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In-Depth Information
0.1
0.01
-4
∼τ
-1
∼τ
0.001
1
×
10
-4
1
×
10
-5
M
t
= 1
M
t
= 2
M
t
= 3
M
t
= 4
10
-6
1
×
1
×
10
-7
1
×
10
-8
1
×
10
-9
-6
∼τ
1
×
10
4
1
×
10
5
1
×
10
6
1
10
100
1000
Waiting time -
τ
- (min)
Figure 2.2.
The distribution density for the time interval between quakes of a given magnitude
M
≥
M
t
=
1
,
2
,
3 and 4. The initial inverse power law with slope
−
1 is Omori's law [
55
], but
after a certain time delay the slope changes to
−
4. The data come from [
73
]. Reproduced with
permission from [
69
].
0.001
0.0001
10
-5
10
-6
10
-7
10
-8
10
-9
10
-10
10
-11
10
100
1000
10000
100000
1000000
10000000
τ
(seconds)
The distribution density of time intervals between solar-flare events is given by the crosses.
The dashed curve is given by a fit to the data using (
1.41
) with normalization constant 30,567,
T
=
8
,
422 and power-law index
β
=
2
.
14
±
0
.
05 [
25
]. Reproduced with permission.
Figure 2.3.
show that for very long times between quakes there is a transition from the slope of
−
1
to an inverse power law with slope
−
4. The location of the transition from the
−
1 slope
to the
4 slope depends on the magnitude of the quake, with quakes of very large mag-
nitude following Omori's law for very long times. Another way to view this moving of
the transition region is that the larger the quake the longer it will be before another quake
of that size occurs. This has led to estimates of the time until the occurrence of a given
quake as being the inverse of the probability of a quake of that magnitude occurring.
Another physical phenomenon in which the distribution in the magnitude of the event
as well as that in the time interval between events follows the hyperbolic distribution
is that of solar flares. In Figure
2.3
the distribution of times between flares is recorded
−
