Open House, ISM in Tachikawa, 2012.6.15統計数理研究所オープンハウス（立川）、H24.6.15ポスター発

Jiancang Zhuang

庄 建倉

English

RISM (Repository of the Institute of Statistical Mathematics) / 統計数理研究所 学術研究リポジトリ

【Abstract】Based on the ETAS (epidemic-type aftershock sequence) model, which is used for describing the features of short term clustering of earthquake occurrence, this poster presentssome theories and techniques related to evaluating the probability distribution of the maximum magnitude in a given space-time window, where the Gutenberg-Richter law forearthquake magnitude distribution cannot be applied directly. It is shown that the distribution of the maximum magnitude in a given space-time volume in long term is determinedby the background seismicity rate and the magnitude distribution of the largest events in each earthquake cluster. The introduced techniques were applied to the seismicity in theJapan region in the period from 1926 to 2009. It is found that the regions most likely to have great earthquakes are along the Tohoku (Northeastern Japan) Arc and the Kuril Arc,both much higher probabilities than the offshore Nankai and Tokai regions.【Description of methods】【Results for the Japan region】JMA catalog:  depth 0 - 100 km, Date 1926-01-01 to 2009-12-31, MJ ≥4.0.【References】Zhuang J. and Ogata Y. (2006) Properties of the probability distribution associated with the largest event in an earthquake cluster and their implications to foreshocks. Physical Review, E. 73, 046134. Vere-Jones D. and Zhuang J. (2008) On the distribution of the largest event in the critical ETAS model. Physical Review E., 78, 047102. Zhuang J. (2012) Long-term earthquake forecasts based on the ETAS model for short-term clustering. Research in Geophysics, in press. DFigure 2. (left panel) Background seismicity rate (occurrence rate of earthquake clusters) [events/(day·deg2)] of earthquakes with magnitude MJ ≥4.0, obtained based on the space-time ETAS model. (right panel) Spatial variations of b-values estimated by variable kernel estimates. Figure 1.  Influence of A, α, and β to function F(m). (a) Parameter A changes, α =1.2 and β =2.4 fixed; (b) Parameter α changes, but A=0.3 and β =2.4 fixed; (c) Parameter β changes, but A=0.3 and α =1.2 fixed. The thin solid, thick solid and dashed curves represent the subcritical, critical and supercritical regimes, respectively.   Estimating the maximum earthquake magnitude through short-term earthquake clustering models庄 建倉 モデリング研究系 准教授2012年6月15日 統計数理研究所 オープンハウスSpace-Time Epidemic-Type Aftershock Sequence (ETAS) model Time varying seismicity rate = "background" + “Triggered seismicity":Magnitude distribution:  the G-R law Time distribution: the Omori-Utsu law Spatial location distribution of children:  Productivity: mean number of childrent: time  (x,y): spatial location m: magnitude∑<−−−+=ttiiiiiiimyyxxfttgmyxyxt :);,()()(),(),,( κμλcmm mmems c ≥= −−    ,)( )(ββ0   ,11)( >⎟⎠⎞⎜⎝⎛ +−=−tctcptgp1   ,11);,( )(22)( >⎟⎟⎠⎞⎜⎜⎝⎛ ++−=−−− qDeyxDeqmyxfqmmmm cc γγπcmm mmAem c ≥= −    ,)( )(ακMaximum magnitude in an earthquake cluster The survivor probability function of the magnitude of the biggest event in a cluster, including the initiating event and all the its descendants, is determined by [Zhuang & Ogata, 2006, Physical Review E, 2006]: Given a space-time windows V, the probability of the maximum magnitudewhere* * * )exp[ ( )( ) 1 ( ,  )  d  ( ]cmcmF m m mm F ms mmκ− −= ≥∫0Pr{at least 1 event greater than  occurs in }1 Pr{all biggest events in each cluster <  in }1 Pr{  clusters occur in total in }          Pr{all event  clusters   clusters in <  | }1nn mm Vm Vn Vn V∞== −×= −=∑( )0( ) ( )( )[1 ( )]!1nn VnV F mVF m ene∞ −Λ=−ΛΛ− −= −∑( ) ( , )d d dVV x y x y tμΛ = ∫∫∫Figure 3 Spatial variations of the occurrence probabilities that at least one earthquake in a 1 yr•deg2 space-time volume is greater than MJ ≥5.0 (left panel), MJ ≥6.0 (middle panel) and MJ ≥7.0 (right panel) . Parameters A=0.323 and α=1.41.

Estimating the maximum earthquake magnitude through short-term earthquake clustering models

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Estimating the maximum earthquake magnitude through short-term earthquake clustering models

Abstract

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RISM (Repository of the Institute of Statistical Mathematics) / 統計数理研究所学術研究リポジトリ

Estimating the maximum earthquake magnitude through short-term earthquake clustering models

Abstract

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Full text

Available Versions

RISM (Repository of the Institute of Statistical Mathematics) / 統計数理研究所 学術研究リポジトリ

RISM (Repository of the Institute of Statistical Mathematics) / 統計数理研究所学術研究リポジトリ