 1992, and we suspect that short-term clock drift might have existed. Thus, we take the records of station GSC in 1992 as an example to assess the performance of its clock. Both Stehly et al. (2007) and Xia et al (2015) studied the stability of a seismometer clock with respect to other high-quality stations. In this study, we choose the station OBN in Russia as the reference station, which records clear 26 s PL signal (Fig. 2) and its clock is stable with variance of a few tenths of a second (Engdahl & Ritzwoller 2001; Wen 2006; Xia et al. 2015). From IRIS/DMC, we download the continuous vertical component broadband waveform data in 1992 and 1993 for stations GSC and OBN. Previous studies found that GSC station clock worked normally in 1993 (Stehly et al2007; Xia et al. 2015), thus we take the NCF between GSC and OBN for entire year 1993 as reference waveform for measuring clock drift in 1992. Mean, trend and instrumental response are removed from the raw data. The sampling rate of the raw data is 20 samples per second (sps), and we interpolate it to 100 sps to improve precision of clock measurement. The continuous waveform data are cut into short segments, either daily or a few hours, as detailed later. SNR of the signal in NCF usually correlates with the length of the waveform record (Yang et al. 2007): longer seismic noise records result in higher SNR. However, there is a trade-off between the accuracy of temporal variation measurement and the SNR of NCF. With more NCFs stacked together, the clock drift could be more smeared. As the duration of the 26 s PL bursting mode is about a few hours (Xia et al. 2015), we calculate the NCFs with different length of records, and find that reliable signals in NCF can be achieved with waveform segment length as short as 3 hr with 50 per cent overlapping. In the following processing steps, we calculate both 1 d and 3 hr long time-domain NCFs to explore the trade-off between window length and measurement precision. Before NCF calculation, we apply running absolute mean time-domain normalization to the waveform data with band-pass filtered in the frequency range of 0.02–0.05 Hz (Bensen et al. 2007). Through comparing different time-domain normalization methods, Bensen et al. (2007) found that the running absolute mean normalization is robust to suppress the interference of irregular signals (e.g. glitches) or strongly correlated signals (e.g. earthquakes). In order to extract broadband surface waves, frequency-domain whitening is usually applied after the time-domain normalization in previous studies. However, if the frequency-domain normalization is applied, the signal of 26 s is also suppressed, just like earthquakes. Instead, we calculate the NCF in this study without frequency-domain whitening. A few examples of daily NCFs are shown in Fig. 3. On some days, almost no 26 s signal can be observed in both time and frequency domains (e.g. 1992 January 17). However, on the other days, the 26 s signal waveforms are quite obvious in both time and frequency domains (e.g. 1992 May 5). The signal arrives around 1600 s in the positive lag of the NCF. Previous studies proposed that the 26 s PL source is located in the Gulf of Guinea (latitude ∼ 0.20°N, longitude ∼6.58°E, Fig. 1) (Xia et al. 2015), which is closer to OBN than GSC with about 6000 km difference. Assuming the Rayleigh wave group velocity of 3.8 km/s (Xia et al. 2013), the 26 s signal would show up around 1600 s in the NCF between OBN and GSC (positive lag), which is consistent with the observation. To quantify the observed 26 s signal on NCFs, we compute its SNR. The SNR is defined as the ratio between the maximum amplitude of the 26 s signal and the maximum amplitude of the background noise. It can be observed that the 26 s signal lasts more than 1000 s on NCFs, which is consistent with its very narrow band (±0.001 Hz) (Fig. 3), according to the uncertainty principle of the data processing (Donoho & Stark 1989). We take a time window of 1200 s around the peak of the 26 s signal to define its amplitude. For example, the 26 s signal on 1992 May 5 is very pronounced with a SNR of 2.8 (Fig. 3). Figure 3. View largeDownload slide The Daily NCFs (left column) and spectra (right column) between OBN and GSC. Dates of the waveform data are displayed in the upper left corner. Figure 3. View largeDownload slide The Daily NCFs (left column) and spectra (right column) between OBN and GSC. Dates of the waveform data are displayed in the upper left corner. We calculate the SNR of the 26 s signals on daily and 3 hr long NCFs for the year of 1992 (Fig. 4). The SNRs for both daily and 3 hr long NCFs are mostly around 1.0, but on occasions they have higher SNR. For example, when SNR is above 2.0, the burst event of the 26 s signal can be observed. The burst events are mostly observed in June, and in February, April, May and July, the burst event occurred with duration time up to 1–2 d (e.g. February 15–16; April 9; May 30–31; July 25–26), which is consistent with those reported by Xia et al. (2015). In Fig. 4, we also show some typical NCFs with different SNRs. The signal with SNR above 1.3 and less than 2 is still recognizable. During the clock error detection, we use 31 NCFs with SNR above 1.3. The moving crosscorrelation is used to measure the time shift of each NCF with high SNR 26 s signals with respect to the reference NCF waveform. We calculate crosscorrelation between each daily NCF and the reference NCF and allow time shifts of up to 30 s, with a time step of 0.01 s. The clock drift is determined from the time when Crosscorrelation Coefficient (CC) achieves maximum (Hauksson & Shearer 2005). To ensure the final quality of the reference NCF, it was computed by stacking the daily NCFs of 1993 with SNR > 1.3 (Fig. 3e). During measurement of clock drift with cross-correlation, the reference waveform window is set to be 1600 s long and centred at the maximum amplitude of the 26 s signal, so as to include most of the 26 s signal wave train. To ensure the quality of clock drift detection, we only keep the measurements with CC above 0.90. Moreover, we also stack the NCF monthly, and measure the clock variation for a comparison with the results by Stehly et al. (2007). Figure 4. View largeDownload slide SNR of the 26 s signal in NCFs (left column) and some example NCFs (right column). (a) SNR of the 26 s signal SNR for daily NCFs (black dots) and 3 hr NCFs (red dots) in 1992. Black and Red dashed lines show the SNR with mean plus two standard error for daily and 3 hr NCFs, respectively. (b)–(e) are the daily NCFs on January 17, April 10, June 10 and July 24, respectively. Figure 4. View largeDownload slide SNR of the 26 s signal in NCFs (left column) and some example NCFs (right column). (a) SNR of the 26 s signal SNR for daily NCFs (black dots) and 3 hr NCFs (red dots) in 1992. Black and Red dashed lines show the SNR with mean plus two standard error for daily and 3 hr NCFs, respectively. (b)–(e) are the daily NCFs on January 17, April 10, June 10 and July 24, respectively. 3 RESULTS The clock variation of GSC station in 1992 with respect to station OBN is displayed in Fig. 5(a). Our measurement (blue dots) with monthly NCF shows small variation of time shift within 0.5 s most of the time, and the clock drift is up to 3 s from April to June. The measurements using burst events of the 26 s PL signal are consistent with the monthly stacked results for most of the months in 1992, implying GSC clock drifts very little or smoothly during the time span. However, in the beginning of June, the daily clock error varies dramatically, for example, from -10, to 8 s, which is not seen in monthly NCF measurements. Probably the monthly NCF smeared the abrupt changes of station clocks, thus leading to much smaller clock drift as compared to daily detection results. Figure 5. View largeDownload slide Clock drift for station GSC in 1992 (a) and June 1992 (b). (a) Black dots are results measured using daily burst events of the 26 s PL signal, green dots are the arrival time differences between GSC and PFO using teleseismic P wave. Red dots are results from monthly NCF measurements and the grey line shows the monthly averaged clock drift between GSC and PFO by Stehly et al. (2007). (b) Black cycles are results measured using 3 hr long burst events NCFs and green diamonds and red stars are shifted up and down by 26 s. Blue diamonds and circles are the clock difference between GSC and PFO and between GSC and PAS using teleseismic P wave, respectively. Dashed ellipses mark measurements on 9, 11, 13, 21 and 23 of June. Figure 5. View largeDownload slide Clock drift for station GSC in 1992 (a) and June 1992 (b). (a) Black dots are results measured using daily burst events of the 26 s PL signal, green dots are the arrival time differences between GSC and PFO using teleseismic P wave. Red dots are results from monthly NCF measurements and the grey line shows the monthly averaged clock drift between GSC and PFO by Stehly et al. (2007). (b) Black cycles are results measured using 3 hr long burst events NCFs and green diamonds and red stars are shifted up and down by 26 s. Blue diamonds and circles are the clock difference between GSC and PFO and between GSC and PAS using teleseismic P wave, respectively. Dashed ellipses mark measurements on 9, 11, 13, 21 and 23 of June. To validate our results, we compare the clock errors with those from Stehly et al. (2007), which is measured from changes of surface-wave arrival in monthly NCFs (Fig. 5a). Stehly et al. (2007) found that the clock between PFO and PAS (close to GSC, see Fig. 1) is consistent, while GSC has a systematic clock drift of ∼0.875 s with respect to PFO and PAS. For our comparison, the baseline drift of theirs is removed. Except June, our daily and monthly clock errors are consistent with those of Stehly et al. (2007), suggesting that GSC clock only drifted little and smoothly. In June, the drastic variation of clock error is not observed in their result that shows a gradually decreasing clock drift. This is generally consistent with our monthly result, which have similar averaging processing. The period band that they used is 5–10 s and 10–20 s, which is different from our monochromatic 26 s, and may cause some bias. We can also use P wave of teleseismic events to verify the short-term clock error of GSC, similar to the work of Anchieta et al. (2011). Here we take advantage of double difference of the P-wave arrival time. The double difference refers to differential P-wave arrival time anomalies between two seismic stations, which can eliminate the error caused by the earthquake mislocation, inaccurate origin time and uncertainty of the velocity model. The double differenced time includes contribution from two factors, the time difference caused by local velocity heterogeneity and the clock drift between the station pair. The time difference caused by the 3-D structure usually does not change temporally, and the variation of the double differenced time would indicate clock change. During the double difference calculation, a close reference station is needed. Following Stehly et al. (2007), we take PFO and PAS as reference stations, which are located within 200 km from GSC (Fig. 1). The P-wave waveform data of 248 earthquakes with magnitude above 5.5 from PDE/USGS earthquake catalogue are downloaded from IRIS data management centre. The epicentral distance of these earthquakes is within 30°–100° (Fig. 1) to avoid rapid change of P-wave slowness due to upper mantle triplication or D″ effects. We use the IASP91 Earth model to calculate theoretical P arrival time. The residual between the observed and theoretical P-wave arrival time is usually less than 2 s (Kennett & Engdahl 1991), and larger residual might hint clock problems. To measure the differential time between station pair more accurately, we also adopt the cross-correlation approach. Figs 6(a)–(f) displays an example to demonstrate the procedures of teleseismic P-wave cross-correlation. The waveforms, band-pass filtered in the frequency band of 0.5–2 Hz, are from an M5.6 earthquake occurring in Fiji-Tonga region on 1992 June 9. A crosscorrelation time window of 12 s is used, including 4 s before P wave to account for 3-D heterogeneity of the Earth and 8 s after P wave to account for source duration of the earthquake. For example, the P-wave residual for station PAS and PFO is within 0.5 s (Figs 6a, b), implying that the clocks for these two stations work normally. However, the P-wave residual between GSC and PAS, or between GSC and PFO is about 17 s, too large for 3D heterogeneity of the Earth. Figure 6. View largeDownload slide Clock drift identification using teleseismic P-wave waveform via cross-correlation (a,f) and regional P-wave waveform. (a,c,e) waveforms are aligned on theoretical P travel-time. (b,d,f) The top trace is aligned on theoretical P arrival and is used as reference trace. The bottom traces are aligned according to time shift measured with cross-correlation. CC and time shift in seconds are also displayed. (a,b), (c,d), (e,f) show station pair of PAS-PFO, PFO-GSC, GSC-PAS respectively. (g) Regional P-wave waveform recorded by PAS, PFO and GSC, respectively. This M3.1 earthquake occurred on 1992 June 24 with depth of 1.1 km (Fig. 1). The waveforms are aligned with theoretical P arrival time (red dashed line). (h) Time shift corrected waveforms using crosscorrelation. Time shifts of PFO and GSC are calculated based on envelope waveforms using a time window of 1.2 s with 0.6 s before first P wave, taking PAS as reference. Figure 6. View largeDownload slide Clock drift identification using teleseismic P-wave waveform via cross-correlation (a,f) and regional P-wave waveform. (a,c,e) waveforms are aligned on theoretical P travel-time. (b,d,f) The top trace is aligned on theoretical P arrival and is used as reference trace. The bottom traces are aligned according to time shift measured with cross-correlation. CC and time shift in seconds are also displayed. (a,b), (c,d), (e,f) show station pair of PAS-PFO, PFO-GSC, GSC-PAS respectively. (g) Regional P-wave waveform recorded by PAS, PFO and GSC, respectively. This M3.1 earthquake occurred on 1992 June 24 with depth of 1.1 km (Fig. 1). The waveforms are aligned with theoretical P arrival time (red dashed line). (h) Time shift corrected waveforms using crosscorrelation. Time shifts of PFO and GSC are calculated based on envelope waveforms using a time window of 1.2 s with 0.6 s before first P wave, taking PAS as reference. We then compute the double difference P-wave arrival times to assess the clock error of GSC in 1992. To ensure accuracy of measurement, the results with larger than 5 as well as with waveform CCs bigger than 0.85 are retained with total amount of 78 events. The clock difference between GSC and PFO is also shown in Fig. 5(a). The results from teleseismic P wave are consistent with those of burst of 26 s PL at most of the time, showing little clock variation. And in June they both have drastic variations, yet, there are also obvious difference between the two sets of measurements. This could be caused by the different time window in measuring clock drift. For P-wave measurements, a short time window of a few seconds is used, while the clock measurement for the burst 26 s PL signal is made for 1 d. To make more compatible comparison, we also show the clock error measured with the 26 s signal using 3 hr long NCFs (Fig. 5b). We only retain the measurements from 3 hr long NCFs with SNR above 1.3 and CC larger than 0.85. Some of the measurements from teleseismic P wave are close to the PL results. However, others are quite different and there seems to be a difference of 26 s, for example, on 9, 11, 13, 21 and 23 of June (Fig. 5b). That is probably due to cycle skipping because the 26 s PL signal is very narrow banded and almost monochromatic in frequency (Xia et al. 2015), and this makes the series of CCs like a sine/cosine function. Thus, the maximum CC sometimes appears in multiples of 26 s away from the true value. To test this hypothesis, we calculated the time shift with one cycle before or after the maximum CC measurement in the cross-correlation. The results with one cycle correction are consistent with the results from P wave (Fig. 5b), implying the mismatch between the result from PL signal and P wave is due to the cycle skipping. The consistence of the result for PL signal and P wave confirms the drastic clock change of GSC station in June 1992, and its error is up to 25 s. But the rapid clock change is not detected using monthly stacked NCFs. 4 DISCUSSION To identify the obvious clock error, we can also use the P wave from local or regional earthquakes. An earthquake with M3.5 occurred within 1° close to GSC on June 24, with focal depth of 1.1 km (Fig. 1). We calculate the theoretical P arrival time based on Western US crustal velocity model (WUS; Herrmann et al. 2011) for GSC, PAS and PFO, respectively. The research by Hauksson et al. (2000) shows that the P-wave time residual in California is usually within 2 s, implying that a larger residual could be caused by clock error. The raw and time shift corrected earthquake waveforms are displayed in Figs 6(g,h). The P-wave arrival residuals for stations PAS and PFO are within 0.5 s, suggesting the velocity model and the station clocks work well. However, for station GSC, the observed P-wave arrives about 23.0 s earlier than the theoretical arrival time, implying a large clock error. This clock error is consistent with measurement from both the teleseismic P wave and the burst of 26 s PL signal, confirming again the observation of the drastic clock error. We have demonstrated that the short-term clock error can be detected using the burst energy of 26 s PL source. However, the burst events do not occur regularly, but randomly with the durations varying from hours to 1 or 2 d. Thus, the measurements of clock variation are only on some random time period. Based on the daily NCFs, the number of high SNR burst events are about 5 per cent of the whole year, which hinder us from continuous measurements of clock error. More short-term clock errors can be obtained combining PL source and teleseismic P waves. It is also worthwhile to determine the accuracy of clock drift detection with the burst event of 26 s source. With ambient noise correlation at local distances, Stehly et al. (2007) was able to achieve an accuracy of 0.2 s in detecting clock errors. We assess the accuracy of clock variation with the 26 s PL signal via computing standard deviations. Assuming the GSC station clock only changed slowly in year 1992 for months other than April to June, we can measure multiple clock errors with 3 hr NCFs, for those days when the 26 s PL is strong. During the calculation, we discard the measurements with NCF having SNR smaller than 1.3 and the CC smaller than 0.9 with the reference waveform, so as to retain only the reliable measurements. It is found that during each day when burst of the PL source occurred, the measurements are relatively stable. The average of the standard errors is about 0.3 s, a little inferior to the 0.2 s accuracy of Stehly et al. (2007). This is not surprising, as the latter is measured over longer time span (one month) while the former is measured daily or in a few hours, again echoing the trade-off between temporal resolution versus accuracy of measurement. Location variation of the 26 s source might influence measurement of clock drift. In order to investigate this issue, we measure the clock variation of station PAS and PFO which are in the same network (TERRAscope) as GSC (Fig. S1). The clock drifts are calculated using the same procedure as for the station GSC. Taking the stacked NCF of the year 1993 as reference NCF, we calculate the time shift between each 3 hr NCFs with the reference waveform using cross-correlation. We observe that the clock drift for station PAS and PFO are mainly close to zero with standard deviation of 0.5 s, and become more stable with increasing CC (Fig. S1). It implies that the location of this 26 s PL source is relatively stable, but it still remains possible that the source location changes. More regional stations and longer seismic records are needed to estimate the location change of this microseism source. As compared to the 0.3 s accuracy for station GSC, the accuracy for PAS and PFO is relatively larger (0.5 s), probably due to further distance of GSC from coast line. The accuracy seems to be related with SNR of 26 s signal in NCF (Fig. S1). Better accuracy can be achieved with higher CC (e.g. 0.99), but less measurements will become available. Overall, this method is probably reliable up to 0.5 s. Although, it is less accurate than Stehly et al. (2007), this method could still be helpful for both global tomography and global earthquake location. For global tomography, travel-time residual after inversion is usually 1.0 s for P wave or even larger for S wave (Spakman et al. 1993). Part of the residual could be caused by inaccurate clock, error in earthquake origin time, or unmodelled 3-D structure. For earthquake location, a clock drift of 0.5 s corresponds to location error of 3–5 km (assuming locating using P wave with apparent traveling velocity of 6–10 km/s), which is relatively small compared with the accuracy of earthquake location of global earthquake catalogs (about 15 km) (Kagan 2003). 5 CONCLUSION In this study, we find that the burst events of the 26 s PL source can be used to detect short-term instrumental clock error for global stations with distances of thousands of kilometres. In April and May of 1992, the clock of GSC station showed gradual drift with the error increasing to 3 s. From June 9, drastic clock error occurred, and was in the range of 25 s, returned to normal in July. We validate the clock error using double difference P-wave arrival time of teleseismic events. The drastic clock error in June is also confirmed by the P wave of a regional earthquake. This method can be used to detect the clock error for seismic station with large station distances, especially in early 1990s when the seismic stations are sparsely distributed. It may also be used to detect the clock error of modern OBS. But the 26 s PL signal seems to azimuth dependent, with stronger signal towards northern Atlantic and weaker towards southern Atlantic (Shapiro et al. 2006). Therefore, it might be very useful for OBS in northern Atlantic. However, due to the limitation of the accuracy, cycle skipping and measurement discontinuity, other methods are needed (e.g. local/teleseismic P waves) to get a continuous and high-accuracy assessment of clock error. Acknowledgements All seismomic data acquired are archived at the Incorporated Research Institutions for Seismology Data Management Center (IRIS DMC) at http://www.iris.edu/dms/dmc/. 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Google Scholar CrossRef Search ADS   SUPPORTING INFORMATION Supplementary data are available at GJI online. Figure S1. Clock drifts for station PAS, PFO using 3 hr long NCF burst event of 26 s signal with different cut-off CC. Figure S2. SNR histogram of 26 s signal for 3 hr long NCFs between OBN and GSC with (red) or without frequency domain whitening (black). (a) Histogram of all data. (b) Histogram for SNR above 3. Please note: Oxford University Press are 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

Assessing the short-term clock drift of early broadband stations with burst events of the 26 s persistent and localized microseism

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Abstract

Abstract Accurate seismometer clock plays an important role in seismological studies including earthquake location and tomography. However, some seismic stations may have clock drift larger than 1 s (e.g. GSC in 1992), especially in early days of global seismic networks. The 26 s Persistent Localized (PL) microseism event in the Gulf of Guinea sometime excites strong and coherent signals, and can be used as repeating source for assessing stability of seismometer clocks. Taking station GSC, PAS and PFO in the TERRAscope network as an example, the 26 s PL signal can be easily observed in the ambient noise cross-correlation function between these stations and a remote station OBN with interstation distance about 9700 km. The travel-time variation of this 26 s signal in the ambient noise cross-correlation function is used to infer clock error. A drastic clock error is detected during June 1992 for station GSC, but not found for station PAS and PFO. This short-term clock error is confirmed by both teleseismic and local earthquake records with a magnitude of 25 s. Averaged over the three stations, the accuracy of the ambient noise cross-correlation function method with the 26 s source is about 0.3–0.5 s. Using this PL source, the clock can be validated for historical records of sparsely distributed stations, where the usual ambient noise cross-correlation function of short-period (<20 s) ambient noise might be less effective due to its attenuation over long interstation distances. However, this method suffers from cycling problem, and should be verified by teleseismic/local P waves. Further studies are also needed to investigate whether the 26 s source moves spatially and its effects on clock drift detection. Seismic Noise, Seismic Interferometry, Seismic Instruments 1 INTRODUCTION Various studies have demonstrated the value of historical seismograms, despite of limited number of seismic stations in the early stage of sparse global network (Kanamori 1988), for example, IDA (Agnew et al.1976), GEOSCOPE (Romanowicz et al.1984), TERRAscope (Kanamori et al.1991), GSN (Butler et al. 2004). These waveforms have been used in studies of focal mechanism solutions and earthquake rupture processes (Alvarado & Beck 2006; Batlló et al. 2010; Kanamori et al. 2010, 2012; Pino 2011; Shiba & Uetake 2011; Kulikova & Krüger 2015; Baştürk et al. 2016; Kulikova et al. 2016). These records would be also important in tomography studies, for example, Hearn (1999) imaged uppermost mantle velocity and anisotropy of Europe with International Seismological Centre arrival data as early as 1960. Similarly, Lü et al. (2011) performed Pn travel-time tomography beneath Tibetan Plateau and adjacent regions using historical travel-time data. Their studies demonstrated that historical earthquakes in low seismicity area improved the ray-path coverage. Besides, through the comparison between historical and recent seismic waveform data, researchers have succeeded in detecting structure changes, such as super rotation of the inner core and topographical variation of the inner core boundary (Song & Richards 1996; Wen 2006). Even though these seismic stations had external synchronization systems (e.g. GPS or OMEGA), clock error of some stations has been found due to hardware or software failure (e.g. Stehly et al. 2007; Xia et al. 2015). When these records are used in studies of earthquake location and seismic tomography, arrival residuals and clock error are usually pre-screened to discard travel-time residual outliers. (Hearn et al. 1991; Hearn 1999; Phillips et al. 2007; Li et al. 2012). Seismometer clock error can be detected via comparison with external timing signals (such as GPS) or using the seismic waves emitted by repeating seismic sources (Stehly et al. 2007). There are mainly two kinds of stable and continuous seismic sources, that is, seismic ambient noise and the Persistent Localized (PL) microseism events (Shapiro et al. 2006). Using the empirical greens function extracted from cross-correlation of ambient noise, Stehly et al. (2007) detected variation of surface-wave travel-times in the period bands of 5–10 s and 10–20 s between regional stations in southern California, USA (inset in Fig. 1, station distance ∼ 200 km). They found that the clock of station GSC is stable most of the time. However, in some months of 1992 it has a clock error of about 2 s. This method has also been used to detect the clock error of Ocean-Bottom-Seismometer (OBS) networks with a relatively small aperture (Sens-Schönfelder 2008; Gouédard et al.2014; Hannemann et al.2014). In addition, Xia et al. (2015) proposed a method of assessing long-term stability of station clocks using the 26 s PL signals from the Gulf of Guinea. Their method can detect clock error with an accuracy of a few tenths of a second via cross-correlation between inter-continental stations, and is applicable for seismic data in early Global Seismographic Network era, because the 26 s signal is much stronger than ambient noise in ambient Noise Cross-correlation Function (NCF) for very large interstation distances. Both methods use stacked waveforms over long time (usually one month) to enhance Signal-to-Noise Ratio (SNR), thus it is difficult to detect the short-term change (e.g. in 1 d) of the instrumental clock. Figure 1. View largeDownload slide Distribution of the stations (triangles), earthquakes (circles) and the 26 s PL microseismic source of the Gulf of Guinea (diamond). Inset shows zoomed in map of stations in California, USA. The open circles are earthquakes within 30° and 100° from station GSC, with magnitude above 5.5. Red circles indicate two earthquakes with waveforms displayed in Fig. 6. One is a local earthquake in California on 1992 June 24 with magnitude of 3.1, and the other is a teleseismic earthquake in Fiji on 1992 June 9 with magnitude of 5.6. Figure 1. View largeDownload slide Distribution of the stations (triangles), earthquakes (circles) and the 26 s PL microseismic source of the Gulf of Guinea (diamond). Inset shows zoomed in map of stations in California, USA. The open circles are earthquakes within 30° and 100° from station GSC, with magnitude above 5.5. Red circles indicate two earthquakes with waveforms displayed in Fig. 6. One is a local earthquake in California on 1992 June 24 with magnitude of 3.1, and the other is a teleseismic earthquake in Fiji on 1992 June 9 with magnitude of 5.6. In contrast, short-term instrumental clock error can be detected using signals excited by events which occur frequently. And such events should be powerful enough to be recorded on seismic stations at large distances. Anchieta et al. (2011) compared the teleseismic P waves between close stations and corrected clock drifts of OBS. For regular and precise monitoring of clock variations, repeating moderate or strong earthquakes for the same source region are required. Otherwise, events from different regions might cause inaccuracy from the heterogeneity of the Earth structure. Besides the frequent natural earthquakes, the PL microseism sources also generate strong seismic signals (Shapiro et al. 2006; Zeng & Ni 2010). For example, Oliver (1962, 1963) found that the 26 s source was particularly strong on 1961 June 6–8, then it merged into background noise. He named these abrupt increasing in amplitude as “storm” of microseism and we refer to them as burst events. However, later studies indeed demonstrated its persistent nature, with episodic strong amplitude and weak excitation in other time (Xia et al. 2013). They behave more or less like repeating events with variable excitation strength, which could be used to monitor short-term clock variation (Shapiro et al. 2006; Zeng & Ni 2010; Xia et al. 2013). In this study, we use the burst signal of PL 26 s source to detect the short-term clock error of GSC station (Fig. 1) in 1992. We begin with calculating the NCF between GSC and a reference station (OBN, Scripps Institution of Oceanography 1986) to get the PL 26 s signal. Burst events are selected with high SNR. The waveforms of all burst events are stacked to obtain a reference waveform. We then measure the differential time between each burst waveform with the reference to detect the clock error. A drastic clock change in June is found, and verified with teleseismic and regional P waves. In the end, we discuss the limitation of this method and its applicability to OBS clocks. 2 INSTRUMENTAL CLOCK ERROR DETECTION USING 26 S PL SIGNAL A few PL microseism sources have been identified on the Earth, for example, the 26 s PL source in the Gulf of Guinea (Fig. 1; Oliver 1962; Holcomb, 1980, 1998; Shapiro et al. 2006; Xia et al. 2013), the 26 s PL source near Vanuatu Island (Zeng & Ni 2014) and the 7–15 s source on Kyushu Island (Zeng & Ni 2010). Among them, the 26 s PL source in the Gulf of Guinea is the strongest one, which is suitable for clock error detection. When burst events occur, this signal can be detected almost all over the globe, especially in Europe and North America (Oliver 1962; Xia et al. 2013). The excitation mechanism of this PL source is still unknown, which is usually attributed to the volcanic process, though oceanic processes have also been proposed to explain its variability in strength (Shapiro et al. 2006; Xia et al. 2013). To demonstrate characteristics of the 26 s PL source, we display ambient noise spectra of stations GSC in Southern California and OBN (IRIS/IDA) in Russia (Fig. 2). The spectra of these two stations are calculated for the same time span. On 1992 May 5, there is a sharp peak at the frequency of 0.038 Hz (26 s). Frequency band of the signal is very narrow, around 0.001 Hz. It distinguishes itself from the weak background spectrum around period of 30 s in the New Low-Noise Model (Peterson 1993). The amplitude of this signal is not constant, and sometimes it is relatively weak (e.g. on 1992 February 16). And occasionally, it becomes strong and can be observed on raw long period seismograms at a global scale, which implies it could be as strong as a M5 earthquake (Oliver 1962). Recent study shows that the burst excitation mode usually lasts hours (Xia et al. 2013). Figure 2. View largeDownload slide Spectra of noise records for stations GSC and OBN. (a,b) Spectra of GSC on 1992 February 16 and May 5, respectively. (c,d) Spectra of OBN on the same days. The length of the ambient noise records are 3 hr long, beginning at 12:00:00 (UTC). The grey area specifies the narrow frequency span of 0.037–0.039 Hz. Figure 2. View largeDownload slide Spectra of noise records for stations GSC and OBN. (a,b) Spectra of GSC on 1992 February 16 and May 5, respectively. (c,d) Spectra of OBN on the same days. The length of the ambient noise records are 3 hr long, beginning at 12:00:00 (UTC). The grey area specifies the narrow frequency span of 0.037–0.039 Hz. Based on the persistence and localization of this 26 s signal, Xia et al. (2015) demonstrated feasibility of using it to detect the long-term instrumental clock error. One month-long NCFs are calculated between inter-continental stations. They measured the differential time between NCF waveform with a reference NCF which is obtained with yearly stacking. But their method cannot resolve clock problems shorter than one month. Stehly et al. (2007) found there are gradual clock drift of GSC station in April, May and June of 1992, and we suspect that short-term clock drift might have existed. Thus, we take the records of station GSC in 1992 as an example to assess the performance of its clock. Both Stehly et al. (2007) and Xia et al (2015) studied the stability of a seismometer clock with respect to other high-quality stations. In this study, we choose the station OBN in Russia as the reference station, which records clear 26 s PL signal (Fig. 2) and its clock is stable with variance of a few tenths of a second (Engdahl & Ritzwoller 2001; Wen 2006; Xia et al. 2015). From IRIS/DMC, we download the continuous vertical component broadband waveform data in 1992 and 1993 for stations GSC and OBN. Previous studies found that GSC station clock worked normally in 1993 (Stehly et al2007; Xia et al. 2015), thus we take the NCF between GSC and OBN for entire year 1993 as reference waveform for measuring clock drift in 1992. Mean, trend and instrumental response are removed from the raw data. The sampling rate of the raw data is 20 samples per second (sps), and we interpolate it to 100 sps to improve precision of clock measurement. The continuous waveform data are cut into short segments, either daily or a few hours, as detailed later. SNR of the signal in NCF usually correlates with the length of the waveform record (Yang et al. 2007): longer seismic noise records result in higher SNR. However, there is a trade-off between the accuracy of temporal variation measurement and the SNR of NCF. With more NCFs stacked together, the clock drift could be more smeared. As the duration of the 26 s PL bursting mode is about a few hours (Xia et al. 2015), we calculate the NCFs with different length of records, and find that reliable signals in NCF can be achieved with waveform segment length as short as 3 hr with 50 per cent overlapping. In the following processing steps, we calculate both 1 d and 3 hr long time-domain NCFs to explore the trade-off between window length and measurement precision. Before NCF calculation, we apply running absolute mean time-domain normalization to the waveform data with band-pass filtered in the frequency range of 0.02–0.05 Hz (Bensen et al. 2007). Through comparing different time-domain normalization methods, Bensen et al. (2007) found that the running absolute mean normalization is robust to suppress the interference of irregular signals (e.g. glitches) or strongly correlated signals (e.g. earthquakes). In order to extract broadband surface waves, frequency-domain whitening is usually applied after the time-domain normalization in previous studies. However, if the frequency-domain normalization is applied, the signal of 26 s is also suppressed, just like earthquakes. Instead, we calculate the NCF in this study without frequency-domain whitening. A few examples of daily NCFs are shown in Fig. 3. On some days, almost no 26 s signal can be observed in both time and frequency domains (e.g. 1992 January 17). However, on the other days, the 26 s signal waveforms are quite obvious in both time and frequency domains (e.g. 1992 May 5). The signal arrives around 1600 s in the positive lag of the NCF. Previous studies proposed that the 26 s PL source is located in the Gulf of Guinea (latitude ∼ 0.20°N, longitude ∼6.58°E, Fig. 1) (Xia et al. 2015), which is closer to OBN than GSC with about 6000 km difference. Assuming the Rayleigh wave group velocity of 3.8 km/s (Xia et al. 2013), the 26 s signal would show up around 1600 s in the NCF between OBN and GSC (positive lag), which is consistent with the observation. To quantify the observed 26 s signal on NCFs, we compute its SNR. The SNR is defined as the ratio between the maximum amplitude of the 26 s signal and the maximum amplitude of the background noise. It can be observed that the 26 s signal lasts more than 1000 s on NCFs, which is consistent with its very narrow band (±0.001 Hz) (Fig. 3), according to the uncertainty principle of the data processing (Donoho & Stark 1989). We take a time window of 1200 s around the peak of the 26 s signal to define its amplitude. For example, the 26 s signal on 1992 May 5 is very pronounced with a SNR of 2.8 (Fig. 3). Figure 3. View largeDownload slide The Daily NCFs (left column) and spectra (right column) between OBN and GSC. Dates of the waveform data are displayed in the upper left corner. Figure 3. View largeDownload slide The Daily NCFs (left column) and spectra (right column) between OBN and GSC. Dates of the waveform data are displayed in the upper left corner. We calculate the SNR of the 26 s signals on daily and 3 hr long NCFs for the year of 1992 (Fig. 4). The SNRs for both daily and 3 hr long NCFs are mostly around 1.0, but on occasions they have higher SNR. For example, when SNR is above 2.0, the burst event of the 26 s signal can be observed. The burst events are mostly observed in June, and in February, April, May and July, the burst event occurred with duration time up to 1–2 d (e.g. February 15–16; April 9; May 30–31; July 25–26), which is consistent with those reported by Xia et al. (2015). In Fig. 4, we also show some typical NCFs with different SNRs. The signal with SNR above 1.3 and less than 2 is still recognizable. During the clock error detection, we use 31 NCFs with SNR above 1.3. The moving crosscorrelation is used to measure the time shift of each NCF with high SNR 26 s signals with respect to the reference NCF waveform. We calculate crosscorrelation between each daily NCF and the reference NCF and allow time shifts of up to 30 s, with a time step of 0.01 s. The clock drift is determined from the time when Crosscorrelation Coefficient (CC) achieves maximum (Hauksson & Shearer 2005). To ensure the final quality of the reference NCF, it was computed by stacking the daily NCFs of 1993 with SNR > 1.3 (Fig. 3e). During measurement of clock drift with cross-correlation, the reference waveform window is set to be 1600 s long and centred at the maximum amplitude of the 26 s signal, so as to include most of the 26 s signal wave train. To ensure the quality of clock drift detection, we only keep the measurements with CC above 0.90. Moreover, we also stack the NCF monthly, and measure the clock variation for a comparison with the results by Stehly et al. (2007). Figure 4. View largeDownload slide SNR of the 26 s signal in NCFs (left column) and some example NCFs (right column). (a) SNR of the 26 s signal SNR for daily NCFs (black dots) and 3 hr NCFs (red dots) in 1992. Black and Red dashed lines show the SNR with mean plus two standard error for daily and 3 hr NCFs, respectively. (b)–(e) are the daily NCFs on January 17, April 10, June 10 and July 24, respectively. Figure 4. View largeDownload slide SNR of the 26 s signal in NCFs (left column) and some example NCFs (right column). (a) SNR of the 26 s signal SNR for daily NCFs (black dots) and 3 hr NCFs (red dots) in 1992. Black and Red dashed lines show the SNR with mean plus two standard error for daily and 3 hr NCFs, respectively. (b)–(e) are the daily NCFs on January 17, April 10, June 10 and July 24, respectively. 3 RESULTS The clock variation of GSC station in 1992 with respect to station OBN is displayed in Fig. 5(a). Our measurement (blue dots) with monthly NCF shows small variation of time shift within 0.5 s most of the time, and the clock drift is up to 3 s from April to June. The measurements using burst events of the 26 s PL signal are consistent with the monthly stacked results for most of the months in 1992, implying GSC clock drifts very little or smoothly during the time span. However, in the beginning of June, the daily clock error varies dramatically, for example, from -10, to 8 s, which is not seen in monthly NCF measurements. Probably the monthly NCF smeared the abrupt changes of station clocks, thus leading to much smaller clock drift as compared to daily detection results. Figure 5. View largeDownload slide Clock drift for station GSC in 1992 (a) and June 1992 (b). (a) Black dots are results measured using daily burst events of the 26 s PL signal, green dots are the arrival time differences between GSC and PFO using teleseismic P wave. Red dots are results from monthly NCF measurements and the grey line shows the monthly averaged clock drift between GSC and PFO by Stehly et al. (2007). (b) Black cycles are results measured using 3 hr long burst events NCFs and green diamonds and red stars are shifted up and down by 26 s. Blue diamonds and circles are the clock difference between GSC and PFO and between GSC and PAS using teleseismic P wave, respectively. Dashed ellipses mark measurements on 9, 11, 13, 21 and 23 of June. Figure 5. View largeDownload slide Clock drift for station GSC in 1992 (a) and June 1992 (b). (a) Black dots are results measured using daily burst events of the 26 s PL signal, green dots are the arrival time differences between GSC and PFO using teleseismic P wave. Red dots are results from monthly NCF measurements and the grey line shows the monthly averaged clock drift between GSC and PFO by Stehly et al. (2007). (b) Black cycles are results measured using 3 hr long burst events NCFs and green diamonds and red stars are shifted up and down by 26 s. Blue diamonds and circles are the clock difference between GSC and PFO and between GSC and PAS using teleseismic P wave, respectively. Dashed ellipses mark measurements on 9, 11, 13, 21 and 23 of June. To validate our results, we compare the clock errors with those from Stehly et al. (2007), which is measured from changes of surface-wave arrival in monthly NCFs (Fig. 5a). Stehly et al. (2007) found that the clock between PFO and PAS (close to GSC, see Fig. 1) is consistent, while GSC has a systematic clock drift of ∼0.875 s with respect to PFO and PAS. For our comparison, the baseline drift of theirs is removed. Except June, our daily and monthly clock errors are consistent with those of Stehly et al. (2007), suggesting that GSC clock only drifted little and smoothly. In June, the drastic variation of clock error is not observed in their result that shows a gradually decreasing clock drift. This is generally consistent with our monthly result, which have similar averaging processing. The period band that they used is 5–10 s and 10–20 s, which is different from our monochromatic 26 s, and may cause some bias. We can also use P wave of teleseismic events to verify the short-term clock error of GSC, similar to the work of Anchieta et al. (2011). Here we take advantage of double difference of the P-wave arrival time. The double difference refers to differential P-wave arrival time anomalies between two seismic stations, which can eliminate the error caused by the earthquake mislocation, inaccurate origin time and uncertainty of the velocity model. The double differenced time includes contribution from two factors, the time difference caused by local velocity heterogeneity and the clock drift between the station pair. The time difference caused by the 3-D structure usually does not change temporally, and the variation of the double differenced time would indicate clock change. During the double difference calculation, a close reference station is needed. Following Stehly et al. (2007), we take PFO and PAS as reference stations, which are located within 200 km from GSC (Fig. 1). The P-wave waveform data of 248 earthquakes with magnitude above 5.5 from PDE/USGS earthquake catalogue are downloaded from IRIS data management centre. The epicentral distance of these earthquakes is within 30°–100° (Fig. 1) to avoid rapid change of P-wave slowness due to upper mantle triplication or D″ effects. We use the IASP91 Earth model to calculate theoretical P arrival time. The residual between the observed and theoretical P-wave arrival time is usually less than 2 s (Kennett & Engdahl 1991), and larger residual might hint clock problems. To measure the differential time between station pair more accurately, we also adopt the cross-correlation approach. Figs 6(a)–(f) displays an example to demonstrate the procedures of teleseismic P-wave cross-correlation. The waveforms, band-pass filtered in the frequency band of 0.5–2 Hz, are from an M5.6 earthquake occurring in Fiji-Tonga region on 1992 June 9. A crosscorrelation time window of 12 s is used, including 4 s before P wave to account for 3-D heterogeneity of the Earth and 8 s after P wave to account for source duration of the earthquake. For example, the P-wave residual for station PAS and PFO is within 0.5 s (Figs 6a, b), implying that the clocks for these two stations work normally. However, the P-wave residual between GSC and PAS, or between GSC and PFO is about 17 s, too large for 3D heterogeneity of the Earth. Figure 6. View largeDownload slide Clock drift identification using teleseismic P-wave waveform via cross-correlation (a,f) and regional P-wave waveform. (a,c,e) waveforms are aligned on theoretical P travel-time. (b,d,f) The top trace is aligned on theoretical P arrival and is used as reference trace. The bottom traces are aligned according to time shift measured with cross-correlation. CC and time shift in seconds are also displayed. (a,b), (c,d), (e,f) show station pair of PAS-PFO, PFO-GSC, GSC-PAS respectively. (g) Regional P-wave waveform recorded by PAS, PFO and GSC, respectively. This M3.1 earthquake occurred on 1992 June 24 with depth of 1.1 km (Fig. 1). The waveforms are aligned with theoretical P arrival time (red dashed line). (h) Time shift corrected waveforms using crosscorrelation. Time shifts of PFO and GSC are calculated based on envelope waveforms using a time window of 1.2 s with 0.6 s before first P wave, taking PAS as reference. Figure 6. View largeDownload slide Clock drift identification using teleseismic P-wave waveform via cross-correlation (a,f) and regional P-wave waveform. (a,c,e) waveforms are aligned on theoretical P travel-time. (b,d,f) The top trace is aligned on theoretical P arrival and is used as reference trace. The bottom traces are aligned according to time shift measured with cross-correlation. CC and time shift in seconds are also displayed. (a,b), (c,d), (e,f) show station pair of PAS-PFO, PFO-GSC, GSC-PAS respectively. (g) Regional P-wave waveform recorded by PAS, PFO and GSC, respectively. This M3.1 earthquake occurred on 1992 June 24 with depth of 1.1 km (Fig. 1). The waveforms are aligned with theoretical P arrival time (red dashed line). (h) Time shift corrected waveforms using crosscorrelation. Time shifts of PFO and GSC are calculated based on envelope waveforms using a time window of 1.2 s with 0.6 s before first P wave, taking PAS as reference. We then compute the double difference P-wave arrival times to assess the clock error of GSC in 1992. To ensure accuracy of measurement, the results with larger than 5 as well as with waveform CCs bigger than 0.85 are retained with total amount of 78 events. The clock difference between GSC and PFO is also shown in Fig. 5(a). The results from teleseismic P wave are consistent with those of burst of 26 s PL at most of the time, showing little clock variation. And in June they both have drastic variations, yet, there are also obvious difference between the two sets of measurements. This could be caused by the different time window in measuring clock drift. For P-wave measurements, a short time window of a few seconds is used, while the clock measurement for the burst 26 s PL signal is made for 1 d. To make more compatible comparison, we also show the clock error measured with the 26 s signal using 3 hr long NCFs (Fig. 5b). We only retain the measurements from 3 hr long NCFs with SNR above 1.3 and CC larger than 0.85. Some of the measurements from teleseismic P wave are close to the PL results. However, others are quite different and there seems to be a difference of 26 s, for example, on 9, 11, 13, 21 and 23 of June (Fig. 5b). That is probably due to cycle skipping because the 26 s PL signal is very narrow banded and almost monochromatic in frequency (Xia et al. 2015), and this makes the series of CCs like a sine/cosine function. Thus, the maximum CC sometimes appears in multiples of 26 s away from the true value. To test this hypothesis, we calculated the time shift with one cycle before or after the maximum CC measurement in the cross-correlation. The results with one cycle correction are consistent with the results from P wave (Fig. 5b), implying the mismatch between the result from PL signal and P wave is due to the cycle skipping. The consistence of the result for PL signal and P wave confirms the drastic clock change of GSC station in June 1992, and its error is up to 25 s. But the rapid clock change is not detected using monthly stacked NCFs. 4 DISCUSSION To identify the obvious clock error, we can also use the P wave from local or regional earthquakes. An earthquake with M3.5 occurred within 1° close to GSC on June 24, with focal depth of 1.1 km (Fig. 1). We calculate the theoretical P arrival time based on Western US crustal velocity model (WUS; Herrmann et al. 2011) for GSC, PAS and PFO, respectively. The research by Hauksson et al. (2000) shows that the P-wave time residual in California is usually within 2 s, implying that a larger residual could be caused by clock error. The raw and time shift corrected earthquake waveforms are displayed in Figs 6(g,h). The P-wave arrival residuals for stations PAS and PFO are within 0.5 s, suggesting the velocity model and the station clocks work well. However, for station GSC, the observed P-wave arrives about 23.0 s earlier than the theoretical arrival time, implying a large clock error. This clock error is consistent with measurement from both the teleseismic P wave and the burst of 26 s PL signal, confirming again the observation of the drastic clock error. We have demonstrated that the short-term clock error can be detected using the burst energy of 26 s PL source. However, the burst events do not occur regularly, but randomly with the durations varying from hours to 1 or 2 d. Thus, the measurements of clock variation are only on some random time period. Based on the daily NCFs, the number of high SNR burst events are about 5 per cent of the whole year, which hinder us from continuous measurements of clock error. More short-term clock errors can be obtained combining PL source and teleseismic P waves. It is also worthwhile to determine the accuracy of clock drift detection with the burst event of 26 s source. With ambient noise correlation at local distances, Stehly et al. (2007) was able to achieve an accuracy of 0.2 s in detecting clock errors. We assess the accuracy of clock variation with the 26 s PL signal via computing standard deviations. Assuming the GSC station clock only changed slowly in year 1992 for months other than April to June, we can measure multiple clock errors with 3 hr NCFs, for those days when the 26 s PL is strong. During the calculation, we discard the measurements with NCF having SNR smaller than 1.3 and the CC smaller than 0.9 with the reference waveform, so as to retain only the reliable measurements. It is found that during each day when burst of the PL source occurred, the measurements are relatively stable. The average of the standard errors is about 0.3 s, a little inferior to the 0.2 s accuracy of Stehly et al. (2007). This is not surprising, as the latter is measured over longer time span (one month) while the former is measured daily or in a few hours, again echoing the trade-off between temporal resolution versus accuracy of measurement. Location variation of the 26 s source might influence measurement of clock drift. In order to investigate this issue, we measure the clock variation of station PAS and PFO which are in the same network (TERRAscope) as GSC (Fig. S1). The clock drifts are calculated using the same procedure as for the station GSC. Taking the stacked NCF of the year 1993 as reference NCF, we calculate the time shift between each 3 hr NCFs with the reference waveform using cross-correlation. We observe that the clock drift for station PAS and PFO are mainly close to zero with standard deviation of 0.5 s, and become more stable with increasing CC (Fig. S1). It implies that the location of this 26 s PL source is relatively stable, but it still remains possible that the source location changes. More regional stations and longer seismic records are needed to estimate the location change of this microseism source. As compared to the 0.3 s accuracy for station GSC, the accuracy for PAS and PFO is relatively larger (0.5 s), probably due to further distance of GSC from coast line. The accuracy seems to be related with SNR of 26 s signal in NCF (Fig. S1). Better accuracy can be achieved with higher CC (e.g. 0.99), but less measurements will become available. Overall, this method is probably reliable up to 0.5 s. Although, it is less accurate than Stehly et al. (2007), this method could still be helpful for both global tomography and global earthquake location. For global tomography, travel-time residual after inversion is usually 1.0 s for P wave or even larger for S wave (Spakman et al. 1993). Part of the residual could be caused by inaccurate clock, error in earthquake origin time, or unmodelled 3-D structure. For earthquake location, a clock drift of 0.5 s corresponds to location error of 3–5 km (assuming locating using P wave with apparent traveling velocity of 6–10 km/s), which is relatively small compared with the accuracy of earthquake location of global earthquake catalogs (about 15 km) (Kagan 2003). 5 CONCLUSION In this study, we find that the burst events of the 26 s PL source can be used to detect short-term instrumental clock error for global stations with distances of thousands of kilometres. In April and May of 1992, the clock of GSC station showed gradual drift with the error increasing to 3 s. From June 9, drastic clock error occurred, and was in the range of 25 s, returned to normal in July. We validate the clock error using double difference P-wave arrival time of teleseismic events. The drastic clock error in June is also confirmed by the P wave of a regional earthquake. This method can be used to detect the clock error for seismic station with large station distances, especially in early 1990s when the seismic stations are sparsely distributed. It may also be used to detect the clock error of modern OBS. But the 26 s PL signal seems to azimuth dependent, with stronger signal towards northern Atlantic and weaker towards southern Atlantic (Shapiro et al. 2006). Therefore, it might be very useful for OBS in northern Atlantic. However, due to the limitation of the accuracy, cycle skipping and measurement discontinuity, other methods are needed (e.g. local/teleseismic P waves) to get a continuous and high-accuracy assessment of clock error. Acknowledgements All seismomic data acquired are archived at the Incorporated Research Institutions for Seismology Data Management Center (IRIS DMC) at http://www.iris.edu/dms/dmc/. 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Google Scholar CrossRef Search ADS   SUPPORTING INFORMATION Supplementary data are available at GJI online. Figure S1. Clock drifts for station PAS, PFO using 3 hr long NCF burst event of 26 s signal with different cut-off CC. Figure S2. SNR histogram of 26 s signal for 3 hr long NCFs between OBN and GSC with (red) or without frequency domain whitening (black). (a) Histogram of all data. (b) Histogram for SNR above 3. Please note: Oxford University Press are 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: Jan 1, 2018

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