Near-field tsunami forecast system based on near real-time seismic moment tensor estimation in the regions of Indonesia, the Philippines, and Chile
- Daisuke Inazu^{1, 2}Email author,
- Nelson Pulido^{2},
- Eiichi Fukuyama^{2},
- Tatsuhiko Saito^{2},
- Jouji Senda^{2} and
- Hiroyuki Kumagai^{3}
Received: 27 January 2016
Accepted: 14 April 2016
Published: 4 May 2016
Abstract
We have developed a near-field tsunami forecast system based on an automatic centroid moment tensor (CMT) estimation using regional broadband seismic observation networks in the regions of Indonesia, the Philippines, and Chile. The automatic procedure of the CMT estimation has been implemented to estimate tsunamigenic earthquakes. A tsunami propagation simulation model is used for the forecast and hindcast. A rectangular fault model based on the estimated CMT is employed to represent the initial condition of tsunami height. The forecast system considers uncertainties due to two possible fault planes and two possible scaling laws and thus shows four possible scenarios with these associated uncertainties for each estimated CMT. The system requires approximately 15 min to estimate the CMT after the occurrence of an earthquake and approximately another 15 min to make the tsunami forecast results including the maximum tsunami height and its arrival time at the epicentral region and near-field coasts available. The retrospectively forecasted tsunamis were evaluated by the deep-sea pressure and tide gauge observations, for the past eight tsunamis (M _{w} 7.5–8.6) that occurred throughout the regional seismic networks. The forecasts ranged from half to double the amplitudes of the deep-sea pressure observations and ranged mostly within the same order of magnitude as the maximum heights of the tide gauge observations. It was found that the forecast uncertainties increased for greater earthquakes (e.g., M _{w} > 8) because the tsunami source was no longer approximated as a point source for such earthquakes. The forecast results for the coasts nearest to the epicenter should be carefully used because the coasts often experience the highest tsunamis with the shortest arrival time (e.g., <30 min).
Keywords
Introduction
Great earthquakes with moment magnitudes (M _{w}) greater than about 8 have often generated disastrous tsunamis with many casualties (ITIC 2015). In particular, the 2004 Sumatra (M _{w} 9.1) and 2011 Tohoku (M _{w} 9.0) tsunamis were extremely disastrous and caused about 200,000 and 20,000 casualties, respectively (e.g., Satake 2014). Practical tsunami early warning systems are necessary for mitigating disasters caused by such great tsunamis.
Seismic waves, crustal deformation, and tsunamis (sea level) are continuously monitored, and these data are mostly available in real time. Seismic waves are primarily observed by onshore seismometers worldwide. Crustal deformations are observed by the global positioning system/global navigation satellite system (GPS/GNSS). Coastal tsunamis are observed at tide gauge stations, and offshore tsunamis are monitored by ocean-bottom pressure gauges (e.g., Rabinovich and Eblé 2015) and GPS sea-surface buoys (e.g., Kawai et al. 2013).
For reliable tsunami warnings, fast-traveling seismic wave data are used to evaluate the sizes of earthquakes and tsunamis, and, if available, offshore tsunami data are then used to reliably evaluate the actual tsunami size before tsunami arrival at the coast. Also, onshore coseismic crustal deformation data (GPS/GNSS) with high sampling (e.g., 1 Hz) can quickly constrain near-field tsunamigenic earthquake sources as presented in recent studies (e.g., Melgar et al. 2013; Tsushima and Ohta 2014).
Rapid earthquake source estimation systems based on real-time seismic observations have been developed and operated (e.g., Okada et al. 2004; Ekström et al. 2012; Duputel et al. 2012b). Earthquake source estimation is essential for the quickest issuing of tsunami warnings and forecasts. The simplest method is to search for a possible scenario in a pre-computed tsunami simulation database according to the estimated earthquake magnitude with its location (e.g., Tatehata 1997; Kamigaichi 2009; Lauterjung et al. 2010; Igarashi et al. 2015). There are various types of earthquake magnitudes, such as local magnitude, body-wave magnitude, surface-wave magnitude, and M _{w} (e.g., Utsu 2001; Shearer 2009). It is important to use the M _{w} for tsunami warning because the M _{w} reflects the fault displacement that is directly related to the tsunami generation. Using the moment tensor with M _{w} can facilitate more reliable tsunami forecasts (e.g., Reymond et al. 2012; Gusman and Tanioka 2014). Tsunami forecast systems based on the estimated centroid moment tensor (CMT) have been installed by the Pacific Tsunami Warning Center (PTWC) (e.g., Wang et al. 2012; PTWC/ITIC 2014) and the French Polynesian Tsunami Warning Center (CPPT: Centre Polynésien de Prévention des Tsunamis) (e.g., Clément and Reymond 2015; Jamelot and Reymond 2015).
Using real-time offshore tsunami observations probably facilitates more reliable forecasts than using observations from seismic data alone. Tsunami forecast systems that use offshore tsunami observations have been developed by the National Oceanic and Atmospheric Administration (NOAA) (e.g., Tang et al. 2009, 2012) and the Japan Meteorological Agency (JMA) (e.g., Tsushima et al. 2009, 2011, 2012). Recently, other reliable forecast methods that use dense offshore observation networks have been also suggested (Baba et al. 2014; Maeda et al. 2015). Forecast systems using tsunami observation can be reliable but require substantially longer times, because it typically takes tens of minutes for a tsunami to reach to the nearest offshore stations (e.g., Tang et al. 2012; Wei et al. 2013). For rapid and reliable forecasts, some studies have suggested that the initial tsunami height based on a finite-fault model inferred from seismic and/or geodetic observations is used as an initial guess, and successive offshore tsunami observations can facilitate a more reliable forecast (e.g., Melgar and Bock 2013; Tsushima et al. 2014).
On the other hand, there are many coastal communities for which offshore tsunami observations are not available for use in early warning because observation points are sparse around the target coastal areas (e.g., Rabinovich and Eblé 2015). So the tsunami forecast system based on seismic observation alone still plays an important role for disaster mitigations of coastal communities.
The tsunami forecast systems of PTWC and CPPT primarily use CMTs estimated by teleseismic body-wave inversions. The robust estimations of these CMTs require at least several tens of minutes after the origin time, especially for great earthquakes (M _{w} > 8) (e.g., Duputel et al. 2011). These tsunami forecast systems require time to estimate the CMT solution and to calculate the tsunami. It is therefore important to reduce the time to estimate CMT and to calculate tsunami for a rapid warning, especially for near-field tsunamis. In order to reduce the CMT estimation time, we prefer to use near-field seismic data, which is available earlier than teleseismic data.
Within the framework of an automatic/manual CMT estimation called the source-parameter determinations based on waveform inversion of Fourier Transformed seismograms (SWIFT) system (Nakano et al. 2008, 2010), the NIED has routinely analyzed the observed seismic data and maintained a database of the estimated CMTs of earthquakes that have occurred throughout the regional seismic networks. The time required for the CMT estimation using the near-field regional seismic data is expected to be shorter than that from the teleseismic data inversion. We have recently implemented an automatic CMT estimation procedure for large earthquakes (M _{w} > 7) into the previous SWIFT system (Nakano et al. 2008) and have incorporated a tsunami forecast system based on the estimated CMT. In the present paper, we briefly describe the automatic CMT estimation procedure, then describe the tsunami forecast system, show the forecast accuracy, and discuss its applicability to disaster mitigation.
SWIFT CMT solution
To estimate the earthquake source, the NIED collects real-time continuous seismic waveform data from 181 broadband seismic stations in Indonesia, the Philippines, Chile, and adjacent regions (Fig. 1) using the SeisComP3 system (e.g., Olivieri and Clinton 2012). The SeisComP3 system estimates in real time, the origin time, hypocenter, and magnitude of detected earthquakes. The estimation triggers the SWIFT system to automatically calculate CMT and source time function of the detected earthquake (Bonita et al. 2015; Punongbayan et al. 2015). The automatically estimated CMT solutions are checked, manually revised, and listed in a searchable database (www.isn.bosai.go.jp). The total number of estimated CMTs is 1488 in the range of M _{w} 4.3–8.6 around Indonesia and the Philippines from June 25, 2007, to December 31, 2015, and 220 in the range of M _{w} 4.0–8.2 around Chile from April 24, 2014, to December 31, 2015 (Fig. 1).
In particular for large earthquakes (M _{w} > 7), we have implemented the following automatic procedure in the SWIFT system to obtain a robust CMT solution as rapidly as possible. Once an earthquake is detected, the SWIFT system obtains available seismic waveform data from the SeisComP3 ring buffer and performs a quality check in terms of signal-to-noise ratio, gaps, clipping, and strong acceleration pulses in the waveform data. A list of datasets (east–west, north–south, and up-down components of the waveform data observed at available seismic stations) that has successfully passed the check is compiled as the accepted data. The SeisComP3 estimation of the origin time, hypocenter, and magnitude is used as an initial guess for the CMT search. For M _{w} < 7 earthquakes, the CMT search is performed using all of the accepted data. The waveform data used are filtered for a passband of 50–100 s. For 7 < M _{w} < 8 earthquakes, the CMT search is performed using accepted data having epicentral distances of 500–1500 km, with a passband of 50–100 s. For M _{w} > 8 earthquakes, the CMT search is performed using accepted data having epicentral distances of 1000–1500 km, with a passband of 50–200 s. The selection criteria of the waveform data with the epicentral distances longer than 1000 km and the passband of 50–200 s for M _{w} > 8 earthquakes are applied to guarantee the point-source assumption for the CMT estimation (Fukuyama and Dreger 2000) and to prevent the use of pulse data that are clipped or too strong, which may worsen the CMT estimate.
Tsunamigenic events for the SWIFT TSUNAMI system
Event with M _{w} | Date (yyyy-mm-dd) | Origin time (UTC) | Latitude (°N) | Longitude (°E) | Focal depth (km) | Fault plane^{a} | Strike (deg) | Dip (deg) | Rake (deg) | Scaling law^{b} | L (km) | W (km) | D (m) | Tsunami data^{c} | Reference | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
DART | Tide Gauge | |||||||||||||||
2012 M _{w} 8.6 off Sumatra earthquake | 2012-04-11 | 08:38:34 | 2.0 | 94.0 | 50 | FP1 FP2 | 201 110 | 54 89 | 1 144 | SC1 SC2 | 207 352 | 103 176 | 10.4 3.6 | 23227, 23401, 56001, 56003 | 1, 2, 4, 7 | Duputel et al. (2012a) |
2007 M _{w} 8.5 Bengkulu earthquake | 2007-09-12 | 11:10:23 | −5.0 | 101.0 | 15 | FP1 FP2 | 314 112 | 10 81 | 112 86 | SC1 SC2 | 184 314 | 92 157 | 9.2 3.2 | 23401 | 6 | Gusman et al. (2010) |
2007 M _{w} 7.7 aftershock of Bengkulu earthquake | 2007-09-12 | 23:49:01 | −2.7 | 100.6 | 30 | FP1 FP2 | 325 126 | 27 64 | 107 82 | SC1 SC2 | 73 125 | 36 62 | 3.7 1.3 | 23401 | – | Gusman et al. (2010) |
2010 M _{w} 7.8 Sumatra earthquake | 2010-04-06 | 22:15:03 | 2.3 | 96.5 | 20 | FP1 FP2 | 306 127 | 7 83 | 89 90 | SC1 SC2 | 82 140 | 41 70 | 4.1 1.4 | 23401, 56001 | 2, 3, 4, 6 | – |
2010 M _{w} 7.5 Mentawai tsunami earthquake | 2010-10-25 | 14:42:21 | −4.0 | 99.8 | 10 | FP1 FP2 | 308 97 | 31 63 | 117 75 | SC1 SC2 | 58 99 | 29 49 | 2.9 1.0 | 56001 | 4, 5, 6, 7 | Satake et al. (2013) |
2012 M _{w} 7.5 Philippine Trench earthquake | 2012-08-31 | 12:47:38 | 10.8 | 127.0 | 40 | FP1 FP2 | 346 206 | 56 41 | 65 122 | SC1 SC2 | 58 99 | 29 49 | 2.9 1.0 | 52405, 52404, 52403 | 8 | Heidarzadeh and Satake (2014) |
2015 M _{w} 8.4 Illapel earthquake | 2015-09-16 | 22:54:29 | −31.2 | 287.2 | 5 | FP1 FP2 | 12 169 | 21 71 | 112 82 | SC1 SC2 | 164 280 | 82 140 | 8.2 2.8 | 32402, 32401, 32412, 32411 | 14–31 | Heidarzadeh et al. (2016) |
2014 M _{w} 8.1 Iquique earthquake | 2014-04-01 | 23:46:49 | −20.1 | 289.2 | 25 | FP1 FP2 | 352 167 | 17 73 | 95 88 | SC1 SC2 | 116 198 | 58 99 | 5.8 2.0 | 32401, 32402, 32412, 32413 | 9–16, 18, 19, 21 | Gusman et al. (2015) |
Tsunami forecast using SWIFT CMT
We have developed a successive automatic tsunami calculation system starting from the automatically estimated CMT using the procedure mentioned in the previous section. The tsunami calculation system is used for both forecast and hindcast. The tsunami calculation system (hereafter the SWIFT TSUNAMI system) is described in this section.
When the estimated SWIFT CMT satisfies the conditions M _{w} > 5.5 and a focal depth shallower than 100 km, the SWIFT TSUNAMI system decides that the detected earthquake is possibly tsunamigenic and performs the following analysis. The tsunami forecast results can be available approximately 30 min after the occurrence of a significant earthquake (i.e., ~15 min to obtain the CMT and ~15 min for the tsunami calculation).
The initial condition of the tsunami simulation is based on a rectangular fault model with a uniform slip. The estimated CMT gives the strike, dip, and rake of the earthquake source with its centroid location (longitude, latitude, and focal depth). In addition, when the length, width, and slip amount of the finite rectangular fault are given, the seafloor deformation is calculated using the Okada’s formula (Okada 1985) with assuming a homogeneous half-space. The center of the rectangular fault is placed at the centroid location. (i) The vertical component of the seafloor deformation due to the faulting primarily determines the seafloor vertical displacement. (ii) A product of the horizontal component and the seafloor gradient at the source region yields an additional seafloor vertical displacement (e.g., Tanioka and Satake 1996). (iii) The tsunami height at the sea surface arises from the seafloor vertical displacement without short-wavelength components. The short-wavelength seafloor vertical displacement is damped by considering a low-pass filtering effect from a local (here 0.5 deg by 0.5 deg) ocean depth (e.g., Saito and Furumura 2009). We use the tsunami height considering (i), (ii), and (iii) as the initial condition of the tsunami simulation. The seawater velocity is assumed to be zero for the initial condition (Saito 2013). The rise time of the faulting is assumed to be zero.
The tsunami simulation is carried out using the initial condition. Here, the simulation is based on a linear long-wave model (Inazu and Saito 2013, 2016). The horizontal resolution is 5 arcmin. The ETOPO1 dataset (Amante and Eakins 2009) is used to configure the bathymetry.
As mentioned above, substantial time is required after the occurrence of a significant earthquake to estimate the robust CMT (~15 min) and the tsunami height with the arrival time (another ~15 min). The results along the coast (Figs. 7, 8, 9) for which the maximum height arrival time is less than 30 min cannot be used for the purpose of forecasting, but are useful for hindcasting and post-disaster evaluations.
Forecast accuracy and uncertainty
Tsunami forecast systems similar to the SWIFT TSUNAMI system have been also developed by PTWC and CPPT. The PTWC system has shown forecast results with successively updated CMT solutions (Wang et al. 2012). The CPPT study has shown forecast uncertainties with respect to CMTs derived from different research institutions (Jamelot and Reymond 2015). We show the forecast uncertainties due to the fault plane selection, the scaling laws used, and other possible factors, especially for greater earthquakes and tsunamis.
We evaluate the forecast accuracy of the SWIFT TSUNAMI system. Eight large earthquakes (M _{w} 7.5–8.6) from 2007 to 2015 were tsunamigenic as detected by the ocean-bottom pressure observations of the Deep-ocean Assessment and Reporting of Tsunamis (DART) system (e.g., Mungov et al. 2013) (Fig. 2). The retrospective forecasts of the eight events based on the SWIFT CMTs are first compared to the DART observations and are then compared to the coastal tide gauge observations.
The tsunami size of the 2010 Mentawai tsunami earthquake was notably underestimated by the SWIFT TSUNAMI system (Figs. 11, 12). The Mentawai tsunami earthquake was estimated as M _{w} 7.5 by the SWIFT estimation, which is significantly smaller than M _{w} ~ 7.8 as derived from the GCMT and USGS solutions (Fig. 3e). If we changed the M _{w} to 7.8 in the SWIFT solution, we confirmed that the underestimation was suitably compensated. Although the automatic SWIFT CMT estimation procedure proposed in the present study is intended for large earthquakes (M _{w} > 7), the procedure may still have difficulty in reasonably evaluating the size of tsunami earthquakes. Improvements especially for reliable M _{w} estimation will be necessary for the proposed procedure to work for tsunami earthquakes. With the exception of the Mentawai tsunami earthquake, the forecasts range mostly within the same order of magnitude as the maximum heights of the tide gauge observations.
We also find that the forecast differences (standard deviation) between the four scenarios increase for the larger events and decrease for the smaller events (Figs. 11b, 12b). The dependence of the forecast differences on M _{w} is recognized in Figs. 7 through 10. For small M _{w} events (e.g., M _{w} 7.5), the differences in the fault plane selection and in the scaling laws used result in relatively small differences in the initial tsunami height condition, indicating that the tsunami source is approximated as a point source and result in small differences in the forecasts (Figs. 9 and 10b). For the larger M _{w} events (e.g., M _{w} > 8.0), however, the tsunami sources significantly deviate from the point source, and the differences in the finite-fault size cause relatively large variations in the forecasts (Figs. 7, 8, 10a). It is worth noting that the dependence of the forecast uncertainty on M _{w} indicates that accurate and robust tsunami forecasting becomes more difficult for larger earthquakes.
Discussion for future perspectives
- (1)
Compiling accurate and reliable bathymetry data with a higher spatial-grid resolution for the simulation is essential to accurate tsunami forecasting at the target regions. Local but high-accuracy multibeam survey data are preferably incorporated into the fundamental ETOPO or GEBCO datasets (e.g., Satake et al. 2013; Eakins and Grothe 2014; Weatherall et al. 2015; Calisto et al. 2015). In the present study, we used the framework of a global tsunami simulation (Inazu and Saito 2013, 2016), but the simulations will be suitably carried out in the regional domain in the vicinity of the SWIFT seismic networks in Indonesia/the Philippines, and Chile, in order to efficiently reduce the computation time with the high grid resolution. Tsunami simulation modeling that includes nonlinear advection with inundation, seafloor friction, and wave dispersion may be also necessary for accurate forecast although the comprehensive modeling requires additional computational time (e.g., Saito et al. 2014; Miyoshi et al. 2015; Baba et al. 2015). A calculated map of the inundation area with height will be required for the forecast products as well. This will be possible using latest supercomputing systems that have shown abilities to facilitate real-time tsunami forecasts with suitable inundation by high-resolution (< 10 m) simulation (Oishi et al. 2015; Musa et al. 2015; Baba et al. 2016).
- (2)
We discuss in detail the uncertainties of the tsunami forecasting based on seismic data alone, especially for great earthquakes. The real-time inferred M _{w} ordinarily involves an uncertainty of ± 0.2 (e.g., Nakano et al. 2010; Jamelot and Reymond 2015; Bonita et al. 2015) and may be significantly underestimated. One striking example was that the JMA issued the earthquake magnitude of 7.9 for the 2011 M _{w} 9.0 Tohoku earthquake (e.g., Ozaki 2011, 2012). The reliable M _{w} estimate is essential. When the estimated M _{w} is reliable, the scaling law used is secondarily important. The 2004 Sumatra and 2010 Tohoku earthquakes involved comparable M _{w} of 9.1 and 9.0, respectively. The tsunami source extended 900 km long for the 2004 Sumatra event (e.g., Fujii and Satake 2007), which can be suitably represented by a large-rupture-area scaling law (e.g., Murotani et al. 2013). The tsunami source for the 2011 Tohoku event, however, extended 300 km long at most (e.g., Gusman and Tanioka 2014), which should be represented by a small-rupture-area scaling law (e.g., Utsu 2001). The difference in the scaling law used for tsunami calculation becomes more notable for greater earthquakes. In addition, as expected for tsunami earthquakes and great-earthquake-induced seafloor failures, the observed tsunami size may be notably larger than that estimated based on the seismic data alone, especially for greater earthquakes (e.g., Tanioka and Seno 2001; Watts et al. 2005; Kawamura et al. 2014). When offshore tsunami observation data (e.g., DART and GPS buoy) are available in near real time, we may be able to reduce the uncertainty and select probable scenarios (e.g., Melgar and Bock 2013; Tsushima et al. 2014).
- (3)
The SWIFT TSUNAMI system has been developed for tsunami disaster mitigation, especially for great tsunamis. We discuss the forecast results from the viewpoint of users. Users should consider the worst-case scenario from the forecasts for early warning and remember that the forecast may underestimate the tsunami size in cases of tsunami earthquakes and great-earthquake-induced seafloor failures. Because we need 30 min from the occurrence of the earthquake to obtain the SWIFT tsunami forecast, we cannot use the estimated results for the forecast at coasts in the vicinity of the epicenter within a 30-min arrival time (Figs. 8, 9). Unfortunately, however, near-field coasts with a short arrival time experience the highest wave in many tsunami events. In addition, seismic waveform analysis and obtaining a reliable CMT solution require substantial time of 10–20 min even though the tsunami calculation time may be reduced. Users should recognize whether their target regions can receive a reliable forecast before or just after a significant earthquake occurrence. The forecast results at the nearest coasts may not be used before the disaster, but will be useful for post-disaster damage evaluations and remediation activities.
Summary
We have described the automatic procedure of the CMT estimation of the SWIFT system for great earthquakes (M _{w} > 7), and the associated tsunami forecast/hindcast system, in the regions of Indonesia, the Philippines, and Chile. The current system requires ~15 min to estimate the CMT of the detected earthquake and another ~15 min for the tsunami calculation; forecast results are available at www.isn.bosai.go.jp.
The retrospectively estimated SWIFT CMT solutions have shown good agreement with the GCMT and USGS solutions for the past seven tsunamigenic earthquakes (M _{w} 7.5–8.6) that occurred throughout the SWIFT seismic networks, excluding the 2010 Mentawai tsunami earthquake. The estimated M _{w} of the SWIFT CMT for this tsunami earthquake was notably underestimated compared to the GCMT and USGS solutions. The calculated tsunami height derived from the SWIFT CMT was also underestimated compared to the offshore and coastal tsunami observations. The current automatic SWIFT CMT estimation procedure may still have difficulty in estimating the size of tsunami earthquakes accurately.
We evaluated the forecast accuracy of the SWIFT TSUNAMI system for the eight tsunamis (M _{w} 7.5–8.6). The system considers forecast uncertainties due to the fault plane selection and the scaling law used and shows four possible scenarios for each tsunamigenic event. The forecast results based on the four scenarios were evaluated by the DART and tide gauge observations. We have shown that the forecasts with associated uncertainties range from half to double the total amplitude of the leading wave of the DART observations and range mostly within the same order of magnitude as the maximum heights of the tide gauge observations. It is also found that the forecast uncertainties become larger for greater earthquakes because the tsunami source is no longer approximated as a point source for greater earthquakes (e.g., M _{w} > 8).
We have discussed the practical applicability of the forecast results as well as the forecast accuracy and uncertainties. Users should judge whether the estimated results can be used for forecasting at the target regions and remember the additional forecast uncertainties for greater earthquakes with associated landslides and tsunami earthquakes. Even if the forecast results cannot be used for forecasting, the results will be useful for post-disaster activities and for enabling researchers to quickly clarify behaviors of the tsunami.
Declarations
Authors’ contributions
DI developed the tsunami calculation system and wrote the majority of the paper. NP developed the earthquake source estimation algorithm and wrote the relevant sections of the paper. EF, TS, and HK contributed extensively to the scientific discussion. JS provided technical help to automate the developed system. All authors read and approved the final manuscript.
Acknowledgements
This present study was supported by the NIED project for “Development of Monitoring and Forecasting Technology for Crustal Activity.” The observed seismic data were obtained through the cooperative research projects with BMKG and PHIVOLCS and through the public servers of IRIS and GEOFON. The DART observation data were downloaded from the NOAA website (http://www.ndbc.noaa.gov/dart.shtml). The tide gauge data were primarily derived from the catalog of the National Tsunami Warning Center (http://ntwc.arh.noaa.gov/about/). Comments from two anonymous reviewers were very useful for improving the manuscript.
Competing interests
The authors declare that they have no competing interests.
Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Authors’ Affiliations
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