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It is well known that direct surface waves of large earthquakes are capable of triggering shallow earthquakes and deep tremor at long-range distances. However, it is not clear whether multiple surface waves circling the Earth could also trigger/modulate seismic activities. Here we conduct a systematic search of remotely triggered microearthquakes near the Coso Geothermal Field in central California following the 2010 Mw 8.8 Chile earthquake. We find a statistically significant increase of microearthquakes in the first few hours after the Chile mainshock. These observations of apparently delayed earthquake triggering do not follow the Omori-law decay with time since the largest ML 3.5 event occurred during the large-amplitude Love waves. Instead, they are better correlated with the first three groups of multiple surface waves (G1 − R1, G2 − R2, and G3). Our observation provides an alternative explanation of delayed triggering of microearthquakes at long-range distances, at least in the first few hours after large earthquakes.
Due to the finiteness of the Earth, surface waves produced by large earthquakes can circle the globe many times [e.g., Stein and Wysession, 2003]. They are denoted as Gn for Love waves, and Rn for Rayleigh waves. The index n denotes the time taken to circle the Earth, with the odd number (G1, G3, etc) corresponding to the shortest path between the source and receiver and the even number (G2, G4, etc) denoting the opposite path. Figure S1 of the auxiliary material shows the record sections for vertical displacement seismograms generated by the Mw 8.8 earthquake that occurred offshore Maule, Chile on 2010/02/27. The R1 to R4 Rayleigh waves are clearly visible, and have peak amplitudes on the order of a few fraction of a centimeter. The associated peak ground velocities for the multiple surface waves is on the order of 0.01 cm/s, which corresponds to a dynamic stress of ∼1 kPa (assuming a nominal phase velocity of 4 km/s and shear rigidity of 40 GPa). These numbers are close to the apparent triggering threshold of a few kPa found from recent systematic studies of triggered microearthquakes and tremor around the world [Brodsky and Prejean, 2005; Peng et al., 2009; Aiken et al., 2010; K. Chao et al., Remote triggering of non-volcanic tremor around Taiwan, submitted to Geophysical Journal International, 2010], suggesting that the later arriving multiple surface waves could have the potential of triggering/modulating microearthquakes.
To test this hypothesis, we examine the continuous seismic recordings near the Coso Geothermal Field (CGF) in central California (Figure 1) ∼12 hours before and after the 2010 Mw 8.8 Chile earthquake. We choose this region mainly because it is one of the most seismically active regions in California [Bhattacharyya and Lees, 2002], and is repeatedly triggered by large regional and teleseismic earthquakes [e.g., Prejean et al., 2004; Aiken et al., 2010]. In particular, Peng et al.  found 4 ML ≥ 2 events listed in the Southern California Seismic Network (SCSN) catalog during the passage of the teleseismic waves of the 2010 Chile mainshock, including an ML 3.5 event that coincides with the 200-s mantle Love wave. In this work, we extend our previous study by manually picking local earthquakes from band-pass filtered seismograms in a longer time frame and examining the correlations with the multiple surface waves produced by the 2010 Chile mainshock.
2. Analysis Procedure
The analysis procedure generally follows that of Peng et al.  and is briefly described here. We use the continuous three-component seismograms recorded by the broadband station JRC2 in the CGF in this study. We first remove the instrument response, integrate into displacement, demean and detrend the displacement data, and then apply a two-pass 4th-order 2–16 Hz Butterworth filter to remove long-period teleseismic signals. We compute the envelopes of the band-pass filtered seismograms, smooth the envelope by a mean operator with a half width of 50 data points (0.5 s), and finally stack the three-component envelopes. Next, we identify earthquakes as high-frequency impulsive seismic energy in the 2–16 Hz band-pass filtered seismograms and double picks in the envelope that correspond to the P and S arrivals. To ensure that the identified events are of local origin, we require that the S − P time for each event is less than 5 s, which roughly corresponds to the epicentral distance of ∼40 km. Next, we find the peak amplitude for each event and use the time corresponding to the peak amplitude as a proxy for the event origin time, as was done by Peng et al. . The actual origin time would be a few seconds earlier, but such a difference is negligible in the following analysis. Overall, we have identified a total of 116 events (Figure 2a) within 12 hour before and after the theoretical P arrival of the Chile mainshock (742.4 s after the origin time 2010/02/27, 06:34:14 UTC), as predicted by the iasp91 model [Kennett and Engdahl, 1991].
It is well known that a ten-fold increase in amplitude generally corresponds to one unit increase in magnitude. Therefore, the measured peak amplitudes of the 116 manually picked events provide good estimation for their magnitudes. Figure 2b shows the magnitude-amplitude relationship for 15 events that are also listed in the SCSN catalog. The magnitudes and log10(amplitudes) follow the 1-1 slope, and the best fitting relationship is M = 0.977 × log10(A) + 6.32, where M is the inferred magnitude, and A is the peak displacement in cm. We use this relationship to convert the peak displacements of all events into magnitudes, without considering the effects of epicentral distances. The median value of the log10 envelope function is −7.32, which roughly corresponds to the inferred magnitude −0.83, denoting the smallest possible events we can identify from this procedure. The manually picked events generally follow the Gutenberg-Richter frequency-size relationship, but the corresponding b-values (Figure 2c) from both least-squares fitting and maximum-likelihood estimates are very low (<0.5). These numbers, however, are marginally within the 1-standard deviations of the b-values estimated directly from the events listed in the SCSN catalog around the occurrence time of the Chile mainshock (Figure S2), suggesting that the low b-value found in this study is not purely an artifact of misidentification of smaller events. The magnitude of completeness Mc value, which is the largest magnitude between those determined from the maximum curvature (MAXC) and the goodness-of-fit (GOF) methods [Wiemer and Wyss, 2000], is −0.4. We only use 99 events with M ≥ Mc value in the subsequent analysis.
3. Relationship Between Local Events and Multiple Surface Waves
Figure 3 shows a comparison of the envelope functions, manually picked events, and the displacement seismograms recorded at station JRC2 around the Chile mainshock. The time windows associated with the group velocities of 4–5 km/s and 3.5–4.5 km/s roughly correspond to the arrivals of the Gn and Rn waves, respectively. We find that nine events occurred between the teleseismic S wave and immediately after the G1 and R1 waves (∼1300–∼3500 s, with 4 listed in the SCSN catalog), as reported by Peng et al. . This is followed by a relative quiescence between ∼3500 and ∼5600 s. There is a strong burst of activity between ∼5600 and ∼7500 s during the G2 waves, and two earthquakes during the subsequent R2 waves between ∼7500 and ∼9000 s. Following these events, there is another brief period of quiescence, and then a strong burst of activity during and immediately after the G3 waves between ∼10500 and ∼12500 s. No clear seismic activity is observed during the R3 waves (i.e., from ∼12500 to ∼14000 s). After that, we could not identify any further correlations with the subsequent Gn and Rn waves. A swarm-like activity occurred about ∼27000 s after the mainshock and does not appear to have any correlations with the teleseismic surface waves (Figure 2).
To further quantify the relationship between the manually picked events and multiple surface waves, we perform two types of statistical analysis. First, we compare the seismicity rate immediately before and after the P wave of the Chile main shock and compute the β-statistic value [e.g., Kilb et al., 2002], which is a measure of the difference between the observed number of events after the main shock and the expected number from the averaged rate before the main shock. The β-value for all the events is 3.4, while the β-value for events above the Mc value is 2.4. Both numbers are slightly above 2, suggesting that there is a moderate increase of seismic activity near Coso following the Chile main shock.
Next, we compute the β-value using a small time window of 1000 s, and slide every 500 s after the teleseismic P waves. The choice of the window length is somewhat subjective, which reflects a compromise between a long-enough window for stable measurements and short-enough window for detailed information. The results from this and other choices of time windows ranging from 500, 2000, to 3000 s (Figure S3) show that the β-values generally track the number of events and are above 2 during the first three groups of the multiple surface waves, suggesting a statistically significant triggering. The β-value during the G4 and R4 waves is less than 2, and hence the apparent triggering is not well established. In addition, the expected β-value outside the multiple surface wave periods is −1.02 when no events occur (Figure S3).
In the second method, we directly measure the β-value from the band-pass filtered envelope functions [Jiang et al., 2010] by summing the log10 amplitudes in different time periods that are above 9 times the maximum absolute deviation (MAD) of the envelope functions (i.e., above −6.6, or inferred magnitude of −0.13). The resulting β-values (Figure 3a) show similar patterns, although the fluctuations are much larger due to the heavy weight towards large-magnitude events. Nevertheless, it is evident from both approaches that there is an apparent correlation between the multiple surface waves of the Chile earthquake and the local seismicity near Coso, at least for the first three groups.
The largest magnitude earthquake during our study period is an ML 3.5 event that occurred during the large-amplitude Love wave [Peng et al., 2010]. To check if the subsequent events could simply be aftershocks of this event [Brodsky, 2006], we compute the seismicity rate relative to this ML 3.5 based on a sliding window technique with a fixed data window of 5 events [Peng et al., 2007]. Figure 4 shows that while the events during the G1 and R1 waves could be considered as aftershocks of the ML 3.5 event (however, with only 3 data points, it is not clear), the events occurred during the subsequent multiple surface waves and the swarm period do not follow the Omori law decay. Hence, these events could not be simply explained as aftershocks of the directly triggered events.
In this short note we showed that multiple surface waves from the 2010 Mw 8.8 Chile earthquake trigger/modulate microearthquake activity at the CGF in central California. To our knowledge, this is the first evidence of earthquake triggering by multiple surface waves, in addition to the abundant observations of triggering from the direct G1 and R1 waves [e.g., Hill and Prejean, 2007]. A few studies in the past have focused on the potentials for free oscillations of the Earth to trigger foreshocks [Costello and Tullis, 1999] or aftershocks [Kamal and Mansinha, 1996], and the results were not consistent. These studies might be relevant to our work if multiple surface waves could be considered as specific modes of free oscillations [e.g., Stein and Wysession, 2003].
Our observations (e.g., Figure 4) suggested that the microearthquake activity in the first few hours at CGF did not follow an Omori's law decay with time since the direct surface waves of the 2010 Chile main shock (i.e., the G1 and R1 waves). Instead, their occurrence times match well with the arrivals of the multiple surface waves circling the Earth (Figure 3). This provides an alternative explanation for the delayed triggering at long-range distances, at least in the first few groups of the multiple surface waves (G1 − R1, G2 − R2, and G3). In this case, the time delay is produced by the propagation of multiple surface waves, rather than at the triggered site as previous models have suggested [Brodsky and Prejean, 2005; Parsons, 2005; Brodsky, 2006; Shelly et al., 2011].
It is worth noting that such effects would probably only work for very large earthquakes (e.g., Mw ≥ 8.0) that are capable of producing multiple surface waves circling the Earth with large-enough amplitudes. Hence, it cannot be applied to explain all observations of delayed triggering. In addition, the triggering effects from multiple surface waves would be most apparent in the first few groups because of the decaying amplitudes and dispersion (Figure 3). The peak displacement and velocity measured during the G3 waves are ∼0.56 cm and 0.017 cm/s, respectively, which corresponds to a dynamic stress of 1.7 kPa. This value is close to the aforementioned triggering thresholds for tremor and microearthquakes found elsewhere [Peng et al., 2009; Aiken et al., 2010; Chao et al., submitted manuscript, 2010], suggesting that the lack of triggering by later arriving surface waves could be due to their small amplitudes.
An interesting distance range for observing triggering by multiple surface waves is at 180° (antipodal distance) or 360° (epicenter). Because the surface wave amplitudes are larger at these distance ranges due to a superposition effect (e.g., Figure S1), we would expect to see higher potential of triggering by multiple surface waves. Recently, Lin  found that one of the large aftershocks of the 2008 Mw 7.9 Wenchuan earthquake occurred during the large-amplitude ScS wave, and proposed that teleseismic waves returning back to the epicentral region could modulate aftershock activity. It remains to be tested whether the multiple surface waves returning back to the epicentral region have the same potential of triggering additional aftershocks. This is an interesting subject that will be analyzed in a follow-up study.
The seismic data and earthquake catalog used in this study are downloaded from the Southern California Earthquake Data Center (SCEDC). We thank Aaron Velasco, an anonymous reviewer, and the editor Ruth A. Harris for their useful comments. This study was supported by the National Science Foundation through award EAR-0956051.