Long-term earthquake forecast

Transcription

1 演 The M9 Tohoku-Oki Earthquake and Statistical Seismology Yosihiko Ogata, Institute of Statistical Mathematics 1.Long-term Probability forecasting and repeating earthquakes 2.Prediction and diagnostic analysis of seismic activity 3.Discrimination of foreshocks and their operational forecasting 30 years after Long-term earthquake forecast The Earthquake Research Committee (ERC) of Japan opens the probabilities that earthquakes will occur in the future at main active faults and subduction-zones in Japan to the public. >90% Long-term evaluation of the subduction-zones Long-term evaluation of the main active faults?% >90% <90% 20% <7% 90%

2 The main focal area of major Earthquakes From Sanriku-Oki to Boso-Oki (ERC, 1999) Miyagi-Ken-Oki Earthquake + f ( x) Time (year) Renewal process models t last f( t tlast ) ( t History) ( ttlast ) 1 F( t t ) last t 30 years probability Present time f( t tlast ) ( ttlast ) 1 F( t t ) a 30 a ( t t ) dt last last What is the BPT renewal process? Probabilistic model for earthquake generation Brownian relaxation oscillator process t last Time(years) Active faults a a years surviving probab. = exp ( Area of ) Fault 1 Fault 2 Fault 3 Fault 4 Fault n present Brownian motion with drift λ S(t): Stress accumulation W(t): Standard Brownian motion λ: Loading rate sf σ: Perturbation rate sf: Failure state s0 s0:ground state S(t) Earthquake Recurrence interval (Brownian passage time)

3 Probability density function What is the BPT renewal process? Brownian Passage Time (BPT) distribution Recurrence interval ( Brownian passage time ) μ Unknown parameters Mean Coefficient of variation α sf s0 Earthquake Recurrence interval (Brownian passage time) Forecasting method by ERC Predictive distribution for interval time from the latest earthquake to the next earthquake Plug-in predictive density MLE from 4 active faults where a lot of earthquakes turned out. or V:slip velocity Mean of past intervals X = (X1 Xn) U:slip size per one earthquake Bayesian predictive density Proposal S. Nomura(SOKENDAI D3) Predictive distribution for interval time from the latest earthquake to the next earthquake Estimation of prior distribution Fault 1 Fault 2 Fault 3 Fault 4 Fault n 現在 Probability density S. Nomura(SOKENDAI D3) μ/t (gamma distribution) posterior density prior density likelihood (BPT renewal process) Merits of proposal method Its predictive performance will be more stable than plug-in methods. Both slip data T=U / V and past intervals X=(X1,,Xn) are used. The estimation of α is not fixed and different among active faults. ABIC and estimated prior distribution Lognormal Gamma Weibull Exp Uniform Lognormal Gamma Weibull Exp Uniform Probability density (Weibull distribution) α (ERC) (MLE from all datasets)

4 Maximum Posterior estimates Mean interval ( 年 ) Coefficient of variation S. Nomura(SOKENDAI D3) Okada, Uchida, Aoki (2011) Renewal model (log Normal) for 163 repeating earthquake sequences Estimation Forecasted for 2010 Result for 2010 Probability density function μ Recurrence interval ( Brownian passage time ) α sf s0 Earthquake Recurrence interval) Stochastic model for repeating earthquakes Brownian relaxation oscillator process (e.g. Matthews et al. 2002) ds t = λdt + σ dw t (W t standard B.M.) S t : shear stress S t λdt :stress loading σdw t : stress perturbation S f : failure stress space-time model Non-stationary loading rates and dispersions ds t = λ(x,y,t) dt + σ(x,y,t) dw t x: 水平位置 λ(x,y,t):loading rate S. Nomura(SOKENDAI D3) (x,y) 繰り返し地震系列 Interval lengths obey the BPT distribution: density S 0 : ground stress t 2 ( x ) mean: ( sf s0)/ f( x, ) exp x 2 x variance: / ( s s ) f 0 y: 深さ の震源位置 震源 (x,y) における繰り返し地震発生時刻 We cannot assume the BPT for the interval distribution. t: 時間

5 Assume the following model ds ( x, y, t) dt ( x, y, t) dw t 0 0 S. Nomura(SOKENDAI D3) λ 0 :Background loading rate σ 0 :Background perturbation rate λ(x,y,t) :space-time rates relative to the background loading rate λ 0 Then we have the BPT intervals for each (x,y) by time transformation t = λ(x,y,t)dt t Parkfield data (Nadeau) S. Nomura(SOKENDAI D3) Micro-earthquakes (HRSN, Magnitude range ー 0.5~2) period 1987/1/1~2004/9/28(preceding 2004 Parkfield) with missing data during 1998/7/1~2001/7/26 λ(x,y,t)is regarded as changes of stress loading velocity, and parameterized by a 3D spline function with smoothness constraints. Objective Bayesian procedure (ABIC) is applied to attain the optimal constraints M M6.0 20km ahead No observation period Result Loading rate change at each sub-region S. Nomura(SOKENDAI D3) Result Spatial change in time S. Nomura(SOKENDAI D3)

6 S. Nomura(SOKENDAI D3) 7 Result on the dispersion coeff.α Dispersion coefficientα(proportional to the perturbation rate σ) is affected by the nearby earthquakes Prediction and diagnostic analysis of seismic activity 低 低 高 高 α Geographical Survey Institute Deformation of Japanese islands Coseismic dislocations of Tohoku-Oki earthquake of M9 Time(Month) M9

7 Triggering Coulomb Stress Sudden Stress Increase FAILURE STRESS FAILURE STRESS Quiescence Sudden Stress Decrease Coulomb s Failure Stress (friction coeff.) X (Epidemic Type Aftershock Sequence model) Ogata (1988, J. Amer. Statist. Assoc.) Omori-Utsu formula for aftershock decay t = Ogata (1988,JASA) Maximize the function ˆ ( ˆ, Kc ˆ, ˆ, ˆ, pˆ) MLE... Computer codes available. Please visit WEB home page of our project team:

8 4 Triggered activities Transformed Time Ordinary Time See the following slides 福島県いわき市付近の誘発地震活動 Northern Nagano Pref. Sakae Vil. M 4.0 M7 M 3.5 M 3.0 M7 M7 FAILURE STRESS Quiescence Stress Rate Decrease

9 7 Foreshocks led by the M7.3 event Foreshocks M 3.0 M 3.5 M 4.0 M 4.5 M 3.0 M 3.5 M Aftershocks Space vs transformed-time plot of the foreshock activity till M9 mega event

10 変換時間変換時間 Aftershocks of Tohoku-Oki Earthquake of M9 14 Aftershocks of Tohoku-Oki Earthquake of M9 (cont.) 2010 Chili Earthquake (Mw8.8)Aftershocks M Sumatra Earthquake (Mw9.0) Aftershocks

11 New Zealand Darfield Earthquake Aftershocks and Christchurch Earthquake E NZ-GNS M 3.5 N S W USGS-PDE M 4.0 Extensive Quiescence before the M9 earthquake 7 (Ogata, 1998, AISM) (Ogata, 2004, JGR and 2011, EPS) Delaunay-based function: an illustration

12 -value K0-value -value Flatness constraints Delaunay-based function: an illustration ρ ( w, w, w, w, w ) L( ) prior( ρ) posterior( ρ) ( ρ) K p q ( ρ) L( ) prior( ρ) d (Likelihood of a Bayesian model; Good 1965) ρ ( ρ) Choose w s that maximize w or minimize M >= p-value M >= K 0 ( x, y ) j j (, t x, y Ht ) ( x, y) p( xj, yj) { j; tj t} ( t tj c) q-value M >= t ( x xj, y yj) S j( x xj, y yj) j j d ( xj, yj)( M j M c ) e q( x, y ) Delaunay-based function: Akaike Bayesian information criterion (Akaike, 1980) M >= M >= Precursory period Delaunay-based function: an illustration Ko Ko Hierarchical Space-time ETAS model (HIST-ETAS) (, t x, y Ht ) ( x, y) { j; tj t} Background rate K( x, y) ( t t c) j p( x, y) ( x x, ) (, ) t q x y j y yj Sj x xj y y j d ( xy, )( M j M c ) e (, ) M 4.0 Shallow 30km p p Stochastic declustering (Zhuang, Ogata & Vere-Jones., 2004 JASA and 2005, JGR) Accept earthquake as a background event with probability: i ( xi, yi) ( ti, xi, yi Hti )

13 M 5.0 Original data A M 5.0 B C Latitude M 5. 0 Time F C A B D E G Time De-clustered data Longitude G F E D Latitude Time Time Longitude Original data T. Kumazawa(SOKEN-DAI D3) 1926 ~ 2011 Mar. M>=5.0 M9 M 5.0 M 5.0 Q Transformed time by ETAS model M9 Q M 5.0 M 4.0 Ordinary Time

14 Geographical Survey Institute (2011) West wards East wards Back slip inversion Okada, Uchida, Aoki (2011) Renewal model (log Normal) for 163 repeating earthquake sequences Estimation Forecasted for 2010 Result for 2010 E-W complession strike slips N-S complession thrust slips Operational Probability Forecasting of Foreshocks and Evaluations: 15 years periods till the Tohoku-Oki Event E-W complession thrust slips N-S complession strike slips

15 (1) How do we recognize that it is initial earthquake of a cluster? (2) What is definition of foreshocks? Earthquakes (M 4.0) in JMA catalog during 1994 ~ Mar are connected by the distance criterion 2 2 dst space ( ctime ) 0.3 (or 33.33km) where c is the constant so as to hold 1day = 1km Cluster types Single-link-clustering , M 4 from the old JMA catalog Cluster Foreshocks Swarms M.A. All clusters member# #c ratio(%) s.e.(%) #c ratio(%) s.e.(%) #c #c ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± Initial earthquakes of clusters or Isolated earthquakes Probability of the initial earthquakes Being foreshock during probability Measuring inter-events concentrations in a cluster and magnitude increments Aftershocks Swarms Foreshocks F A S F F Others freq. Foreshocks freq. Forecasted results for 1994 Mar Forecast 0-2.5% 2.5-5% 5%- All Foreshocks Others All types Ratio(%) Diff. entropy = 22.7 Diff. AIC = 40.0 (cross-table) Probability forecast (%) Relative frequencies A S F

16 Time difference, Distance & Magnitude difference Normalization (t, r, g) () in [0,1] 3 Time Interval Transformation Epicenter Separation Transformation 1exp{ min( r,50) / 20} Magnitude Difference Transformation Normalized time differnce, distance & magnitude difference in the unit cube Algorithm of foreshock probability calculations in case of plural earthquakes in a cluster For plural earthquakes in a cluster, time differences t ij (days),epicenter separation r (km),magnitude difference g ij are transformed into the unit cube ij ( t, r, g ) (,, ) [0,1] i, j i, j i, j i, j i, j i, j Probability p c is calculated sequentially logit( p ) logit ( x 1, y k k k c 1) 1 k i, j k i, j k i, j #{ i j} a b c d ij k1 k1 k1 Here (x, y) indicates probability of initial earthquake at location (x,y),and the 2 nd term calculates arithmetic mean of polynomials of the normalised space-time magnitude variables for all pairs of earthquakes (i < j) in a cluster, where the coefficients a, b, c, d are as follows. Ogata, Utsu and Katsura, 1996, GJI) k ak bk ck dk ただし 6709, Forecasted sequence and evaluation ( Mar ) # F? #C Pc ENTRPY CU~ENT P1 P2 P3 P4 P5 P6 P7 P8 P9 P % % % % 12.66% % % % % % % % % % % 11.17% 7.87% 9.82% % % % % % % % % 27.8% 27.7% 20.1% 14.0% 14.2% 13.6% 11.6% 15.7% 11.9% 10.1% 8.2% 10.1% 11.7% 10.9% 10.6% 11.5% 11.1% 9.9% 8.2% 7.2% 6.8% 7.6% 7.3% 7.4% 6.7% 7.0% 7.0% 8.0% 8.5% 8.6% 8.2% 8.0% 8.1% 8.4% 7.8% 7.3% 7.5% 7.8% 8.1% 8.1% 7.8% 7.4% 7.7% 7.8% 7.6% 7.2% 7.2% 6.9% 6.8% 6.7% 7.4% 8.0% 7.8% 7.6% 7.7% 8.3% 9.0% 8.7% 8.5% 8.6% 8.3% 8.4% 8.2% 8.2% 8.0% 7.9% 7.9% 8.4% 8.4% 8.6% 8.5% 8.6% 8.4% 8.2% 8.4% 8.3% 8.3% 8.1% 7.9% M7.3 Foreshock of 9 Mar 2011 M9.0 Probability forecast (%) 100% 10% 1% 0.1% Mc % Earthquake number in a cluster Probability forecast (%) 100% 10% 1% 0.1% 0.01% Earthquake number in a cluster M main 6.5 Mc 4.0 Earthquake number in a cluster M7.3 Foreshock of 9 Mar 2011 M % % 4.77% 6.21% 3.42% 1.74% 1.24% 1.04% 0.90% 0.83% 0.97% 1.03% % % 0.25% 0.51% 0.83% 2.77% 2.21% 2.02% 3.19% 2.78% 2.50% 2.43% 3.07% 2.92% 2.74% 2.84% 2.68% % % 0.79% 1.70% 2.06% 1.90% 1.90% 1.88% % % % % % % 7.42% 4.88% 3.98% 3.56% 4.05% 4.49% % % % % % % % % *Entropy0 = ; 2*Entropy = : 2*Entropy = Relative frequencies Others freq. Foreshocks freq 年 年 3 月 Probability forecast (%)

17 Thank you very much for your attention. How foreshock forecast probabilities (BLUE LINES) changed after actual mainshock occurred in case of foreshock-mainshockaftershock sequence? 100% Software available for the ETAS fitting, diagnostic analysis and its manual. Please visit WEB home page of our project team: Very soon, computer programs are available for the Hierarchical Space-Time ETAS (HIST-ETAS) by a Bayesian procedure (ABIC). Probability forecast (%) 10% 1% 0.1% 0.01% Mc 4.0 Single foreshock case Plural foreshocks case Mc 4.0 Mc Earthquake number in a cluster Earthquake number in a cluster Single-link-clustering , M 4 from the old JMA catalog Cluster Foreshocks Swarms M.A. All clusters member# #c ratio(%) s.e.(%) #c ratio(%) s.e.(%) #c #c ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± Single-link-clustering , M 4 from the new JMA catalog Cluster Foreshocks Swarms M.A. All clusters member# #c ratio(%) s.e.(%) #c ratio(%) s.e.(%) #c #c ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±

18 前震の確率は本震が起きてからどのように変わったか?. 青線が本震直前以降の確率変化 左図が一個の前震の場合で右図が複数個の前震 ( 赤線 ) の場合 群れの先頭 ( 孤立地震を含む ) が前震である確率の地域性 JMA old JMA old % 10% Probability forecast (%) 1% 0.1% Mc 4.0 JMA new JMA new Mc 4.0 Mc % Earthquake number in a cluster Earthquake number in a cluster

19 Thank you very much for your attention Software available. Please visit WEB home page of our project team: