1. Time-dependent b value 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)}

7. Determination of Mc －Wiemer (2000)

8. b-value and p-value

9. 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.

10. Evaluation of the PAH map - Phi coefficient
Alarming for M≧ M0 aftershocks in the grids with P ≧ P0
Number of grids
Alarming area
Total
Yes No
After-shock a b
a+b c d
c+d
a+c
b+d
a+b+c+d

11. Phi coefficients for alarming M≧5
Phi coefficients for alarming M≧5.0 aftershocks based on the RJ-PAH map ←

12. 2. Distribution of aftershock- magnitude

14. 3. Modified Reasenberg-Jones model

15. Sequential prediction

18. 4. Comparison of RJ and MRJ models