For a future potential radar sounder mission to small celestial bodies like comets and asteroids, it is important to understand the interaction between propagating waves and interior geophysical structures. In general, it is not easy to build a software model capable of handling relevant dimensions with high numerical accuracy. Researchers often rely on a scaled-down model that cannot fully represent physical phenomena.

The objectives of this work were to develop three-dimensional (3D) forward electro-magnetic (E&M) modeling and fully coherent back-projection imaging tools for future potential radar sounder missions to small primitive solar system bodies like comets and asteroids. The forward propagation modeling tools are for accurately describing the propagation of E&M waves both inside and outside of a small celestial body, while minimizing numerical computations and suppressing numerical errors below –60 dB, compared with the strength of incident waves. The back-projection imaging tools are for building 3D interior structures using simulated radar echoes (3D tomography) as well as evaluating its performance. The forward and back-projection tools would enable understanding of radar echograms (radargrams) from internal reflections of the incident waves, and derive geophysical parameters such as internal dielectric properties and losses at the resolution of a wavelength.

The tools achieved high computational efficiency using MATLAB’s parallelized matrix operations. The 3D tools consisted of a wrapper and core computational subroutines. The wrapper allowed users to construct a 3D comet in any shape and size as well as specify basic radar-related parameters such as wavelength and source (dipole antenna) location. The 3D comet model included real and imaginary permittivity values at a regularly spaced 3D grid.

The first step of the forward modeling was to compute the exact electric and magnetic dipole fields near the source, and then project them onto the top surface of the simulation domain via an analytic method. Until this time, there were no numerical calculations and errors; everything was analytic. Once the dipole fields were injected, corresponding 3D electric and magnetic fields were allowed to numerically propagate in time while satisfying Maxwell’s equations inside and outside the comet. Electric and magnetic fields were all 3D MATLAB matrices, allowing each field matrix to be updated simultaneously. At the boundaries of the simulation domain, Perfectly Matched Layers (PMLs) were added so that any E&M fields leaving the simulation domain were almost entirely absorbed. The amount of reflected power from the PMLs was weakened by about 100 dB. The PMLs were designed to be flexible enough so that their effectiveness could be controlled after taking into account the size of the simulation domain or computational time. This was the most critical part of the 3D forward modeling work that was not found in commercial tools.

Once the incident fields were scattered by the 3D comet body, the resulting waves propagated outward in all directions. To collect E&M fields at the sensor location where the incident fields were originally generated, a near-field to far-field transform (NFFT) was implemented. This used the initial field projection layer as a sensing layer. Any fields detected at the sensing layer were projected back to the source via NFFT. This avoided numerical errors from a long-distance propagation from the simulation domain to the source, as well as minimized memory resource and computational load. By employing both the analytic source field projection and the NFFT, numerical simulations were confined around the comet body, although the source could be located far away — 20-100 km.

This work was done by Darmindra Arumugam and Xiaoqing Wu of Caltech for NASA’s Jet Propulsion Laboratory. This software is available for license through the Jet Propulsion Laboratory, and you may request a license at: . NPO-49985