Jökull - 01.06.2000, Page 42

Foulger and Field
The total error estimated from the first three
sources is shown in Figure 6d. These estimated err-
ors are conservative and would scale up or down if the
true errors in the LET model and the Bouguer density
are larger. The error field has an RMS Bouguer anom-
aly of 1.48 mGal. The Comparing Figures 6c and 6d,
the main area of discrepancy is a zone of residual low
gravity corresponding to the Ftengill system and the
northern part of the Hrómundartindur system.
APPLICATION TO THE KRAFLA AREA
A Bouguer reduction density of 2,300 kg/m3 was used
by Schleusener et al. (1976) and Karlsdóttir et al.
(1978). A Bouguer density of 2,300 kg/m3 was also
obtained for the Krafla area using the Parasnis met-
hod. This value was thus used in the present study.
The Bouguer anomaly field is somewhat complicated
(Figure 7a) and thus a value for the regional gradient
of 0.5 mGal/km taken from Schleusener et al. (1976)
was subtracted from the data (Figure 6b). The Bougu-
er anomaly field was then normalised to zero by add-
ing the appropriate constant value to all stations.
In calculating the simulated gravity field from the
LET model, the poorest resolved parts were not inclu-
ded since they represented a relatively large part of the
study volume. The part of the Hengill-Grensdalur stu-
dy volume that was poorly resolved was much smaller
in comparison.
Because the gravity station spacing was small in
the Kraíla area, a lot of detail is seen that cannot
be reproduced by modelling the LET model, which
is only reliable below sea level, i.e. ~500 m below
the surface. For this reason, the simulated and obser-
ved Bouguer anomaly fields upward continued to
1 km above sea level are compared. The gravity mea-
surements were resampled onto a 200 x 200 m grid to
prevent instabilities in the continuation process.
The observed and simulated Bouguer anomaly
maps are shown in Figure 8. The amplitudes of the
anomalies in each are about the same, being about
±1 mGal in the observed field and ±1.5 mGal in the
simulated field. The first-order features in the obser-
ved field are gravity highs at the W, SW and NE parts
of the caldera rim and at Leirhnjúkur and low gravity
at the N caldera rim and S of the caldera. The simula-
ted field is characterised by gravity highs at the W and
NE caldera rims and low gravity S of the caldera.
The observed and simulated fields correlate to
some extent. The gravity highs at the W and NE of
the caldera rim and low gravity S of the caldera are
common to both fields. However, the gravity highs
in the observed field at the SW caldera rim and at
Leirhnjúkur are not reproduced in the simulated field.
On the whole the correlation is poorer than for the
Hengill-Grensdalur area.
Despite the upward continuation, the two fields
are dominated by anomalies which are most likely
caused by bodies at different depths. The observed
field is dominated by anomalies with half-widths of up
to ~ 1 km, which roughly corresponds to the maxim-
um depths to the centres of the causative bodies (Bott
and Smith, 1958). This suggests that the maximum
depths to the tops of the bodies causing the observed
gravity anomalies may be approximately at sea level.
The main high-gravity anomalies in the simulated
field, on the other hand, are caused by deeper bodies,
as the LET has virtually no resolution at shallow
depths. Subtracting the simulated field from the obser-
ved did not significantly decrease the RMS anomaly.
For this reason, the observed and simulated fields are
not very comparable and we used a different approach
in our joint analysis from that used with the Hengill-
Grensdalur data.
An estimate of the maximum depth to the causati-
ve bodies for the observed field was made using the
spectral method of Granser et al. (1989). This method
utilises the equation
lnJ5(k) = [A0(k)]2 — 2|k|^o
where -E(k) is the power spectrum, Aq (k) is the
spectrum continued to the maximum source depth,
k is the wavenumber vector and Zq is the maximum
depth to the causative bodies.
This equation exploits the fact that gravity anom-
aly pattems are largely determined by the depths
and volumes of their causative bodies rather than
by details of their boundaries. It is strictly valid for
situations where there are large numbers of bodies,
though in practice it is found to work well for cases
where there are no more than five or six bodies
40 JÖKULL No. 48