Recent advances in planetary surface characterization using modeling of radar scattering

Introduction

Planetary radar observations provide a powerful tool for the post-discovery characterization of the physical and dynamical properties of asteroids, comets, the Moon, and terrestrial planets. Radar observations of near-Earth objects (NEOs) [e.g., 1] have increased our understanding of the diversity of NEO sizes, shapes, binarity, and composition. These characteristics are crucial also to planetary defense as they play a role in the selection of the optimal mitigation technique. Planetary radar systems can be used for range-Doppler imaging by mapping the reflected power as a function of the Doppler frequency and the range (based on the signal’s round-trip time), which allows imaging resolutions finer than 10 meters at best, and thus direct observations of morphologic features and possible moons. The data can be obtained at two orthogonal polarization states.

Due to the penetration depth of several wavelengths and the wide parameter space in scattering inversion problems, understanding the physical characteristics of NEOs based on their radar scattering profiles requires extensive numerical modeling. Traditionally, circular polarization ratio has been used as a first-order gauge to the surface roughness, but more recent advances in numerical modeling demonstrate that analyzing the reflectivity information in parallel with the polarization information is crucial (e.g., [2-3]). This allows distinguishing different scattering processes. For example, the disk function of (101955) Bennu shows little to no specular component, which indicates that wavelength-scale particles dominate the surface; a fact not available from the polarization ratio information alone. For contrast, the Moon has a strong quasi-specular spike, which is consistent with the fact that fine-grained regolith dominates the lunar surface.

Analytically derived scattering models typically assume that the surface is composed primarily of fine-grained regolith or a solid surface that forms a gently undulating interface with few or no wavelength-scale scatterers. This assumption has been reasonable for the surfaces of the terrestrial planets and moons but is not sufficient for asteroids that have often a “rubble-pile structure” and, as such, the asteroid surfaces have often a significantly greater coverage of centimeter-to-decimeter scale regolith than planets or moons. Empirical laws lack understanding of the meaning of the empirical fit parameters. In this presentation, I discuss the recent advances in scattering modeling methods and future requirements for improved interpretation of radar observations.

Aims

Here, we present recent advances in the modeling efforts of radar scattering for the characterization of planetary bodies. The goal is to improve planetary surface characterization by better interpretation of radar observations. As research has shown, examples of physical properties that can be derived include the near-surface density, regolith size-frequency distributions of centimeter-to-decimeter scale particles, and subsurface permittivity contrast that provides clues to the internal structure and composition.

Methods

The radar scattering processes in planetary bodies includes two components: Scattering by the undulating surface and scattering by the wavelength-scale particles. As the main part of this work, we conducted numerical computations of scattering properties of rough polyhedral particles 1) in touch with a surface to simulate surface particles [6], and 2) embedded in a host medium. In the first case, we investigate the roles of size parameter (x=2πr/λ, where r is the effective particle radius and λ is the wavelength) and the refractive properties. We selected two different refractive indices for comparative analysis: 2.17 + 0.004i and 2.79 + 0.0155i (particles) on a substrate with 1.55 + 0.004i, and two polyhedral morphologies with statistically distinct levels of roundness. In the second case, the refractive contrast relative to the host medium is compared for 1.4 and 1.8. Also, the effect of the particle packing density is investigated for the radiative transfer approximation with and without coherent backscattering included. The size-frequency distribution of regolith typically follows a power-law distribution with a power index of 2.5–3.5; a comparable size distribution range is used also in our numerical simulations. The range of sizes extends from sub-wavelength scale to several wavelengths.

For scattering by a fine-grained regolith substrate, we built synthetic rough surfaces and simulated radar scattering as a function of incidence angle using a geometric-optics approximation [4]. We used self-affine fractal surfaces, which are described using a horizontal-scale-dependent height standard deviation and Hurst exponent, because they have been shown to be more realistic for rocky surfaces than stationary surfaces. Research has shown that the Gaussian scattering law provides a good approximation for scattering by self-affine fractal surfaces [4,5].

Summary of the results

This work discusses and illustrates the different scattering processes taking place in planetary surfaces and what role they play in the observable parameters. The main part of the work discusses the role of particles on surfaces and below the surface. We find that for surface particles with a refractive index above 2.17, the refractive index plays an insignificant role in comparison to the particle abundance and shape, and that the surface-particle interaction is weak [6]. For particles embedded in the substrate, the contrast between the particles and host medium plays a noticeable role in the observed polarization and reflectivity. Coherent backscattering produces a significant enhancement, as expected. We discuss how to identify coherent backscattering – a signature of low-absorption substances such as water ice – when observations at a range of phase angles are not available.  

References

[1] Virkki, A. K. et al. (2022), Planetary Science Journal, 3, 222.

[2] Virkki, A. K. & Bhiravarasu, S. S. (2019), Journal of Geophysical Research: Planets, 124, 11.

[3] Hickson, D. C., et al. (2021), Planetary Science Journal 2, 30.

[4] Virkki, A. K. (2024), Remote Sensing 16, 890.

[5] Shepard M. K. et al. (1995), Journal of Geophysical Research 100, E6, 709.

[6] Virkki, A. K. & Yurkin, M. A. (2025), In revision. Pre-print available at https://arxiv.org/abs/arXiv:2501.10019.