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Time-dependent b value for aftershock sequences

Time-dependent b value for aftershock sequences. Yuh-Ing Chen Institute of Statistics National Central University Chungli, Taiwan. Statsei4, Japan, 2006/1/10. Outline. Reasenberg-Jones (RJ) model Distribution of aftershock-magnitude Modified Reasenberg-Jones (MRJ) model

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Time-dependent b value for aftershock sequences

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  1. Time-dependent bvalue for aftershock sequences Yuh-Ing Chen Institute of Statistics National Central University Chungli, Taiwan Statsei4, Japan, 2006/1/10

  2. Outline • Reasenberg-Jones (RJ) model • Distribution of aftershock-magnitude • Modified Reasenberg-Jones (MRJ) model • Comparison of RJ and MRJ models

  3. 1. Reasenberg and Jones model Gutenberg-Richter (1944) law log N(M)= a- bM, for M≧ Mc, where N(M) is the number of earthquakes with magnitude M or larger and Mc is the cut-off magnitude. The distribution of M is left-truncated exponential with survival distribution S(M)=exp {-β(M -Mc)} , M≧ Mc

  4. Modified Omori’s Law(Utsu, 1961)

  5. Reasenberg-Jones(1989)model P = P{At least one aftershock with magnitude between and occurs in (S, T)}

  6. Determination of Mc－Wiemer (2000)

  7. b-value and p-value

  8. Probabilitic aftershock hazard (PAH) map－Wiemer (2000) The probability that at least one M≧5.0 aftershocks occurred during [t+1, t+7) days after the Chi-Chi earthquake for 2≦t≦5 Days.

  9. Evaluation of the PAH map - Phi coefficient Alarming for M≧ M0 aftershocks in the grids with P ≧ P0

  10. Phi coefficients for alarming M≧5.0 aftershocks based on the RJ-PAH map ← 2.326

  11. 2. Distribution of aftershock- magnitude

  12. 3. Modified Reasenberg-Jones model

  13. Sequential prediction

  14. 4. Comparison of RJ and MRJ models

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