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Earthquake Sequence 1973–1996 in Bárðarbunga volcano
APPENDIX
Stress-drop of Bárðarbunga earthquakes relative
to regular tectonic earthquakes in Iceland.
Seismic stress drop is a factor that can account for difference
in corner frequency of earthquakes of similar size. A priori,
the corner frequency of e.g. the larger, Vatnafjöll event, is
expected to be lower than that of the smaller Bárðarbunga
1996 event. It turns out that corner frequency of the Vatna-
fjöll event is three times as high as the Bárðarbunga event
of 1996 (Table 2). Similarly the corner frequency of the
larger Skagafjörður 1994 event (MW =5.5) is twice as high
as that of Bárðarbunga 1995 event (MW =5.4) (Table 2). The
Vatnafjöll earthquake nucleated in the lower crust, with cen-
troid depth of 6.6 km (Bjarnason and Einarsson, 1991), but
it is argued here that the unusually low corner frequencies of
the Bárðarbunga medium size earthquakes do suggest shal-
low sources as previous authors have suggested (Einarsson,
1991, Nettles and Ekström, 1998; Konstantinou et al., 2003;
Tkalc̆ić et al., 2009).
Categorizing stress drop in Bárðarbunga earthquakes,
three principal methods come to mind: Static stress drop es-
timates; dynamic stress drop from source time functions de-
termined with moment tensor inversion; and dynamic stress
drop from corner frequency:
Static stress drop
Calculation of static stress drop ∆σstatic = CgµD/A
1/2
(eq. 1) is not feasible because of lack of information on most
of the parameters that it depends on, fault area (A), fault
geometry (Cg), and average slip (D). However, the shear
modulus (µ) in the fault region is assumed to be equal to the
average modulus for the Central and North Iceland Volcanic
zones (Bjarnason and Schmeling, 2009).
Dynamic stress drop and source time function
Nettles and Ekström (1998) reported unusually long source-
time functions (4–7 s) for the intermediate Bárðarbunga
earthquakes in the years 1976–1996, with 5 s for the 1996
event. Fichtner and Tkalc̆ić (2010) concluded that the
source duration of the 1996 event could not be well con-
strained, in spite of the higher frequency resolution of local
broadband recordings used (HOTSPOT array, Foulger et al.,
2001). The duration in the range of 3–8 s was estimated by
these authors, with maximum moment release in the first
3.5 s. Konstantinou et al. (2003) estimated∼5 s long source
time function for the 1996 event. All these estimates sug-
gest long source duration, and 5 s duration of the 1996 event
is 3/4 longer than average for earthquakes of that size (Ek-
ström et al., 1992). Although longer than average source
time function may be an indicator of low stress drop event,
as the Brune model suggests, firm theoretical or empirical
relations with observations are still lacking (see e.g. Scholz,
1990; Bizzarri, 2010). There is even a case of very long
source duration event compared to the average that may not
have been with low stress drop (Ekström et al., 1992). It is,
however, generally agreed that longer than average source
duration indicates low rupture velocity (Vr).
For the estimated 12 km long rupture in the 1996 event,
assuming unilateral rupture (reasonable assumption based
on Stefánsson et al. (1996) aftershock distribution), the rup-
ture velocity (maximum velocity) is 2.4 km/s, which is a
low value. Assuming a normal value ratio of rupture ve-
locity to source shear velocity to be Vr/β = 0.9, this gives
source depth of 2.0–2.5 km, and Vr/β = 0.7, a source depth
of ∼5.0 km, using the shear velocity structure of Bjarna-
son and Schmeling (2009) for Central Iceland. It is not rea-
sonable to assume Vr/β to be lower than 0.7, because that
would place the source at unreasonable depth in the lower
crust or even in the mantle. As stress drop (eq. 1) is a linear
function of the shear modulus there is an indication that a
shallow source earthquake would tend to have lower stress
drop. In the laboratory this effect is observed: At low con-
fining pressure (equivalent to shallow depth) the material
friction is smaller than at greater pressure, and hence the
loading force (stress) needed for slip is smaller. As stress
drop is proportional to the loading force (Scholz, 1990), it
follows that the stress drop is also lowered. Therefore, it is
concluded, that these observations do indicate a low stress
drop of a shallow (2.0–5.0 km) event. It seems unlikely
that the rupture depths of the other Bárðarbunga events,
with similar source properties, would deviate much from the
above depth range.
Dynamic stress drop and corner frequency
The relationships of corner frequency f of earthquake spec-
tra of a circular crack model of Sato and Hirasawa (1973)
were reviewed by Aki and Richards (1980) [p. 820–821].
The Sato and Hirasawa (1973) model spectra have a Brune
(1970) like ω−2 asymptote beyond the corner frequency.
The dependence of azimuthally averaged P-wave corner fre-
quency 〈fp〉, is 2π〈fp〉 = Cpα/R (eq. 2), where α is
P-wave velocity at the source, R is radius of the circular
crack, and Cp is a scaling constant that depends on the ra-
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