The backscatter coefficient of a surface changes with the wavelength,
polarization, and incidence angle of the radar energy. The magnitude
of the echo and the variation in the return with changes in the
above parameters can be linked to surface roughness, to the bulk
dielectric constant of the material, and occasionally to subsurface
scattering when the dielectric losses in the material are low.
Surface roughness can in turn be treated as a combination of scatterers
at a wide range of spatial scales, whose effect on the backscatter
varies. Therefore, numerous possible explanations exist for variations
in backscatter; however, we can make some general statements based
on terrestrial radar studies.
ROCKY SURFACES (THOSE HAVING NO SOIL COVER): At incidence angles >30o, the changes in HH (horizontal transmit, horizontal receive) backscatter coefficient are directly correlated with roughness at the scale of the wavelength and the bulk dielectric constant of the surface. The effect of the two changes is illustrated in figure 2 with results from Hawaii. This plot shows that changes in wavelength-scale roughness will likely be the dominant cause of radar brightness variations in areas of Venus where the dielectric constant is <10 (that is, everywhere below about 6,053 km in planetary radius). Values of 8-9 are the maximum found for terrestrial dense basalt samples.
At incidence angles near or below 30o, the HH backscatter
cross section may not represent the wavelength-scale roughness
of the surface, because large "quasi-specular" facets
begin to play a role in the measured echo. For terrestrial lava
flows, this can lead to a complete loss of roughness discrimination
or contrast reversals between smooth and rough terrain at angles
of 20-30o. Dielectric effects are similar to those
seen at more oblique angles, in that we expect a linear variation
in backscatter with changes in the Fresnel reflectivity. This
loss in discrimination, for lava flows on Kilauea,
is shown on figure 3. In using the Magellan images at these incidence
angles, one can expect that many lava flow fields will appear
rather featureless relative to those viewed at more oblique angles.
SURFACES HAVING A POROUS COVERING: At all incidence angles, the backscatter cross section will drop as a result of attenuation by loose mantling material. The average dielectric constant will also fall if the soil is simply a less dense version of the base rock (see the emissivity sections below). If the soil is deep (>1 m), has a low loss factor, and contains wavelength-size rocks, the observed backscatter could be much higher than that of a solid smooth surface having the same population of rocks per unit area. Such deep-soil scenarios do not seem likely on Venus (although they are common on the Moon), but shallow soils almost certainly occur in some areas. An estimate of the amount of loss within soils can be obtained using equations found in Ulaby et al. [1987, p. 67, 847]. For two-way passage through a layer, the power (P) lost due to attenuation will be
where h is the layer depth,
is the radar wavelength in vacuum (12.6 cm for Magellan),
is the real part of the soil dielectric constant,
is the incidence angle in the soil (after refraction), and
is the microwave "loss tangent" of the soil. Loss tangent
is the ratio of the imaginary and real parts of the complex dielectric
constant, and typical values for dry lunar soil at radar wavelengths
are 0.002 to 0.02. This equation can provide an estimate of the
depth of a mantling layer if there is a good estimate of the backscatter
coefficient of an unmantled surface (for example, a lava flow
which is partially covered by fine crater ejecta [see Campbell et al., 1992]).
PRESENTATION OF DATA: What does this mean for mapping conventions? There are clearly problems in trying to make comparisons between rock units seen at widely varying geometries, and mappers working with data at smaller incidence angles can expect to see a diminished dynamic range between rough and smooth surfaces. Rather than try to force a set of interpretive conventions on everyone, a radar correlation chart may be produced, which presents the mean backscatter properties of various units in comparison to the Venus average and selected terrestrial analog terrains. Sources for these comparative values can be found in Plaut , Arvidson et al. , Campbell and Campbell , and Gaddis . A sample plot of this type is shown in figure 4, where scales in angle and cross section are recommended as a template for use on Venus maps. When multiple-angle data are available, units can have a portion of their backscatter function plotted on this diagram. The correlation chart serves the dual purpose of helping the mapper make informed judgements as to what are real changes in surface roughness within their areas (versus the subjective effects of image contrast stretching) and provides readers with a means to extrapolate results from one map to another at their own peril.
The radar backscatter coefficients for the Hawaiian lava flows and the Muhleman scattering law used in figure 4 are available as ascii data files over the Internet (app. 3), and it is suggested that all correlation charts use at least these comparison curves. If the radar behavior of other terrestrial terrains is needed to illustrate unit properties (for example, echoes from silicic domes or dry soil layers), mappers should feel free to add them to the diagram. The 12.6-cm (S-band) lava flow echoes shown were interpolated from 6-cm (C-band) and 24-cm (L-band) AIRSAR data using the relationship
The unit description should contain only the data product from which the backscatter information was obtained (for example, C1-30n045) and the latitude and longitude boundaries of the example site (pixel values within an image should not be used, since the reader may wish to examine the site using a different product). Actual values of backscatter coefficient and other parameters (emissivity, rms slope, Fresnel reflectivity, and elevation) should be placed in tables on the map sheet. For any given unit, the mapper should provide the mean, standard deviation, pixel scale, and the number of samples used to find the backscatter coefficient of the example site. Situations may arise where the standard deviation of the backscatter data is larger than the mean value, which may indicate a poorly chosen or very small test site that has widely varying brightness or a skewed probability distribution.
A single example area may not represent the full range of behavior within a given terrain unit, such as a volcano with interfingered bright and dark lava fields. If the mapper feels that the range of backscatter is significant, two averages could be quoted to illustrate the variation in properties across the unit. Map reviewers will need to check the selection and description of these example sites to ensure consistency. The interpretation section of the unit label should include a discussion of the significance of these results to the nature of the unit, particularly where surface properties appear to diverge significantly from the average behavior. An example data table corresponding to the Venus sample sites plotted in figure 4 is shown in table 2; all of these data were produced using the two programs (mgn_data and anc_data) discussed in the Appendixes.