Jökull - 01.01.2021, Page 51

Bedrock and tephra layer topography within the Katla caldera
the cube is the travel time of the reflected radar wave,
with time interval corresponding to double sampling
frequency (0.625× 10−9 s for data acquired with 80
MHz sampling frequency in 2013 to spring 2017 and
2021 and 0.4167× 10−9 s for data acquired with a
new receiver recording at 120 MHz from autumn 2017
to 2019). The interpolated cube also covered a 50 m
wide area on each side of the cube corresponding to
the area just before and after turning the snowmobile
180◦ to measure a new line (Figure 4a). The inter-
polated cube mimics the RES-survey point matrix at
the surface with positions (M) corresponding to the
exact column locations of the cube with the receiver
and transmitting antenna placed along the first axis of
the cube at distance A/2 behind and in front of M.
Therefore, all survey points where the driving direc-
tion deviates more than 10◦ from the profile direction
were omitted before the interpolation. If the input data
at a given position near the edge of the cube were in-
sufficient for linear interpolation, the corresponding
column was left with zero values.
Next a 3D Kirchoff migration (e.g. Schneider,
1978) was applied on the regularly interpolated cube,
using cgl=1.68× 108 m s−1 and 250 m search radius.
Additional input required for the migration are the po-
sitions and elevations for each interpolated radar-shot
in the cube for the receiver and transmitter; the eleva-
tion values were extracted from a surface DEM inter-
polated from the simultaneous DGNSS survey. The
output yields a set of profile images identical to the
ones obtained with 2D migration in terms of axis def-
inition (x=distance, y=elevation) and pixel dimension
(dx=5 m, dy=1 m). The output profiles correspond to
those in the pre-planned survey route (20 m apart), ex-
cluding the profiles at the edges. At the edges of the
area spanning the migrated profiles the search radius
extended outside the input data. To compensate for
this, the migrated output data was scaled by the recip-
rocal of the number of input survey points from the
interpolated cube.
When tracing reflections in the 3D migrated data
(Figure 4) the same approach was adopted as for the
2D migrated data, using each migrated profile ob-
tained in the track direction. The tracing results were
also revised by comparing cross track images ex-
tracted from the 3D migration with the posted tracing
(Figure 4g–i). Sometimes further tracing was con-
ducted from cross track profiles. A systematic ele-
vation difference was sometimes observed between
traced bed reflections of different surveys (typically
1–3 m), attributed to different transmitters used, inac-
curacies in tracing, or temporal changes in the prop-
agation velocity of the radar wave. To minimise to-
pographic artefacts, which may arise when data from
different times are used, a master data set was de-
fined (Table 1). The median difference between the
elevation of traced reflections from master and in-
dividual slave data set at fixed locations was calcu-
lated for sub-sections of three neighbouring along-
track profiles and used as correction for the corre-
sponding slave profiles. After applying such correc-
tion, where needed, the lowermost trace was consid-
ered as the bedrock elevation and other traces omit-
ted. Traced reflections significantly above the as-
sumed bed elevation (based on all available data) were
likely reflections from the top of subglacial water bod-
ies (Figure 4d–e). At a few locations, the traced re-
flections were considered to be from water bodies for
all surveys, hence the corresponding location was left
without traced bedrock (e.g. common location of cyan
lines in Figure 4d–e).
The bedrock traces from 3D migrations were at
this point exported as a list of coordinates, x,y,z, (east-
ing and northing in ISN93 Lambert projection (EPSG
code 3057, National Land Survey of Iceland) and
bedrock elevation in metres above sea level (ISH2004,
National Land Survey of Iceland)) and used with-
out further revision as input into interpolation of the
bedrock DEM (Figure 3).
Revision of bedrock data and construction of
bedrock DEM
The traced reflections of the 2D migrated data were
filtered with a 25 m wide triangular filter and down-
sampled at 20 m interval along the profile (Magn-
ússon et al., 2016) prior to extracting a coordinates
list identical to the one obtained from the 3D mi-
grated data (see above). All points derived from the
2D migrated data, located within the areas of 3D mi-
grated data, were omitted. Cross-point mismatches
with bedrock elevation difference of 5 m or higher,
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