Numerical computation of radar echoes measured by MARSIS during phobos flybys

Computing low‐frequency radar surface echoes for planetary radar using Huygens‐Fresnel's principle

“…While planetary radar echoes are commonly used like seismograms to visually recover structural features, we propose to work with signal phases and amplitudes using equations derived from boundary integral expressions of the planetary surface scattered electromagnetic fields. Similar works have been carried out previously using Huygens's principle, in the acoustic approximation [e.g., Kobayashi et al , ], for specific setups [e.g., Fa et al , ], using numerical integration [e.g., Plettemeier et al , ], coupling numerical surface integrations and ray tracing [e.g., Jin , ; Zhang et al , ], or with approximate geometries [e.g., Nouvel et al , ]. The latter is currently implemented as a routine to quantitatively assess Mars's ionosphere and Mars's surface permittivity [e.g., Mouginot et al , ] from the increasing amount of data acquired with MARSIS.…”

“…Any piecewise complex function on S can be approached through a set of constant over elementary surface elements. In general, this formulation is used to numerically compute Huygens‐Fresnel's integral [e.g., Plettemeier et al , ; Kobayashi et al , ].…”

“…Fundamentally, their differences arise in the geometry of the facet element used (triangular or square mostly) and in the nature of the quantities associated to each facet used to describe the fields on the surface. In the zeroth‐order series expansion case [e.g., Jin , ; Plettemeier et al , ; Zhang et al , ], quantities are sets of constant vector (i.e., independent of the position on a facet element) associated to each facet element, which is fundamentally a numerical integration. Whereas in higher‐order series expansion cases, quantities are vector fields associated to each facet (i.e., vectors' amplitude and phase can vary with the position where they are evaluated on a facet element).…”

“…This method is very easy to implement and most flexible but can be time consuming due to the numerous facet elements needed to describe the surface [Jin, 2012;Kobayashi et al, 2002]. Typically, this requires that each element does not exceed ∕10 in length, which is usually computationally exhaustive [e.g., Plettemeier et al, 2009].…”

Considering Nonsurface Scattering in Physical Optics Approximations

“…This approach has been applied successfully in many applications, e.g. astrophysical simulations [34]- [36] or in the design of military airplanes and ships [37]- [39]. One of the disadvantages of the PO compared to the FDTD or FEM is that it does not address any volume effects which can have a significant impact on the overall scattering.…”