Jökull - 01.01.2017, Page 13

Zeinab Jeddi et al.
Figure 5. Gutenberg-Richter relation for the eastern
activity. Open circles are the cumulative number of
events. Crosses are non-cumulative. Dotted line
shows the estimated MC . Blue line demonstrates
b-value fit. – Stærðardreifing jarðskjálfta austan í
Kötlu. Opnir hringir sýna fjölda skjálfta upp að
hverri tiltekinni stærð. Rauðir krossar sýna fjöldann
við hverja stærð. Brotalínan sýnir mat lágmarks-
stærðar þar sem skjálftar eru skráðir að fullu (MC
= magnitude of completeness). Hallatala bláu lín-
unnar er veldisstuðull (b-gildi) þeirrar veldisfalls-
dreifingar sem best lýsir dreifingunni.
lected a short time window (∼0.5 sec) around them.
We then correlated (separately for P and S phases) the
windows of the template event with all other events.
We applied this cross-correlation process to all three
components and selected the component resulting in
the highest correlation coefficient as the best estimate.
This allowed us to estimate P and S differential ar-
rival times between the template event and all other
events and also absolute arrival times based on cross-
correlation with the template waveform using careful
absolute picks of the templates.We then used the dif-
ferential times for the relative location and the abso-
lute times for the non-linear absolute location.
In order to obtain a better estimate of the hypocen-
tral locations, the cross-correlation times were se-
lected by setting a lower threshold of R as high as
0.7 and only event pairs with at least 5 time measure-
ments were used. This reduced the number of events
to 155 in family 1, but did not affect family 2. Fur-
thermore, we checked for outliers by inverting for the
relative location of all the events that passed the above
criteria. The histogram of residuals resembles an ex-
ponential distribution (Figure 6) with clear outliers at
residuals larger than 0.05 s. Those outliers may be
due to cycle skipping in the correlation measurements,
thus they were removed. This reduced the number of
events in family 1 to 132. We defined a proxy for the
uncertainty for each relative time measurement based
on R, with the uncertainty assumed to be proportional
to (1-R). This measure of the relative uncertainty was
then used to define relative weights of the data in the
relative-location inversion. The relative weight is the
inverse of the relative uncertainty.
Absolute Locations
The eastern events were located in the 3-D local ve-
locity model by Jeddi et al. (2016) using manually
picked absolute arrival times. The resulting hypocen-
tral locations were concentrated in a small area near
the rim of Sandfellsjökull glacier, with a wide depth
distribution between 0 and 6 km bsl. Since the wave-
forms are similar, the spread of hypocenters is big-
ger than expected. Therefore, we tried to improve the
absolute locations by using a probabilistic, non-linear
method to map the likelihood function for each event
with a grid search around a defined center (chosen to
be the center of mass of the distribution shown in Fig-
ure 6) (Lomax et al., 2000). The error distribution of
the arrival times is unknown, but assumed to be Gaus-
sian. We also assume increasing uncertainty with in-
creasing distance (linearly), and so we used inverse
distance weighting for the stations farther than 12 km.
Ultimately, the residual errors were used to calibrate
the data error estimates that were used to calculate the
location uncertainty. This was done assuming that the
total residual misfit represents the combined error of
observation and prediction.
We constructed a local 1-D velocity model to use
with the non-linear location method based on the to-
mographic model in the area (Jeddi et al., 2016) by
averaging over a 9 km2 area around the source region.
We referenced the depth to the average elevation in
the source region (0.3 km). We also applied station
corrections in order to absorb effects of lateral het-
erogeneity. We did this with an iterative procedure,
which alternately locates events and reevaluates sta-
8 JÖKULL No. 67, 2017