• Sorsa, Liisa-Ida

Abstract

Full-wave radar tomography of complex small solar system bodies, such as asteroids, presents a challenging mathematical and computational inverse problem starting from the selection of the method of how to compute the forward problem of wave propagation through the target domain, and continuing to the selection of the appropriate inversion technique. The challenge is further augmented when such tomographic measurement is conducted in deep space with radar-carrying satellites with limited power supply and positional control. This leads to a set-up in which data can be measured in a sparse measurement configuration, and there are a number of possible sources of error starting from the ambiguity of the exact measurement position and orientation, and continuing to the measurement noise caused not only by the instrument but also the cosmic radiation environment.<br/><br/>The aim of this thesis is to advance the mathematical and computational methods for full wave radar tomography by applying the finite element time domain (FETD) method to compute wave propagation in realistic asteroid interior models built inside the shape of the asteroid Itokawa. Tomographic reconstructions of the simulated forward data are computed with the total variation inversion procedure, which is shown to detect the deep interior details such as voids, cracks, boulders, and low contrast details within the asteroid model. Higher-order Born approximation was formulated and implemented to the 2D FETD solver to investigate the effect of the higher-order scattering and measurement configuration on the quality of the reconstructions. To validate the numerical results with the Itokawa model, permittivity-controlled asteroid analogues were manufactured to compare the simulation results to laboratory measurements with microwave radar on the same target shape and structure. The computational tools to model wave propagation in the 2D and 3D target domains, and a toolbox to create a wireframe structure with controlled permittivity distribution for 3D-printing, were published as open source software packages.<br/><br/>The numerical results show that a low-frequency tomographic radar can detect deep interior details inside a realistic asteroid interior model with the shape and size of the asteroid Itokawa, in which the largest dimension is 535 meters. The bistatic and multistatic measurement configurations provide more robust reconstructions in comparison to the monostatic case. The laboratory experiment was designed to investigate a 5 MHz centre frequency and 2 MHz bandwidth radar for an Itokawa-sized target. Based on the results, the simulations model the measured time domain signal well, and the interior details can be detected in the locations predicted by wave traveltimes, giving evidence that numerical simulations can be used to model the real measurements in such a target. Furthermore, it was shown that even a single-point backprojection of the measured data can reveal interior details such as a void.<br/><br/>The current methodology and computational resources can model the full-wave radar tomographic problem for low frequency radars operating at 10 MHz for a target of size 260 meters, or 20 MHz for a target which size is approximately 130 meters. To increase the target size, the memory requirement for the computations may present a limit depending on the available high-performance computing resources. Increasing the measurement frequency to 50-60 MHz would require refining the finite element mesh to increase the accuracy of the forward modelling stage. This would also increase the system size and hence memory requirement, and requires specialised high-performance computing resources and further development of the presented solvers to fully utilise the now available and developing high-performance computing capacity.

Topics

• impedance spectroscopy
• experiment
• simulation
• tomography
• crack
• void