The Venus Geologic Mappers' Handbook

Overview of Data Sources

Mission Summary

Magellan's global data on Venus have been acquired as part of a series of spacecraft investigations of the inner planets (Mercury, Venus, Earth, and Mars). The data are more complete than similar data for Earth (whose largely unmapped ocean floors make up 70 percent of its surface). The Magellan images, altimetry, and data on the physical-electrical properties of the surface of Venus were acquired at a wavelength of 12.6 cm and are very different from images and data acquired at optical wavelengths that have been employed for planetary geologic mapping and studies. The properties of surfaces that influence reflection of radio waves are not the same as those that influence the reflection at optical wavelengths. This factor must be considered when interpreting synthetic aperture radar (SAR) images and surface properties measured at radio wavelengths and when preparing geologic maps.

In this section we briefly discuss (1) the Magellan mission, (2) the radar instruments, (3) data acquisition and processing, and (4) data products that are or will become available. For detailed information, please see the Recommended Reading.

The Magellan radar mapping mission to Venus has provided SAR images of 98.3% of the planet's surface, as well as data on topography, small-scale surface roughness, radar reflectivity, and thermal emissivity--all of which cover similar percentages of the surface (Saunders and others, 1992). The images and the ancillary data are the resource materials for the VMAP program.

The Magellan spacecraft went into orbit around Venus with an orbit period of 3 hr. 25 min. and inclination of 85. This corresponds to about 7.5 orbits per day and a total of 1,790 orbits during one 243-day rotation period (a 'cycle' in Magellan parlance). Periapsis of the orbit was at lat 9.9 N. and the motion of the spacecraft was from north to south during data acquisition. The altitude of the spacecraft was 294 km at periapsis and 2,100 km over the north pole. The 85o inclination angle for the orbit was chosen to allow imaging of the polar regions.

After orbit insertion, the first four weeks of the mission were devoted to engineering tests, but some test images were acquired as well. Systematic data collection began on 15 September 1990. Coverage was completed in cycle 1 on 15 May 1991, and in cycle 2 on 14 January 1992. Cycle 3, the last cycle in which systematic SAR data were obtained, ended on 14 September 1992. Cycle 4 mission operations focused on the collection of gravity data. Continuation of the Magellan mission beyond cycle 4 involved aerobraking to a low-altitude (250 km) circular orbit, acquiring high-resolution gravity data, and special experimenting.

Images of 83.7% of the planet's surface were obtained during cycle 1 with the SAR antenna looking to the east of the orbit plane (left-looking) (see Michaels, 1992, fig. 2); 54.5% was covered during cycle 2 with right-looking images and some left-looking images (Michaels, 1992, fig. 3); and 22.8% was covered during cycle 3 with left-looking images (chiefly for stereometric use with cycle 1 images). Coverage of Venus with SAR images is summarized in Ford and others (1993; figs. 2.2, 2.4, 2.5, and 2.6).

The Magellan Radar Sensor

Many geologists are familiar with the techniques of photogeologic mapping and have a working knowledge of standard aerial photography, satellite images, and stereoscopy. Magellan SAR images are basically similar to photographs and images acquired in the visible wavelengths in that they faithfully portray landforms and topography. However, there are important differences between the SAR images and images acquired at visible wavelengths because of the source of illumination, the manner in which the radar echoes are translated into map distances, and the large wavelength of the radar. The surface is illuminated by the Sun for aerial photography and satellite imagery, whereas the SAR provides its own illumination. Geometric distortions or relief displacements in aerial photographs and satellite images are radial to the nadir, whereas those in SAR images are in the direction of the radar antenna. The large wavelength (12.6 cm) of the Magellan SAR results in scattering properties of the surface that are much different than those at visual wavelengths; these scattering properties vary with several parameters such as wavelength, polarization, and incidence angle of the transmitted radar waves and the fine- to coarse-scale roughness and physical-electrical properties of the surface. Thus, geologic mappers will need to be familiar with the characteristics of the Magellan radar system, how the data were acquired and processed, and responses of natural surfaces to incident radar energy so that they can intelligently analyze the data.

The Magellan spacecraft carries a single scientific instrument-a multi-mode radar sensor that operates in burst cycles. Each burst cycle consists of sequential synthetic aperture radar (SAR), altimetry, and radiometry measurements (Saunders and others, 1990, fig. 2; Saunders and Pettengill, 1991; Ford and Pettengill, 1992; Michaels, 1992, table 1 and fig. 1). The SAR and altimeter are active sensors that transmit radar waves and measure the radar echoes from the surface (backscatter or reflectivity) in oblique and vertical (near-nadir) viewing geometries, respectively (Pettengill and others, 1991). The radiometer passively measures the thermal emission from the surface at 12.6-cm wavelength by sampling the SAR receiver between radar echoes. The SAR and the radiometer operate through a narrow bandwidth, high-gain antenna (HGA), while the altimeter uses a separate, smaller horn antenna (ALTA) positioned to the side of the HGA. Magellan's SAR operates at angles of incidence between about 17o and 45.7o from the local surface normal. Incidence angles are smallest toward the poles and largest at periapsis (Pettengill and others, 1991; Saunders and others, 1992; Tyler and others, 1992). During each orbit the SAR imaged a strip about 20 km wide and 17,000 km long, alternately from the north pole to 57o S (intermediate swaths) and from 70o N to 70o S (delayed swaths). The three Magellan radar modes are briefly discussed below.

Synthetic aperture radar (SAR). Synthetic aperture radar (fig. 2) is a method of acquiring images of a surface (Tyler and others, 1992). Illumination of the surface is provided by transmitting radar energy to the surface through the SAR antenna and receiving the echoes or backscattered energies with the same antenna. Echoes are associated with specific areas on the surface (resolution cells) because of the known topography, spacecraft orbital parameters, large incidence angles, and motion of the spacecraft. This situation allows separation of echoes by time delay or range and by Doppler shift or azimuth (fig. 2). The range direction is called cross-track and the azimuth direction is called along-track.

Figure 2. Method of data acquisition by the Magellan synthetic aperture radar (SAR) system; see text for discussion. (Reprinted from Engineering & Science, Spring 1991, v. LIV, no. 3, p. 16)

Several parameters control Magellan SAR image quality. The most important are spatial resolution, the number of "looks," amplitude resolution, signal-to-noise ratio, and incidence angle. The SAR was designed to produce a 120-m along-track or azimuth resolution. Cross-track or range resolution is governed by normal techniques of pulse encoding common to most radars and is a function of radar bandwidth and incidence angle. Range resolution varies from about 120 m near periapsis to about 280 m near the poles (Michaels, 1992, figs. 16, 17). These two resolution dimensions constitute a resolution cell. The backscattered echoes were resampled at a pixel spacing of 75 m for the construction of images. Each measurement of the power backscattered from a resolution cell is a single estimate of a random variable whose mean is the backscatter radar cross section. For Magellan, the number of looks (N) ranged from 5 near the equator to 15 near the poles (Saunders and others, 1992, table 3). If these estimates or looks are averaged to obtain a mean, then the standard deviation of this measurement of the mean is equal to the mean divided by N1/2. The angle between the incident radar waves and the surface normal was varied to maintain an acceptable ratio of signal-to-noise as the altitude of the spacecraft above the surface varied. Decreasing the angle of incidence increases the returned power because of Venus' scattering law at 12.6-cm wavelength, and thus the decreased angle compensates for the increased signal loss as the distance to the surface increases (Pettengill and others, 1991).

Image pixel values (DN) are normalized backscatter cross sections and equal to the ratio of the measured mean backscatter cross section to the value predicted by the Magellan project scattering law (Saunders and others, 1992). Predicted values closely match empirically derived average backscatter behavior of the surface of Venus as a function of incidence angle (Muhleman, 1964). The pixel (DN) values range between 1 and 251, and each increment of 1 DN corresponds to an increment of 0.2 decibels (dB). Relative accuracy of the radar cross section is less than 1 dB in the cross-track direction and 2 decibels (dB) in the along-track direction. Performance checks during the mission verified that the radar sensor was operating according to sensitivity specifications.

The backscatter coefficient (also called backscatter cross section, sigma-zero, or ) is a measure of the power of an echo from the surface. Because backscatter coefficients are of interest to mappers (as discussed later), a procedure for calculating them is given here. Normalized backscatter cross sections ( ) are ratios of backscatter coefficients to the expected backscatter cross section ( )) for a horizontal, level surface at the incidence angle ( ) of the Magellan SAR image:

Normaized backscatter cross sections ( ) are related to DN values by:


where . The normalizing equation used by the Magellan project for the expected backscatter cross section is given by:


Sigma-zero ( ) is the product of and (i.e., ) and gives the value of in decibels.

The key parameters of Magellan's radar imaging system, as well as those for previously acquired radar data, are given in Table 1 of Michaels (1992).

Altimeter. The altimeter on Magellan measures the round-trip time of the transmitted signal and its echo (and therefore, the distance) between the spacecraft and the surface (Pettengill and others, 1991). Because of the orbital altitude and the need to improve the signal strength, the Magellan radar altimeter was designed to transmit 17 pulses and then to "listen" for their echoes. The pulses were transmitted and their echoes received through the altimeter horn antenna, which was pointed down toward the nadir. The strongest echoes usually come from smooth, level surfaces at the nadir, but in rough regions the echoes can be contaminated with echoes from nearby areas. The altimeter "footprint" is large (8 x 11 km at periapsis to 20 x 29 km near the poles), and several techniques are used to determine the spacecraft-to-surface distance. The altimetry data are combined with information on the spacecraft position relative to the planet's center of mass to produce a topographic map, which shows elevations in terms of planetary radii (Ford and Pettengill, 1992).

Shapes of the time-dispersed and (or) frequency-dispersed echoes and their amplitudes for each transmitted pulse from the altimeter horn antenna are dependent on the surface roughness at both wavelength and larger scales and on the surface reflectivities of the areas within the altimeter footprint. The shapes of the echoes (that is, the amplitudes as a function of time or frequency) are measures of the meter-scale surface roughness within the antenna footprint and can be fitted to several theoretical scattering functions (the scattering laws); delays or frequencies correspond to incidence angles from zero to about 10 or 30 (Tyler and others, 1992). The integrated power in the echoes provides an estimate of the backscatter cross sections at normal incidence.

Radiometer. The Magellan SAR antenna is used to estimate the brightness temperature of the surface in a passive mode. The procedures for making these estimates are beyond the scope of this handbook, but they are discussed by Pettengill and others (1992), who also list footprint dimensions. The estimated brightness temperatures at 12.6-cm wavelength are then compared with the black-body or physical temperatures of the surface. Physical temperatures of the surface are known from previous experiments (Pettengill and others, 1992).

Analysis of Magellan Radar Data

SAR images. SAR images are similar to aerial photographs and images acquired at visual wavelengths, because all three portray the morphology and moderate- to coarse-scale topography of the surface and its landforms. Morphology and topography are evident in SAR images because of the modulation of echo strengths by slopes. Echo strengths tend to increase with decreasing incidence angle. Thus, echoes from slopes facing the radar antenna are stronger and appear brighter in the images than those facing away from the radar antenna, but the magnitudes of the echo modulations also vary with surface properties. Some landforms with little or no relief, such as lava flows, can be recognized by patterns of backscatter that differ from those of the adjacent surfaces.

Magellan SAR echoes are thought to result primarily from two scattering mechanisms: quasi-specular and diffuse. Quasi-specular echoes are produced by mirrorlike reflections from facets oriented perpendicular to the SAR antenna (Hagfors, 1964; Tyler and others, 1991) that are much larger than the wavelength of the radar (12.6 cm). Quasi-specular scattering dominates echoes at small incidence angles, but echo strengths decrease rapidly with increasing incidence angle and become weak to nonexistent relative to the diffuse echo at incidence angles near 10 to 30 or so (depending on the root-mean-square slope). Quasi-specular echoes are rare in Magellan SAR images because of the large incidence angles. Diffuse scattering is produced by wavelength-size roughness elements at and near the surface, which scatter the incident radar energy in all directions so that diffuse echoes are received at all incidence angles. Diffuse scattering dominates echoes at large incidence angles that are typically greater than ~30, and the echoes also tend to become weaker with increasing incidence angle. However, this tendency is a function of the attributes of the wavelength-size scatterers on the surface (such as concentration, size-probability distribution, and dielectric properties). Diffuse echoes dominate the Magellan SAR images because of the large incidence angles.

Other applications and aspects of SAR data are discussed in the following numbered sections. This discussion highlights the derivation of several parameters and measurements and their relevance to geologic mapping, as well as important topographic effects, so that the mapper can make fullest use of the data.

1. Backscatter coefficient. The backscatter coefficient, as noted previously, is a measure of the power of an echo from the surface. The backscatter coefficient is a function of incidence angle, , of the transmitted radar energy with the surface and the physical-electrical properties of the surface materials. Backscatter coefficients of planar level surfaces tend to be larger at small incidence angles than at larger incidence angles; similarly, surfaces tilted toward the radar tend to have large backscatter coefficients than surfaces tilted away from the radar. Concentrations of wavelength-size roughness elements at and near the surface also affect the backscatter coefficient. Roughness elements include rocks, surfaces of aa lava flows, near-surface voids, and other wavelength-size discontinuities. Large concentrations of roughness elements produce larger coefficients than smaller concentrations. Magellan SAR images contain quantitative information on backscatter coefficients because the DN values, as noted previously, are normalized by values of backscatter (Saunders and others, 1992). Of importance to the mapper is the information that can be gained about the properties of geologic map units. Some terrestrial data illustrating this application are given in figure 3; the literature should be consulted for further possibilities.

Figure 3. Backscatter coefficient (also known as sigma-zero or ) as a function of incidence angle for the average Venus surface and four terrestrial surfaces at 12.6-cm wavelength (after Plaut, 1991). Note that the aa flow, a strong diffuse scatterer, has large coefficients that are nearly independent of incidence angle, and the playa, a weak diffuse scatterer, has small coefficients that are a strong function of incidence angle.

2. Identification resolution. The identification resolution of a SAR image is larger than the resolution stated in terms of pixel or cell size (120 m x 120 to 280 m) and is a function of landform shape, size, and backscatter properties and SAR incidence angles. Analyses of lunar radar images suggest that an observer begins to identify crater landforms when they are about four times the cell size of the radar (Moore and Thompson, 1988). Experience with spacecraft images at visual wavelengths yields similar results (Dial and Schaber, 1981). For Magellan SAR images, geologic mappers will learn by experience the sizes of landforms that they can identify.

The mapper's ability to identify linear features also depends on their orientations. Linear landforms that are transverse to the illumination or look direction are often prominent, but those that are parallel to the illumination or look direction may not be evident (see Wise, 1969; Yamaguchi, 1985). Other asymmetrical landforms, such as sand dunes, may be more evident in one look direction than they are in the opposite look direction because of their shapes. Similar phenomena may occur at scales that are finer than the resolution of the images (Plaut and others, 1992).

3. Geometric distortion. Geologic mappers should be aware that topography appears distorted in SAR images because of the translation of echo-time delay into horizontal distance. The effect is most noticeable for small features with large relief. Slopes that face the SAR antenna are foreshortened (or compressed), and those that face away are elongated (or expanded). Thus, peaks, hill tops, and crests of ridges are displaced toward the radar antenna in the look direction relative to their true positions. Distortion increases with decreasing incidence angle (see Ford and others, 1989, fig. 29). When the angles of radar-facing slopes exceed the incidence angle, echoes from the tops of slopes are received before those from the base of the slopes; thus the relative positions of the tops and bases are transposed in the image (see Ford and Pettengill, 1992, figs. 4 and 5). The resulting transposition, called layover, is an extreme case of geometric distortion or relief displacement.

Although a minor nuisance to geologic mappers, geometric distortions in single images (monoscopic) can be used advantageously to estimate the relief and slopes of landforms that are symmetrical in the cross-track direction (Michaels, 1992, fig. 15). Foreshortening and elongation due to relief of landforms in different images of the same scene acquired with different incidence angles also provide a means of estimating with parallax measurements the relief of the landforms.

4. Radar shadows. Radar shadows are produced when no echoes are received because slopes are not illuminated by the SAR antenna. This effect is produced when slopes facing away from the antenna are greater than ninety degrees minus the incidence angle. Many slopes that face away from the radar have weak backscatter echoes and appear dark in the images, but true radar shadows are rare in Magellan images.

5. Stereoscopy. The principal value of stereoscopic viewing of image pairs of Venus is the enhanced ability to interpret landforms, structures, and geologic relations between rock units. Topographic relief can be perceived by simultaneous viewing of image pairs of the same scene acquired with different incidence angles because of the differences in geometric distortions or parallax. Such relief is best perceived when the image pairs have the same look direction but different incidence angles (see also Leberl and others, 1992). In some cases, relief can be perceived when the look directions are opposite.

Nearly all cycle 3 images are left-looking with smaller incidence angles than those of cycle 1 and can be paired with images of the same scenes for stereoscopic viewing. For most of these image pairs with north up, the image with the smaller incidence angle (cycle 3) should be viewed with the right eye and the image with the larger incidence angle (cycle 1) should be viewed with the left eye in order to attain the correct sense of relief. A reversed viewing arrangement is necessary for images of Maxwell Montes, where cycle 3 images have larger incidence angles than those of cycle 1. Mountains, hills, and domes appear to lean toward the antenna in the look direction. In attempts to view stereoscopically opposite-side images with north up, the left-looking image should be viewed with the right eye and the right-looking image with the left eye.

6. Parallax relief. Relief of landforms can be estimated because of the parallax engendered by different geometric distortions of landforms in image pairs of the same scene acquired with different incidence angles or look directions. Such estimates are particularly important for landforms and local relief at scale lengths that are too small for altimetry and for terrain that is complicated and difficult to decipher with altimetry.

Geometric relations and equations for making such estimates are illustrated for same-side or left-looking image pairs in figure 4 and opposite-side or right- and left-looking image pairs in figure 5. Of particular importance is the identification of "conjugate-image" points (the same points on the surface in each image of the pair). This identification is more readily achieved with same-side image pairs than with opposite-side image pairs. Measurements and calculations on digital displays in terms of pixels with subsequent translations to meters are recommended, but such measurements can be made with stereoscopes, parallax bars, and suitably oriented hardcopy images or their equivalents. It is also important to demonstrate that the look directions of the two images are roughly parallel, say within 10 of each other, because relief displacements are cross-track in the direction of the antenna.

Figure 4. Vertical profile of surface in the cross-track plane illustrating geometry of relief displacement and parallax for left-looking image pairs. A, a point on the surface at scale of image; As, point A in image with smaller incidence angle (usually cycle 3); Al , point A in image with larger incidence angle (usually cycle 1); B, a second point on the surface at scale of the image; Bs, point B in image with smaller incidence angle (usually cycle 3); Bl, point B in image with larger incidence angle (usually cycle 1); , smaller incidence angle; , larger incidence angle; P, parallax; h, relief from A to B.

Figure 5. Vertical profile of surface in the cross-track plane illustrating geometry of relief displacement and parallax for left- and right-looking image pairs. A, a point on the surface; Ar, point A in image with right-looking incidence angle (cycle 2); Al, point A in image with left-looking incidence angle (usually cycle 1 or 3); B, a second point on the surface; Br, point B in right-looking image (cycle 2); Bl, point B in left-looking (usually cycle 1 or cycle 3); , incidence angle of right-looking image; , incidence angle of left-looking image; P, parallax; h, relief from A to B.

Parallax measurements have been used to estimate the relief of lava flows (Moore and others, 1992), of crater rims above their floors (Schaber and others, 1992; Moore and others, 1993), and of volcanic edifices (Moore and others, 1993; Plaut, 1993). An excellent discussion of the method is given in Ford and others (1993).

Some caution must be exercised in applying parallax measurements, because there may be significant image displacements related to navigational boundaries (differences in orbital parameters between uploads or each group of eight swaths). These displacements can be recognized by rotating the image pairs 90 and viewing them stereoscopically. Because of this problem, we recommend that parallax measurements be confined to small landforms or images that have been corrected for spurious image displacements. There are plans for correcting the Magellan images, but usable products may not be available in time for use in The Venus Geologic Mapping Program.

Altimetry. The nominal mission provided 3 x 106 altimetry measurements from between lat 85 with a vertical resolution of about 80 m. Cycle 2 measurements were halfway between those of cycle 1 so that more complete coverage could be attained. A global topographic dataset and a map with a 5-km pixel size have been produced from these measurements (Ford and Pettengill, 1992, plate 1). Overall, the Magellan altimetry data refined the general hypsometry of Venus (first determined by Pioneer Venus). Venus has a unimodal distribution of elevations; about 80% of the surface is within 1 km of the mean planetary radius (6051.84 km). Steep coarse-scale slopes (> 30o) are measured along the mountain fronts of Maxwell and Danu Montes and in Diana and Dali Chasmata in the equatorial highlands (Ford and Pettengill, 1992).

Altimetry data suitable for most geologic mapping are furnished to the mapper of each quadrangle in two forms: (1) in the same projection (Mercator, Lambert Conformal, or Polar Stereographic) as the mapper's quadrangle at 1:5,000,000 scale, and (2) a reduced color-transparency version of (1). A reduced-scale black and white transparency of the SAR image with the same scale and projection as the altimetry color transparency is also furnished to the mapper of each quadrangle to facilitate correlations and comparisons. The data are also available on CD-ROMs, which include global data sets in both sinusoidal and Mercator projections (GTDR.SINU and GTDR.MERC files) and ancillary data for those wishing more quantitative information; pixel size is about 4.6 km at the equator.

Reflectivity. Magellan coverage of Venus with reflectivity data closely matches that of the altimetry because both types of data are obtained from the same echoes. The Magellan data on reflectivity have systematic errors from an unknown source that cause the values to increase northward and southward from periapsis. Some data files have been empirically corrected for these systematic errors, but others have not (see below).

Normal reflectivity (for brevity, simply "reflectivity") is the ratio of quasi-specular echo power received from a surface at normal incidence and the power transmitted to the same surface. For Magellan, reflectivities are estimated by using the equation of Hagfors (1964; see for example, Tyler and others, 1992):

where is the total cross section, is the normal reflectivity, C is a surface-roughness parameter, and is the incidence angle. C-1/2 is interpreted as root-mean-square slope (see below). Diffuse scatterers on and at the surface effectively reduce the surface area available for quasi-specular echo scattering (Evans and Hagfors, 1964; Pettengill and others, 1988); some Magellan reflectivity data sets have been corrected for this effect by using SAR backscatter data (see below).

Of particular importance to geologic mappers are the relations between reflectivity and dielectric constant and model-dependent relations between relative dielectric constant and the physical-electrical properties of the reflecting materials. The relation between reflectivity ( ) and relative dielectric constant ( ) is given by the Fresnel reflection coefficient:

Relative dielectric constant (also called dielectric permittivity) is the ratio of the dielectric constant of a material to that of free space or a vacuum.

There are a variety of model-dependent relations between the relative dielectric constant and physical-electrical properties of natural materials. Olhoeft and Strangway (1975) advocated the Lichtenecker mixing formula (see Saint-Amant and Strangway, 1970) and showed its applicability to lunar rocks and regoliths and their bulk densities; Garvin and others (1985) offered a modest modification to the equation of Olhoeft and Strangway. Campbell and Ulrichs (1969) applied the Rayleigh mixing formula to their data on dielectric constants and porosities of rocks, meteorites, and dry powders of these materials and cited references for other models. Selected relations are illustrated in figure 6 to give the mapper an appreciation for the significance of reflectivity.

Figure 6. Relations between normal reflectivity and bulk density of rocks and dry rock powders or regoliths. Rayleigh mixing curve assumes a "parent rock" with a relative dielectric constant of 7.7 and a bulk density of 3,100 kg/m3 (see Campbell and Ulrichs, 1969); curve extrapolated to a reflectivity of 0.25. Olhoeft and Strangway (1975) curve is based on experimental measurements of lunar rocks, aggregates, and regolith samples; light curves indicate one standard deviation. Relative dielectric constants (permittivities) calculated with the Fresnel reflection coefficient (see text). Conducting inclusions are not considered in these calculations.

Inclusions of electrical conductors, such as the mineral pyrite, in rocks and regoliths may have a profound effect on their dielectric constants (Pettengill and others, 1988). Rocks and regoliths containing such inclusions have been called "loaded dielectrics." This phenomenon may be an important factor contributing to the large radar reflectivities and low emissivities of Venusian surfaces at high elevations. The effects of conducting inclusions are presented by Pettengill and others (1988) and illustrated in figure 7.

Figure 7. Relation between ratio of dielectric constants of a "loaded" dielectric and host material and the volume fraction of electrical conducting inclusions in the "loaded" dielectric (after Pettengill and others, 1988). For a volume fraction of conducting inclusions of 0.1, if the dielectric constant of the host is 5.0, the ratio is 4.87 and the dielectric constant of the "loaded" dielectric is 24.4.

Reflectivity data suitable for most geologic mapping purposes are furnished to the mapper of each quadrangle in a color-transparency with the same scale and projection as the SAR-image and altimetry transparencies mentioned above. The data are also available on CD-ROMs, which include global data sets in both sinusoidal and Mercator projections (GREDR.SINU and GREDR.MERC files) and ancillary data for those wishing more quantitative information; pixel size is about 4.6 km at the equator. It is important to realize that only the GREDR.MERC files have been corrected for both the systematic errors and diffuse scattering mentioned above (P.G. Ford, personal communication, 1992).

Root-mean-square (RMS) slope. Quasi-specular echoes received by the altimetry antenna are spread or broadened in delay and Doppler frequency according to the probability distribution of tilted facets on the surface that are larger than the wavelength of the radar (about 10 to 250 wavelengths; see for example, Moore and others, 1980). Smooth, gently undulate level surfaces with small RMS slopes produce narrow echoes with sharp peaks. Rough, hummocky level surfaces with large RMS slopes produce broad echoes with broad peaks. To a crude approximation, RMS slope is analogous to the algebraic standard deviation of a slope-probability distribution. Regional surface tilts cause shifts in echo peaks from the delay and Doppler expected for level surfaces. Coverage of the Venusian surface is similar to that of the altimetry because both employ the same antenna. The mean RMS slope of Venus is 2.84; values range from about 0.5 to 11 (Ford and Pettengill, 1992). A pair of slope-probability distributions of lunar maria samples derived from images and radar are illustrated in figure 8 to give the mapper an appreciation of the significance of RMS slope.

Figure 8. Slope-probability distributions of part of Mare Serenitatis obtained by using Apollo 15 panoramic camera photography and bistatic radar; (a) photogrammetry, 25-m slope length, and (b) bistatic radar, 13-cm wavelength. Incremental probability shown by bars, cumulative probability shown by solid line; hypothetical Gaussian cumulative probability for algebraic standard () shown by dashed line. Note that actual cumulative curves are larger than Gaussian curves at large slope angles (reprinted from Moore and others, 1976, upper part of fig. 43).

Inversions of the delay and Doppler-frequency spectra show that the probability distributions of slopes of Venusian surfaces between 0 and 10 can be described with exponential, Hagfors, and Gaussian distribution functions (Tyler and others, 1992). In the analyses, contributions of diffuse echoes are justifiably assumed to be negligible. For nominal analyses (Ford and Pettengill, 1992), the echo spectra are fit with the Hagfors' scattering function noted above to obtain RMS slopes.

RMS-slope data from nominal analyses that are suitable for most geologic mapping purposes are furnished to the mapper of each quadrangle in a color transparency with the same scale and projection as the SAR-image, altimetry, and reflectivity transparencies mentioned above. The data are also available on CD-ROMs, which include global data sets in both sinusoidal and Mercator projections (GSDR.SINU and GSDR.MERC files) and ancillary data for those wishing more quantitative information; pixel size is about 4.6 km at the equator. The results of Tyler and others (1992) will be available on CD-ROMs in the future.

Emissivity Emissivity (e) is the ratio of the radiance of a gray body and the radiance of a black body at the same temperature. For the hot Venusian surface and the frequency of the Magellan radar, the Rayleigh-Jeans approximation, or the ratio of the brightness temperature at 12.6-cm (Tb) and the physical temperature of the surface (Tp), is a close estimate of the emissivity (that is, e = Tb/Tp ; see Schmugge, 1980; Pettengill and others, 1992, 1988). The mean emissivity of the Venusian surface at 12.6-cm wavelength is about 0.845 (Pettengill and others, 1992); the value is consistent with a dry, moderately dense, basaltic material. However, at elevations above about 6,054 km, most surfaces have very low emissivities (0.3-0.7) (Pettengill and others, 1992). Current explanations invoke elevation-dependent weathering processes that result in phase changes of inclusions of iron-bearing minerals to produce loaded dielectrics (Klose and others, 1992) or a material of average dielectric properties with many large voids that cause multiple scattering (Arvidson and others, 1992; Pettengill and others, 1992). The floors of some large impact craters also have low emissivities that result from compositional differences or other causes (Weitz and others, 1992). To an approximation, the Fresnel reflection coefficient ( ) is the complement of the emissivity (e) (see Pettengill and others, 1988, 1991):


This approximate relation between reflectivity and emissivity should be viewed with some caution, because the incidence angles for reflectivities (altimeter antenna) and emission angles for emissivities (SAR antenna) are not the same. Both reflectivity and emissivity are affected by surface roughness, and emissivity varies with incidence angle (Pettengill and others, 1992).

Emissivity data suitable for most geologic mapping purposes are furnished to the mapper of each quadrangle in a color transparency with the same scale and projection as the SAR-image, altimetry, reflectivity, and RMS-slope transparencies mentioned above. The data are also available on CD-ROMs, which include global data sets in both sinusoidal and Mercator projections (GEDR.SINU and GEDR.MERC files) and ancillary data for those wishing more quantitative information; pixel size is about 4.6 km at the equator.

Magellan Data Products

SAR image data records. Magellan radar data are processed and mosaicked into spatial image products to facilitate scientific analysis. The standard data products include image mosaics and ancillary data. Other special products include altimetric, rms slope, reflectivity, and radiometric datasets in image form for science analysis. A particularly useful portrayal is the superposition of color-coded datasets on the SAR backscatter data records (for example, Arvidson and others, 1991; Tyler and others, 1991; Kirk and others, 1992; Pettengill and others, 1992; Sandwell and Schubert, 1992). SAR mosaics are further processed to generate the scaled quadrangles that are used for map bases in the VMAP program. Both synthetic and real parallax stereopairs of Magellan image mosaics are being produced as well; the synthetic ones have parallax offsets generated by computer on the basis of Magellan altimetry data.

One Full-Resolution Basic Image Data Record (F-BIDR) was produced for each Magellan orbit; 1,790 orbits complete one mapping cycle (360 of longitude). (For the primary mission, solar conjunction prevented the return of SAR data for 110 orbits.) An additional 10 percent was lost during the nominal mission because of solar heating of electronic components (the spacecraft's solar reflectors had lost much of their efficiency), failure of one of the spacecraft's two tape recorders, and problems affecting spacecraft attitude. One F-BIDR contains nearly 60 Mbytes of 8-bit image data and less than 10 Mbytes of ancillary data. The F-BIDR format is 75 m/pixel resampled from the original 120-m cross-track and along-track resolutions and transformed into Sinusoidal Equal-Area projection; within 10 of the poles, the data are in oblique Sinusoidal projection (the F-PIDR format). Each F-BIDR forms a strip about 300 pixels wide by about 220,000 pixels long. In turn, about 30 F-BIDRs (or more at higher latitudes) are used to generate a mosaic, which has 7,168 lines by 8,192 samples. The mosaics are called Full-Resolution Mosaicked Image Data Records (F-MIDRs). Each F-MIDR is identified by center latitude and longitude and covers 5 of latitude and >5 of longitude (depending on latitude; see Michaels, 1992, figure 4). A "venetian blind" effect is commonly evident in mosaicked F-BIDRs because of border mismatches in backscatter intensity caused by minor errors in spacecraft pointing and navigation, in the topography model, and in processing.

To provide image-mosaic coverage for larger areas, the data are compressed in successive operations in which nine pixels are averaged and replaced by one pixel and then reprojected. The Once-Compressed Mosaicked Image Data Record (C1-MIDR) consequently has a resolution of 225 m/pixel and covers 15 of latitude and >15 of longitude (see Michaels, 1992, figure 5). In turn, successive compressions result in the 675 m/pixel C2-MIDRs (45 of latitude by >45 of longitude; Michaels, 1992, figure 6) and the 2,025 m/pixel C3-MIDRs (80 of latitude by >120 of longitude). Polar data records (F-PIDRs) and projections (P-MIDRs) portray areas at >80 latitude.

The various MIDR products are being distributed as photographic prints and digital files on CD-ROM disks. The CD-ROMs released by the Magellan Project are available to the planetary geoscience community through the National Space Science Data Center in Greenbelt, Maryland.

Synthetic stereopairs and merged databases. Synthetic parallax stereoimages of most of Venus based on C1-MIDR image mosaics have been produced by the U.S. Geological Survey for the Magellan Project as preliminary tools in assessing the global geology of Venus. These synthetic stereoimages are produced by (1) geometrically registering to a single Magellan image mosaic the best available altimetry dataset (8 x 11 km to 20 x 29 km resolution, depending on spacecraft altitude), and (2) introducing parallax into the MIDR, as controlled by the registered geometry (that is, shifting pixels left or right by a distance proportional to the altitude relative to the average altitude in the MIDR, so that the overall average shift is zero pixels). Vertical exaggerations have been produced at 10X and 50X. These stereoimages will be important for interpretations of the broad topography, which will be valuable in analyzing the larger landforms associated with volcanism and tectonism.

In addition, perspective views can be generated from the merged topography and SAR image mosaics. Other radar databases (emissivity, reflectivity, rms slope, etc.) can be colorscaled and combined with black-and-white SAR mosaics for normal or perspective views or for synthetic stereo analysis.

Map projections. To assist in various cartographic endeavors, formal map series are being produced at various standard scales and projections. Such maps will be used as base materials for geologic mapping. The VMAP program is sponsoring geologic mapping of the 1:5,000,000-scale series that consists of 62 quadrangles (fig. 1). The series includes Mercator (<25 latitude), Lambert Conformal Conic (25 to 75), and Polar Stereographic (>75) projections. All are conformal projections, which retain the approximate shape of small landforms. However, all are distorted across larger regions. The Mercator base, visualized by a cylinder perpendicular to the equator, is conveniently rectangular, but scale changes rapidly with latitude (Batson, 1990, fig. 3.1). For Venus, the cylinder intersects at 15.9 latitude, where the true 1:5,000,000 scale occurs. The Lambert Conformal Conic projection is represented by a cone tangential to the globe whose apex intersects the spin axis of the planet (Batson, 1990, fig. 3.3). The latitudes of cone-globe intersection are called standard parallels. Scale changes with latitude. For Venus, two rows of these projections occur in each hemisphere with standard parallels at 34 and 73, where true 1:5,000,000 scale occurs. Polar Stereographic projections represent planes tangent to the axial pole (where true scale occurs). The scales of the projections are the same where they join (at lats 25 and 75).

Other map series that are being produced for Venus contain 340 sheets (Sinusoidal) at 1:1,500,000 scale, 8 sheets (6 Mercator and 2 Polar) at 1:10,000,000 scale, 3 sheets (2 Mercator and 1 Polar) at 1:25,000,000 scale, and 1 sheet at 1:50,000,000 scale. For more information, refer to Batson (1990).

Non-Magellan Radar and Other Data

Since the early 1960s, Venus has become one of the planets most visited by spacecraft. Fifteen Soviet and six U.S. missions have probed its sulfurous clouds to measure atmospheric structure and composition. Other investigations disclosed a lack of water vapor and the absence of a magnetic field. Seven of the Soviet craft were landers that conducted chemical analyses of rocks, which indicated that some have compositions similar to basalt and thus may be of volcanic origin. One of the landers, Venera 9, gave us our first glimpse of the surface when, in 1975, it relayed a panoramic view. These early explorations were enhanced by observations in the field of radio astronomy that indicated that Venus is a perpetual furnace; surface temperatures reach 482 C (~900 F), and the atmospheric pressure is 90 times that of Earth's (Young, 1990).

The 1978 U.S. Pioneer Venus Orbiter (PVO) was the first spacecraft to carry a radar (SAR-type) sensor to Venus, and the altimetry of 92 percent of the surface was mapped at a resolution of 50 to 140 km. For the first time, planetary scientists had a global map of Venus. Continent-size highlands, hilly plains, large mountains looking like volcanoes, and flat lowlands were revealed (Masursky and others, 1980). Much of the initial scientific results from the Pioneer Venus mission were published in a special issue of the Journal of Geophysical Research dedicated to that mission (December 1980, v. 85, no. A13, p. 7575-8337).

Five years after Pioneer Venus went into orbit, the Soviet Venera 15 and 16 spacecraft used radar to map about 25 percent of Venus (lat 25-90 N.) at a resolution of 1.2 to 2.4 km. These images revealed evidence of abundant volcanism, impact craters, and complex tectonic deformation, including coronae--large, oval features of apparent volcanotectonic origin previously unrecognized on other bodies in the Solar System (Kotelnikov, 1989). The geoscience investigations of Venera 15 and 16 are described in many publications (see Recommended Reading).

Earth-based radar observations of some regions of Venus have been made primarily from the Arecibo Radio Observatory and the Goldstone receiving station since the mid-1960s (see, for example, Jurgens and others, 1980, 1988a, b; Burns and Campbell, 1985; Campbell and others, 1989, 1990; Campbell and Campbell, 1992; Plaut and Arvidson, 1992). The Goldstone radar coverage is restricted to lat 23 S. to 23 N. and long 260 to 32 E. (Plaut and Arvidson, 1992), while that from the Arecibo Observatory is limited to most of the area between lat 67 and long 265 to 35 E., about 23 percent of the surface (Campbell and others, 1990). In all, about 40 percent of Venus has been mapped from these radar stations (Campbell and others, 1990).

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