Deterministic and Non-deterministic Behavior of Earthquakes and Hazard Mitigation Strategy Hiroo Kanamori Seismological Laboratory, California Institute of Technology
Earthquake Process Deterministic Non-deterministic
Deterministic Behavior Elastic Rebound Δε s (about 10000:1) Strain change in an earthquake: Δε s 2x10-5 to 2x10-4
Strain rate Plate boundary Plate interior ε ε =2x10-7 /year =2x10-8 /year Strain Change in Earthquake Δε s =2x10-5 to 2x10-4 Repeat Time, Plate boundary Plate interior τ τ = ε ε s 100 to 1,000 years 1,000 to 10,000 years
Recent progress Strain measurements with GPS.
1998 to 1999 Shortening of Honshu near Sendai 3 cm/yr (3 m/100yr, 30 m/1000yr)
Then, what happened on March 11, 2011 is:
Middleton Is., Alaska, Terraces courtesy of Dr. George Plafker
Middleton Is. Terraces Intervals: 500 to 1,350 years Height: 3.5 to 9 m 1964 Alaskan earthquake, Mw=9.2
c c c v c v c Deterministic Case c Kamaishi Repeater v Uchida, Matsuzawa et al. c(2012) c v c c c
Stress (strain) Change and Earthquake Sequence Strain or ε Δε s Strain or
Non-deterministic Behavior Complexity in plate boundary structure
Great Earthquakes rupture zones asperities interacting elements
Implication of multiple events Earthquake Sequence in Colombia-Ecuador 1906 Mw=8.8 1942, 1958, 1979 1906 11/15/2004 1906 M 0 =2x10 22 N-m 1979 1958 M 0 of 1906 x5 of (1942+1958+1979) 1942 Kelleher(1972), Kanamori and McNally (1982)
Earthquake Process Deterministic Part Scale Length Space: Fault dimension Time: Plate motion Regularity, Predictable Plus Non-deterministic Part Fault Interaction Nonlinearity of rock Complex system, unpredictable (magnitude-frequency relation (G-R relation), predictable only in a statistical sense)
Non-deterministic behavior Interaction of many elements in a large system Percolation Cellular automata Slider-block etc Turcotte et al. (2009) Magnitude-Frequency Relation (Gutenberg-Richter relation) Power Law
Magnitude-frequency Relation discrete (interval) cumulative log(n), log(n) characteristic log(n), log(n) non-characteristic M M log(n), log(n) general M discrete (interval) log[n(m)]=a-bm cumulative log[n(m)]=a -bm M and M+ΔM M
Kamaishi Uchida et al. Repeating (characteristic) earthquakes
Nankai trough M. Ando, written communication, 1999
If deterministic element dominates, some forecasts are possible. Forecast: 1. Measure strain build up, ΔԐ, with GPS in an area, S. 2. If ΔԐ is comparable to the estimated seismic strain change, ΔԐ s, Forecast of an earthquake with M w which depends on S and ΔԐ s. Uncertainties in ΔԐ s and S (e.g., interaction between patches) cause uncertainties in M w etc.
Example: 2010 Chile, 175 years since the 1835 (Charles Darwin) event Ruegg et al. (2009): Fully coupled (blue zone), a slip deficit of ~12 m, M w = 8 to 8.5 2010 M w =8.8, Red region, Aftershock area (From Lay, 2011)
Similar forecasts were made for the 2012 Costa Rica and the 2011 Tohoku-Oki E. In (2012) Mw=7.8 was forecast. Mw=7.6 occurred in 2012 Forecast underestimated. S and Δε s were underestimated
Scientific forecasts are useful for long-term hazard mitigation practice, if the uncertainties are properly considered. Scenario earthquake approach Average scenario events can be defined by existing scaling laws. However, outliers always exist, and it is important to understand what causes outliers. One of the most objectively determined scaling relations: source duration vs. moment (M 0 =µds)
Duration-Moment scaling relation Duputel et al. (2012) 8 1/3 0 t = 1.2x10 M c Source function t c : half duration (sec) M 0 =μsd : seismic moment t c 2t c Theoretically: 1/3 2/3 C α 1 1/3 = M γ V σ V: rupture speed, Δσ: stress drop, α: aspect ratio etc 1/3 0
Scale-invariant relation Duputel et al. (2012) Small V (rupture speed) Small Δσ (stress drop) Large α (aspect ratio) Large V Large Δσ Small α t c
The scaling relation gives the average scenario earthquakes, and outliers give the range. The physics causing the anomalous behavior can be inferred, if not uniquely.
Nankai trough Scenario Earthquake (Cabinet Office, Government of Japan, 2013)
Diversity of subduction-zone earthquakes Subduction-zone earthquakes in different domains Slightly modified from Lay et al. (2012) and Ye et al. (2013)
Diversity 1896 Sanriku Earthquake, M S =7.2 Run-up 30 m 200 km Hatori, 1967
2006 Java tsunami earthquake Minor shaking damage Heavy tsunami damage Courtesy of Professor Jim Mori
Diversity of subduction-zone earthquakes Subduction-zone earthquakes in different domains Slightly modified from (2013) Lay et al. (2012) and Ye et al.
Variation of source spectrum Green Box intra-plate earthquakes (Domains I and II)
Comparison of ground motion acceleration Tohoku-Oki earthquake Intra-plate earthquake
1939 Chillan earthquake (Ms=7.8, H=80-100 km) Beck et al. (1998), death toll 28,000 2009 Padang earthquake (M W =7.6, H=78 km ) death toll 1,115 EERI Special Earthquake Report December 2009,
Ground-motion from great earthquakes Source spectrum of large and great earthquakes Moment, N-m 2011 Tohoku-oki M w =9.0 2010 Chile M w =8.8 2004 Sumatra M w =9.2 2003 Tokachi-oki M w =8.3 M w =9.0 reference 0.001 0.01 0.1 1 Frequency, Hz
During the 2011 Tohoku-Oki earthquake, the roof of the Sakishima Building in Osaka, about 800 km from the epicenter, swayed 1.37 m. 52 story, 256 m
Ground motion acceleration NS (low passed at 0.2 Hz (5 sec)) cm/sec 2 Sendai (MYGH08) Red: downhole Black: surface Downhole 100m Osaka (OSKH02) Downhole 2 km Time, sec
Ground motion variation from Sendai to Osaka building x14 surface 2 km x30 1/30 Sato et al. (2012, 2013); Sato (2014) Source+path+site
Real-time application To cope with unexpected events, real-time methods are required.
Tsunami warning Modern broad-band records contain the complete source information in the first few minutes. Rapid (less than a few minutes) identification of tsunami source is now feasible.
Use of close-in stations for rapid retrieval of source parameters Rivera, Duputel, and others.. Source MR Function 150 s Δ=10, 2m30s ABU Z disp. Δ=5, 1m20s W phase window, 180 s M w =9.1
Earthquake Early Warning (far more difficult than tsunami warning) JMA type system is already working. Most important is warning at ground zero. Automated system is necessary. Bullet train Elevator control Protection of workers Protection of machinery
Bullet trains At the time of the earthquake 24 trains were running in the Tohoku Shinkansen system 9 seismic sensors along the coast, and 44 sensors along the train track - from Asahi detected the initial tremor; automatic shutdown of power; activation of the emergency brakes all trains stopped without derailment they did not sustain any damage on bridges and tunnels, and could restore the operation very quickly
Concept of onsite threshold warning (2011 Tohoku-Oki, MYG006) Can the initial amplitude tell us the peak amplitude? cm/sec 2 Vertical acceleration Initial amp. Trigger threshold (60 cm/sec 2 ) Warning time, 13 sec Peak amp. Horizontal velocity amplitude cm/sec Target PGV, 20 cm/s Time, sec
missed alarm successful alarm 100 PGV (total), cm/sec 10 Pa3, cm/sec 2 successful no alarm false alarm 1 1 10 100 Pa3, cm/sec 2 (gal)
Example of onsite early warning, P-trigger=60 cm/sec 2, Target PGV=20 cm/sec successful alarm false alarm successful no alarm missed alarm 2011 Tohoku-Oki 20km Mw=9.1 2004 Chuetsu, 13km Mw=6.6
Need to develop (1) Updating mechanism (to reduce missed alarms) (2) Cancellation mechanism (to reduce the impact of false alarms) (3) Automated control system
Conclusion 1. Earthquake process has Deterministic and Non-deterministic elements. 2. Where deterministic element dominates, forecasts can be made. 3. Large uncertainties are inevitable because of nondeterministic elements. 4. Seismic scaling relation helps to define scenario earthquakes and outliers. 5. Diversity needs to be considered for effective hazard mitigation strategy. 6. To cope with unpredictable nature of earthquakes, effective real-time systems need to be developed.
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