Data Set Overview
    =================
      The Global Vector Data Record (GVDR) is a sorted collection of
      scattering and emission measurements from the Magellan Mission.
      The sorting is into a grid of equal area 'pixels' distributed
      regularly about the planet.  For data acquired from the same
      pixel but in different observing geometries, there is a second
      level of sorting to accommodate the different geometrical
      conditions.  The 'pixel' dimension is 18.225 km.  The GVDR is
      presented in Sinusoidal Equal Area (equatorial), Mercator
      (equatorial), and Polar Stereographic (polar) projections.
 
      The GVDR is intended to be the most systematic and comprehensive
      representation of the electromagnetic properties of the Venus
      surface that can be derived from Magellan data at this
      resolution.  It should be useful in characterizing and comparing
      distinguishable surface units.
 
 
    Parameters
    ==========
      The Magellan data set comprises three basic data types: echoes
      from the nadir-viewing altimeter (ALT), echoes from the oblique
      backscatter synthetic aperture radar (SAR) imaging system, and
      passive radiothermal emission measurements made using the SAR
      equipment.  The objective in compiling the GVDR is to obtain an
      accurate estimate of the surface backscattering function
      (sometimes called the specific backscatter function or 'sigma-
      zero') for Venus from these three data types and to show its
      variation with incidence (polar) angle, azimuthal angle, and
      surface location.
 
      The ALT data set has been analyzed to yield profiles of surface
      elevation [FORD&PETTENGILL1992] and estimates of surface Fresnel
      reflectivity and estimates of meter-scale rms surface tilts by
      at least two independent methods [FORD&PETTENGILL1992;
      TYLER1992].  The 'inversion' approach of [TYLER1992] provides,
      in addition, an empirical estimate of the surface backscatter
      function at incidence angles from nadir to as much as 10 degrees
      from nadir in steps of 0.5 degrees.
 
      Statistical analysis of SAR image pixels for surface regions
      about 20 km (across track) by 2 km (along track) provided
      estimates of the surface backscatter function over narrow
      angular ranges (1-4 degrees) between 15 and 50 degrees from
      normal incidence [TYLER1992].  By combining results from several
      orbital passes over the same region in different observing
      geometries, the backscatter response over the full oblique
      angular range (15-50) could be compiled.  In fact, the number of
      independent observing geometries attempted with Magellan was
      limited, and some of these represented changes in azimuth rather
      than changes in incidence (or polar) angle.  Nevertheless, data
      from many regions were collected in more than one SAR observing
      geometry.  Histograms of pixel values and quadratic fits to the
      surface backscattering function over narrow ranges of incidence
      angle were computed by [TYLER1992].
 
      Passive microwave emission by the surface of Venus was measured
      by the Magellan radar receiver between ALT and SAR bursts.
      These measurements have been converted to estimates of surface
      emissivity [PETTENGILLETAL1992].  With certain assumptions the
      emissivity derived from these data should be the complement of
      the Fresnel reflectivity derived from the ALT echo strengths.
      In cases where the two quantities do not add to unity, the
      assumptions about a simple dielectric (Fresnel) interface at the
      surface of Venus must be adjusted.
 
 
    Processing
    ==========
      The processing carried out at the Massachusetts Institute of
      Technology (MIT) to obtain altimetry profiles and estimates of
      Fresnel reflectivity and rms surface tilts has been described
      elsewhere [FORD&PETTENGILL1992].  In brief it involves fitting
      pre-computed templates to measured echo profiles; the
      topographic profiles, Fresnel reflectivities, and rms surface
      tilts are chosen to minimize differences between the data and
      templates in a least-squares sense.  The estimates of emissivity
      require calibration of the raw data values and correction for
      attenuation and emission by the Venus atmosphere
      [PETTENGILLETAL1992].  These data have been collected by orbit
      number on a set of compact discs [FORD1992] and into a set of
      global maps, also distributed on compact disc [FORD1993].
 
      ALT and SAR data have been processed at Stanford University
      using 'inversion' methods, whereby the radar equation is
      converted to a matrix-vector relationship and that is solved
      (using least-squares techniques) to obtain an 'empirical'
      scattering function for each radar echo [TYLER1992].  In the
      case of ALT data, stability of the solution requires
      considerable attention; in the case of SAR data, it is the
      variability of the surface scattering itself that leads to the
      most uncertainty.  Stanford has also independently confirmed the
      results of the MIT processing of emissivity data but without
      developing separate algorithms.
 
      At MIT the primary input data were ALT-EDR tapes from the
      Magellan Project.  The echoes themselves were used to obtain the
      altimetry and fitting results.  SAR block quantization data were
      used to obtain a coarse estimate of high-angle scattering
      efficiency and that was applied to adjust the near-nadir
      Fresnel reflectivity.  Raw radiometry measurements from the SAR
      burst headers were the input to the emissivity calculations.
 
      At Stanford ALT-EDR tapes were the input for calculation of
      near-nadir empirical backscattering functions.  For oblique
      backscatter, C-BIDR tapes from the Magellan Project and F-BIDR
      files obtained via Internet from Washington University were the
      input products.  Output was collected on an orbit-by-orbit basis
      into a product known as the Surface Characteristics Vector Data
      Record (SCVDR).  The SCVDR has been delivered to the Magellan
      Project for orbits through 2599; processing of data beginning
      with orbit 2600 and continuing through the end-of-Mission is
      pending completion of the first version of the GVDR.
 
 
    Tabulated Data
    ==============
      The GVDR data set comprises several 'tables' of results based on
      analysis of each of the data types described above.  These
      include:
 
        (1)  Image Data Table
        (2)  Radiometry Data Table
        (3)  MIT ALT Data Table
        (4)  Stanford ALT Data Table
 
 
      (1) Image Data Table
      --------------------
        This table contains results from analysis of SAR image strips.
        The results are parameterized by the azimuth angle, the
        incidence (polar) angle, and the polarization angle.
        Quantities include the number of image framelets used to
        compute the scattering parameters; the median, the mode, and
        the one-standard-deviation limits of the pixel histogram; and
        the three coefficients and the reference angle of the
        quadratic approximation to sigma-zero as a function of
        incidence angle.
 
 
      (2) Radiometry Data Table
      -------------------------
        This table contains results from MIT analysis of the
        radiometry data.  The results are parameterized by the azimuth
        angle, the incidence angle, and the polarization angle.  The
        results include the number of radiometry footprints used to
        compute the estimate of thermal emissivity, the emissivity,
        and its variance.
 
 
      (3) MIT ALT Data Table
      ----------------------
        This table contains results derived from the MIT altimetry
        data analysis.  The results include the number of ARCDR ADF
        footprints used in computing the estimates of scattering
        properties for the pixel and estimates (and variances) of
        radius, rms surface tilt, and Fresnel reflectivity from the
        ARCDR.
 
 
      (4) Stanford ALT Data Table
      ---------------------------
        This table contains results from the Stanford analysis of
        altimetry data.  Results include the number of SCVDR
        footprints used in computing the estimates of surface
        properties for this pixel, the centroid of the Doppler
        spectrum, the derived scattering function and the angles over
        which it is valid, variance of the individual points in the
        derived scattering function, and results of fitting analytic
        functions to the derived scattering function.
 
 
    Ancillary Data
    ==============
      Ancillary data for most processing at both MIT and Stanford was
      obtained from the data tapes and files received from the
      Magellan Project.  These included trajectory and pointing
      information for the spacecraft, clock conversion tables,
      spacecraft engineering data, and SAR processing parameters.  For
      calibration of the radar instrument itself, Magellan Project
      reports (including some received from Hughes Aircraft Co.
      [BARRY1987; CUEVAS1989; SE011]) were used.  Documentation on
      handling of data at the Jet Propulsion Laboratory was also used
      [BRILL&MEISL1990; SCIEDR; SDPS101].
 
 
    Coordinate System
    =================
      The data are presented in gridded formats, tiled to ensure that
      closely spaced points on the surface occupy nearby storage
      locations on the data storage medium.  Four separate projections
      are used: sinusoidal equal area and Mercator for points within
      89 degrees of the equator, and polar stereographic for points
      near the north and south poles.  The projections are described
      by [SNYDER1987]; IAU conventions described by [DAVIESETAL1989]
      and Magellan Project assumptions [LYONS1988] have been adopted.
 
 
    Software
    ========
      A special library and several example programs are provided in
      source code form for reading the GVDR data files.  The general-
      purpose example program will serve the needs of the casual user
      by accessing a given GVDR quantity over a specified region of
      GVDR pixels.  More advanced users may want to write their own
      programs that use the GVDR library as a toolkit.  The library,
      written in ANSI C, provides concise access methods for reading
      every quantity stored in the GVDR.  It conveniently handles all
      geometric and tiling transformations and converts any compressed
      quantities to a standard native format.  The general purpose
      program mentioned above provides an example of how to use this
      library.
 
 
    Media/Format
    ============
      The GVDR will be delivered to the Magellan Project (or its
      successor) using compact disc write once (CD-WO) media.  Formats
      will be based on standards for such products established by the
      Planetary Data System (PDS) [PDSSR1992].

Overview
    ========
      The GVDR is intended to be the most systematic and comprehensive
      representation of the electromagnetic properties of the Venus
      surface that can be derived from Magellan data at this
      resolution.  Nevertheless, there are limitations to what can be
      done with the data.
 
 
    Review
    ======
      The GVDR will be reviewed internally by the Magellan Project
      prior to release to the planetary community.  The GVDR will also
      be reviewed by PDS.
 
 
    Data Coverage and Quality
    =========================
      Because the orbit of Magellan was elliptical during most of its
      mapping operations, parts of the orbital coverage have higher
      resolution and higher signal-to-noise than others.
 
 
      Cycle 1 Mapping
      ---------------
        During Mapping Cycle 1, periapsis was near 10 degrees N
        latitude at altitudes of approximately 300 km over the
        surface.  The altitude near the poles, on the other hand, was
        on the order of 3000 km.  For all data types this means lower
        confidence in the results obtained at the poles than near the
        equator.
 
        Further, the spacecraft attitude was adjusted so that the SAR
        antenna was pointed at about 45 degrees from nadir near
        periapsis; this was reduced to near 15 degrees at the poles.
        The objective was to compensate somewhat for the changing
        elevation and to provide scattering at higher incidence angles
        when the echo signal was expected to be strongest.  The ALT
        antenna, at a constant 25 degree offset from the SAR antenna,
        followed in tandem but at angles which were not optimized for
        obtaining the best altimetry echo.
 
        During Mapping Cycle 1 almost half the orbits provided SAR
        images of the north pole; because of the orbit inclination,
        ALT data never extended beyond about 85N latitude in the north
        and 85S in the south.  No SAR images of the south pole were
        acquired during Mapping Cycle 1 because the SAR antenna was
        always pointed to the left of the ground track; the Cycle 1
        SAR image strip near the south pole was at a latitude
        equatorward of 85S.
 
 
      Cycle 2 Mapping
      ---------------
        During much of Mapping Cycle 2, the spacecraft was flown
        'backwards' so as to provide SAR images of the same terrain
        but with 'opposite side' illumination.  This adjustment also
        meant that the SAR could image near the Venus south pole (but
        not near the north pole).  The ALT data continued to be
        limited to latitudes equatorward of 85N and 85S.
 
 
      Cycle 3 Mapping
      ---------------
        During Mapping Cycle 3 the emphasis was on obtaining SAR data
        from the same side as in Cycle 1 but at different incidence
        angles (for radar stereo).  In fact, most data were acquired
        at an incidence angle of about 25 degrees, which meant that
        the ALT antenna was usually aimed directly at nadir instead of
        drifting from side to side, as had been the case in Cycle 1.
        These Cycle 3 data, therefore, may be among the best from the
        altimeter.  Dynamic range in SAR data was larger than in Cycle
        1 because the incidence angle was fixed rather than varying to
        compensate for the changing spacecraft height.
 
 
      All Cycles
      ----------
        It is important to remember that, since the SAR and ALT
        antennas were aimed at different parts of the planet during
        each orbit, building up a collection of composite scattering
        data for any single surface region requires that results from
        several orbits be integrated.  In the case of data from polar
        regions, where only the SAR was able to probe, there will be
        no ALT data.  When scheduling or other factors interrupted the
        systematic collection of data, there may be ALT data for some
        regions but no comparable SAR or radiometry data (or vice
        versa).
 
        Note that for all Cycles outages played an important role in
        determining coverage.  For example, although a goal of Cycle 3
        radar mapping was radar stereo, early orbits were used to
        collect data at nominal incidence angles that had been missed
        during Cycle 1 because of thermal problems with the
        spacecraft.  A transmitter failure during Cycle 3 caused a
        loss of further data.  It is not within the scope of this
        description to provide detailed information on data coverage.
 
 
    Limitations
    ===========
      Both the template fitting approach and the inversion approach
      will have their limitations in estimating overall surface
      properties for a region on Venus.  The template calculation
      assumes that scattering is well-behaved at all incidence angles
      from 0 to 90 degrees and that a template representing that
      behavior can be constructed.  The Hagfors function [HAGFORS1964]
      used by MIT, however, fails to give a finite rms surface tilt if
      used over this range of angles, so approximations based on a
      change in the scattering mechanism must be applied
      [HAGFORS&EVANS1968].  The inversion method [TYLER1992] is
      susceptible to noise at the higher incidence angles and this
      will corrupt solutions if not handled properly.
 
      Users of this data set should be aware that radar echoes are
      statistically variable and that each result has an uncertainty.
 
      A nominal nadir footprint can be assigned to altimetry results,
      but this footprint is biased near periapsis because the ALT
      antenna is rotated about 20 degrees from nadir (during Cycle 1).
      Over polar regions in Cycle 1, the ALT antenna is rotated about
      10 degrees to the opposite side of nadir.  A more important
      consideration in polar regions is that the area illuminated by
      the ALT antenna is approximately 100 times as large as near
      periapsis because of the higher spacecraft altitude.  The region
      contributing to echoes in polar regions -- and therefore the
      region over which estimates of Fresnel reflectivity and rms
      surface tilts apply -- is much larger than at periapsis.