Jökull - 01.01.2010, Page 79

Intraplate earthquake swarms in Central Europe
then variations of the P and T axes of the resultant
source mechanisms relative to orientation of the axes
of the maximum (σ1) and minimum (σ3) local tec-
tonic stress (Figure 8a) reflect various orientations of
the fault planes with respect to the σ1 and σ3. We infer
that in case of a favourably oriented fault plane, pres-
surized fluids reduce normal stress σn and thus bring
the fault to a critical state. The running swarm activ-
ity is then mainly governed by the co-seismic stress
changes, which could be the case of the 2000 swarm
and of the first phase of the 1997 swarm. Provided
a less favourably oriented fault plane, additional ten-
sile force is needed to bring the fault to rupture, as it
happened probably in the second phase of the 1997
swarm.
Scaling relations
It is generally assumed that the magnitude-frequency
distribution is the primary attribute differentiating
the earthquake swarms from ordinary mainshock-
aftershock sequences. A causality of the main shock
and aftershocks is reflected by the b-value of the Gut-
enberg-Richter law ≤1. As opposed to mainshock-
aftershock sequences, several larger earthquakes have
similar magnitudes in swarms, and the smaller events
are not associated with any identifiable mainshock;
the consequence is a high b-value of the Gutenberg-
Richter law, which typically exceeds 1 and reaches
up to 2.5 (e.g., Lay and Wallace, 1995). For ex-
ample, the ML≤2.1 swarm-like episode beneath Ey-
jafjallajökull in South Iceland in 1996 was charac-
terized by a b-value∼2.5, a bit lower b-value∼2.1
was found for the ML≤2.2 microearthquake swarm
at Upptyppingar in North-East Iceland (Jakobsdóttir
et al., 2008). But this is not true in case of the
West Bohemia/Vogtland swarms. The magnitude-
frequency distributions of the swarms of 1997, 2000
and 2008 show b-values∼1.0, practically the same b-
values were reported by Neunhöfer and Hemmann
(2005) for the 1908, 1962, 1985/1986 swarms. But
the b-value is not steady during individual swarms as
shown by Hainzl and Fischer (2002) who reported
the b-value variations of 0.8<b<1.4 in the swarm
of 2000. Nevertheless, we can conclude that the
West Bohemia/Vogtland earthquake swarms are char-
acterized by b-values around 1.0 which are typical
for mainshock-aftershock sequences at tectonic-plate
boundaries.
Local or moment magnitudes ML and Mw, and
seismic moment M0 are basic measures of size of
the earthquake source. It is generally assumed that
ML∼=Mw, and Mw∝2/3logM0 in the whole extent
of ML estimated. However, a relation between ML
and M0 of small earthquakes and micro-earthquakes
still remains an open question (e.g., Braunmiller et
al., 2005; Deichmann, 2006). To clarify this issue we
evaluated the relation between M0 and the WEBNET
magnitude ML. We benefited from the knowledge of
the scalar moments M0, which were estimated for 70
events of the 1997 swarm and for 100 events of the
2000 swarm. Using the linear regression we obtained
the relation;
log10M0=1.0ML+11.3 (1)
for the 0.3≤ML≤2.9 events of the 1997 swarm and
for the 1.6≤ML≤3.3 events of the 2000 swarm,
where M0 is measured in N-m (Figure 9b). However,
the definition of the moment magnitude Mw given by
Kanamori (1977);
log10M0=1.5 Mw + 9.1 (2)
shows fairly different scaling between moment and
magnitude. If we combine the equations (1) and (2)
we get ML=1.5Mw–2.3. This points to the inconsis-
tency of the ML and Mw scales and underestimation
of ML as discussed by Deichmann (2006). Besides,
different scaling of the ML and Mw magnitudes af-
fects also the b-value of the magnitude-frequency dis-
tribution log10N = a − bM . We can write a rela-
tion bL = bW /1.5 where bL and bW stand for the b-
value determined from the local magnitude ML and
moment magnitude Mw, respectively. If we used
a moment magnitude Mw for statistical analysis of
the West Bohemia/Vogtland earthquake swarms we
would obtain the b-value of ∼1.5. The relation of
log10M0∝ML, where ML is local magnitude esti-
mated by the SIL network (e.g., Jakobsdóttir, 2008),
was also found for the micro-earthquakes in South
Iceland (R. Slunga, pers. comm.). This underlines
a significance of discussing the discrepancy between
the local and moment magnitudes which should be a
subject of further study.
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