Jökull - 01.01.2021, Page 50

Magnússon et al.
is the travel time of received backscattered transmis-
sion relative to the triggering time of the measure-
ment; the receiver measurement is triggered by the
direct wave propagating along the surface from the
transmitter (Figure 1b). The centre position, M, be-
tween transmitter and receiver for each RES-survey
was obtained using the GNSS timestamp obtained by
the receiver unit for each RES-survey, and the corre-
sponding position of the DGNSS on the snowmobile
projected back along the DGNSS profile by a fixed
distance (Figure 1b). This distance corresponds to
the half the antenna separation (a/2) plus the mea-
sured distance b, from the RES-receiver sledge to the
snowmobile (location of the DGNSS antennae). b
was 20–22 m in the surveys described here. Except
when taking sharp turns, the horizontal accuracy of
M is expected to be < 3 m. Errors are mainly due to
variation in distance to the snowmobile, inexact tim-
ing of each RES-survey (the survey plus processing
time of the stacked measurements varies slightly but
is typically ∼1 s), and inaccuracy in how well the
towed sledges follow the snowmobile path. The ver-
tical accuracy in surface elevation measured with the
DGNSS, is typically a few decimetres. The strong di-
rect waveform is estimated as the average wave form
measured over several km long RES-profile segments
and then subtracted from the corresponding segment
of the raw RES-measurements. The remaining part
of the measured backscatter, mostly from englacial
and subglacial reflectors, was amplified as a func-
tion of the travel time in order to have the backscat-
ter strength as independent as possible of the reflector
depth. The next processing steps depend on whether
2D or 3D migration was applied.
2D migrated RES-data
In case of 2D migration, the amplified RES-data along
with the 3D location, M, for each measurement and
corresponding transmitter and receiver 3D positions
(a/2, behind and in front of M, respectively, along the
DGNSS profile) were used as inputs into a 2D Kirch-
hoff migration (e.g. Schneider, 1978), programmed
in MATLAB(®Mathworks). The migration was car-
ried out assuming propagation velocity of the radar
signal through the glacier, cgl=1.68× 108 m s−1 and
500 m width of the radar beam illuminating the glacier
bed. The value of cgl is the same as obtained by
comparison of a borehole survey and RES-data in the
eastern Skaftár cauldron located in the accumulation
area of Vatnajökull (Magnússon et al., 2021) and only
slightly lower than the value used in previous mapping
of Mýrdalsjökull by Björnsson et al., (2000), which
used the value cgl=1.69×108 m s−1. The 2D migra-
tion results in profile images like the ones shown in
Figure 2e. The x- and y-axis of these images corre-
spond to driven profile length and elevation in metres
above sea level, respectively. The image pixel dimen-
sions, dx=5 m and dy=1 m, roughly correspond to
the horizontal sampling density when measuring with
∼1 s interval at∼20 km hour−1, and the 80 MHz ver-
tical sampling rate (in 2012–2017 and in 2021; it is
120 MHz for a new receiver unit used in 2018–2019).
Backscatter from the glacier bed is usually recog-
nised as the strongest continuous reflections at depth
in the 2D migrated amplitude images. They were
traced with an automatic tracing algorithm, pro-
grammed in MATLAB (®Mathworks). The algorithm
traces the bed reflection by using the maximum cor-
relation with the bed reflection at the chosen starting
point. The obtained traces were manually checked
and rejected where the algorithm failed. This pro-
cess was repeated until all clear bed reflections had
been traced for each profile of an individual survey.
At sharp turns in the survey profiles reflections were
rejected. The assumption of fixed distance between
transmitter and receiver fails at these turns and the 2D
migration is not expected to result in an accurate depth
of reflector.
3D migrated RES-data
The input into the first specific processing step of the
3D migration is the RES-data, amplified as function
of the travel time, acquired for a dense set of paral-
lel profiles, 20 m apart (Figure 4a). The surveys were
carried out by manually following a pre-planned route
in the navigation instrument of the snowmobile. The
survey point positions (M) deviate slightly from the
pre-planned route (Figure 4a). At this stage a 3D ma-
trix (a cube) was linearly interpolated from the survey
data, with first axis in the direction of the planned sur-
vey tracks (5 m node interval) and second axis in cross
track direction (10 m node interval). The third axis of
48 JÖKULL No. 71, 2021