Multi-domain pseudo-spectral time-domain method based optimization approach to the CoNSERT inverse scattering problem

Details Multi-domain pseudo-spectral time-domain method based optimization approach to the CoNSERT inverse scattering problem Multi-domain pseudo-spectral time-domain method based optimization approach to the CoNSERT inverse scattering problem

Dec 2011

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2011agufm.p13g..07p&link_type=abstract

American Geophysical Union, Fall Meeting 2011, abstract #P13G-07

Statistics

Computation

[0629] Electromagnetics / Inverse Scattering, [0689] Electromagnetics / Wave Propagation, [6210] Planetary Sciences: Solar System Objects / Comets

Scientific paper

The scope of CoNSERT, short for Comet Nucleus Sounding Experiment by Radio Transmission, is to perform a sounding of the comet 67P/C-G's core. This will be achieved by launching a lander, called Philae, onto the comet's surface. It will act as a receiver for the sounding signal emitted by Rosetta, and retransmit the received and processed signal to Rosetta. With these data, a three dimensional model of the comet's core (i.e., the material distribution with regard to the dielectric permittivity ɛ) is to be reconstructed. The problem of reconstructing the permittivity distribution from electromagnetic field data is a classical inverse scattering problem. We formulate this inverse problem as an optimization problem with the complex dielectric permittivity as our target parameter. The target functional j for this gradient-based optimization approach is based on the normalized envelope of the time-dependent measured field at a finite number of orbit positions. Due to the normalization we can adapt to amplitude distortions on the measured signal. Errors due to the small number of measurement positions are handled by multi-scale regularization and sparsity induction by L1-regularization. The application of Lagrange's method with Maxwell's equations as the constraints of the target functional results in the gradient necessary for the optimization. The accompanying direct- and adjoined problems necessary for the computation of the gradient inside the comet are solved with the multi-domain pseudo-spectral time-domain method (PSTD) while the propagation between comet and orbiter is solved by free-space-transforms. With this method and a baseband approach, i.e., simulation of the signal-envelope instead of the modulated signal, we were able to reconstruct a whole artificial-data-comet-model of approximately 6km in diameter. Simulation of the modulated signal is possible for the grazing-incidence case of electromagnetic wave propagation in boundary regions of the comet, i.e. an area of about 600 m around the lander position. With this tool at hand, we were able to investigate the influence of the permittivity model on the inversion procedure as well as the influence of the spacecraft orbit on the uniqueness of the solution.

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