Geology Reference
In-Depth Information
A simple numerical experiment shows that
for
a
<
b
the slider motion is jerky, that is, it is
characterized by phases of rapid slip separated by
stick intervals, as illustrated in Fig.
10.6
Starting
from a stationary contact, the spring force to
normal stress ratio,
F
s
/¢, will increase linearly
until the current value of the static friction co-
efficient
s
is attained. At this point, a velocity
spike occurs and the spring shortly starts relax-
ing. When
F
s
/¢ falls below the dynamic friction
coefficient , the slider starts decelerating and
quickly stops. As shown in Fig.
10.6
during the
stick time intervals, the static friction coefficient
increases logarithmically, while the state variable
increases linearly.
Also the spring force increases linearly during
a stick interval. In fact, if at any time
t
D
t
0
the
slider stops at location
u
0
D
u
(
t
0
), then during the
subsequent stick interval we have:
At any time
t
in the stick interval, this force
could
potentially
accelerate the slider to velocity:
Z
t
F
s
t
0
dt
0
v
.t/
D
t
0
2
KV
0
t
2
t
0
K
u
0
.t
t
0
/ (10.11)
1
D
However, the slider will effectively restart
only when the dynamic friction corresponding
to this potential velocity is less than the applied
spring force. In conclusion, a plausible though
qualitative explanation of the seismogenic mech-
anism can be obtained combining Reid's elastic
rebound idea with the modern theory of friction
and analog spring-slider modelling. However, it
is important to note that this representation of
earthquake nucleation cannot be used to predict
the short-term occurrence of seismic events.
The reason is that a fault generally includes
several stick regions with different geometry
and different normal loads. This complexity
clearly affects the regularity of stick-slip motion.
Furthermore, an earthquake associated with
rupture of a stick zone usually modifies the
stress field of other stick regions, determining
a delay or an advance of the subsequent rupture.
Therefore, earthquake prediction cannot be
based on rigorous geophysical laws, but must
be considered as a statistical problem.
F
s
.t/
D
K.
u
0
V
0
t/
D
F
s
.t
0
/
C
KV
0
.t
t
0
/
I
t
t
0
I
stick time
(10.10)
10.2
Faults and Focal Mechanisms
Fig. 10.5
The spring-slider analogy for earthquake nu-
cleation. A spring with stiffness
K
is pulled at con-
stant velocity
V
0
. The elastic force exerted by the
spring on the attached slider is opposed by the friction
stress
£
(
t
) D
An important step in the study of earthquake
dynamics consists into the determination of the
location of the rupture area along a fault plane.
¢
(
t
). This system may exhibit stick-slip
instability
Nm
1
,
Fig. 10.6
Frictional response, slider velocity, and state
evolution in a numerical stick-slip motion experiment. A
spring-slider system is pulled at velocity
V
0
D 0.01 ms
1
.
It
The
parameters
are
set
as
follows:
K
D 12
D 1Pa,
dt
D 0.0005 s,
L
D 10
5
¢
m,
a
D 0.005,
b
D 2
a
,
ms
1
,
0
D 0.6.
v
0
D 0.1
F
s
D
K
[
u
(
t
)
V
0
t
]isthe
is
assumed
that
the
slider
is
at
rest
for
t
D 0.
spring force
