Titolo della tesi: Super-Resolution applied to Radar Sounders: Theory and Implications for Surface and Subsurface characterization
This thesis focuses on the design and implementation of a super-resolution technique to enhance radar sounder renge resolution to support geophysical and geological interpretation of planetary surfaces. The developed processing, called Ultra-Wide Band processing (UWB), has been designed according to the Mars Advanced Radar for Surface and Ionospheric Sounding (MARSIS) instrument data acquisition design and is suitable to be applied to multi-frequency radar sounders. The processing operates on the two spectra acquired almost simultaneously on the same geological target. The adjoining bandwidths are first merged to fill the missing gap samples by means of Bandwidth Interpolation (BWI) techniques. This augmented bandwidth is then broadened by a factor three through the use of Bandwidth Extrapolation techniques (BWE) based on the Burg algorithm. The resulting bandwidth enables an enhancement of the radar vertical resolution up a factor six, leading for the case of MARSIS to 25 m free space resolution against the nominal 150 m.
The development of the UWB processing, prior to BWI, requires the correction of ionospheric dispersive effects along free space propagation: constant and linear phase offset and attenuation. Linear phase distortion is corrected in the time domain by means of a retracking procedure. The constant phase offset is recovered by means of extrapolation techniques: the two spectra are extrapolated to overlay and via a Least Square (LS) minimization, the constant phase shift to guarantee coherence of the augmented spectrum is selected. Finally, signal attenuation is compensated in the frequency domain by means of ionospheric modeling.
In order to guarantee the reliable application of the technique it has been necessary to constrain its applicability conditions, set by the precision of the retracking procedure in identifying the surface echo. By using via ray-tracing simulations of MARSIS data at different frequencies, it has been obtained that the developed processing can be reliably applied on moderately flat surfaces guaranteeing a retracking error below the expected data resolution after super-resolution.
Finally, the UWB algorithm is applied to experimental MARSIS products acquired on areas of geological interest on Mars: Elysium Planitia on the equator and the South Polar layered deposits (SPLD). By comparison with the SHAllow RADar (SHARAD) products acquired on parallel orbits, it has been possible to validate the detection of shallow interfaces not visible in the standard product.
The capacity of the UWB processing has been brought to the limit by its application to simulated data from REASON (Radar for Europa Assessment and Sounding: Ocean to Near-surface), with the aim of filling a $56.5$ MHz frequency gap by using a 1 MHz and a $10$ MHz. This attempt ended in the failure of applying both BWI and UWB techniques in case of excessive gap between the acquired spectra.
The application of the UWB band processing to data acquired in Elysium Planitia enabled the detection of a subsurface layer at ~1 $\mu s$ depth. With the aim of characterizing its composition, multi-band inversion techniques have been applied jointly to super-resolved MARSIS and SHARAD products, deriving a surface loss tangent associated to mafic/basaltic terrain. The performance of Joint Data Inversion for the attenuation and loss tangent estimation has been evaluated by means of a statistical approach based on Monte Carlo simulations by varying realizations of noise and considering a two-layer scenario.
With the aim of validating the loss tangent estimation, a model-based technique for the estimation of planetary surfaces roughness characteristics has been developed. The technique employs a model derived from the Kirchhoff approximation and exploits the deviation of the acquired sounder waveform from the nominal shape for estimating dimensional surface roughness parameters (root mean squared height $\sigma_h$ and correlation length $L$) and the compensation of the power lost due to scattering effects. The method has been tested on sounder waveform simulations employing Gaussian surfaces and data from the Martian Digital Elevation model MOLA (Mars Orbiter Laser Altimeter).
Finally, the utility on super-resolution techniques is demonstrated on altimetric data acquired by the Cassini RADAR data, which the application of extrapolation techniques enabled the enhanced characterization of the inclusions within Titan's seas and lakes. An analytical model for the Surface-to-Volume Power Ratio (SVR) has been developed, incorporating principles of radiative equilibrium and Mie scattering theory. This model accounts for extinction phenomena and enables the extraction of information regarding the presence of dust particles or bubbles in the liquid bodies of Titan. By leveraging the absence of volume scattering in altimetric waveforms, thanks to BWE technique, constraints are placed on the maximum density at various radii, pertaining to the potential presence of nitrogen bubbles or solid particles, including water ice, nitriles, and tholins.