Jökull - 01.12.1976, Page 13

tance did not record all the earthquakes re-
corded by the other 4 stations. Therefore, to
maintain a homogeneous internally consistent
data set, only the 4 near stations were used for
locating the earthquakes near the volcano. The
two distant stations were used as an indepen-
dent check on the reliability of locations of
more distant events.
The 4 near stations were used in two dif-
ferent combinations of 3 stations to locate
events by the tripartite array method. For events
outside of the array, azimuth and apparent velo-
city are calculated from the P-wave time dif-
ferences between the stations, and distance is
estimated from the apparent velocity and the
S-P times. The limitations of this method are
discussed by Ward and Gregersen (1973):
1. Small errors in reading the P-wave arrival
times can cause large errors in calculated ap-
parent velocities and azimuths. Depending on
the geometry of the array, these errors are func-
tions of the apparent velocities and the azi-
muths.
2. Uncertainty in picking the S-waves corre-
sponds to uncertainty in the distance of the
earthquake from the array. In a complex vol-
canic region the wave of an earthquake can
be quite irregular, and identifying the S-wave
constitutes a major problem.
3. Assuming a crustal structure with flat lying
layers with constant velocities introduces a pro-
blem of nonuniqueness for the location of an
earthquake if the first arriving P-wave is cri-
tically refracted. It is therefore necessary to
assume a crustal structure of flat lying layers
with constant velocity gradient and without any
first order velocity discontinuities. The constant
gradient model is chosen so as to approximate
the constant velocity model determined by con-
ventional seismic refraction methods.
4. The most severe error cause is any un-
known irregularity in the crustal structure. To
estimate the magnitude of this error it is neces-
sary to set off explosions in a number of places
at different azimuths and distances, preferably
near the epicenters of the earthquakes to be
located.
In this study the main sources of P-time read-
ing errors are considered to be the finite sam-
pling frequency of the FM recorder and irre-
gularities in the speed of the recording and
play-back instruments. The center frequency of
the magnetic tape recorder was 84.4 Hz, which
corresponds to a reading error of ± 0.006 sec.
Irregularities in the speed of the recorder and
the play-back instruments can produce uncer-
tainties as large as ± 0.01 sec in the interpola-
tion between second marks on the records. The
total error is therefore estimated to be ±0.01
sec, which corresponds to an error of approxi-
mately ±8° in azimuth and ±0.3 km/sec in
apparent velocity for most of the near earth-
quakes located with this method.
The magnitude of the error in location
caused by the uncertainty of picking the S-
wave is more difficult to estimate. If we assume
that the S-wave is picked correctly the error of
that reading is the same as the error in read-
ing the P-wave. If the S-wave is not identified
correctly, however, the error is difficult to pre-
dict. An experienced interpreter would hardly
mispick an S-wave by more than ± 0.3 sec
corresponding to an error of ± 2.5 km in dis-
tance for most of the earthquakes located in
this study.
The seismic velocity model of the crust used
for locating the earthquakes was based on velo-
city measurements by Pálmason (1971). One of
his refraction profiles runs about 10—30 km
northeast and east of Hekla. The velocity model
adopted is shown in Table 1. This model differs
from Pálmason’s results only in the thickness of
layer 1. The necessity of this modification will
be discussed below.
Layer TABLE 1 P-velocity km/sec Thickness km
0 2.1 0.6
1 4.1 2.3
2 5.1 2.5
3 6.5 3.5
4 7.2
In order to calibrate the seismometer array
three explosions were set off in a lake about
11 km to the northeast of the array. For these
blasts apparent velocities of 3.8 to 4.0 km/sec
were measured across the array. These velo-
cities are not significantly different from the
velocity in layer 1 measured by Pálmason (1971).
Assuming a P-velocity of 2.1 km/sec for layer 0
and using the absolute P-wave travel time for
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