Jökull - 01.01.2019, Page 76

Variation in b-value of caldera earthquakes of Bárðarbunga Volcano
shown for the period immediately following the col-
lapse of the caldera, from April 1 to December 23,
2015. The seismic activity was low in the beginning
but increased towards the autumn. The period con-
tains 1000 events. The other curve shows the mag-
nitude distribution in the period October 29, 2016, to
June 4, 2017, also containing 1000 events. The fig-
ure show that the earthquakes during these periods
follow the linear Gutenberg-Richter relationship quite
well. The plots show similarity, a regular slope be-
tween magnitude 1 and 3 and a steeper curve above
the knee at magnitude 3. Similar curves are found in
various tectonic environments, showing lack of large
events and therefore steepening of the curve towards
higher magnitudes (see e.g., Einarsson, 1986). There
is visible difference, however, between the b-values
of the two curves, far exceeding the 95% confidence
interval of the slope, ±0.03 and ±0.05, respectively.
For comparison, the distribution curves for the
collapse period are plotted in Figure 3, both for the
number of events and the cumulative number, N.
These plots show a very different behavior from that
of the inflation period. The curve of cumulative fre-
quency has two kinks, upwards at magnitude around
2.5 and downwards at magnitude 4. This is a very un-
usual behavior. A closer inspection of the frequency
plot reveals that the first kink is due to an increase in
the frequency of events of magnitude 4–5 compared to
lower magnitude events. The earthquake population
appears to be a sum of two populations, one follow-
ing a power law according to Gutenberg-Richter, and
the other with something resembling a normal distri-
bution of magnitudes. A simulation of such a sum
of distributions was attempted using the R functions
rexp() and rnorm() with 80000 values from an expo-
nential distribution with λ = 1 and 20000 values from
a normal distribution with µ = 4 and σ = 0.5. The sim-
ulated lists were then combined and a histogram pro-
duced (Figure 4). All values were chosen ad hoc to
produce the desired qualitative result. The simulation
does not include a dropoff in frequency for smaller
earthquakes such as would be expected from mea-
surement data, and is clearly seen in Figure 3. This
simulation is not the only way to model the distribu-
tion, but it shows that such a simulation is possible.
In particular, we stress that a simulation by two expo-
nential distributions according to Gutenberg-Richter
is not possible.
Figure 3. Magnitude distribution for the collapse period, August 16, 2014 to February 28, 2015, both frequency
(left) and cumulative frequency (right), N, as a function of M. The clear increase in the frequency of earth-
quakes above magnitude 3.5 is anomalous. – Stærðardreifing skjálfta fyrir hruntímabilið frá 16. ágúst 2014 til
28. febrúar 2015, bæði tíðni einstakra gilda og uppsafnaður fjöldi, sem fall af stærð M. Fjölgun skjálfta fyrir
ofan stærðina 3,5 er mjög afbrigðileg.
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