1. Earthquake Statistics Gutenberg-Richter relation
Frequency-Magnitude relation
b is an important parameter that varies in time and space ranging around 1
a accounts for the background seismicity rate

2. Frequency-magnitude relation from seismic moment

3. Aftershocks Aftershock decay rate follows the OMORI law
K is the productivity
p is close to 1
c account for magnitude completness

4. 2017/4/26 3
Omori (1894)
1891 Nobi Earthquake of M8.1

5. ｔ : Ｋ，ｃ，ｐ : The Omori-Utsu formula for aftershock decay rate
2017/4/26 4
Utsu (1961)
The Omori-Utsu formula
for aftershock decay rate
ｔ :
Elapsed time from the mainshock
Ｋ，ｃ，ｐ :
constant parameters

6. Aftershocks occur on faults close to failure.
Dieterich ‘94 model
Aftershocks occur on faults close to failure.
100
100 80 80 60 60
sec-1x10-7 40 40 20 20
rate (events/time)
close to failure
far from failure
perturbed seismicity
background seismicity
time

7. Earthquake Probability

8. 1992 Landers Earthquake
INGV
r(x,y)
m(x,y)
reference
background

9. ‘Permanent’ Probability
Single Fault : probability of failure after a stress step t0
clock-advance
‘Permanent’ Probability
P(telapsed< t <telapsed+Dt) =
= ∫ f(t) dt
probability density
telapsed+Dt
telapsed
time
telapsed
telapsed+Dt
previous earthquake
Clock-advances shorten the mean recurrence time, increasing the probability.