Supporting Information for
The Bathymetry of a Titan sea
Geophysical Research Letters
Marco Mastrogiuseppe, Valerio Poggiali, Alexander Hayes, Ralph Lorenz, Jonathan
Lunine, Giovanni Picardi, Roberto Seu, Enrico Flamini, Giuseppe Mitri, Claudia
Notarnicola, Philippe Paillou, Howard Zebker.
Introduction
We analyzed T91 Cassini RADAR altimeter echoes reflected from the bottom of
Ligeia Mare in order to derive bathymetry and loss tangent of the liquid hydrocarbons
filling the basin. The bathymetry was obtained by means of super resolution
techniques (MEM method via Burg algorithm). The loss tangent was estimated using
nominal range resolution and incoherent data processing (13 modulus squared radar
echoes average within each burst) in order to improve the radiometric resolution and
thus the accuracy on the radar parameters estimation.
1. Burg’s MEM Application for Subsurface Detection Improvement
In order to improve the detection of the subsurface reflected echoes and obtain a
more accurate bathymetry of the sea we applied the Burg’s MEM for Cassini
bandwidth extrapolation, and a coherent processing to the Cassini bursts. First we
applied the method on a two layer model Cassini simulated signal and we verified the
effectiveness improvement on distinguish the peaks generated at interfaces below the
nominal radar range resolution, see Figure S1.
1
Figure S1. Burg Algorithm applied on simulated Cassini radar signal received from a
two layer model. The simulated methane - water ice interfaces are placed to a distance
below the radar resolution. In the right panel we can see the extrapolated spectrum of
the simulated signal. In the left panel the resolution system has been improved by a
factor of 3 via Burg algorithm and the second peak appear separated from the first
one.
Second, we investigated the reliability on reconstructing bandwidth by
extrapolating one third of the spectrum from the pulses of Burst n. 248036994 and
then we compared the reconstructed signal with the original one, see Figure S2. We
find a high degree correlation for extrapolation bandwidth factor of 3 which decreases
for higher order factors.
2
Figure S2. The reconstructed and original Cassini burst n° 248036994. Large
correlation is obtained from extrapolation of the spectrum by a factor of 3
2. Two-Layers Model Cassini Radar Data Simulation
Cassini radar response was simulated over a two-layers model scenario in order to
compare the simulated signals to the echoes collected over Ligeia Mare.
We simulated the radar echo obtained from burst ID#248037009 where the subsurface
was detected at a two-way transit time ∆τ equal to 1.3 μs from an altitude of 1700 km.
As geophysical parameters we imposed a hydrocarbons dielectric constant equal to
1.75 at the surface, a loss tangent of 3 ∙ 10−5 and a subsurface dielectric constant of
1.9. We applied the nominal processing (range compression and taper function) by
considering the taper function (Taylor taper) used by Cassini Processing of Altimetric
Data system (CPAD) for the generation of Titan altimetric profiles and a dedicate
taper (Blackman taper) able to suppress the lateral lobes of the first strong reflection
up to 60 dB in order to improve the subsurface returns.
3
Figure S3. Simulated vs real Cassini data. Right panel: Cassini data simulated over a
two-layer scenario composed by 150 m of liquid hydrocarbons. Left panel: the real
Cassini Burst# 248037009, the upper image is obtained by using Taylor taper and the
bottom image using Blackman taper. The upper image is processed by means of
Taylor taper and the bottom image using Blackman taper.
It is worth to note that both simulated and real data show that a dedicate taper
function such as Blackman or Kaiser Bessel, improves the detection of subsurface
return thanks to a better lateral lobes suppression of the first strong surface return
(Figure S3).
3. T91 Data Analysis: Loss Tangent Estimation of Ligeia Mare
Cassini collected 38 echoes along 280 km over the sea, several radar returns were not
used for the inversion analysis because they were acquired over a shallow portion of
the sea (North part of Ligeia Mare) or in presence of significant subsurface roughness.
We selected the reliable echoes for loss tangent measurements by investigating to the
shape of reflected surface and subsurface pulses.
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The criterion was based on the selection of pulses having SNR greater than 8 dB (see
Figure S4) with the following shape characteristics:
-
Only radar pulses that show Gaussian behavior measured at – 3 and –6 dB as
asymmetry of the shape respect to the central peak position, with a tolerance
of ±30%;
-
Only radar pulses that show pulse width (measured at – 3 and –6 dB) smaller
than the flat response + 30%.
These characteristics of the echo shape correspond in the near - nadir non coherent
Cassini echo model to a radar response acquired over a surface with standard heights
deviation less than 20 m and off - nadir angle less than 0.2° from an altitude of ~1700
km. As a result we obtained 8 radar pulses, collected most of them along a portion of
80-90 km from 77° to 79° in latitude, indicating this region to have moderate
stationary subsurface roughness and thus to be suitable for our inversion procedure
analysis. Three more pulses belong to the same area but do not completely satisfy the
second pulse shape selection. Anyway we decided to include them into the analysis as
they do not change results but only increase sample size. The rest of the radar echoes
were not selected since most of them are partially or completely merged to the surface
pulse.
We investigated the loss tangent by means of a standard technique adopted on
sounder and GPR (Campbell et al. 2008; Matsouka et al. 2010) able to estimate the
radio signal attenuation respect to the depths of the sea bottom. Assuming the bottom
of the sea to be homogeneous, we measured the subsurface peak power relative to the
surface (Ps/Pss) as function of the two-way surface/subsurface transit time ∆τ.
Through linear regression applied to the radar measurements of Ps/Pss vs. ∆τ (see
5
Figure S5), we found specific attenuation value equal to 11±4 (dB/μsec) and along
with the formula:
k ( ) dB /  sec  27  tan  sea ( )  f 0 MHz
(1)
where k(τ) is the specific attenuation in dB/μsec, f0 is the carrier frequency in MHz,
we estimated the loss tangent tanδsea of Ligeia Mare be in order of 3 ∙ 10−5 ±30%.
Figure S4. SNR of the seabed detected echoes after coherent and incoherent
processing algorithm. Coherent processing tends to improve the resolution and the
subsurface SNR. The measurements acquired over the central portion of the
bathymetry are the less reliable since the SNR is very low due to the large depths.
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Figure S5. Linear regression of subsurface relative power (Ps/Pss) vs two-way transit
time Δτ. The linear regression suggests that Cassini signal specific attenuation caused
by the propagation through the sea is in order of 11 dB/μsec.
4. Upper Bound on Loss Tangent from Magnitude of Secondary Echo Peak
As described in the main text, we applied an alternate analysis for estimating the
loss tangent by ascribing the difference in magnitude of the surface and subsurface
echoes entirely to absorption in the medium and differences in the surface and seabed
reflections caused by variations in liquid vs. seabed dielectric constants assuming
specular interfaces. In particular, along with formula F2, we computed the maximum
relative subsurface expected magnitude (minimum Ps/Pss) in absence of non-nadir
scattering terms (fs/fss=0 dB) (see Picardi et al. 2007 for more details):
 SS
dB
 S
dB
 1   S 
2
dB
 K dB 
fS
f SS

dB
PS
PSS
dB
(F2)
We imposed the expected minimum surface reflectivity (ΓS) equal to ~ -19 dB
(which corresponds to surface dielectric constants equal to 1.6) and the maximum
subsurface reflectivity (ΓSS) equal to ~ -12 dB (which corresponds to seabed dielectric
constants equal to 4.8) by investigating the possible materials present on Titan as
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measured by Cassini radiometry and Scatterometry (Wye et al. 2007). The difference
of Ps/Pss from the observed data respect to this theoretical value was attributed
completely to the attenuation into the medium. This upper limit of attenuation along
with the relative measurement of ∆τ and through formula (F1) was used to constrain
the upper limit of loss tangent echo by echo. Results for this analysis are shown in
Figure S6, where we solve for the depth from the delay of the sea bottom peak (top
panel) and record the magnitude of the bottom peak compared to the surface echo
(center panel). Since the surface scatters nearly specularly, this yields an upper bound
on the loss through the medium (bottom panel).
As we expected from the pulse shape analysis, the region from 77°N to 79°N we
previously found for the better estimate of loss tangent, results be the more stable
even among the upper bound loss tangent measurements. In this region the upper
bound reaches values of ~9 ∙ 10−5 . A more realistic scenario which include
subsurface roughness and/or other kinds of materials can only have loss tangent lower
than this last quantity.
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Figure S6. Loss tangent upper bound using all Ligeia echoes. (top) Estimate of depth
from time delay of second peak. (center) Relative magnitude of subsurface echo.
(bottom) Upper bound on loss tangent. Plots have been obtained by means of noncoherent processing.
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