Jökull - 01.06.2000, Blaðsíða 40

Foulger and Field
cube. These velocities were used to calculate a density
for each cube. The expression for the gravitational ef-
fect of a rectangular parallelepiped (Talwani, 1973)
was used to calculate the effect of each cube at the
surface and the effects of all the cubes were summed
to give the simulated Bouguer anomaly fields.
The observed Bouguer anomaly fields were
calculated from the original gravity measurements.
The Parasnis method was applied to estimate a
Bouguer reduction density for each area. This met-
hod is described in detail by Parasnis (1962) and in-
volves rearranging the Bouguer anomaly equation to
express gravity at the stations as a function of heig-
ht and density and the Bouguer anomalies as random
errors.
, APPLICATION TO THE
HENGILL-GRENSDALUR AREA
A bulk rock density of 2,400 kg/m3 was obtained
using the Parasnis method. This compares with a
Bouguer reduction density of 2,600 kg/m3 used by
Þorbergsson et al. (1984). Laboratory measurements
of the wet densities of 15 rock specimens from
the Hengill-Grensdalur area were also available. The
specimens were collected from Nesjahraun, a post-
glacial lava flow NE of Hengill, and from hyalocl-
astite units within the Hrómundartindur system and
the Grensdalur central volcano. Large samples were
split into 5 or 6 blocks 6-10 cm3 in volume
and individual determinations made for each. The
wet densities of the samples vary from 2,110 to
2,800 kg/m3 and the porosities lie in the range 8-40%.
The results illustrate the large variation in the physical
properties of the near-surface rocks. The average wet
density of the whole suite is 2,465 ± 100 kg/m3. On
the basis of all the information available, a Bougu-
er density of 2,450 kg/m3 was used to calculate the
observed Bouguer anomaly field (Figure 5).
A NE-SW regional gradient of approxiamtely 20
mGal occurs over the area. This was removed us-
ing the quadratic surface which minimises the RMS
gravity residual, and a constant was added to all the
Bouguer anomaly values so the field had a mean value
of zero (Figure 6a).
The observed and simulated Bouguer anomaly
fields (Figures 6a,b) may only be compared in a relati-
ve sense since the datum of each is arbitrary. Bearing
this in mind it may be seen that the simulated gra-
vity field bears considerable similarity both spatially
and in amplitude to the observed field. Positive anom-
alies occur of about 1-2 mGal at (2,13) over Húsmúli
and 3-4 mGal at about (8,6) in the Grensdalur area.
The Bouguer lows south and north of Hengill and over
Hrómundartindur in the observed field are, on the ot-
her hand, absent in the simulated field.
The simulated Bouguer anomaly field was su-
btracted from the observed field and the residual is
illustrated in Figure 6c. The residual field contains
fewer and smaller anomalies than the real field. The
most serious discrepancies occur south of Hengill (at
about 1,10) and at Hrómundartindur (12,7). The RMS
anomaly for the real field is 2.05 mGal compared with
1.81 mGal for the residual field.
In order to assess how much of the significant
Bouguer anomaly field is unexplained by the LET
model, an error budget was made. The most serious
uncertainties arise from 6 sources:
1. the values of measured gravity,
2. the density used to make the Bouguer and terrain
corrections (the Bouguer density),
3. the LET velocity model,
4. variations in the density above sea level,
5. variation in the velocity : density relationship for
rocks below sea level, and
6. errors in detrending the Bouguer gravity field.
Errors in the values of gravity are estimated by
Þorbergsson et al. (1984) to be occasionally up to
about 0.5 mGal. The error in the LET velocity model
was conservatively assumed to be about 0.1 km/s, alt-
hough repeat LET indicates that it may be still higher.
The error in the Bouguer density used for the whole
area was assumed to be 100 kg/m3, a figure that
is again conservative compared with the variation in
Bouguer densities used by other authors (e.g., Þor-
bergsson et al. 1984; Hersir et al. 1990). Quantifying
the errors from the last three sources is not straight-
forward. In particular, the density of the material abo-
ve sea level is known to vary over the area (Hersir et
al. 1990).
38 JÖKULLNo. 48