Geology Reference
In-Depth Information
Fig. 10.1
The seismic
cycle in the elastic rebound
model. The
red line
represents a reference
marker on two tectonic
plates,
A
and
B
,whichis
progressively deformed
during the time interval
between two earthquakes
(
top, inter-seismic phase
).
There is no slip along the
fault plane during the
interseismic phase. During
an earthquake (
co-seismic
phase
), the displacement
field is maximum along the
fault (
bottom
), so that the
shape of the marker is
restored on each plate
changes of strain field in seismically active re-
gions (known as the
secular strain rate
).
A simple physical mechanism explaining the
seismic cycle and the elastic rebound theory
is known as the
stick
-
slip model
of frictional
instability. This theory is based upon the
observation that earthquakes do not form as a
consequence of shear cracking (i.e., fracturing)
of rocks, but they are ultimately frictional
phenomena (Brace and Byerlee
1966
). Therefore,
the seismic cycle is viewed as a combination
between a “stick” interseismic phase of elastic
strain energy accumulation and a coseismic “slip”
along an
existing
fault plane. The observation
of Brace and Byerlee (
1966
) was followed by
a number of laboratory friction experiments,
with the objective to study the dynamics of
sliding instability and determine a constitutive
law of friction. These experiments showed that
constant but depends on the duration of the stick
interval, so that if the two surfaces are kept in
static contact under load for a time interval
t
,
then
s
increases as log
t
(Dieterich
1972
).
The quantity
s
is an important parameter for
understanding earthquake mechanics, because as
we saw in Chap.
7
it represents the threshold ratio
of shear to normal stress triggering sliding along a
fault plane. During sliding, the friction coefficient
decreases to a new value, , which is termed the
dynamic friction coefficient
. Another significant
result of the experiments was the determination
of the dependence of from the sliding velocity
v
, which was found to be:
/
log
v
. Finally,
it was found that variations of sliding velocity
determined state transitions over a characteristic
distance
L
(for a review of the major experimental
results, see Scholz
1998
). At the same time, the-
oretical modelling of stick-slip motion revealed
that the instability of frictional slip depends from
a reduction of the friction force during sliding.
This phenomenon was called
slip weakening
.
Modelling efforts led to the formulation of
an empirical constitutive law for the dynamic
friction coefficient, which is known as the
rate
-
and
-
state friction law
(or
Dieterich-Ruina law
).
According to this law, starting from a
steady
