Otober 1-1,, Beijing, China A NEW AGNITUDE ESTIATION ETHOD BASED ON PREDOINANT PERIOD AND PEAK APLITUDE Li Shanyou 1 and Song Jindong 1 Proessor, Institute o Engineering ehanis, China Earthquake Administration, Harbin. China Email: shanyou@iem.a.n, shanyou@iem.a.n Graduated Student, Institute o Engineering ehanis, China Earthquake Administration, Harbin. China Email: iemsjd@1.om, iemsjd@1.om ABSTRACT: Earthquake Early Warning (EEW) is a useul tool or pratial real-time seismi hazard mitigation at present. The ritial tehnology o EEW is determining the size o an earthquake and the predited ground motion at given site, rom the irst ew seonds o the P waves. Currently, there are two dierent approahes to the EEW magnitude estimation, predominant period method and amplitude method. However, both methods have some disadvantages, suh as signiiant unertainty and saturation at great magnitude. To improve the estimation o magnitude, a new united predominant period τ and amplitude P method is developed and the ormula is = a*log P +b*logτ +*log Δ +d Where a, b,, and d are onstants, Δ is epientral distane. The magnitude estimation results o the irst three seond P wave o NSP strong motion data indiate that, the estimation preision o new method is higher than those o the two methods mentioned above, and the saturation at great magnitude is improved. eanwhile, or short hypoentral distanes, a simpliied united predominant period τ and amplitude P method is presented, the ormula is = a*log P +b*logτ +d KEYWORDS: Earthquake Early Warning (EEW), agnitude, Predominant Period, Amplitude 1. INTRODUCTION In the past several deades, researh on earthquake early warning (EEW) has undergone a rapid development. At present EEW is beoming a useul tool or pratial real-time seismi hazard mitigation, with its appliations in Japan (Nakamura,1; Horiuhi et al.,; Kamigaihi,,), Taiwan (Wu and Teng,; Wu and Kanamori,a), exio (Espinosa-Aranda et al.,1,), United States (Bakun,1; Allen and Kanamori, ; Allen,), Romania(Wenzel et al.,), and Turkey(Erdik et al.,). The haraterization o an earthquake or early warning inludes most importantly estimates o its size and loation (Allen and Kanamori, ), in this two researh areas a lot o researh results have been made in reent years (Nakamura,1; Allen and Kanamori,; Odaka et al.,; Rydelek and Pujol,; Kanamori, ; Wu and Kanamori, a,b; Olson and Allen,; Horiuhi et al., ; Wu et al.,; Zollo et al.,; Satriano et al, ). The deterministi relationships between the earthquake magnitudes and some waveorm properties, suh as the predominant period and peak amplitude, o the irst ew seonds o P waves, an be used to estimate magnitude. Olson and Allen () suggested that the inal magnitude o an earthquake is determined by the irst ew seonds o the rupture proess and the state o stress in the region surrounding the ault plane. This model provides a physial basis or the deterministi nature o earthquake magnitudes and or EEW appliations. Currently, there are two dierent approahes to the EEW magnitude estimation. One is the predominant period method (Nakamura, 1; Allen and Kanamori, ; Kanamori, ; Wu and Kanamori, a; Olson and Allen, ), another is the amplitude method (Odaka et al., ; Wu and Kanamori, b; Wu et al., ; Zollo et al., ).However, both methods have signiiant unertainty and the saturation at great magnitude. So,
Otober 1-1,, Beijing, China here we are onerned with obtaining the high-point o magnitude estimation and simultaneously the less unertainty as time passes ater the irst triggered arrival rom the event, improving the underestimate at great magnitude. To ahieve the objetive, a new single station earthquake magnitude estimation method united amplitude and predominant period is developed.. ETHOD In the single station approah, the relationships between the magnitudes o earthquakes and some observational properties o the irst ew seonds o the P waves, inluding the predominant period τ (Nakamura, 1; Allen and Kanamori, ; Kanamori, ; Wu and Kanamori, a; Olson and Allen, ) and the peak amplitudes Pd (Odaka et al., ; Wu and Kanamori, b; Wu et al., ; Zollo et al., ) were ind out..1 Predominant Period ethod The predominant period τ, that is similar to the one used by Nakamura (1), is deined in terms o the waveorms o the irst ew seonds o the P waves as ollows. First we ompute r by r τ = τ u& u () t dt () t dt (.1) Where u(t) is the ground-motion displaement and the integration is taken over the time interval (, τ ) ater the onset o the P wave. Usually, τ is set at s. Using Parseval s theorem, ˆ ( ) ( ) d π u d r = = π uˆ Where is the requeny, û( ) is the requeny spetrum o u(t) and by û( ). Then, is the average o (.) weighted π 1 τ = = (.) r Previous studies have shown that the predominant period relet the sizes o earthquakes (Kanamori, ; Wu and Kanamori, a) as ollows. ( τ ) = A*logτ + B (.) est Where A and B are onstants, est (τ ) is the estimation magnitude determined by predominant periods τ.. Amplitude ethod The quantity P is the peak amplitude o waveorm within the irst ew seonds (again usually se) ater the arrival o the P wave. P is an amplitude parameter and relets the attenuation relationship o the ground motion with distane. Thereore, i we an determine the attenuation relationship o P, then we an use P to estimate the magnitude when the hypoentral (or epientral) distane is available.
Otober 1-1,, Beijing, China Wu and kanamori (b), Wu et al. () ound a good linear relationship among the peak displaement amplitude Pd, the magnitude, and the hypoentral distane R an be represented by A Pd B R C ' ' ' Pd = *log + *log + (.) Zollo et al. () also obtained the similar results. Odaka et al. () hoose a novel onstant B instead o hypoentral distane. They ind that logb is linearly proportional to -log Δ, and the linear relationship between B and magnitude. In this study, using ormula ( P, Δ ) = A *log P + B *log Δ+ C (.) est ' ' ' instead o equation (.).Where A, B and C are onstants, P is the peak amplitude o aeleration waveorm within the irst three seonds ater the arrival o the P wave, Δ is epientral distane that an be determined using real-time loation proedures as, or instane, the method proposed by Odaka et al. () or Horiuhi et al.(), est (P, Δ ) is the estimation magnitude determined by P and Δ.. United Amplitude and Predominant Period ethod The relationships between magnitude and the two methods above-mentioned are deterministi. However, both methods have some shortomings, suh as signiiant unertainty (Greksh and Kumpel, 1; Allen and Kanamori, ; Olson and Allen, ) and saturation at great magnitude (Wu et al., ). So, a new approah that an improve these disadvantages is neessary. The duration and the predominant period o the shaking is proportional to the earthquake s magnitude (Nakamura, 1), whih means that the larger the predominant period, the greater the magnitude. Also, under the same distanes onditions, the previous studies (Wu and Kanamori, a; Wu et al., ) indiate that the larger the amplitude, the greater the magnitude. Wu and kanamori (b) onsidered that τ *Pd is a good quantity o threshold EEW and Wu et al () propose that a ombination o Pd and τ analyses to be used or single station or onsite EEW operation. eanwhile, rom the pioneer deinition o the magnitude, it is a quantity determined by the amplitude and period (Rither, 1). On the basis o the physial basis, a new magnitude estimation method united predominant period and amplitude is introdued as ollowed. ( P, τ, Δ ) = a*log P + b*log τ + *logδ+ d (.) est Where a, b,, and d are onstants, est (P,τ, Δ ) is the estimation magnitude determined by P, τ, and Δ.. DATA The U.S. Geologial Survey National Strong-otion Projet (NSP) has the primary Federal responsibility or reording eah damaging earthquake in the United States on the ground and in man-made strutures in densely urbanized areas to improve publi earthquake saety. The Projet maintains a national ooperative instrumentation network, a national data enter, and a supporting strong-motion data analyses and researh enter in support o this responsibility. The waveorms used in this study are olleted rom 1 earthquakes ourring between 1 and rom NSP. All o the events have magnitudes rom.1 to. and oal depths o less than km, and all o these epientral distanes are rom km to 1 km. Vertial omponent reordings were used in this study. Aeleration was integrated one to obtain veloity and twie to obtain displaement. A. Hz Butterworth high-pass ilter was applied to remove the low-requeny drit ater the integration. We used an automati P wave piker similar to that desribed by Allen (1) to detet the P wave arrival. To reognize the seismi
Otober 1-1,, Beijing, China arriving time automatially, on the basis o seismi phase reognition by using the method proposed by Allen (1), a searhing method in a window whih is beore arriving time at trigger threshold is developed. Then, we omputed predominant periods τ rom the irst -seond-lonsg iltered signals ater the P wave arrival. The peak aeleration amplitudes P was also omputed in the same time window. Table.1 Events used in this study Origin Time (UTC) Lon. (W) Lat. (N) Depth (km) N /1/ 1::.1 1.... //1 1::.1 1.... //1 ::.1 1.... // ::.1 11.1. 1.. // 1::. 1.... //1 1:1:1. 11.1. 1.. /1/1 :1:. 11....1 /11/ 1::1.1 1.. 1.. // 1:1:. 1..1.. /11/ :1:1. 1..1.. //1 1::. 1.... // 1::1. 11..1.. 1//1 1:1:11. 1..1.. 1// 1::. 1..1 1.. 1/1/1 1::.. 1... 11 1//1 1::1. 1.... 1// 1::. 1..... RESULTS The results we obtained or the relationships among the peak amplitudes o aeleration within the irst three seonds ater the arrival o the P wave P, the predominant periods τ, epientral distane Δ, and the magnitude is shown in Figure 1a to Figure 1d. Figure 1a shows the relationship between est (τ ) determined rom the predominant periods τ versus the inal magnitude o the earthquake. Estimation standard deviation level is. magnitude units, whih is larger than the one obtained rom the previous studies (Wu and Kanamori, a; Wu et al, ). It is to be remarked, we hoose single stations τ instead o multi stations average τ. The linear regression or the relationship between the est (τ ) and τ leads to ( τ ) =.*logτ +. (.1) est Figure 1b shows the relationship between est (P, Δ ) determined rom P obtained rom the irst three seond P wave seismograms reorded by strong motion instruments and epientral distane Δ versus the inal magnitude o the earthquake. Estimation standard deviation level is. magnitude units. Aording to the igure, the unertainty o amplitude method is smaller than the one o predominant period method. The linear regression or the relationship among the est (P, Δ ), P and Δ leads to ( P, Δ ) = 1.*log P +.1*log Δ. (.) est Figure 1d shows the relationship between est (P,τ, Δ ) determined rom united amplitude and predominant period method versus the inal magnitude o the earthquake. Estimation standard deviation level is. magnitude units. As is shown in the igure in evidene, the new method has less unertainty and simultaneously
Otober 1-1,, Beijing, China Standard Deviation=. Standard Deviation=. est(τ) est(p,δ) a b Standard Deviation=. Standard Deviation=. est(p,τ) est(p,δ,τ) d Figure 1 est (vertial axis) versus (horizontal axis). Solid line shows the 1:1 linear relationship between est and, two dashed lines show one magnitude units deviation. (a) the relationship between est (τ ) determined rom the predominant periods τ versus the inal magnitude o the earthquake (b) the relationship between est (P, Δ ) determined rom P obtained rom irst three seond P wave seismograms reorded by strong motion instruments and epientral distane Δ versus the inal magnitude o the earthquake () the relationship between est (P,τ ) determined only rom peak amplitudes P and predominant periods τ versus the inal magnitude o the earthquake (d) the relationship between est (P,τ, Δ ) determined rom united amplitude and predominant period method versus the inal magnitude o the earthquake the saturation at great magnitude is improved. The linear regression or the relationship among the est (P,τ, Δ ), P, τ and Δ leads to ( P, τ, Δ ) = 1.*log P +.1*logτ + 1.*log Δ+. (.) est
Otober 1-1,, Beijing, China The harateristi o earthquake early warning is issue warning message only using irst several triggered stations. The denser the seismologial monitoring network in the soure region, the less the epientral distane o these stations. It will redue the impat o amplitude attenuation aused by short hypoentral distanes. For short hypoentral distanes, equation (.) has a simpliied version, ( P, τ ) = 1.1*log P + 1.*logτ +. (.) est whih is similar to Xu() and by whih we ould estimate magnitude only using predominant period and amplitude, regardless o the impat o distanes. Figure 1 shows the relationship between est (P,τ ) determined only rom peak amplitudes P and predominant periods τ versus the inal magnitude o the earthquake. Estimation standard deviation level is. magnitude units, whih is similar to amplitude method, equation (.). Under the less epientral distanes, suh as -km upper limit, the results o equation (.) must be ontinued to be onsidered.. DISCUSSION AND CONCLUSION In this study, a new method united predominant period and amplitude is developed, whih is based on the ahievement o previous studies and deinition o the magnitude. We determined the relationship among magnitude, predominant periods τ and peak aeleration amplitudes P observed rom the irst three seonds o P waves. Compared with predominant period method or amplitude method, the new method has less unertainty and simultaneously the underestimate at great magnitude is improved, using the NSP strong motion data. The result o preliminary numerial validation o new method only using a small number o seismi reords is presented in this study. It is unknown that the rationality o large amounts o data. eanwhile, or short hypoentral distanes stations data, a simpliied united predominant period τ and amplitude P method is presented. The results o the rationality o large amounts o data and the simpliied method must be ontinued to be onsidered. ACKNOWLEDGEENT We wish to thank U.S. Geologial Survey National Strong-otion Projet (NSP), or we used the strong motion data obtained rom USGS. This researh was supported by National Natural Siene Foundation o China(No:). REFERENCES Allen, R.. (). The ElarmS earthquake early warning methodology and its appliation aross Caliornia, In "Earthquake Early Warning Systems", P. Gasparini, G. anredi, J. Zshau (Eds), p. 1-, Springer, ISBN-1 ----. Allen,R.., Kanamori.H. (). The potential or earthquake early warning in southern Caliornia, Siene, :. Allen, R. V. (1). Automati earthquake reognition and timing rom single traes, Bull. Seismol. So. Am.,, 11 1. Bakun, W. H, Fisher. F. G., Jensen, E. G., VanShaak, J. (1). Early warning system or atershoks. Bull. Seism. So.Am.,,-. Espinosa-Aranda, J., Jimenez, A., Ibarrola, G., Alantar, F., Aguilar, A. (1). exio City seismi alert system. Seismol. Res. Lett.,,. Espinosa-Aranda J, Rodriguez FH. (). The seismi alert system o exio City[]. In International
Otober 1-1,, Beijing, China Handbook o Earthquake & Engineering Seismology, ed.whk Lee, H Kanamori, PC Jennings, C Kisslinger, San Diego:Aademi Press, pp. 1-. Erdik,.et al, (). Istanbul Earthquake Rapid Response and The Early Warning System, Bulletin o Earthquake Engineering 1: 1 1. Greksh, G., Kumpel, H. J. (1). Statistial analysis o strong-motion aelerograms and its appliation to earthquake early-warning systems. Geophys. J. Int. 1:11. Horiuhi S, Negishi H, Abe K, et al. (). An Automati Proessing System or Broadasting Earthquake Alarms, Bull. Seism. So. Am,, -1. Kamigaihi, O. (). JA earthquake early warning, Journal o Japan Assoiation or Earthquake Engineering, Vol., No.,1-1. Kamigaihi, O. (). Earthquake Early Warning-Provision to General Publi and Future Prospet, Fith International Conerene on Urban Earthquake Engineering,Tokyo, Japan, 1-. Kanamori, H. (). Real-time seismology and earthquake damage mitigation, Annu. Rev. Earth Planet. Si.,, 1 1. Nakamura, Y. (1). On the Urgent Earthquake Detetion and Alarm System (UrEDAS), th world onerene on earthquake engineering, Vol. VII, pp. -. Odaka, Y., Ashiya, K., Tsukada, S., Sato, S., Ohtake, K., Nozaka, D., (). A new method o quikly estimating epientral distane and magnitude rom a single seismi reord, Bull. Seismol.So. Am.,. Olson.E.L., and Allen, R.. (). The deterministi nature o earthquake rupture., Nature,, 1-1. Rihter, C. F. (1). An instrumental earthquake magnitude sale. Bull. Seism. So. Am.,,1-. Rydelek, P. and Pujol, J. () Real-Time Seismi Warning with a Two-Station Subarray, Bull. Seism. So. Am,, 1-1. Satriano C., Lo A.,Zollo,A. (). Real-Time Evolutionary Earthquake Loation or Seismi Early Warning, Bull. Seism. So. Am,, 1-1. Wenzel, F. (). An Earthquake Early Warning System or the Romanian Capital, Perspetives in odern Seismology. Editor: Friedemann Wenzel, Leture Notes in Earth Sienes, Springer, vol. 1, p.1-1. Wu, Y.., and Teng, T. L. (). A virtual sub-network approah to earthquake early warning. Bull. Seism. So. Am.,, -1,. Wu, Y.. and Kanamori, H. (a). Experiment on an onsite early warning method or the Taiwan early warning system, Bull. Seism. So. Am.,, -. Wu, Y.. and Kanamori, H. (b). Rapid Assessment o Damaging Potential o Earthquakes in Taiwan rom the Beginning o P Waves, Bull. Seism. So. Am.,, 111-11. Wu, Y.., Yen, H. Y., Zhao, L., Huang, B. S., and Liang, W. T. (). agnitude determination using initial P waves: A single-station approah, Geophys. Res. Lett.,, L. Xu Yang, Wu Zhong-liang, et al. (). Estimating the size o an earthquake using short-period seismograms o the irst three seonds: A simulated experiment using the 1 Chi-Chi earthquake sequene, Ata Seismologia Sinia, Vol.1, No., 1~1. Zollo,A., Lanieri,. and Nielsen, S. (). Earthquake agnitude Estimation From Peak Amplitudes o Very Early Seismi Signals on Strong otion Reords, Geophys.Res.Lett. Vol., No., L1.