Capability of Tokai Strainmeter Network to Detect and Locate a Slow Slip: First Results
The Tokai Strainmeter Network (TSN), a dense network deployed in the Tokai region, which is the easternmost region of the Nankai trough, has been designed to monitor slow slips that reflect changes in the coupling state of the plate boundary. It is important to evaluate the current capability of TSN to detect and locate slow slips. For this purpose, the probability-based magnitude of completeness developed for seismic networks was modified to be applicable to the evaluation of TSN’s performance. Using 35 slow slips having moment magnitudes M5.1–5.8 recorded by TSN in 2012–2016, this study shows that the probability that TSN detected and located a M5-class slow slip is high (> 0.9) when considering a region in and around the TSN. The probability has been found to depend on the slip duration, especially for M5.5 or larger, namely the longer the duration, the lower the probability. A possible use of this method to assess the network’s performance for cases where virtual stations are added to the existing network was explored. The use of this application when devising a strategic plan of the TSN to extend its coverage westwards is proposed. This extension that allows TSN to cover the entire eastern half of the Nankai trough is important, because the historical records show that the eastern half of this trough tends to rupture first.
KeywordsCrustal deformation earthquake prediction fault slip plate boundary seismicity statistical methods
The Nankai trough earthquakes occurred with a return period of about 90–200 years. More than 70 years have passed since the last series of Nankai trough earthquakes occurred, the 1944 Tonankai earthquake and the 1946 Nankai earthquake, both belonging to a magnitude eight class. The possibility of large earthquakes in the Nankai trough has now increased. The earthquakes often occurred in pairs, where a rupture was followed by a rupture elsewhere: for example, the 1854 Ansei-Tokai earthquake and the 1854 Ansei-Nankai earthquake the next day, and the 1944 Tonankai earthquake, followed by the 1946 Nankai earthquake. On the other hand, the fault for the 1707 Hoei earthquake is considered to rupture along its entire length. The history of the Nankai trough earthquakes shows that the eastern half of this trough tends to rupture first (Kanamori 1972; Ando 1975; Ishibashi 2004; Working Group on Disaster Prevention Response when Detecting Anomalous Phenomena along the Nankai Trough 2018). This historical tendency, with current seismic and geodetic observation, implies that the eastern part will rupture earlier than the western part also in the next series of earthquakes, although we cannot say how long the time-lag will be (Nanjo and Yoshida 2018).
Slow slips that grow over time may result in large earthquakes, as was observed for the 2011 Tohoku-oki earthquake of moment magnitude M9 (Kato et al. 2012). As another example of a precursor phenomenon just before an earthquake occurs, tilting associated with the 1944 M8-class Tonankai earthquake has been observed (Mogi 1984). A remarkable precursory tilt started 2 or 3 days before the earthquake. The precursory amount of change corresponds to about 30% of the amount of change at the time of the earthquake. In contrast, many studies using strainmeters and tiltmeters located close to the eventual earthquakes have concluded that a precursory slip, if any, is very small, < 1%, for many California earthquakes (Wyatt 1988; Kanamori 1996) such as the 1987 Whittier Narrows earthquake (M = 6.0), the 1987 Superstition Hills earthquake (M = 6.6), the 1989 Loma Prieta earthquake (M = 6.9), and the 1992 Landers earthquake (M = 7.3).
Scholz et al. (1972) made detailed laboratory measurements on frictional characteristics of granite. In the condition where the stick–slip predominated, the stick–slip was preceded by a small amount of stable slip, which accounted for about 2–5% of the unstable slip that followed. Lorenzetti and Tullis (1989) used mechanical models of faulting during an earthquake cycle that was based on the rate- and state-dependent friction law, and predicted that the amount of pre-seismic moment release was < 0.5% of the earthquake moment for most simulations. Using a simulation of the earthquake cycle in the Tokai region, Kato and Hirasawa (1996) did not directly estimate M of a precursory slow slip. However, their result indicates that M varies, depending on values given for different parameters. Furthermore, in their earthquake-cycle simulation, it was commonly seen that remarkable abnormal crustal movements started to appear over a wide area several days to several hours before the occurrence of an earthquake.
It is difficult at present to determine M of slow slips that are precursory phenomena to the Nankai trough earthquake, but it is necessary to assume a severe situation. Based on the discussion provided above, a precursor slip would be assumed to be < 0.5–1% of the earthquake. As the Nankai trough earthquakes belong to a M8-class or larger, the final precursory slow slip with < M6–6.5 is assumed. Under this assumption, it could be of high value to detect and locate slow slips when they are still small. In this study, we estimated the capability of TSN to detect and locate a slow slip.
The approach was based on the Probabilistic Magnitude of Completeness (PMC) method, which had been developed for seismic networks (e.g., Bachmann et al. 2005; Schorlemmer and Woessner 2008; Nanjo et al. 2010; Schorlemmer et al. 2018). This study is the first to be applied to a strainmeter network. This PMC-based method relies on empirical data. Station probability (Pst), which is the probability that a station was used to detect and locate a slow slip of a given magnitude M at a given distance L, where L is distance in the three spatial dimensions, is derived. From the Pst for all stations, we obtain the probability (Pdl) of detecting and locating slow slips of M at a point (x) for three or more stations. If this method is applied to TSN, the product is a map of Pdl for M. A feedback for JMA network operators is foreseen by providing a tool to infer spatial heterogeneity of current monitoring ability. This tool will be used as a basis to help future planning for optimizing network coverage.
The Japan Meteorological Agency, with a similar motivation as that shown in this study, mapped the lower-limit M (MLL) to detect and locate slow slips in the Nankai trough (Research Committee for Forecast Ability of Large Earthquakes along the Nankai Trough 2017). This mapping calculated crustal deformation due to a slow slip of given M at a point x on the plate interface using the method of internal deformation due to shear fault in an elastic half-space (Okada 1992). The strike and dip of a fault at x were determined in such a way that the fault is a tangent plane to the plate boundary interface at x (Kobayashi 2000). The slip angle of the fault was based on the direction of plate convergence (Heki and Miyazaki 2001). If crustal deformation due to a slow slip of M at x causes strain changes that are satisfied by a criterion that the signal-to-noise ratio is larger than a predefined value at three or more stations, then this slow slip is considered to be detected and located. For each x, the MLL to be satisfied with the criterion is searched, and this is mapped at x. However, it is nontrivial to assign noise levels for each station because tidal correction (Ishiguro et al. 1984; Tamura et al. 1991), geomagnetic correction (multicomponent strainmeters) (Suganuma et al. 2005; Miyaoka 2011), and precipitation and atmospheric-pressure correction (volumetric strainmeters) (Hikawa et al. 1983; Ishigaki 1995; Gebauer et al. 2010) are applied as pre-processes for each analysis, where the geomagnetic correction is needed, because multicomponent strainmeters use magnetic sensor to measure radical deformation (volumetric ones do not use this sensor), so that the output is affected by magnetic fields. These noise levels for each station vary with time (Miyaoka and Yokota 2012). Moreover, setting a criterion of signal-to-noise ratio, for example, 2 or 3 as was done in Miyaoka and Yokota (2012), is arbitrary when calculating MLL.
The significance of this research is that a criterion was not predefined for the signal-to-noise ratio, nor was the noise level assigned to each station, even though both are critical for the computation of MLL. In other words, the Pdl computation requires no assumption once Pst is determined based on empirical data. Thus, mapping Pdl provides an alternative to mapping MLL. This adds value to the current state of the art of reliable estimation of detection-location capability of a slow slip because changes in the coupling state of the plate boundary will not be missed even if they are small from the viewpoint of disaster prevention measures. The results obtained in this study show general agreement with JMA’s results, although both methods are based on different ideas and approaches, which are outlined in the Sect. 5.
The PMC-based method relies on two sources of data: (1) station data describing the location for each station in the network; (2) the slow-slip catalogue describing the location, time, and M for each slow slip including data describing which stations were used to detect and locate this slow slip. The method is divided into an analysis part and a synthesis part. See (e.g., Bachmann et al. 2005; Schorlemmer and Woessner 2008; Nanjo et al. 2010; Schorlemmer et al. 2018) for applications to seismic networks.
2.1 Analysis Part
Pst(M, L) was smoothed by applying a simple constraint: Pst cannot decrease with smaller L for the same M (e.g., Schorlemmer and Woessner 2008; Nanjo et al. 2010; Schorlemmer et al. 2018). This smoothing accounts for high probabilities at short distances (Fig. 3b). Another constraint, namely that the smoothed probability cannot increase with decreasing M at the same distance, was not applied because imposing this constraint would lead to an overestimation of Pst(M, L).
One problem arises for stations that have never been used for event detection and location even though these stations were in operation. They were relatively far from the slow slips during the observed period (2012–2016), assuming that JMA only uses these stations if slow slips occur near them. Consequently, Pst(M, L) was assigned for all stations in operation, regardless of whether or not they have been used for event detection and location.
2.2 Synthesis Part
In the synthesis part, basic combinatorics were used to obtain Pdl(M, x) for detecting and locating a slow slip of M at location x, given a specific network configuration (e.g., Bachmann et al. 2005; Schorlemmer and Woessner 2008; Nanjo et al. 2010; Schorlemmer et al. 2018). Pdl(M, x) for TSN is defined as the probability that three or more stations detect changes in a strain associated with a slow slip of M to locate the event at x. Only two are needed if admitting that a slow slip occurs on the plate boundary interface, where the depth contours are shown by red curves in Fig. 1. However, JMA requires at least three stations (Research Committee for Forecast Ability of Large Earthquakes along the Nankai Trough 2017; Miyaoka and Yokota 2012). The minimum number of stations must be adjusted if the condition of the TSN is based on another number of stations.
If Pdl is larger than a threshold, this is considered as an indication that a slow slip will not be missed. Previous researchers (Schorlemmer and Woessner 2008; Nanjo et al. 2010; Schorlemmer et al. 2018) took several values among 0.99 ~ 0.99999 as a threshold. Given the considerable uncertainty in all phenomena such as tectonic strain accumulation, slow slips, and others in this study, the threshold needs to be as high as possible to secure that a slow slip will not to be missed. We assumed a conservative value of Pdl = 0.9999, where the complementary probability Q (= 1 – Pdl) that a slow slip will be missed is 0.0001 (= 1 – 0.9999). We avoided smaller Q because of possible computational artifacts: our preliminary study experienced that the solution often did not converge when taking Pdl = 0.99999 as the threshold.
The Japan Meteorological Agency is recording short-term slow slips in the Tokai region with the TSN, one of the densest networks in Japan, operating 11 multicomponent strainmeter stations and 16 volumetric strainmeter stations (Fig. 1). The former strainmeters are generally buried in boreholes at depths of 400–800 m, while the latter ones are in the range of 150–250 m. The station list can be obtained from JMA. Note that for the time being, there is no tiltmeter included in the TSN (Japan Meteorological Agency 2017b).
Short-term slow slips in the Tokai region release energy over a period of a few days to a week, rather than seconds to minutes which is characteristic of a typical earthquake. Long-term slow slips that slip over a period of a few months to several years were recorded by GNSS (Global Navigation Satellite System). In the Tokai region, long-term slow slips of M7.0 and M6.8 occurred in 2001–2005 and 2013–2017, respectively. Short-term slow slips can be seen at depths of about 30–40 km, down-dip side of the long-term slow slips at a depth of about 20–30 km. There is interest in knowing the capability of TSN to detect and locate small slow slips. This study used the short-term slow-slip catalog (Kimura and Miyaoka 2017), which includes 35 events for M5.1–5.8 with depths 26–41 km from 2012 to 2016 in the Tokai region (Fig. 1). Based on the slow-slip catalog and the list of strainmeter stations, data triplets were compiled.
To compute Pst(M, L), data triplets were used, each having M and L close to a given pair (M, L). Triplets were selected by measuring the distance between each triplet and pair (M, L). To measure such a distance, a metric in the M–L space needed to be defined. Schorlemmer and Woessner (2008) proposed the use of an attenuation equation for magnitude-based determination of earthquakes located in a given local seismic network, and redefined a metric in the transformed magnitude–magnitude space. In this study, we followed this idea and used the attenuation equation used by JMA (Tsuboi 1954; Schorlemmer et al. 2018). The magnitude of a slow slip is defined by the moment magnitude (M), and not by the JMA magnitude (MJMA). However, when M exceeds 5, MJMA can be considered statistically equivalent to M, while below M = 5, MJMA is smaller than M (Japan Meteorological Agency 2003; Scordilis 2005). The slow slips that were analyzed in this study had M > 5. Thus, it was assumed, for our case, that the attenuation equation used by JMA is directly applicable to define a metric in the transformed magnitude–magnitude space. Given this metric, we selected all triplets that obey the criterion of a metric smaller than or equal to 0.2, which is a usual magnitude error.
This approach assumes that single slow slips occur at different times because multiple slow slips that had occurred at different locations at the same time were not reported by JMA during 2012–2016.
Figure 3a, b show the distribution of stacked data triplets and the corresponding distribution of Pst(M, L), respectively. There is no triplet for short distances (L < 35 km) due to the distances from stations to the plate interface on which slow slips occurred. Despite this, Pst > 0.9 (dark green) is seen, irrespective of M. This is because the smoothing constraint described in Sect. 2.1 was applied. General patterns of Pst for M = 5.1–5.4 are similar to each other: there is a band of Pst ~ 0.8 (yellow) around L = 40 km, above which Pst decreases with L (red). It was observed that the patterns for M = 5.5–5.8 were different from those for M = 5.1–5.4: events of higher M can be observed at greater distances, thus Pst is higher, while events of lower M are observable only at shorter distances and thus have lower Pst at long distances L > 40 km. Before applying Pst to create the maps of Pdl, simple sensitivity checks on dependence of volumetric and multicomponent strainmeters were conducted on the distribution of data triplets, which are shown in the next section.
4.1 Sensitivity Checks on the Dependence of Volumetric and Multicomponent Strainmeters Affect Distribution of Data Triplets
4.2 Mapping Pdl in and Around TSN: Current Capability of TSN to Detect and Locate a Slow Slip
We confirmed the expectation that a region of high probabilities (Pdl ≥ 0.9) for M = 5.1–5.8 almost covers the TSN. Detailed characteristics are as follows. As expected from Pst in Fig. 3, the spatial patterns of Pdl for M = 5.1 and 5.3 are similar to each other (Fig. 8a, b). The pattern of very high probabilities (Pdl ≥ 0.9999) is spatially heterogeneous: a noticeable feature is that Pdl ≥ 0.9999 is not seen at the near-coast offshore around 137.5° E but around other longitudes. This may be due to the lack of stations around 137.5° E near the coast. Above M = 5.4 (Fig. 8c, d), the region of Pdl ≥ 0.9 increased with M. The anticipated source zone (grey chain line) of the Tokai earthquake, the easternmost segment in the Nankai trough, is covered by a region of Pdl ≥ 0.9 for M = 5.8 (Fig. 8d). When considering Pdl ≥ 0.9999 as an indication that a slow slip will not be missed, a slow slip with M ≤ 5.8 would likely be missed in a southern part of the anticipated source zone.
4.3 Dependence of Duration of a Slow Slip on Pst and Pdl: the Longer the Duration, the Greater the Difficulty in Detecting and Locating a Slow Slip
For a short duration (Fig. 9e), Pst at large distances (e.g., L > 40 km) increased with M, but it did not increase for a long duration (Fig. 10c). The difference in Pst between short duration (Fig. 9e) and long duration (Fig. 10c) is clear for M = 5.6–5.8. As expected from Pst, Pdl(M = 5.5, x) in Fig. 9c is similar to that in Fig. 10a. A comparison between Figs. 9d and 10b for M = 5.8 shows that the capability of detecting and locating a slow slip is lower for a long duration (> 5 days) than for a short duration (≤ 5 days). Changes in strain produced by a long-duration slow slip were more gradual than that by a short-duration slow slip. The former changes were more difficult to be distinguished from background levels in strain than the latter changes. This is plausibly the reason why the detection and location of a slow slip is more critical for a long duration than for a short one.
4.4 Virtual Installation of one or more Stations into TSN
To infer the effect of adding station(s) to the TSN on Pdl, scenario computations were performed by virtually placing additional stations to the network configuration. A fundamental problem is the definition of Pst that is used for individual stations installed for the virtual case. As was applied for stations that have never been used for event detection and location even though these stations were in operation, Pst(M, L) was assigned for virtual stations.
As pointed out in the “Introduction” section, it is a standard practice to make severe assumption that a precursor slip would be < 0.5–1% of the earthquake. The final precursory slow slip with < M6–6.5 to the Nankai trough earthquakes belonging to a M8-class or larger is assumed, if it exists. This assumption implies that it is not necessary for precursory slips to have an observable size (e.g., the occurrence of slips of M4-class or smaller is a possibility). Furthermore, the current study used only 35 slow slips and presented the first attempt of applying the PMC-based method to the evaluation of TSN’s performance. Thus, readers should be careful about extrapolating these results to precursory slips of a megathrust earthquake in the Nankai trough. However, if the primary purpose of the TSN is considered, it is important to monitor changes in the coupling state of the plate boundary by detecting and locating slow slips. The estimation made in this study of the capability of TSN to detect and locate a slow slip provides the first results. Future research would use much more data to constrain Pdl with sufficient certainty.
The early detection-location capability of a slow slip has not yet been considered. Data obtained by strainmeters under TSN are being monitored continuously at JMA, so that rapid earthquake information is in operation in real-time (Japan Meteorological Agency 2017a). Miyaoka and others developed a stacking method in which data at different strainmeter stations are added to increase the signal-to-noise ratio for early detection of crustal deformation associated with slow slips (Miyaoka and Yokota 2012; Miyaoka and Kimura 2016). This method, in combination with the PMC-based approach reported in this study, will lead to a more realistic evaluation of TSN’s performance regarding the early detection-location capability of a slow slip.
A conventional assessment of MLL has been applied to the entire Nankai trough (Research Committee for Forecast Ability of Large Earthquakes along the Nankai Trough 2017) by using a model assumption that the medium is elastic and that the strainmeters record elastic strain changes caused by slow slips (Okada 1992). This paper addressed a fundamental question, namely whether this PMC-based method and the conventional method gave similar results. The map of MLL for the Nankai trough was created based on the TSN operated by JMA and the network operated by AIST (National Institute of Advanced Industrial Science and Technology). Since only three AIST stations are in operation in the Tokai region, it was assumed that the spatial pattern of MLL based on this hybrid network was comparable to the maps of Pdl purely based on TSN. Values of MLL ≤ 5.8 fall in and around the hybrid network in the Tokai region, where slip duration was not taken into consideration for the MLL computation. Given that Pdl ≥ 0.9999 is an indication that a slow slip will not be missed, the probability map of M = 5.8 (Fig. 8d), where values of Pdl ≥ 0.9999 fall in and around TSN, shows consistency with the MLL map. When a small magnitude (M = 5.5) was assumed, this again demonstrated general agreement between the region of Pdl ≥ 0.9999 (Fig. 8c) and the region of MLL ≤ 5.5, although detailed differences in patterns demonstrate that the former region spreads wider toward offshore at 138.0–138.5° E than the latter region. Regardless of the different approach used in this study relative to a conventional approach, the results were generally similar to each other. However, these constitute the first results that need to be supported by much more data in future.
Monitoring changes in the coupling state of the Nankai trough plate boundary may provide researchers with qualitative information on the increased (or decreased) possibility of the occurrence of an impending large earthquake (Japan Meteorological Agency 2017a). It is important to estimate the coupling state through the occurrence of slow slips. Moreover, for such an estimation, it is vital to reliably evaluate monitoring ability of slow slips, as was shown in this study and in a previous study (Research Committee for Forecast Ability of Large Earthquakes along the Nankai Trough 2017). However, forecasting M and timing of an earthquake involves large uncertainty from a scientific viewpoint. For example, if slow slips have a duration of 5 days, could there be knowledge about “precursor” to the eventual great earthquake that might occur after these 5 days or later? In other words, what is the time span until the eventual one would happen? Based on the present research, we cannot say what time span is left until the earthquake starts, implying no knowledge about time to evacuate people from the future Nankai trough earthquake. Thus, considering that earthquakes occur suddenly is a major premise to implement disaster prevention measures, but the remaining damage can be huge even if a response occurs. When abnormal phenomena related to plate coupling are observed, it is necessary to make full use of such information for reducing disasters. For example, it is known, from a study of a scenario of Nankai trough earthquakes, that the predicted time elapse until a 1 m tsunami wave arrives, is a few minutes to several tens of minutes (Shizuoka Prefecture 2014). If the possibility of the occurrence of an impending large earthquake is judged to increase, this information may be used as a trigger to evacuate, in advance, elderly people who live near the coast to a safe place where they are expected to stay for a certain period (Working Group on Disaster Prevention Response when Detecting Anomalous Phenomena along the Nankai Trough 2018).
The current capability of TSN to detect and locate a slow slip was evaluated in this study. The PMC method for seismic networks was modified to be applicable to the evaluation of TSN’s performance. A currently available catalog, in which 35 slow slips with M = 5.1–5.8 (depth of 26–41 km) in 2012–2016 had been recorded by TSN, was used. It was confirmed that a region of high probabilities (Pdl ≥ 0.9) that TSN detected and located a slow slip of M = 5.1–5.8 almost covered the TSN. In more detail, the spatial patterns of Pdl for M = 5.1–5.4 were similar to each other (Fig. 8a, b). Above M = 5.4 (Fig. 8c, d), the region of high Pdl values (Pdl ≥ 0.9) increased with M. If Pdl ≥ 0.9999 is interpreted as an indication that a slow slip will not be missed, a slow slip with M ≤ 5.8 would likely be missed in a southern part of the anticipated source zone of a future Tokai earthquake.
It was further shown in Figs. 9 and 10 that Pdl is generally lower for slips of long duration (> 5 days) than for those of short duration (≤ 5 days), where the duration was defined by subtracting the starting time of a slip from the ending time of the slip. This result implies that the longer the duration, the greater the difficulty in detecting and locating a slow slip. Gradual changes in strain produced by a long-duration slow slip were difficult to be distinguished from background levels, compared with the changes in strain by a short-duration slow slip. This is a physically plausible reason of the findings that possibilities of detecting and locating a slow slip event are higher when the duration of the event is shorter. The Pdl maps created by using slow slips regardless of their duration (Fig. 8) are considered to show the average capability of TSN to detect and locate slow slips over short- and long-durations.
Given the reported rupture history (Kanamori 1972; Ando 1975; Ishibashi 2004; Working Group on Disaster Prevention Response when Detecting Anomalous Phenomena along the Nankai Trough 2018, Nanjo and Yoshida 2018) described in Sect. 1, it is desirable to explore the possibility of making a strategic plan for TSN to extend its coverage westwards to the entire eastern half of the Nankai trough. Note that for the entire eastern half of the Nankai trough, the detection-location capability of a slow slip is currently low, except for the Tokai region and a part of the Kii Peninsula (Research Committee for Forecast Ability of Large Earthquakes along the Nankai Trough 2017). For this purpose, a tool proposed in this study can help on network planning with simulation of virtual station installation (Fig. 11). However, it is understood that the effectiveness of this tool needs to be investigated in more detail as it is a non-trivial task to assume a station characteristic for a new station. Additional information such as local site conditions and geological parameters need to be available. Nonetheless, as a rule of thumb, the PMC-based method can help, with reduced costs, to estimate network performance and infer locations for future stations.
Cases where additional submarine stations are virtually placed in offshore regions were not considered because it was assumed that Pst for a virtual seafloor station was not the same as that used for an inland station. As seen in Sect. 4.4, virtual installation of one or more inland stations would certainly increase Pdl in far-offshore regions, but the effect is limited. Two seafloor strainmeter stations under DONET (Dense Oceanfloor Network system for Earthquakes and Tsunamis), not involved in TSN, are operating in a far-offshore region from the Kii peninsula near the trough axis (33.0–33.5° N, 136.0–136.5° E) (Araki et al. 2017). Eight slow slips in 2011–2016 have been recorded thus far. The next generation for evaluating TSN’s performance may make use of information of seafloor strainmeter records.
The author thanks two anonymous reviewers for their useful comments. The author would also like to acknowledge H. Kimura and K. Miyaoka for providing slow-slip and strainmeter-station catalogs (Kimura and Miyaoka 2017), and Y. Ishikawa and J. Kasahara for discussions. Strainmeter stations in TSN were installed by JMA, except for the stations “Hamamatsu Haruno” and “Kawanehonshou Higashifujikawa” that were installed by Shizuoka Prefecture. This work was partially supported by JSPS KAKENHI Grant Number JP 17K18958 and the Ministry of Education, Culture, Sports, Science and Technology (MEXT) of Japan, under its Earthquake and Volcano Hazards Observation and Research Program. Some figures were produced by using GMT software (Wessel et al. 2013). Data are available upon reasonable request.
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