Geology Reference
In-Depth Information
11
Seismic Deformation
of the Lithosphere
Abstract
Here the principles of seismic deformation are illustrated, which represent
an essential tool to unravel the kinematics of subduction. In particular, the
classic Kostrov and Brune formulae are presented, as well as the more
advanced representation of Molnar, based on an asymmetric strain tensor.
Finally, this chapter introduces the application of these techniques to the
study of slab deformation in subduction zones.
11.1 Kostrov's Formula
In the previous chapters, we have learnt that
lithosphere deforms both by viscous creep, at the
time scale of millions of years, and elastically
in the short range (up to thousands of years).
Therefore, at first glance seismicity does not
provide a relevant source of data for studying
neither the long-term pattern of deformation of
tectonic plates nor plate motions. In this chapter,
we are going to prove that such an appearance
is misleading, because earthquakes supply both
valuable qualitative information about the
style
of deformation (e.g., the modes of deformation
of slabs), and a quantitative measure of the long-
term strain rate under external loads.
The first attempt to link earthquakes to long-
term tectonics was done by Brune (
1968
)ina
seminal paper. This author considered the seis-
micity along a large shear zone with total surface
S
, consisting into a series of earthquakes with
scalar moment
M
(
k
0
(
k
D
1,2, :::,
n
), rupture sur-
face
S
k
, and average displacement
u
.k/
(Fig.
11.1
).
M
.k/
0
S
k
u
.k/
D
(11.1)
Therefore, if the overall displacement,
u
,
along the entire shear zone is calculated taking
the weighted average of these quantities, with
weights given by the size of the individual rupture
areas, we have:
S
X
k
S
X
k
1
1
M
.k/
0
u
.k/
S
k
D
u
D
(11.2)
This is called
Brune
'
sformula
. Assuming that
the observed seismicity is relative to a sufficiently
long time interval
T
, the formula can be used to
estimate the average
rate of seismic slip
along a
shear zone:
ST
X
k
@
u
@t
D
1
M
.k/
0
(11.3)
