Tsunami amplitudes estimation from numerical simulations and empirical laws

Transcription

1 Tsunami amplitudes estimation from numerical simulations and empirical laws Sixth International workshop on tsunami, Guayaquil sept 2007 Dominique Reymond CEA/DASE/LDG BOX 640 Papeete French Polynesia Emile A. Okal Northwestern University Evanston IL , USA Hélène Hebert CEA/DASE BP 12 Bruyères-Le-Chatel France

2 Tsunami warning : What are the essential informations for Civil Defense and the emergency plan? The tsunami warning centre (TWC) must be able to provide: 1) Information on the earthquake itself: Location (routinely) Focal depth (not trivial) Magnitude (not trivial for slow and giant earthquakes) 2) Information on the potential tsunami hour of tsunami arrival (routinely) Importance of the tsunami (i.e estimation of amplitude of the tsunami) 3) Seriousness of the warning Evaluation of the danger : major, ocean wide, moderate, local effects only,..etc.

3 Parenthesis: The case of slow earthquakes Nicaragua sept 1992: mb = 5.3, Mw = 7.6 Java 2 June 1994: mb = 5.5, Mw = 7.8 Peru 21 Feb 1996 : mb = 5.8, Mw = 7.5 Java 17 Jul 2006: mb = 5.5, Mw = 7.7

4 Sumatera Mm = 8.5, Mw=8.4 Sumatera 12 sep 2007 Mm = 7.0, Mw = 7.3

5 The BSSA-89 relation: a first estimation of tsunami amplitude Okal & Talandier (An algorithm for automated tsunami warning in French Polynesia based on mantle magnitude, BSSA, vol 79, 1989): TS = 0.3 Mo 1E20 Δ 90 sin( Δ) Where: * Mo is in N.m Δ in degree * TS is in cm This formula derived from normal mode theory, gives: * Tsunami amplitude in far field * In deep ocean * In the direction of maximum of radiation * For a source at 20 km depth, with thrust 45 faulting

6 Application to Papeete harbor Theoretical Log log formula gives: log TS = log(mo) 0.5 log (Δ sin Δ) with TS in m, Mo in N.m Difference Obs Cal: 0.13! Experimental linear fit gives: log TS = log(mo) 0.5 log (Δ sin Δ) with TS in m, Mo in N.m The 0.13 unit of difference between theory-empirical, traduces that PPT is not an amplificating site Finally we retain for Papeete: log TS MAX = log(mo) 0.5 log (Δ sin Δ) 21.0 Max log TS Aver = log(mo) 0.5 log (Δ sin Δ) 21.4 Average log TS Min = log(mo) 0.5 log (Δ sin Δ) 21.8 Min

7 Observed peak-peak tsunami amplitude in Papeete harbour ( ) normalized at 90 of distance Aleutian 1 avril 1946 Peak-peak amplitude (m) Tonga 1982 Tonga 2006 Kuril 15 Nov 2006 Hokaido 2003 Peru 2001 Aleutian 1965 Alaska 1964 Chili 1960 BSSA 89: Log10 H = Log10 Mo 0.5log10(Δ sinδ) E E E E E+24 Seismic moment Mo (N.m)

8 Application of BSSA-89 relation to a tsunami measured in several places Tonga 3 May 2006 : Observed tsunami heights NukuAlofa, Tonga NIUE Log10 H = Log10 Mo 0.5log10(Δ sinδ) 21.4 Peak-peak tsunami m PagoPago, Samoa Port Vila, Vanuatu Noumea, NC Papeete,PF Kahului, Hawaii Crescent City, CA H_Min (m) c-c H_Moyen (m) c-c H_Max (m) c-c Observ Nuku Hiva, M i Hiva Oa, Marquises Rikitea, Gambier Santa Barbara CA King cove Alaska San Francisco Directivity effect Epicentral distance deg

9 First partial conclusions BSSA-89 relation works not only for PPT harbor, but also for various sites in the Pacific; Comparison of BSSA-89 gives good agreement with observed tsunami amplitudes, except for : Strong amplificating sites (Marquesas, Hawaii, Crescent City etc..), BSSA-89 under-estimates the amplitudes. Sites in nodes of directivity : BSSA-89 over-estimates the amplitudes. Thus the idea would be to add functions for taking into account : 1. Directivity, 2. Amplification of site, 3. Focusing effects, 4. Focal depth excitation. (Must also remind that source mechanism is not taken into account)

10 Method 1. Compute numerical simulations from a ten of classical sources (Chile 60, Aleutian 46, etc.) for a large number of virtual gauges, in various locations in the Pacific 2. Compare numerical simulations amplitudes with the BSSA-89 formula 3. Compare both above with observed tsunami amplitudes 4. Define a relation of the type: logts = CSource + CDist + CFocal + CSite + C0 Source Propagation Receiver

11 Location of studied sources Alaska 64 Kuril 2006 Aleutian 46 Mexico 1995 Tonga May 2006 Peru 2001 Chile 95 Chile 60 Generic source Earthquake

12 The 57 virtual gauges used for simulations

13 Virtual gauges around Marquesas

14 Example of source: Aleutian Isl. 1st April 1946

15 Example of comparison of BSSA-89 with computed amplitudes on the 57 sensors Aleutian H tsunami m Tsunami amplitude computed at for a 5000 m ocean depth: η2 = η1 (H2/H1)0.25 Sensor Capteur over sur 400m m de of profondeur ocean depth TS BSSA MAX m H5000 TS /2 TS / Hauteur Amplitude ramenée calculated à 5000 for m5000 m Directivity effect Distance deg

16 Example of correction of directivity Cor_Az Discutable! Back azimut % radiated along the fault azimuth 1 / Cor_AZ cor_azm Cor_AZ = cos( (ϕ strike +/- 90) - ϕ station )

17 The subductions zones in the Pacific for the pre-computed corrections of directivity

18 Aleutian 1 apr 1946 amplitudes are corrected from azimuth of strike H tsu m (cr-cr) TS BSSA A_cor_az TS /4 TS /2 Application of the correction of directivity distance deg Chile 30 jul 1995 amplitudes are corrected from azimuth of strike Mo = 1.2 E21 N.m Depth = 36 km 0.40 H tsu m (cr-cr) TS BSSA A_cor_az TS /4 TS / distance deg

19 Second partial conclusion : the BSSA-89 relation strongly over-estimates tsunami amplitudes for giant EQ. (Mo > 1E23 N.m) Chile 1960 H tsunami m TS BSSA MAX m H5000 TS /2 TS / Distance deg

20 Fitting the coefficient α to the BSSA-89 law TS = α Mo/1E20 *[Δ sin(δ/90)]0.5 ) * C_DIR 0.40 log10 TS best fit logaz_cor distance deg Log10(α ) vs log10(mo) log10(α ) log alpha Linéaire (log alpha) Y = X Log10(Mo)

21 1.20 Normalized excitation of tsunami vs depth and period Influence of s 758s 908s 1134s Average the focal depth Polynomial degree 2, as a function of focal depth Excitation tsunami vs depth T= 908s (15 min) 1.2 TS = α(mo) * Mo/1E20 * [Δ/90 sin(δ)] -0.5 * C_DIR(ϕs-ϕ ) * Excit(H) Excitation (normalized) y = -9E-05x x R 2 = s Polynomial (908s) focal depth km log TS = 0.53 log Mo log([δ/90 sinδ] + logc_dir(ϕs-ϕ) + logexcit(h) (A) TS tsunami amplitude in deep sea, crest-to through in m, Mo in N.m

22 Comparisons with observed amplitudes for 21 tsunamis recorded à Nuku Hiva (Marquesas)

23 Adjusting the constant of site CSite example for Marquesas Nuku Hiva Log Mo vs log tsunami amplitude at log Ampl (m) normalized Chile 1995 CSITE = y = x R 2 = Hokkaido log Mo loga90 logts 90 Linéaire (loga90)

24 Log ratio : obs / calc Comparison : tsunami amplitude observed vs estimated Nuku Hiva bay: ratio tsunami amplitude observed/estimated Peru2007 Kuril2007 Kuril2006 Tonga2006 Rat Island2003 Hokkaido2003 Peru2001 Kamchatka97 Santa Cruz97 Aleutian96 Peru96 Kuriles95 Mexique95 Solomon95 Chili95 Honshu89 Alaska87 Alaska64 Chili60 Kuriles58 Aleutian57 Aleutian Amplification Amplification

25 The site amplification factor: CSite (tsunami amplitude in deep ocean to tsunami amplitude in a given bay/harbor) The constant giving an average ratio close to 1.0 (without strong the focalization data (like Chile 95, Peru..etc) and without strong deficient amplitude (like Japan 2003 ) is: For Nuku Hiva (Marquesas): CSite =7.95 (# 8.0) Papeete (Tahiti, Society) : CSite = 2.7

26 Conclusions: final formula SOURCE PROPAGATION RECEIVER logts = CSource + CDist + CFocal + CSite + C0 TS : Tsunami amplitude crest-to-throught in m CSource = 0.53 log Mo + log C_dir(ϕstation-ϕstrike) + log Excit(H) Mo : seismic moment in N.m C_dir(ϕstation-ϕstrike) : correction of directivity Excit(H) : correction of excitation with focal depth CDist = log([δ/90 sinδ] : correction of distance CFocal : correction of focalization CSite : Constant of site C0 = -12.7

27 Conclusions : constant values CSite : Constant of site : CSite = 8.0 for Taiohae (Marquesas) CSite = 2.7 for Papeete (Tahiti) CFocal Constant of Focalization Marquesas Region CFocal Central Aleut. 4.6 Central Chile 5.2 Central Peru 2.3 Kurils 2.0 CFocal Constant of Focalization Papeete Region CFocal Central Aleut. 4.7 Tonga 2.7 Kurils 2.0 C_Excit(H) = -9E-5 H² H , H is focal depth in km

28 Next steps 1. Refine the constant of focalization (CFocal) with generic sources located in the main Peri- Pacific subduction zones 2. Refine the constant of site amplification (CSite), with use of detailed simulations 3. Improve the directivity function C_dir(ϕstation- ϕstrike), by taking into account distance and source dimensions.

29 END Thank you for your attention