TCThe CryosphereTCThe Cryosphere1994-0424Copernicus PublicationsGöttingen, Germany10.5194/tc-12-2969-2018Coherent large beamwidth processing of radio-echo sounding dataProcessing of radio-echo sounding dataHeisterAntonanton.heister@dlr.deScheiberRolfGerman Aerospace Center (DLR), Microwaves and Radar Institute, Wessling, GermanyAnton Heister (anton.heister@dlr.de)19September20181292969297923March201818April201819August201822August2018This work is licensed under the Creative Commons Attribution 4.0 International License. To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/This article is available from https://tc.copernicus.org/articles/12/2969/2018/tc-12-2969-2018.htmlThe full text article is available as a PDF file from https://tc.copernicus.org/articles/12/2969/2018/tc-12-2969-2018.pdf
Coherent processing of radio-echo sounding data of polar
ice sheets is known to provide an indication of bedrock properties and detection
of internal layers. We investigate the benefits of coherent processing of a
large azimuth beamwidth to retrieve and characterize the orientation and
angular backscattering properties of the surface and subsurface features.
MCRDS data acquired over two distinct test areas in Greenland are used to
demonstrate the specular backscattering properties of the ice surface and of
the internal layers, as well as the much wider angular response of the
bedrock. The coupling of internal layers' orientation with the bed topography
is shown to increase with depth. Spectral filtering can be used to increase
the SNR of the internal layers and mitigate the surface multiple. The
variance of the bed backscattering can be used to characterize the bed return
specularity. The use of the SAR-focused RES data ensures the correct azimuth
positioning of the internal layers for the subsequent slope estimation.
Introduction
Radio-echo sounding (RES) is a well-established technique for remotely
measuring the thickness of ice sheets. The use of synthetic aperture radar
(SAR) focusing improves gain and azimuth resolution of the echograms.
Overall, state-of-the-art SAR processing offers information about the
spatial properties of the ice sheet and the strength of the response, which
is used to determine ice thickness, internal layers' orientation and bedrock
conditions, i.e., presence or absence of water. There exist several SAR
algorithms for focusing RES data, among them 1-D matched filtering
, the ω-k migration , 2-D
matched filtering , and multilook time-domain
back-projection . Additionally, offer
a method for improving SAR focusing of internal layers by introducing a
correction of attenuation, migration and radial spreading for the returns
from tilted internal layers.
Previous studies of angular backscattering properties of the ice sheet and
bed were performed in
.
offer a technique for studying the backscattering properties of the ice sheet
and bed using a special subaperture SAR approach. The authors study the
dependency of the surface and bed return power on the incidence angle and the
effect of the surface slope on the surface return power. They show that the
response of the internal layers is specular and propose incoherent
summation of subapertures to
improve the signal-to-noise ratio (SNR) of internal layers.
estimates an optimal value for the SAR beamwidth based on the bedrock SNR.
offer an approach for detecting the presence of
subglacial water at the bed based on its angular backscattering
characteristics. The authors estimate the specularity of the bed returns by
comparing power contributions in two HiCARS 60 MHz
SAR echograms with synthetic apertures of 700 and
2000 m. introduce two new methods for estimating the
slope of internal layers, among them the Doppler centroid method, which
leverages the fact that internal layers' returns are highly specular. The
authors use azimuth Fourier transform of short overlapping range-compressed
RES data blocks, and derive the slope of internal layers from the wavenumber
of the corresponding Doppler centroids.
introduce a novel approach for SAR processing of RES data,
where the processing chain generates a number of SAR echograms, each
corresponding to a particular incidence angle in along-track. A subset of the
echograms with the highest SNR is then selected for further processing.
In this paper we introduce a new flexible technique to analyze the angular
backscattering properties of the ice sheet and bed, which can be applied to
previously conventionally SAR-focused complex-valued echograms. A better
understanding of those properties allows us to offer novel strategies for
improving internal layer and possibly bed SNR, to mitigate the surface
multiple return and to train sparsifying dictionaries for model-based
cross-track focusing methods such as .
This paper begins with a description of the employed SAR-focusing
algorithm for RES data in Sect. . After that we
introduce the technique for analyzing angular backscattering properties of
the ice sheet and bed in Sect. . In
Sect. we analyze the processing results for two RES surveys
collected by the Center for Remote Control of Ice Sheets (CReSIS),
Kansas, USA using their Multi-Channel Radar Depth Sounder
(MCRDS) during the Greenland
campaign in 2008 . Based on the results of
Sect. , we discuss and demonstrate approaches for improving
internal-layer visibility and for mitigating the surface multiple in
Sect. . Potential impacts for the scientific
evaluation of SAR-focused RES data with large beamwidth are discussed in
Sect. . Finally, a summary and conclusions
are given.
SAR focusing
We perform SAR focusing of RES data using a modification of the
range-Doppler algorithm. The processing is done in overlapping 8000 m long
azimuth blocks, with each block processed as described in
Algorithm . For each block we assume the platform to
fly with a constant velocity v, the ice surface to have a constant
along-track slope ψ, and the ice sheet to have a constant refractive
index nice=1.78 with an equivalent real part of relative
permittivity εice=3.17. We also assume that the
electromagnetic wave propagation obeys Snell's law for a two-layer air-ice
model shown in Fig. . The number of azimuth samples
in each block is selected to satisfy at least twice the desired SAR beamwidth
of Δθ=30∘. We additionally assume that the azimuth
antenna pattern is broad enough so that its variation for incidence angles in
the interval θ=[-15∘,15∘] can be safely ignored.
We now describe the algorithm inputs using the notation where τ denotes
range time, fτ denotes range frequency, η denotes
azimuth time, and fη denotes azimuth frequency (Algorithm 1).
Range compression, which is a signal-processing technique for improving the
radar range resolution, is implemented using a matched filter
HRC equal to a complex conjugate of the Fourier transform of
the transmitted signal weighted by Hamming or Blackman windows for the
side-lobe suppression.
The range-Doppler algorithm assumes a linear motion trajectory of the
platform; therefore the motion compensation, a procedure that corrects the
platform's trajectory deviation from a linear reference trajectory, is
needed. We implement it using a filter HMOCO, which only
corrects for a vertical component of the platform's deviation from a
reference track in the range frequency domain.
SAR focusing
raw data DATA, filters HRC, HMOCO, and HREF, amount of RCM ΔRRCM.
SAR-focused echogram DATASAR
DATA:=FFTrange(DATA)
DATA:=DATA⋅HRC⋅HMOCO
DATA:=IFFTrange(DATA)
DATA:=FFTazimuth(DATA)
forfη∈[-Baz/2,Baz/2]do
DATA[:,fη]:=interp(DATA[:,fη],ΔRRCM[:,fη])
endfor
DATA:=DATA⋅HREF
DATASAR:=IFFTazimuth(DATA)
returnDATASAR
As the platform moves in azimuth, the response from a target spreads across
multiple range bins. Range cell migration correction (RCMC) is an operation
that removes this range variation, bringing the target response to a fixed
range bin at every azimuth position. RCMC is performed in the range-Doppler
domain. During RCMC every range line is shifted by the time corresponding to
the amount of range cell migration ΔRRCM. The spatially
variant shift in range is implemented using a sinc interpolator with Lanczos
window (a=2) and the length exceeding 3 times the maximal ΔRRCM. Finally, azimuth
compression is done by applying the HREF filter. We now derive
equations for ΔRRCMC and HREF.
Along-track geometry.
From Fig. the optical path length R from the radar
at azimuth x=η⋅v to a point target at depth d is
R(d,η)=Rair+niceRice,
where the geometric lengths that the electromagnetic wave travels in air and
ice are
Rair=(R02+s⋅tanψ)2+(x-s)2,Rice=s2+(d-s⋅tanψ)2.
Both Eqs. () and () depend on an
unknown location of the refraction point s, which is a function of time
η and depth d. The refraction point s can be found by solving a
fourth-order polynomial equation or, more
efficiently, by using Newton's optimization method, which iteratively finds
s that minimizes (Eq. ) with the following update
rule at (i+1)th iteration:
si+1=si-R′(s)/R′′(s),
where we initialize the refraction point with s0=0.
Knowing s, we calculate the phase shift of the received signal with respect
to the time η=0, when the platform crosses the origin of the x axis
Δϕ(η)=4πλ0ΔR(η)=4πλ0(R(η)-R(0)),
where λ0 is the wavelength of the transmitted wave in the air.
The Doppler frequency shift of the received signal is proportional to the
derivative of Eq. () in time:
Δf(η)=12π∂ϕ(η)∂η.
Knowing Eq. () for each depth d and azimuth position x,
we compute the amount of range cell migration in the range-Doppler domain
ΔRRCM(d,fη) by interpolating its time domain
counterpart ΔRRCM(d,η)=τ⋅c0/2-ΔR(d,η) onto a regularly sampled azimuth frequency grid fη∈[-Baz/2,Baz/2], where fη=±Baz/2 corresponds to incidence angles θ=±15∘.
Finally, we compute Δϕ(fη) by interpolating
Eq. () onto fη and calculate the
matched filter for SAR-focusing HREF as
HREF(τ,fη)=exp(-jΔϕ(fη)).
We note that more precise and less restrictive SAR-focusing algorithms for
ice-sounder data exist, such as time-domain back-projection
; our choice of a particular approach described above is
based on simplicity of implementation and its sufficiency for the subsequent
analysis of the ice sheet and bed angular backscattering properties.
Multiple subbands processing
In order to analyze the dependency of the backscattering properties of the
ice sheet and bed on the incidence angle, we divide the azimuth spectrum of
an echogram into N overlapping subbands of beamwidth Δθsub=2∘ and an overlap between two adjacent
subbands of 1∘, with each subband weighted by a rectangular window.
The central frequency of the n∈(1,N) subband, f0(θn),
corresponds to the incidence angle of interest θn∈[-14∘,14∘]:
f0(θn)=2vsinθnλ0.
Each subband is then accordingly zero-padded in azimuth so that all N
subbands have the same size. An inverse azimuth Fourier transform is then
applied to each subband to get a set of N echograms In, each containing
returns coming predominantly from the corresponding incidence angle
θn.
The positions of ice-sheet features of interest, such as surface, internal
layers and bed, are then manually selected from an echogram
Iincoh, calculated as the incoherent sum
Iincoh=∑n=1N|In|.
We note that the ice sheet features can be tracked semi-automatically or
automatically; however, for the small amount of data we analyze in the paper,
manual selection is feasible.
Greenland MCRDS data
We apply the approach presented in Sect. to RES data
collected by CReSIS using their MCRDS system
. The main parameters of the radar and the
acquisitions are summarized in Table . Two
chirps with different durations were transmitted alternately on a
pulse-to-pulse basis, with a 3 µs chirp intended to capture the
surface and the shallow internal-layer returns (shallow mode), and a
10 µs chirp intended to capture deeper internal layers and bed
returns (deep mode). We employ the availability of multiple cross-track
channels of MCRDS to increase the SNR of nadir returns by combining
the SAR echograms of the cross-track channels using conventional delay and
sum beamforming.
We select two tracks, both flown over Greenland in summer 2008 and
approximately 70 km long. The track flown from the inland towards
Jakobshavn Glacier is referred to as track 1, the track flown over
south-eastern Greenland in a north-easterly direction is referred to as track 2.
The regions of interest, their topography and flight trajectories are shown
in Fig. . These particular surveys are chosen to
demonstrate how different bed topography affects the reflective properties of
the internal layers; the bed in track 1 has depth varying in the interval
dbed∈[2170m,3030m] and slopes varying in
the interval ψbed∈[-35∘,33∘]. The
corresponding intervals for track 2 are dbed∈[640m,1970m] and ψbed∈[-62∘,65∘]. Here we calculate the slopes of the bed and the internal layers
as
ψbed/layer(x)=tan-1∂dbed/layer(x)∂x⋅nice,
where nice scales the geometric slope to correspond to the
incidence angle observed by the radar.
Parameters of MCRDS acquisitions.
ParametersTrack 1Track 2Central frequency150 MHz Chirp bandwidth20 MHz Chirp duration3/10µsSampling frequency120 MHz Effective PRF78 Hz156 HzNumber of cross-track channels166Effective cross-track aperture14.34 m4.79 mAcquisition date20 June 20081 August 2008Acquisition start UTC18:32:2916:49:49Acquisition end UTC18:47:3317:07:23Average height over surface160 m800 mAverage velocity78ms-165ms-1
MCRDS surveys on a map. The map of Greenland is plotted using a
stereographic projection with a central meridian of 41∘ W and a
central parallel of 72∘ N. Isolines on maps correspond to a
surface elevation change of 250 m.
Backscattering characteristics of the ice sheet and bed for track
1.
Backscattering characteristics of the ice sheet and bed for track
2.
The full bandwidth echogram of track 1 is shown in
Fig. a. To produce the figure we combine echograms of
the shallow and deep modes, average the intensities of each eight adjacent
azimuth samples, downsample the result in azimuth by a factor of 8, and add a
depth-dependent amplitude ramp of 20 dB km-1 to improve the visibility of
the deep internal layers and the bed. The internal layers are visible to
d≈2 km. The gaps in internal-layer visibility occur at azimuth
positions where the bed slope is the steepest.
First, we investigate reflective properties of the ice surface.
Figure b shows the normalized reflectivity power of the
surface as a function of incidence angle. The surface response is specular,
with the incidence angle corresponding to the maximum intensity
θmax(I), varying slowly in azimuth.
To study backscattering properties of internal layers we select a single
internal layer tracked with a solid red line in Fig. a. A
deep layer is selected in order to avoid undesired contributions of the
off-nadir surface returns. Figure c shows the internal
layer's normalized power together with its slope, computed from
Eq. () and drawn as a white line. We use bicubic interpolation to
plot the figure. The internal-layer response is specular, with
θmax(I) proportional to the layer's geometric slope.
A further insight into the behavior of the internal layer's response is given
in Fig. d, where for each pixel of Iincoh we
color coded the incidence angle corresponding to the maximum intensity
θmax(I). Prior to plotting, we additionally applied a median
filter of size (5,5) and bicubic interpolation. The black lines on the
figure correspond to the surface and bed return positions. The figure shows a
correlation between θmax(I) and the bed slope, with the
blue and the red color appearing at azimuth positions with negative and
positive bed slope correspondingly. Moreover, for a given azimuth position
x0 the absolute value of θmax(I) increases with depth;
therefore, according to Fig. d,
the absolute value of internal layers' slope also increases with depth. This
implies that the deeper the internal layer is located, the more its shape
resembles the shape of the bed.
Figure e shows the normalized power of the bed response,
where, prior to the normalization, we additionally compensate for the two-way
propagation power loss of 20 dB km-1. The incidence angle
θmax(I) of the bed response varies in azimuth, and overall the
response is wide, meaning the bed is a rough surface for a radar with
λ0=2 m.
Figure shows the dependency of the
return power of the previously selected internal layer and bed at four fixed
azimuth positions. Those particular positions are selected to demonstrate the
variety of shapes of reflective signatures for the bed and the persistent
signature shape for the internal layer.
Internal layer (a) and bed (b) returns for track 1
at azimuth positions x=(3,9,46,59) km, marked with vertical red lines
in Fig. a. Quadratic interpolation was applied to smooth
the signatures.
The full bandwidth echogram for track 2 is shown in
Fig. a, where we add a depth-dependent amplitude ramp of
20 dB km-1. Here the bed topography varies more compared to
track 1, the internal layers are visible close to the bed with gaps
appearing at azimuth positions where the absolute value of bed slope is the
highest, and the surface multiple is also present in the echogram.
Figure b shows the normalized reflectivity power of the
surface. The surface response is similar to the one for track 1, with
higher variation of θmax(I) starting from azimuth x=65 km.
Reflective properties of a single internal layer tracked with a solid red
line in Fig. a are shown in Fig. c.
Here we select a shallow layer because θmax(I) for deeper layers
would lie outside the interval θn∈[-14∘,14∘]
previously selected in Sect. . The incidence angle
θmax(I) in Fig. c varies more strongly and
frequently compared to that in Fig. c.
Figure d is plotted similarly to
Fig. d. As expected, we observe larger color gradients
for internal layers for track 2, whereas incidence angles of the
surface multiple lie around θn≈0∘ in white,
corresponding to the ice surface.
The normalized power of the bed response for track 2 is shown in
Fig. e.
In Fig. we compare the responses
of the previously selected internal layer and bed at four fixed azimuth
positions. We again observe specular reflections from the internal layer and
wider reflections from the bed, with θmax(I) for the bed and the
internal layer positively correlated for each selected position.
Internal layer (a) and bed (b) returns for track 2
at azimuth positions x=(3,25,32,54) km, marked with vertical red lines
in Fig. a. Quadratic interpolation was applied to smooth
the signatures.
For both tracks the mean value of the surface and the layer beamwidth at the
-6 dB level is 2.2∘. The shape of the bed response varies and
does not necessarily have a prominent single peak; therefore we do not
calculate its beamwidth. We suggest using the variance of the bed angular
response to quantify its spread when the bed roughness or the presence of
basal water is of interest. For more details we refer the readers to
Sect. .
Enhancement of SAR echograms
In this section we offer two straightforward applications of the results
provided in Sect. to improve the SAR-focused RES data.
First, the fact that an internal-layer response is narrow means that for a
given depth and azimuth it contributes only to a limited azimuth frequency
range of a SAR echogram spectrum. For the azimuth spectrum of a small block
of a SAR echogram we see that at each depth internal-layer contribution is
clustered around the frequency corresponding to the layer slope, which is
demonstrated in Fig. . This allows us to use
spectral filtering to improve the SNR of the internal layers. We perform the
filtering using 250 m azimuth blocks with a 70 % overlap. We apply a
Fourier transform in azimuth to each block, after which for each depth we
select a frequency corresponding to the maximum spectrum intensity
fmax(I)(d) and fit it to a piecewise linear regression with
npieces=3 to make the estimate f^layer(d) of
the internal layers' frequency flayer(d) more robust against
outliers. Depending on the shape of flayer(d), other values for
npieces as well as other types of regression (e.g., polynomial
regression) might be used to calculate f^layer(d). After
that we nullify the part of the spectrum at frequencies lying outside the
interval f^layer(d)±0.05Baz, whereas the
part of the spectrum lying inside the interval is kept intact. Finally we
apply an inverse Fourier transform in azimuth to each block and re-assemble
the overlapping blocks. We apply this method to the track 1 SAR
echogram. The results are shown in Fig. .
Azimuth spectrum of a 250 m long SAR block in track 1, azimuth
position x=59 km. The frequency interval f^layer(d)±0.05Baz is marked with white lines.
Improvement of internal-layer visibility for track 1. The subsets of
the SAR echogram before and after the processing are shown at the top and the
bottom correspondingly.
The procedure results in a 21.8 % sharpness improvement in terms of
intensity squared metric (Eq. )
with the mean intensity of the echograms normalized prior to the comparison.
s(I)=∑i,jIi,j⋅Ii,j*
Figure depicts the antenna power pattern, the layer
power spectrum centered around flayer, and the power spectrum
of the noise. The noise power is proportional to the integral of its power
spectrum. Prior to the spectral filtering, this frequency range contains the
entire processed bandwidth Baz, whereas after the
filtering the interval is fη∈[flayer-0.05Baz,flayer+0.05Baz]. Assuming
white Gaussian noise, and that the signal energy is not affected by the
filtering, the SNR improvement is 10 dB.
Noise reduction for internal-layer SNR
improvement.
Second, according to the Fig. d, the contribution of the
surface multiple return, which is a multipath reflection from the ice surface
as well as from the upper internal layers and the bottom of the aircraft
fuselage and wings, can be mitigated by identifying and filtering out its
contribution in the azimuth frequency domain, therefore revealing previously
masked internal layers. This approach, however, only works in areas where the
θmax(I) for internal layers and the surface multiple differ.
To demonstrate the approach we process a subset of a SAR echogram of
track 2. The processing is done in blocks with similar parameters as
for internal-layer visibility improvement. In each block we locate the
strongest surface multiple contribution at a depth dmult
corresponding to the doubled height of the aircraft over the ice surface, and
at azimuth frequency fmult which corresponds to the frequency
of strongest surface return. After that in each block we apply a 2-D notch
filter located at depth d∈[dmult,dmult+100m] and at frequency fη∈[fmult-0.05Baz,fmult+0.05Baz].
The results are shown in Fig. .
Mitigation of the surface multiple for track 2. The subsets of the
SAR echogram before and after the mitigation are shown at the top and the
bottom correspondingly.
Scientific utility of large beamwidth SAR processing
In this section we discuss the practical benefit of large beamwidth SAR
processing of RES data for two scientific applications, namely basal water
detection and estimation of internal-layer slope.
Presence of water bodies can be detected in RES data using either amplitude
or angular information. The amplitude detection is based on the fact that
the basal water produces stronger reflection compared to the grounded bed.
However this method is prone to errors as the radar
attenuation depends on the chemical composition of the ice as well as its
temperature . The analysis of the angular backscattering
distribution of the bed return, on the other hand, is free of the
aforementioned limitations, and a specular bed response indicates the
presence of basal water.
In order to quantify specularity of the bed return,
introduce the specularity content, a measure which is calculated as a ratio
of energies of the bed return in two SAR echograms, I1 and I2,
focused with synthetic apertures L1=700 m and L2=2000 m
correspondingly. The echogram I1 contains specular returns, whereas the
echogram I2 contains both specular and non-specular returns. For a
typical height above the ice surface R0=500 m and ice thickness
d=2km used in the survey , L1 and
L2 respectively correspond to beamwidths Δθ1≈10∘ and Δθ2≈28∘.
We compare the specularity content used so far with the variance of angular
backscattering of the bed, which is a measure of the bed angular distribution
spread, introduced in Sect. . We calculate the specularity
content using Δθ1=10∘ and Δθ2=30∘. To calculate the variance we normalize the energy of the angular
backscattering in each azimuth position. In Fig. the
specularity content is low at azimuth positions A and D, failing to detect
specular bed reflections located outside of Δθ1; the
specularity content is high at azimuth positions B and C, but decays rapidly
as the bed reflection moves outside of Δθ1. The variance, on the
other hand, is insensitive to an angular shift of the reflected energy,
therefore making it possible to detect additional specular reflections. Using
the variance instead of the specularity content can potentially lead to
better detection and mapping of subglacial water bodies, especially in areas
where the bed is tilted in azimuth.
Specularity content and variance as measures of specularity of the
bed return for track 2. For comparison we take two parts of track 2
each 2.3 km long. The power of the angular energy returns (a)
and (c) is normalized with respect to the highest value of the
distribution at each azimuth position. The area inside the dashed horizontal
lines in (a) and (c) corresponds to Δθ1.
Internal layers, frequently observed in RES echograms, are widely attributed
to the changes of electrical conductivity within the ice sheet. Owing to the
fact that the internal layers are considered isochrones ,
when tracked in RES data, they provide information about changes in the ice
flow and snow accumulation rate in the past
. The availability of a large amount of RES data and
the fact that the semi-automatic layer tracking is prohibitively expensive
motivate the development of automatic layer-tracking
algorithms.
Some of the tracking algorithms use reflection slope to predict the internal
layering, which in turn simplifies subsequent tracing.
introduce two new methods for the slope estimation, namely horizontal phase
gradient and Doppler centroid methods. Both methods use coherent RES data
(phase preserved). As stated in currently the data have
been range compressed but without SAR focusing. The use of range compressed
as opposed to SAR-focused RES data might lead to erroneous estimation of the
slope due to the displacement of internal layers in azimuth. The displacement
is due to the fact that the internal-layer reflection is specular, which in
turn means that prior to SAR focusing the return from an internal layer
appears at the azimuth position, where the incident energy is normal to the
layer's surface. SAR focusing registers the return at its zero Doppler
position, which corresponds to the nadir direction.
Figure schematically illustrates this
effect with two examples. For the sake of simplicity we ignore the ray
bending due to the difference in refractive properties of the air and ice.
The azimuth positions at which the layer returns are registered in range
compressed and SAR-focused data are marked with circles and squares,
respectively. A convex internal layer in Fig. a
appears stretched in azimuth in range-compressed data, whereas a concave
internal layer in Fig. b appears shrunk (in
extreme cases reflections from the left and the right would be overlaid).
Azimuth displacement of a tilted internal layer in range-compressed
data.
The amount of the displacement Δx depends on the layer's geometric
slope α, its depth d, platform height above the surface R0, the
refractive index of the ice nice, and the surface slope ψ.
When ψ=0∘, the displacement is calculated as
Δx=R0tan(sin-1(nicesinα))+nicedtanα.
Figure shows the dependency of Δx
on the layer geometric slope α and depth d when the height over
the surface is R0=800 m, the ice refractive index is nice=1.78, and ψ=0∘.
Internal-layer displacement in azimuth.
Real data examples for both cases are demonstrated in
Fig. , where we compare range-compressed and SAR-focused
subsets of RES data for track 2. For the range-compressed data, the internal
layers appear stretched in azimuth in areas A and C, whereas for the area B
the layers shrink and even overlay at the lower depth.
Stretching and shrinkage of internal layers in range-compressed data
of track 2. The range-compressed echogram is shown in (a), the SAR-focused echogram is shown in (b).
Summary and conclusions
In this paper we offered a new approach to study scattering characteristics
of ice sheets, which is based on the division of a conventionally focused
large beamwidth ice sounder SAR echogram into a set of subbands, each of which
correspond to a particular incidence angle in an along-track direction. We
estimated and compared scattering characteristics of the ice surface,
internal layers and bed for two surveys in Greenland. For those surveys, the
surface and internal layers have narrow responses, which correspond to a
smooth specular surface, while the bed response is wide, which corresponds to
a rough surface. The scattering properties carry information which can be
used to estimate characteristics of the bed roughness , with
the specular bed response indicating the likely presence of subglacial water
at the bed .
Based on the scattering characteristics of internal layers, we offered a
post-processing technique to improve their visibility. By taking a small
azimuth block of a SAR echogram, within which the orientation of internal
layers varies slightly in along-track, we observe that the internal
layer's contribution to the block's azimuth spectrum is sparse and is clustered
around the frequency corresponding to the internal layer's slope. This
observation directly suggests a way to improve internal layers' SNR by
keeping only those spectral components where the internal layers'
contributions are present. This post-processing technique can improve spatial
tracking and interpretation of both horizontal and tilted internal layers. As
a subject for further studies, we suggest that denoising all ice sheet
features in a SAR echogram is possible by finding a sparse representation of
the echogram given a sparsifying dictionary learned on patches with high SNR.
We also demonstrated a way to reduce the undesired contribution of the
surface multiple return, which masks internal layers at corresponding depths.
The reduction is possible whenever the surface multiple and the masked layer
contributions come from different incidence angles, in which case they are
separable in the azimuth frequency domain.
Finally, we discussed the potential benefit offered by the analysis of RES
data focused using large beamwidth SAR with regards to the bed specularity
characterization and for the correct azimuth positioning of the tilted
internal layers.
The raw MCRDS data used in the paper are available from CReSIS
upon request.
The authors declare that they have no conflict of
interest.
Acknowledgements
We acknowledge the use of data from CReSIS generated with support from
the University of Kansas, NASA Operation IceBridge grant
NNX16AH54G and NSF grant ACI-1443054. The authors would also
like to thank John Paden of CReSIS for answering the sensor and data-related questions.The article processing
charges for this open-access publication were covered by a
Research Centre of the Helmholtz Association. Edited by: Joseph MacGregor Reviewed by: John
Paden and one anonymous referee
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