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.

A review of Mars radar data obtained through the 1973 opposition confirms that the surface of the planet has many diverse characteristics. Analysis of the quasi-specular echo component shows changes in apparent reflectivity of at least 5 to 1. If attributed entirely to variations in surface material, these correspond to dielectric constants between 1.6 and 4.0. Values of rms surface slope on 1- to 100-m scales range from as low as 0.5° in tablelands near Vlles Marineris to more than 3.0° (the upper limit for which these analysis techniques are appropriate) in certain other areas such as inside Coprates Chasma itself. There is weak correlation between the small-scale surface characteristics inferred from radar and those inferred from Mariner 9 images, geologic maps derived from those images, and other remote sensing data sets. Topography, a large-scale surface characteristic for which good correlation exists between radar and other data sets, was not considered in this study. A search for guidelines which would allow extrapolation of radar properties to new areas on the basis of those studied has been singularly unsuccessful. Data obtained during the 1973 opposition at Arecibo, Goldstone, and Haystack Observatories indicate that the scattering behavior of Mars varies little over the 70- to 3.8-cm wavelength range. Comparison of 1971 and 1973 Goldstone results shows no detectable variation with time.

Lunar surface slopes distributions from bistatic radar, photogrammetric and photoclinometric measurements by Explorer 35, Surveyor, Lunar Orbiter and Apollo spacecraft

On 9 April 1994 the Clementine spacecraft high-gain antenna was aimed toward the Moon's surface and the resulting 13-cm wavelength radio echoes were received on Earth. Using these data, we have found that the lunar surface generally follows a Lambertian bistatic scattering function cO = KD cos0i cos0s with KD---0.003 for the opposite (expected) sense of circular polarization and Ktr-0.001 for the same (unexpected) sense. But there are important deviations---of up to 50% in some parts of the echo spectrum---from this simple form. Based on an earlier analysis of these same data, Nozette et al. [ 1996] claimed detection of an enhancement in echoes with right circular polarization from regions near the South Pole in a near-backscatter geometry. Such behavior would be consistent with presence of perhaps large quantities of water ice near the Pole. We have been unable to reproduce that result. Although we find weak suggestions of enhanced echoes at the time of South Pole backscatter, similar features are present at earlier and later times, adjacent frequencies, and in left circular polarization. If enhanced backscatter is present, it is not unique to the South Pole; if not unique to the Pole, then ice is less likely as an explanation for the enhancement.