Hyperbola fitting is a mainstream interpretation technique used in ground penetrating radar (GPR) due to its simplicity and relatively low computational requirements. Conventional hyperbola fitting is based on the assumption that the investigated medium is a homogeneous half-space, and that the target is an ideal reflector with zero radius. However, the zero-radius assumption can be easily removed by formulating the problem in a more generalized way that considers targets with arbitrary size. Such approaches were recently investigated in the literature, suggesting that hyperbola fitting can be used not only for estimating the velocity of the medium, but also for estimating the radius of subsurface cylinders, a very challenging problem with no conclusive solution to this day. In this paper, through a series of synthetic and laboratory experiments, we demonstrate that for practical GPR survey, hyperbola fitting is not suitable for simultaneously estimating both the velocity of the medium and the size of the target, due to its inherent nonuniqueness, making the results unreliable and sensitive to noise.
The Echus-Kasei region on Mars has been exposed to different episodic volcanic, fluvial, and glacial events in Amazonian time. The goal of the present work is to demonstrate the usefulness of radar instruments to find preserved late Amazonian subsurface structures that may have been encapsulated underneath recent lava flows on Mars. We have analysed 27 radar observations of the SHAllow RADar (SHARAD) instrument on board the Mars Reconnaissance Orbiter (MRO), over the region of Echus Chasma. We discovered the presence of subsurface reflectors in five consecutive SHARAD radargrams at a depth from 35 to 79 m beneath the structure of a lava fan that formed about 59 ± 4 Ma ago. Some vents are preserved above the surface of this lava flow, which stands at a height of 80 m above the surrounding surface. A few kilometres to the north, we find other subsurface reflectors at a depth of about 30 m and a long pit chain formed by the collapse of a lava tube. These kinds of subsurface late Amazonian structures are of interest for astrobiology because they date from the last period when the planet still experienced intense volcanic activity over regions that were previously extensively covered by water.
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