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(e.g., Kiratzi and Papazachos 1996 ) or subducting
slabs (e.g., Kiratzi and Papazachos 1995 ), and
at large scale to build global strain rate mod-
els for the lithosphere (Kreemer et al. 2000 ).
Although ( 11.4 ) appears as a generalization of
( 11.3 ) (and Kostrov himself considered his for-
mula this way), this interpretation is not com-
pletely correct. As pointed out by Molnar ( 1983 ),
Kostrov's formula leads to results that differ from
those obtained using Brune's formula when the
former is applied to a block that deforms along
a unique shear zone (which is the situation con-
sidered by Brune). To understand the difference
between the two formulations, let us consider the
deformation field associated with the coseismic
slip along a fault plane. The sudden non-elastic
displacement during an earthquake can be viewed
as a rotation of one block relative to the opposing
block about an axis perpendicular to the fault
plane. Clearly, conservation of the angular mo-
mentum requires that the moment associated with
slip be balanced by an opposite moment with
equal magnitude. Such a complementary moment
will determine elastic deformation in the region
surrounding the rupture area border. Brune's for-
mulation allows to calculate the net rotation as-
sociated with seismic slip independently from
the elastic deformation occurring near the fault
ends. In this instance, the strain tensor will be
identically zero, while the displacement field can
be described uniquely by an antisymmetric rota-
tion tensor ¨ ij (see Sect. 7.2 ) . Consequently, this
model cannot completely describe the deforma-
tion within a 3-D volume. Conversely, in his
formulation Kostrov assumed that the deforma-
tion was pure shear (i.e., without any rotational
component). In fact, the symmetric strain rate
tensor that results from summation of symmetric
moment tensors excludes any rotational displace-
ment. As a consequence, Kostrov's model cannot
describe situations where any of the faults in the
deforming region intersects the region boundary.
In particular, it cannot describe the simple shear
of a block. In the next section, we shall consider
a more general formulation that combines both
approaches.
Fig. 11.1 Average long-term seismic slip in the Brune's
model
Differently from Brune ( 1968 ), Kostrov
( 1974 ) considered the problem of describing
the seismic deformation within a finite volume
V , rather than dislocations along a planar plate
boundary. In this instance, earthquakes are
not confined to a planar surface, individual
faults within the deforming region have
different orientations, and slip along these faults
occurs along distinct directions. Therefore,
the contribution of each event to the overall
deformation must include the source focal
mechanism parameters or, alternatively, the
components of the moment tensor. Kostrov
( 1974 ) proved that the components of the average
strain rate tensor due to seismic slip are related to
the moment tensor components of the individual
earthquakes, M ( k )
ij , by the following expression:
2VT X
k
2VT X
k
1
M 0
M .k/
m .k/
ij
P © ij D
ij D
(11.4)
where M 0 is the average scalar seismic mo-
ment and m ij is the geometrical part of the mo-
ment tensor, which can be expressed in terms of
strike, dip, and rake (see 10.58 ) . This formula has
been widely used to determine at regional scale
the seismic deformation of continental blocks
 
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