Orbiter-to-orbiter tomography: a potential approach for small solar system bodies

Abstract

The goal of this paper is to advance mathematical and computational methodology for orbiter-to-orbiter radio tomography of small planetary objects. In this study, an advanced full waveform forward model is coupled with a total variation based inversion technique. We use a satellite formation model in which a single unit receives a signal that is transmitted by one or more transponder satellites. Numerical results for a 2D domain are presented.Index Terms-Radio Tomography, Small Planetary Objects, Inverse Problems, Waveform Imaging. t 0 ∇u(τ, x) dτ yields the first order system arXiv:1608.06566v1 [astro-ph.IM]

Far-Field Inversion for the Deep Interior Scanning CubeSat

“…where g = ( g (1) , g (2) , g (3) ) with g (j) = t 0 ∇Ei(τ, x) dτ for j = 1, 2, 3 and f, v; Ω = Ω f v dV . The bilinear forms a and b correspond to the right-hand sides of the equations (34) and (35), respectively, and v ∈ H 1 (Ω), w = ( w (1) , w (2) 3 are test functions. Under regular enough initial conditions this weak form [3] has a unique solution E : [0, T ] → H 1 (Ω) [40].…”

“…In this study, the process of finding an estimate ε * r for the relative permittivity εr, the unknown of the inverse problem, consists of the following three stages presented in [3]: 1) Forward Simulation. For each transmission and/or measurement position, the signal can be propagated using the leap-frog iteration.…”

“…Running the wave simulation for a single source position took about 71 and 184 minutes in the case of the background and exact data, respectively. The matrix-vector products including the inverse of the mass matrix [3] were evaluated using the preconditioned conjugate gradient method with the lumped diagonal preconditioner, i.e., a matrix with row sums on its diagonal. The system matrices required a total of about 4 GB memory of which the mass matrix took 0.62 GB.…”

“…The aim of this study is to advance Computed Radar Tomography (CRT) [1], [2] for reconstructing the deep interior structure of a small solar system body (SSSB) [3]- [7]. The first such attempt, the Comet Nucleus Sounding Experiment by Radio-wave Transmission (CONSERT), was made as a part of the ESA's Rosetta mission to comet 67P/Churyumov-Gerasimenko.…”

Bistatic Full-wave Radar Tomography Detects Deep Interior Voids, Cracks, and Boulders in a Rubble-pile Asteroid Model

“…Such a model is constructed similar to the detailed, structural models with the difference that the interior permittivity is constant, here ε (bg) r = 4. We utilize a linearized forward model given by Pursiainen & Kaasalainen (2016):…”