Radar scattering from the icy galilean satellites is marked by unusually high backscatter cross sections and polarization ratios at wavelengths lambda(0) = 3.5-70 cm. The persistence of exotic scattering behavior over this large a wavelength range suggests that the responsible mechanisms remain at least partially effective as the wavelength approaches or exceeds the size of individual scatterers. We examine two models previously analyzed in the geometrical optics limit-radar glory from buried craters (Eshleman, 1986, Science 234, 587-590) and refraction scattering from subsurface lenses (Hagfors et al., 1985, Nature 315, 637-640)-at wavelength scales using three-dimensional finite-difference time-domain (FDTD) numerical simulations. We include craters with rough walls and lenses with random inclusions of heterogeneous material. For hemispherical craters spanning up to 3lambda(0) in diameter, we observe none of the exotic backscatter behavior attributed to the geometrical optics models. Nonspherical refraction scatterers can produce circular polarization ratios mu(C) > 1 and linear polarization ratios mu(L) = 0.5-0.8 at diameters as small as similar tolambda(0), but the density of such inclusions must be high if refraction scattering alone is to account for the measured cross sections. (C) 2003 Elsevier Inc. All rights reserved.

Numerical finite-difference time-domain (FDTD) techniques allow computation of diffuse radiowave scattering from discrete, wavelength-scale surface and subsurface objects, such as rocks, having complex shape and material inhomogeneities. Details of the methodology for twoand three-dimensional simulations are discussed in Wong et al. [1996] and Baron [2001]. Here we focus on the backscatter properties of a variety of 3-D objects, including spheres, ellipsoids, and digitized models of actual rocks, as a function of burial depth and size distribution. Figure 1 shows backscatter as a function of incidence angle for one of the rocks in our collection, labeled “B” here, whose physical characteristics are discussed in more depth in [Baron, 2001]. The rock (dielectric constant 4) is positioned either perched on the surface (dielectric constant 2.56) or buried tangentially beneath the surface. Circularly polarized waves are transmitted; both the polarized (opposite circular, or OC) and depolarized (same circular, or SC) responses are calculated. The backscatter cross sections have been averaged over sizes ranging up to kaeq 5:3, where k is the free-space wave number and aeq is the radius of an equivalent-volume sphere.

Reanalysis of rock population data at the Mars Viking Lander sites has yielded updated values of rock fractional surface coverage (about 0.16 at both sites, including outcrops) and new estimates of rock burial depths and axial ratios. These data are combined with a finite difference time domain (FDTD) numerical scattering model to estimate diffuse backscatter due to rocks at both the Lander 1 (VL1) and Lander 2 (VL2) sites. We consider single scattering from both surface and subsurface objects of various shapes, ranging from an ideal sphere to an accurate digitized model of a terrestrial rock. The FDTD cross‐section calculations explicitly account for the size, shape, composition, orientation, and burial state of the scattering object, the incident wave angle and polarization, and the composition of the surface. We calculate depolarized specific cross sections at 12.6 cm wavelength due to lossless rock‐like scatterers of about 0.014 at VL1 and 0.023 at VL2, which are comparable to the measured ranges of 0.019–0.032 and 0.012–0.018, respectively. We also discuss the variation of the diffuse cross section as the local angle of incidence, θi, changes. Numerical calculations for a limited set of rock shapes indicate a marked difference between the angular backscattering behavior of wavelength‐scale surface and subsurface rocks: while subsurface rocks scatter approximately as a cosine power law, surface rocks display a complex variation, often with peak backscattering at high incidence angles (θi = 70°–75°).

Reanalysis of rock population data at the Mars Viking Lander sites has yielded updated values of rock fractional surface coverage (about 0.16 at both sites, including outcrops) and new estimates of rock burial depths and axial ratios. These data are combined wih a finite difference time domain (FDTD) numerical scattering model to estimate diffuse backscatter due to rocks at both the Lander 1 (VL1) and Lander 2 (VL2) sites. We consider single scattering from both surface and subsurface objects of various shapes, ranging from an ideal sphere to an accurate digitized model of a terrestrial rock. The FDTD cross-section calculations explicitly account for the size, shape, composition, orientation, and burial state of the scattering object, the incident wave angle and polarization, and the composition ofhe surface. We calculate depolarized specific cross sections at 12.6 cm wavelength due to lossless rock-like scatterers of abou 0.014 at VL1 and 0.023 at VL2, which are comparable to the measured ranges of 0.019-0.032 and 0.012-0.018, respectively. We also discuss the variation of the diffuse cross section as the local angle of incidence, Oi, changes. Numerical calculations for a limited set of rock shapes indicate a marked difference betweenhe angular backscattering behavior of wavelength-scale surface and subsurface rocks: while subsurface rocks scatter approximately as a cosine power law, surface rocks display a complex variation, often with peak backscattering at high incidence angles (Oi = 70ø-75ø).

A major difficulty in physical interpretation of radio wave scattering from geophysical surfaces is the lack of detailed information on the signatures of geologically plausible discrete objects, Although the aggregate response will never be dominated by any single object, differences in the population of discrete objects on or near the surface (their sizes and shapes, for example) can change the character of a radio echo markedly. When the average surface is modeled as a flat, homogeneous half-space, the field that ''drives'' the scattering process is a composite consisting of the incident plane wave and the reflected and transmitted plane waves, all of which are known quantities; the total field can then be defined as the sum of the driving field and the scattered field. When a discrete object is near the surface, the total field can be calculated using finite-difference time-domain (FDTD) techniques, and the scattered near field can be calculated accordingly, The Green's functions for electric and magnetic currents above and below the surface, obtained by Sommerfeld theory and employed in conjunction with Huygens' principle, transform the local scattered fields to the far field. The FI)TD implementation accommodates discrete lossy dielectric and magnetic scatterers in the vicinity of a dielectric surface; extension to a lossy halfspace is straightforward. Two-dimensional results for scattering from perfectly conducting circular cylinders above and below a dielectric surface agree with moment method solutions within a few percent. Results for scattering from a dielectric wedge exhibit expected forward diffraction and internal reflection phenomena.

Finite-difference time-domain (FD-TD) techniques allow practical numerical computation of radiowave scattering by a wide range of objects (e.g., rocks) on or in a planetary regolith. Numerical models are evaluated for two-dimensional (2-D) cases in which burial depthDand object sizeRof a single scatterer vary and for which the separation distanceLbetween two scatterers varies. A buried object typically has a significantly weaker scattering response than the same object resting on the surface, although the strongest response may occur when the scatterer is partially buried. Large objects scatter strongly and in complex ways, but the bounds on solutions appear to be well-defined; this should be useful in predicting aggregate behavior of ensembles of scatterers. The response of closely spaced objects differs significantly from the response of the objects calculated separately, but the coupling decreases rapidly with separation. Two-dimensional wavelength-scale objects (R≊ λ0) separated byL≥ 15Reffectively behave as independent scatterers. Computations in 2-D can be adapted for three- dimensions (3-D); preliminary results are consistent with measured radar backscatter cross sections for the Moon and Venus and with estimates of block population densities on the Moon. The FD-TD code generalizes to 3-D, permitting the set of case studies to be expanded for interpretation of data such as those from Magellan.