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1 2016 年全球地震海啸监测预警与数值模拟研究 1, 任智源 2 1, 2,, 原野 3 1, 2,, 赵联大 3 1, 2,, 王培涛 3 1, 2,, 侯京明 3 1, 2,, 徐志国 3, 1, 2, 高义 3 1,, 李宏伟 2 1,, 闪迪 2 1,, 王君成 2 1,, 范婷婷 2 1, 2, 王宗辰 (1., ; 2., ; 3., ) 摘要 : 回顾了国家海洋环境预报中心 ( 国家海洋局海啸预警中心 ) 2016 年全球地震海啸监测预警的总体状况, 并基于震源生成模型和海啸传播数值模型的计算结果详细介绍了几次主要海啸事件及其影响特性 2016 年全年国家海洋环境预报中心总共对全球 6.5 级 ( 中国近海 5.5 级 ) 以上海底地震响应了 45 次, 发布海啸信息 81 期, 没有发生对我国有明显影响的海啸结合精细化的数值模拟结果和浮标监测数据, 重点介绍了苏门达腊 7.8 级地震海啸厄瓜多尔 7.8 级地震海啸新西兰 7.1 级和 7.8 级地震海啸, 以及所罗门 7.8 级地震海啸的波动特征和传播规律, 模拟结果与实测海啸波符合较好针对厄瓜多尔 7.8 级地震海啸事件, 本文比较分析了均匀断层模型和多源有限断层模型对模拟结果的影响 ; 针对新西兰 7.1 级地震海啸, 探讨了色散效应对海啸波在大水深远距离传播过程的影响规律关键词 : 地震海啸 ; 海啸预警 ; 数值模拟 ; 浅水波方程 ; Boussinesq 方程中图分类号 : O352 文献标识码 : A 文章编号 : (2017) DOI: /hykx ,, [1], 90% [2-3],, , M w =9.2, 30 [4-6] 2010 M w = M w =9.0 [7], [8] Mansinha Lmylie [9], Volterra, COMCOT Okada [10-11],, [12],,, Cauchy-Poisson Fourier Laplace,, [1] Lynette Liu [13] Boussinesq [14] Madsen [15], Euler, [16] : ; : : (2016YFC ); ( ); (1604); [Foundation: The Public Science and Technology Research Funds Projects of Ocean, No ; the National Key Research and Development Plan, No. 2016YFC ; Opening fund of State Key Laboratory of Ocean Engineering, No. 1604; Technology Foundation for Selected Overseas Chinese Scholar] : (1986-),,,,,, : , zhyren@foxmail.com 98 / 2017 / 41 / 6

2 ,, Boussinesq MOST [17] GeoClaw [18] COMCOT [19] TUNAMI [20] N-S(Navier-Stokes),,,, Boussinesq,, Boussinesq,, FUNWAVE [21] CULWAVE [22], Boussinesq, [8, 23-25], [26-27], Carrier Greenspan [28], Synolakis [29], Carrier [30],, Tadepalli Synolakis [31-32] N (, N), N N Madsen Schffer [33] N, Zhao [34] N,,, Satake [35], Wei [36], Liu [37] 39, COMCOT Ren [38],,,, [39-41], Wang Liu [42-43],, (), , 2016, ( 1), , 7.8 1, Bird [44] PB2002, 18,,,,,, 2016 表 ~2016 年地震海啸预警响应频次 ( 中国海洋灾害公报 2010~2016) Tab. 1 Response times on tsunami warning from 2010 to 2016 (From Chinese Bulletin of Marine Hazards ) () () Marine Sciences / Vol. 41, No. 6 /

3 [44] Fig. 1 The distribution of the earthquake source which we have released tsunami information [44] AF: ; AM: ; AN: ; AR: ; AU: ; CA: ; CO: ; EU: ; IN: ; NZ: ; NA: ; OK: ; PA: ; PS: ; SA: ; SO: ; SU: ; YA: AF: plates of Africa; AM: plates of Amur; AN: plates of Antarctica; AR: plates of Arabia; AU: plates of Australia; CA: plates of Caribbean; CO: plates of Cocos; EU: plates of Eurasia; IN: plates of India; NZ: plates of Nazca; NA: plates of North America; OK: plates of Okhotsk; PA: plates of Pacific; PS: plates of Philippines; SA: plates of South America; SO: plates of Somalia; SU: plates of Sunda; YA: plates of Yangtze 1 研究方法 1.1 实测数据 DART (Deep-ocean Assessment and Reporting of Tsunamis)(PMEL, Pacific Marine Environmental Laboratory) DART 15 s1 min15 min, 15 min 15 s, 1 min,,,,, 1.2 数值模型, Okada [10-11],,,,,, [18] : h t x y hu hv 0 (1) b hu hu gh huv gh x (2) t x 2 y x b hv huv hv gh gh y (3) t x y 2 y, t, h(x, y, t), b(x, y), u(x, y, t) v(x, y, t) x y, g x y : 2 2 2, x gn hu hu hv 7/3 y 2 gn hv hu hv 7/3 2 2 h h (4) n,, (limiter) Wei Kirby [46] Boussinesq, TVD(Total Variation Diminishing), R-K(Runge-Kutta) [21], 100 / 2017 / 41 / 6

4 Nwogu [47] Boussinesq Peregrine [48] Boussinesq,, Boussinesq 1 Ht Hu Hv cos r cos z h h z h A B 2 r cos z h hcos z h A B 0 2 r g u fv u u v u t r0cos r0 r0cos (5) (6) 2 1 z Cd z A 0 2 t Bt u u r 2 0 cos H 1 1 g vt fu uv vv r0cos r0 r0 (7) 2 1 z Cd z A 0 2 t Bt u u r 2 H 0 ( hu ) ( hv cos ) ( u) ( v cos ) A, B (8) cos cos, H, r 0, (u α, v α ), η, C d,, f 0.39, z 0.53 h Boussinesq 年典型地震海啸模拟研究 2.1 苏门达腊 7.8 级地震海啸 (UTC ), M w = E, 4.9 S, 800 km, 24 km(usgs, United States Geological Survey), N m- 600 km, - 55 mm USGS,,,, , , DART-56001DART-23401, DART cm 15 cm (Hanimadhoo) 40 cm(sabang) DART, 1 cm USGS NOAA, : 96, 84, 170, 100 km, 50 km, 3.0 m Okada,, 2, 2a (),,,,, 3 h, 4 h 2b,, 4 DART ( E, S) DART ( E, S)DART ( E, N), DART ( E, N),, 4 DART, 2.2 厄瓜多尔 7.8 级地震海啸 (UTC ), M w =7.8 USGS, W, 0.37 N, 170 km, 20 km N m, 61 mm Marine Sciences / Vol. 41, No. 6 /

2 2016 7.8 Fig. 2 Numerical results of the 2016 Sumatra Earthquake Tsunami of M w 7.

5 Fig. 2 Numerical results of the 2016 Sumatra Earthquake Tsunami of M w 7.8 a: ; b: a: Distribution of the maximum tsunami wave amplitude and traveling time; b: Comparison of the tsunami wave series at DART locations between the measurement (black line) and numerical results (red line), La Libertad 0.12 m, 0.24 m USGS ( 160 km, 60 km, 29, 15, 123 ), Okada (Finite fault model, 240 ), 4 min, 0.5 min 0.25 min 3, 3a,,,,,, 22 h 3b,, 32411( W, N) 32413( W, S) 1 cm, DART ( W, N), 102 / 2017 / 41 / 6

5 cm La Libertad (89.319 W, 13.4851 N),,, DART51407, 1 mm 3 2016 7.8 Fig. 3 Numerical results of the 2016 Ecuador Earthquake Tsunami of M w 7.

6 5 cm La Libertad ( W, N),,, DART51407, 1 mm Fig. 3 Numerical results of the 2016 Ecuador Earthquake Tsunami of M w 7.8 a: ; b: a: Distribution of the maximum tsunami wave amplitude and traveling time; b: Comparison of the tsunami wave series at DART locations between the measurement (black line), numerical results of the uniform earthquake source (red line), and the finite fault model (green line) 2.3 新西兰 7.1 级地震海啸 (UTC ), M w = E, S,, 50 km, 20 km N m, 47 mm/a, 6 28, Marine Sciences / Vol. 41, No. 6 /

7 East Cape( E, S) Tauranga( E, S), 23 cm 5 cm USGS : 60 km, 40 km, 19 km, 351, 26, 145, 0.6 m, 0.5, 4a, East Cape 30 min, 4 4b,,, 13 h, boussinesq 4c,,, 2.4 新西兰 7.8 级地震海啸 (UTC ), M w = E, S,, 56 km, 22 km(usgs) N m,, Kaikoura( E, S) Wellington( E, S) 233 cm 46 cm : 100 km, 50 km, 15 km, 219, 38, 128, 3.0 m,, 5a, 30 min,, 4 5b, 200 km,, 14 h, 18 h 2.5 所罗门群岛 7.8 级地震海啸 (UTC ), M w = E, S,, (Kirakira) 69.1 km, 41.0 km (USGS) N m,, 96 mm USGS ( E, S) 55023( E, S) 100 km, 50 km USGS : 41 km, 290, 44, 67, 3.0 m 6a,, 5 cm,,,, 3 讨论 2016,,,, ,,, 7.8,, 104 / 2017 / 41 / 6

4 2016 7.1 Fig. 4 Numerical results of the 2016 New Zealand Earthquake Tsunami of M w 7.

8 Fig. 4 Numerical results of the 2016 New Zealand Earthquake Tsunami of M w 7.1 a: ; b: ; c: a: Comparison of the tsunami wave series at coastal locations between the measurement and numerical results; b: Distribution of the maximum tsunami wave amplitude and traveling time; c: Difference of maximum amplitude between the shallow water equation and the Boussinesq equation Marine Sciences / Vol. 41, No. 6 /

5 2016 7.8 Fig. 5 Numerical results of the 2016 New Zealand Earthquake Tsunami of M w 7.

9 Fig. 5 Numerical results of the 2016 New Zealand Earthquake Tsunami of M w 7.8 a: ; b: a: Comparison of the tsunami wave series at coastal locations between the measurement (black line) and numerical results (red line); b: Distribution of the maximum tsunami wave amplitude and traveling time,, [49] 7.8,,,, [50-51] : = A h (9) 2 3 6h L (10),,,, A, h, L, λ, 1 m, ;, 1 cm, ,,, m 30 m, 1 m, 100 km, (A 1 /A 2 = (h 2 /h 1 ) 1/4 ) ε 4000 = , ε 30 =0.11, 10,, (4 000 m), (100 km), km 106 / 2017 / 41 / 6

10 Fig. 6 Numerical results of the 2016 Solomen Earthquake Tsunami of M w 7.8 a: ; b: a: Comparison of the tsunami wave series at coastal locations between the measurement (black line) and numerical results (red line); b: Distribution of the maximum tsunami wave amplitude and traveling time km τ Glimsdal [51], τ 0.1,, m, 100 km, km,, 4c 2011 [21],,, [18],, 2 43 Ou h, 100 m,, [52] 4 结论 2016, Boussinesq, , , 8.0, 7.8 4,,,,,, Marine Sciences / Vol. 41, No. 6 /

11 , 致谢 : 感谢上海交通大学何友声教授和加州理工学院吴耀祖教授 (Theodore Yao-Tsu Wu) 的鼓励与支持对上海交通大学刘桦教授和丹麦科技大学 Per A. Madsen 教授的指导和帮助表示衷心感谢本文得到了国家重点研发计划 (2016YFC ), 国家海洋公益性行业科研专项项目 ( ), 海洋工程国家重点实验室开放课题 (1604) 和留学人员科技活动项目择优资助的支持 : [1]. [D]. :, Ren Zhiyuan. Numerical simulation of tsunami in South China Sea[D]. Shanghai: Shanghai Jiao Tong University, [2],,,. [J]., 2012, 34(2): Wang Peitao, Yu Fujiang, Zhao Lianda, et al. Numerical simulation of trans-oceanic tsunami and its impact analysis on Chinese coasts[j]. Acta Oceanologica Sinica, 2012, 34(2): [3],,. [J]., 2005, 22(S1): Ye Lin, Yu Fujiang, Wu Wei. The disaster and warning of tsunami in China and the suggestion in future[j]. Marine Forecasts, 2005, 22(S1): [4] Titov V, Rabinovich A B, Mofjeld H O, et al. The Global Reach of the 26 December 2004 Sumatra Tsunami[J]. Science, 2005, 309(5743): [5] Grilli S T, Ioualalen M, Asavanant J, et al. Source constraints and model simulation of the December 26, 2004, Indian Ocean Tsunami[J]. Journal of Waterway, Port, Coastal, and Ocean Engineering, 2007, 133(6): [6] Wijetunge J J, Wang X, Liu P L-F. Indian Ocean Tsunami on 26 December 2004: numerical modeling of inundation in three cities on the south coast of Sri Lanka[J]. Journal of Earthquake and Tsunami, 2008, 2(2): [7] Melgar D, Allen R M, Riquelme S, et al. Local tsunami warnings: Perspectives from recent large events[j]. Geophysical Research Letters, 2016, 43(3): [8],,,. [J]., 2015, 3: Liu Hua, Zhao Xi, Wang Benlong. Numerical simulation of tsunami and tsunami warning methods for South China Sea region[j]. Chinese Quarterly of Mechanics, 2015, 3: [9] Mansinha L, Smylie D E. The displacement fields of inclined faults[j]. Bulletin of the Seismological Society of America, 1971, 61(5): [10] Okada Y. Surface deformation due to shear and tensile faults in a half-space[j]. Bulletin of the Seismological Society of America, 1985, 75(4): [11] Okada Y. Internal deformation due to shear and tensile faults in a half-space[j]. Bulletin of the Seismological Society of America, 1992, 82(2): [12] Dao M H, Tkalich P. Tsunami propagation modelling-a sensitivity study[j]. Natural Hazards and Earth System Science, 2007, 7(6): [13] Lynett P, Liu P L F. A numerical study of submarine landslide generated waves and run up[j]. Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences. The Royal Society, 2002, 458(2028): [14]. Boussinesq [D]. :, Wang Benlong. Mathematical modelling of surf zone based on the high order Boussinesq equations[d]. Shanghai: Shanghai Jiao Tong University, [15] Madsen P A, Bingham H B, Liu H. A new Boussinesq method for fully nonlinear waves from shallow to deep water[j]. Journal of Fluid Mechanics, 2002, 462: [16]. [D]. :, Zhao Xi. Numerical simulation of generation, propagation and runup of tsunamis[d]. Shanghai: Shanghai Jiao Tong University, [17] Titov V V, Synolakis C E. Numerical modeling of tidal wave runup[j]. Journal of Waterway, Port, Coastal, and Ocean Engineering, 1998, 124(4): [18] Leveque R J. Tsunami modelling with adaptively refined finite volume methods[j]. Acta Numerica, 2011, 20: [19],,. [C]//.. :, 2013: Ren Zhiyuan, Zhao Xi, Liu Hua. Advances in tsunami warning technology and tsunami warning method in South China Sea[C]// Wu Yousheng. Article Collection of 25th National Symposium on Hydrodynamics. Beijing: China Ocean Press, 2013: [20] Imamura F, Shuto N, Goto C. Numerical simulations of the transoceanic propagation of tsunamis[c]//iahr, Sixth Congress of the Asian and Pacific Regional Division of the International Association for Hydraulic Research proceedings. Kyoto: Local organizing committee of the congress, 1988: / 2017 / 41 / 6

12 [21] Kirby J T, Shi F, Tehranirad B, et al. Dispersive tsunami waves in the ocean: Model equations and sensitivity to dispersion and Coriolis effects[j]. Ocean Modelling, 2013, 62(62): [22] Lynett P J. Nearshore wave modeling with high-order Boussinesq-type equations[j]. Journal of Waterway, Port, Coastal, and Ocean engineering, 2006, 132(5): [23] Madsen P A, Schäffer H A. Higher order Boussinesq type equations for surface gravity waves: derivation and analysis[j]. Philosophical Transactions of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, 1998, 356(1749): [24] Gobbi M F, Kirby J T, Wei G. A fully nonlinear Boussinesq model for surface, waves. Part 2. Extension to O(kh) 4 [J]. Journal of Fluid Mechanics, 2000, 405(4): [25] Madsen P A, Bingham, Liu H. A new Boussinesq method for fully nonlinear waves from shallow to deep water[j]. Journal of Fluid Mechanics, 2002, 462(1): [26] Bai Y, Cheung K F. Dispersion and nonlinearity of multi-layer non-hydrostatic free-surface flow[j]. Journal of Fluid Mechanics, 2013, 726: [27] Fang K, Liu Z, Zou Z. Modelling coastal water waves using a depth-integrated, non-hydrostatic model with shock-capturing ability[j]. Journal of Hydraulic Research, 2015, 53(1): [28] Carrier G F, Greenspan H P. Water waves of finite amplitude on a sloping beach[j]. Journal of Fluid Mechanics, 1958, 4(4): [29] Synolakis C E. The runup of solitary waves[j]. Journal of Fluid Mechanics, 1987, 185: [30] Carrier G F, Wu T T, Yeh H. Tsunami run-up and draw-down on a plane beach[j]. Journal of Fluid Mechanics, 2003, 475: [31] Tadepalli S, Synolakis C E. The run-up of N-waves on sloping beaches[j]. Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences. The Royal Society, 1994, 445(1923): [32] Tadepalli S, Synolakis C E. Model for the leading waves of tsunamis[j]. Physical Review Letters, 1996, 77(10): [33] Madsen P A, Schaeffer H A. Analytical solutions for tsunami runup on a plane beach: single waves, N-waves and transient waves[j]. Journal of Fluid Mechanics, 2010, 645: [34] Zhao X, Wang B, Liu H. Characteristics of tsunami motion and energy budget during runup and rundown processes over a plane beach[j]. Physics of Fluids, 2012, 24(6): [35] Satake K. Inversion of tsunami waveforms for the estimation of a fault heterogeneity: Method and numerical experiments[j]. Journal of Physics of the Earth, 1987, 35(3): [36] Wei Y, Cheung K F, Curtis G D, et al. Inverse Algorithm for Tsunami Forecasts[J]. Journal of Waterway, Port, Coastal, and Ocean Engineering, 2003, 129(129): [37] Liu P L-F, Wang X, Salisbury A J. Tsunami hazard and early warning system in South China Sea[J]. Journal of Asian Earth Science, 2009, 36(1): [38] Ren Z Y, Liu H, Wang B L, et al. An investigation on multi-buoy inversion method for Tsunami Warning System in South China Sea[J]. Journal of Earthquake and Tsunami, 2014, 8(3): [39] Okal E A, Piatanesi A, Heinrich P. Tsunami detection by satellite altimetry[j]. Journal of Geophysical Research, 1999, 104(B1): [40] Smith W, Scharroo R, Titov V, et al. Satellite altimeters measure tsunami[j]. Oceanography, 2015, 18(2): [41] Hamlington B D, Leben R R, Godin O A, et al. Could satellite altimetry have improved early detection and warning of the 2011 Tohoku tsunami?[j]. Geophysical Research Letters, 2012, 39(15): L [42] Wang B, Liu H. Kinematic dynamo by large scale tsunami waves in open ocean[j]. Theoretical and Applied Mechanics Letters, 2013, 3(3): [43] Wang B, Liu H. Space-time behaviour of magnetic anomalies induced by tsunami waves in open ocean[j]. Proceedings of the Royal Society A Mathematical Physical & Engineering Sciences, 2013, 469(2157): [44] Bird P. An updated digital model of plate boundaries[j]. Geochemistry, Geophysics, Geosystems, 2003, 4(3): [45] Rabinovich A B, Candella R N, Thomson R E. The open ocean energy decay of three recent trans Pacific tsunamis[j]. Geophysical Research Letters, 2013, 40(12): [46] Wei G, Kirby J T. Time-dependent numerical code for extended Boussinesq equations[j]. Journal of Waterway, Port, Coastal, and Ocean Engineering, 1995, 121(5): [47] Nwogu O. Alternative form of Boussinesq equations for nearshore wave propagation[j]. Journal of Waterway, Port, Coastal, and Ocean engineering, 1993, 119(6): [48] Peregrine D H. Long waves on a beach[j]. Journal of Fluid Mechanics, 1967, 27(4): [49] Ulutas E. Comparison of the seafloor displacement from uniform and non-uniform slip models on tsunami simulation of the 2011 Tohoku Oki earthquake[j]. Journal of Asian Earth Sciences, 2013, 62(30): Marine Sciences / Vol. 41, No. 6 /

13 [50]. [J]., 2001, 31(3): Wu T Y. Advances in water wave mechanics[j]. Advances in Mechanics, 2001, 31(3): [51] Glimsdal S, Harbitz C B, Løvholt F. Dispersion of tsunamis: does it really matter?[j]. Natural Hazards and Earth System Sciences, 2013, 13(6): [52] Ren Z Y, Wang B L, Fan T T, et al. Numerical analysis of impacts of 2011 Japan Tohoku tsunami on China Coast[J]. Journal of Hydrodynamics, 2013, 25(4): Monitoring, early warning and numerical study of global tsunamis in 2016 REN Zhi-yuan 1, 2, YUAN Ye 1, 2, 3, ZHAO Lian-da 1, 2, 3, WANG Pei-tao 1, 2, 3, HOU Jing-ming 1, 2, 3, XU Zhi-guo 1, 2, 3, GAO Yi 1, 2, 3, LI Hong-wei 1, 2, SHAN Di 1, 2, WANG Jun-cheng 1, 2, FAN Ting-ting 1, 2, WANG Zong-chen 1, 2 (1. National Marine Environmental Forecasting Center, Beijing , China; 2. State Oceanic Administration Tsunami Warning Center, Beijing , China; 3. Key Laboratory of Research on Marine Hazards Forecasting, National Marine Environmental Forecasting Center, Beijing , China) Received: Feb., 14, 2017 Key words: Tsunami; Tsunami early warning; numerical modeling; shallow water equation; Boussinesq equation Abstract: This study reviewed global earthquake tsunami warnings in 2016, monitored by the National Marine Environmental Forecasting Center (National Tsunami Warning Center, SOA), and introduced the five typical tsunami events-basedon tsunami generation and propagation numerical models. We have responded from 45 submarine earthquakes, above a magnitude of 6.5 (M w > 5.5 in the coastal region of China), and released 81 times of earthquake information in No tsunami affected Chinese Coasts. This study has focused on the Sumatran tsunami of M w 7.8, the Ecuadorian tsunami of M w 7.8, the New Zealand tsunamis of M w 7.1 and 7.8, and the Solomon tsunami of M w 7.8, and presented maximum tsunami wave distribution and wave fluctuation data based on refined numerical results and measurements. The numerical results could reproduce the tsunami scenarios and match the measured data well. Comparison between the uniform fault model and the finite fault model with the multi-plate for the Ecuadorian tsunami of M w 7.8 is presented. The dispersion effect on tsunami propagation is discussed based on the simulation results of the New Zealand tsunami of M w 7.1 with Boussinesq equation. ( 本文编辑 : 李晓燕 ) 110 / 2017 / 41 / 6

Fig. 1 1 The sketch for forced lead shear damper mm 45 mm 4 mm 200 mm 25 mm 2 mm mm Table 2 The energy dissip

Fig. 1 1 The sketch for forced lead shear damper mm 45 mm 4 mm 200 mm 25 mm 2 mm mm Table 2 The energy dissip * - 1 1 2 3 1. 100124 2. 100124 3. 210018 - ABAQUS - DOI 10. 13204 /j. gyjz201511033 EXPERIMENTAL STUDY AND THEORETICAL MODEL OF A NEW TYPE OF STEEL-LEAD DAMPING Shen Fei 1 Xue Suduo 1 Peng Lingyun 2 Ye