Dataset Overview
    ================
      The imaging system on each Viking Lander consisted of two
      identical cameras.  These cameras operated throughout the
      mission, returning nearly 6600 images.  Rocks were identified
      in the images, and their locations and dimensions were
      determined.  Statistical distributions for the rocks were
      derived.
 
      This data set includes a table giving locations and dimensions
      of 425 rocks (plus 2 possible outcrops) located near VL1 (file
      VL1ROCKS.TAB) and a second table of 499 rocks near VL2 (file
      VL2ROCKS.TAB).  It also includes derivative tables showing
      number density and areal coverage as a function of rock
      diameter (VL1NORML.TAB and VL2NORML.TAB, respectively).  The
      VL1 population, with the two 'outcrops' omitted, has also been
      included as a 'VL0' set of files.  These rock size-frequency
      and size-area distributions are updated versions of earlier
      work [MOORE&KELLER1990] and [MOORE&KELLER1991].
 
      Intermediate products -- tables of axial ratios and areas for
      rocks and of rock distributions according to surface type --
      have also been included.  These may be of interest to users
      seeking more details of the statistical analysis or alternative
      descriptors of the rock population.  Tables of axial ratios
      have file names of the form VL*AXRAT.TAB; tables of rock
      distribution by surface type have names of the form
      VL*SURFS.TAB.
 
 
    Parameters
    ==========
      The basic tables cover 425 rocks and 2 possible outcrops at the
      Lander 1 site and 499 rocks at Lander 2.  They include three
      types of information: (1) the xyz-coordinates; (2) the lengths,
      widths, and heights; and (3) a descriptor of the apparent burial
      state of each rock.  Length  L  is the longest visible
      (horizontal) dimension, width  W  is the orthogonal horizontal
      dimension, and height  H  is the vertical exposure of the rock
      above the surrounding surface.  The burial descriptors are
      subjective and include three categories: 'perched,' 'partly
      buried,' and 'deeply buried.' For construction of rock size-
      frequency and area-size distributions, the average rock diameter
      D  is taken to be the geometric mean of the length and width;
      the corresponding rock area is approximated as  (PI/4)*(D**2).
 
      Derivative tables include parameters such as the average axial
      ratio for rocks computed from each pair of rock dimensions
      and the number density and areal coverage of rocks as a
      function of diameter.
 
 
    Processing
    ==========
      The rock size-frequency and size-area distributions were
      obtained from images and maps of surface materials by
      estimating the areas occupied by materials within the
      camera fields of view.  The process involved several steps.
      Measurements on the smallest, closest rocks were combined
      with measurements of large rocks over great distances to
      obtain a composite distribution function for about 80 square
      meters at each site.
 
      First, maps of surface material were divided into two regions.
      The 'near field' extended to about 3 meters in front of each
      Lander and was approximately within reach of the surface
      sampler arm.  The 'far field' extended to about 9 meters.
 
      Data on rock dimensions and locations for the near field came
      from three sources: (1) 1/10-scale base maps that showed the
      sizes and locations of rocks [MOOREETAL1987]; (2) unpublished
      working maps and data; and (3) Lander camera images.  Rocks
      and clods with dimensions larger than about 0.01 meter could
      be measured and located in the near field.
 
      Data on dimensions and locations for the far field also came
      from three sources: (1) 1/20-scale contour maps [LIEBES1982];
      (2) Lander camera mosaics with overlaid contours [LIEBES1982];
      and (3) Lander camera images.  Large rocks were located
      directly on the contour maps and the mosaics; then they were
      measured directly from the maps.  Smaller rocks that were not
      intersected by contours were located using stereometric
      procedures; their sizes were calculated from their ranges and
      from the angles they subtended.
 
      Second, different types of surface materials were identified.
      Three types of materials were mapped at both Lander sites:
      (1) fine materials, (2) soil-like materials, and (3) rocks.
      For the far fields of both landers, fine material included
      uniform-appearing materials that were free of small rocks
      and clods except along contacts with other soil-like
      materials.  The thickness of deposits of fine material in
      the far field, which were superposed on soil-like materials
      and rocks at both sites, were estimated to range from 0.01
      or 0.02 meters to more than 0.25 meters at Lander 1 and from
      0.01 meters to about 0.3 meters at Lander 2.  Known locations
      of large rocks permitted delineation of areas covered by fine
      materials and rock outcrops by visual inspection.  These
      areas were obtained graphically from the maps; allowances for
      areas occupied by rocks within the areas of fine and soil-like
      materials were computed.  The area of fines near footpad 2 of
      Lander 1 were included with fines of the far field because
      they were thick and free of small rocks.  The soil-like areas
      in the near fields of Landers 1 and 2 contained rocks as small
      as, or perhaps even smaller than, 0.022 meters.  Two areas at
      the Lander 1 site were mapped as outcrops [BINDERETAL1977],
      but it is possible that they could be large rocks
      [SHARP&MALIN1984] or a single rock about 3 meters long.
 
      Third, cumulative rock distribution functions at each Lander
      site were obtained by combining the measured distributions in
      the near field, far field, and fine areas.  All rocks with
      average diameters greater than 0.25 meters in the near and far
      fields were included in the cumulative distribution.  Rocks
      smaller than 0.25 meters in the near field were considered to
      be representative of that size range in both the near and far
      fields -- except where fine materials were mapped.  That is,
      since small rocks are not resolved in the far field, areas
      between moderate and large rocks in the far field were assumed
      to have the same distribution as in the near field.  All rocks
      within the deposits of fines were assumed to be large enough
      to have been measured accurately and were included in the
      cumulative distribution.
 
      The cumulative rock distribution function was then the
      distribution of rocks larger than 0.25 meters everywhere, plus
      the total rock distribution from fines areas, plus the
      distribution of rocks smaller than 0.25 meters in the near
      field scaled to 'fill in' the spaces among rocks larger than
      0.25 m in the far field; this total was then normalized by the
      total area (about 80 m**2 at both sites).  The results are
      presented in the tables VL*NORML.TAB; the contributions from
      the different surface types are tabulated in VL*SURFS.TAB.
 
 
    Data
    ====
      Two tables contain basic rock population data derived from
      images, maps derived from images, and other data.  Tables
      VL1ROCKS.TAB  and  VL2ROCKS.TAB  contain the data for Landers
      1 and 2, respectively.  Each row in the table contains an ID
      keyed to hand-drawn overlays for the atlas of lander images
      [LIEBES1982], an indicator of the environment in which the rock
      was located (near field, far field, outcrop, drift material,
      or excluded from statistical tabulations because of anomalous
      settings), the XYZ coordinates of the rock based on the
      Local Gravity-Normal (LGN) map grid in [LIEBES1982] in meters,
      estimates of the dimensions of the rock (meters) and its
      orientation in the LGN frame, a subjective evaluation of its
      burial state (perched, partly buried, buried, or unknown),
      and miscellaneous notes such as names associated
      with certain well-known rocks.  The data fields are in 11
      columns totaling 82 bytes each; each row is terminated with
      an ASCII carriage-return line-feed pair.  Each table is
      accompanied by a detached PDS label which fully describes
      its format and content.
 
      VL0ROCKS.TAB  is identical to  VL1ROCKS.TAB  except that the
      two 'outcrops' have been omitted.  It is accompanied by
      detached PDS label  VL0ROCKS.LBL.
 
      VL1AXRAT.TAB  is a table of binned results of calculations based
      on VL1ROCKS.TAB.  The area of each rock and three axial ratios
      were computed and binned as follows:
 
       AREA = L*W*PI/4           binned according to   DLW = SQRT(L*W)
       ARLW = MIN(L,W)/MAX(L,W)  binned according to   DLW = SQRT(L*W)
       ARWH = MIN(W,H)/MAX(W,H)  binned according to   DWH = SQRT(W*H)
       ARLH = MIN(L,H)/MAX(L,H)  binned according to   DLH = SQRT(L*H)
 
      where
           ARxy  denotes axial ratio of dimensions  x  and  y
           Dxy   denotes average diameter using dimensions  x  and  y
           L = estimated longest dimension of the rock
           W = estimated width of the rock (orthogonal to length)
           H = estimated vertical exposure of a perched rock, or
                twice the exposure of a partly buried rock (see below
                for discussion of buried rocks)
      and
           MIN(X,Y) is the smaller of X and Y
           MAX(X,Y) is the larger of X and Y
 
      The lowest bin boundary was set at 1/128th meter; boundaries
      then increased by powers of SQRT(2) (0.008, 0.011, ... , 1.000,
      1.414 m).  The area reported in VL1AXRAT.TAB is the sum of the
      areas of all the rocks assigned to that bin.  For axial ratios
      the quantity reported for each bin is the average and standard
      deviation of the axial ratios of the rocks in that bin.  The
      results are tabulated separately according to surface type
      (drift area, far field, near field, and excluded) and burial
      state (perched, partially buried, buried, and unknown).
      Cumulative results for all bins were then computed for each
      surface type and burial state combination; these are shown in
      summary lines in the table.
 
      Since there are three dimensions for each rock, axial ratios
      were calculated using each of the three possible pairings.
      Because the height of buried rocks is very uncertain, axial
      ratios based on heights of buried rocks were excluded from the
      averages and standard deviations; instead, those rocks were
      assigned to a special 'undefined' bin (bin number 1).
 
      VL1AXRAT.TAB is composed of 16 sub-tables, one for each
      combination of surface type and burial state. Each sub-table
      has 19 rows; the first is for rocks which could not be binned
      (e.g., the computation required  H  for a buried rock),
      the next 17 are for bins in increasing average diameter, and
      the last is a summary for all diameters.  VL1AXRAT.TAB is
      accompanied by a detached PDS label which fully describes both
      its content and format (VL1AXRAT.LBL).
 
      VL1SURFS.TAB  is a table of VL1 rock numbers and areal coverage
      (both incremental and cumulative) in decreasing order of rock
      diameter for each of the three surface types -- drift material,
      far field, and near field.
 
      For each surface type (drift material, far field, and near
      field) rocks were sorted into bins according to diameter (square
      root of length times width), the area covered was estimated
      (diameter squared times pi divided by 4), and a running sum was
      accumulated.  Total area and area covered by rocks for
      each surface type at VL1 were:
 
          Surface Type    Total Area  Area Covered    Area Covered
                                        by Rocks    by Rocks >0.25m
          --------------  ----------  ------------  ---------------
          Drift Material  15.27 m**2   0.4102 m**2    0.0534 m**2
          Far Field       57.85 m**2   6.7229 m**2    5.4397 m**2
          Near Field      10.48 m**2   1.3153 m**2    0.0560 m**2
 
      The inter-rock area in the far field was 52.4103 m**2, where
      inter-rock was taken to mean area not covered by a rock of
      diameter 0.25 meters or larger.  Inter-rock area in the near
      field was 10.4240 m**2.  Ratio of the total inter-rock area
      (far field plus near field) to the near field inter-rock area
      was 6.0278; this was the scale factor used to multiply the
      near field distribution for diameters less than 0.25 m in
      constructing the VL1NORML.TAB table below.
 
      VL1SURFS.TAB is accompanied by a detached PDS label which fully
      describes both its content and format (VL1SURFS.LBL).
 
      VL1NORML.TAB  is a table of rock number and area density for
      the entire VL1 site.  A distribution function is first formed
      by summing the following:
 
        (1) the near field distribution of rocks larger than 0.25 m
        (2) the far field distribution of rocks larger than 0.25 m
        (3) 6.0278 times the near field distribution of rocks smaller
              than 0.25 m
        (4) the total distribution of rocks in the drift material
 
      Then the density is derived by dividing the distribution by
      the total area (83.60 m**2).  The table has columns for the
      rock number and rock area distribution per bin, the cumulative
      rock number and rock area as a function of bin, the rock number
      and rock area density per bin, and the cumulative rock number
      and rock area density per bin.  VL1NORML.TAB replicates the
      results reported earlier by [MOORE&KELLER1990] and
      [MOORE&KELLER1991], with minor corrections.
 
      VL1NORML.TAB is accompanied by a detached  PDS label which
      fully describes both its content and format (VL1NORML.TAB).
 
      VL2AXRAT.TAB, VL2SURFS.TAB, and VL2NORML.TAB are the
      respective files for the Viking Lander 2 site.  Each is
      accompanied by a detached PDS label.
 
      VL0AXRAT.TAB, VL0SURFS.TAB, and VL0NORML.TAB are the
      respective files for the Viking Lander 1 site but with the
      two 'outcrops' omitted.  Each is accompanied by a detached PDS
      label.
 
 
    Ancillary Data
    ==============
      None.
 
 
    Coordinate Systems
    ==================
      The photogrammetric reference points of the two cameras on each
      Lander were separated by 0.822 m [LIEBES&SCHWARTZ1977].  If the
      Lander were resting on a perfectly flat surface, the origin of
      the Lander Aligned Coordinate System (LACS) would be 1.583 m
      below the midpoint of this line and 0.470 m to the rear (toward
      Footpad 1, or in the LACS -Z direction).  The line from Camera
      2 to Camera 1 would point in the +Y direction. LACS +X was down,
      making a right-handed orthogonal system.  The LACS was fixed
      with respect to the body of the Lander.
 
      The LGN origin coincided with the LACS origin, but its Z axis
      pointed toward zenith.  Its +Y axis pointed in the direction
      of the LACS +Z projection onto the horizontal plane.  The LGN
      +X axis completed the right-handed orthogonal frame.  Loosely
      quoting [LIEBES1982]: 'To the extent that lander tilt may be
      considered small, the LGN may be visualized as having its
      x-axis approximately anti-parallel to the LACS y-axis (and thus
      pointing roughly parallel to the direction from Camera 1 to
      Camera 2).  The LGN y-axis points roughly parallel to the LACS
      z-axis, or in the horizontal direction outward and approximately
      forward from the lander, and roughly perpendicular to the
      intercamera baseline.'
 
      For Lander 1, north was 141.91 degrees counter-clockwise about
      the LGN Z-axis, from the LGN Y-axis.  The Lander 1 deck was
      tilted 2.99 degrees at azimuth 285.17 degrees (clockwise) from
      north.  For Lander 2, north was 29.14 degrees counter-clockwise
      about the LGN Z-axis, from the LGN Y axis.  The Lander 2 deck
      was tilted down 8.21 degrees at azimuth 277.70 degrees
      (clockwise) from north [LIEBES1982].
 
      Rock positions are given with respect to the Local Gravity-
      Normal (LGN) map grid defined in [LIEBES1982].  Rock
      orientations indicate the direction of the long axis of the
      rock and are measured clockwise from the LGN Y-axis.
 
 
    Software
    ========
      The SOFTWARE directory includes FORTRAN 77 source code for a
      single program which will carry out a statistical analysis
      of the basic rock data (e.g., VL1ROCKS.TAB) and generate the
      corresponding derivative files (e.g., VL1AXRAT.TAB,
      VL1SURFS.TAB, and VL1NORML.TAB).  Note that the table formats
      produced by the program will be in somewhat different than
      formats for the tables in the data set.
 
      During assembly of the data set, the software was compiled
      under SunSoft FORTRAN 77 4.0 and executed under Solaris 2.5.1.
      During PDS peer review the software was compiled (but not run)
      using Fortran PowerStation 4.0 under Windows95 and on a
      workstation running SunOS 4.1.4.
 
      Bin boundaries start at 1/128 m and increase by factors of
      sqrt(2)[MOORE&KELLER1990][MOORE&KELLER1991]; results can be
      conveniently displayed on log-log plots.  The software
      included with this archive (see below) can easily be modified
      for other bin definitions.

Confidence Level Overview
    =========================
      Compilation of maps of surface materials based on images
      from stationary cameras on landed spacecraft is limited
      primarily by obscuration of the surface.  First, sides of
      large rocks may be hidden from the field of view of cameras.
      Second, areas that contain small rocks may be hidden by
      large rocks, by surfaces that slope away from the cameras,
      and by spacecraft parts.  Third, many small rocks in the
      far field simply cannot be mapped because of the decrease
      in camera resolution with increasing distance and the
      overwhelming number of rocks.  These problems become more
      severe with increasing distance.  Hence, only rocks larger
      than about 0.03 to 0.05 m could be mapped in the far field,
      and the maps were confined to areas roughly 9 m by 15 m.
      Areas behind very large rocks were excluded from analyses
      except where interpretation of the images suggested that
      uniform deposits of fine materials could be confidently
      inferred.
 
 
    Data Coverage and Quality
    =========================
      As mentioned above, the burial status of each rock at a
      landing site was defined to be either perched, partially
      buried, or deeply buried.  Roughly 60 percent of rocks at
      VL-1 are partially buried, with the remaining 40 percent
      evenly split between perched and deeply buried.  For each
      burial depth and sample region, the mean and standard
      deviation of the axial ratios  W/L  and  H/L  were
      calculated.  The  H/L  ratio was not calculated for deeply
      buried rocks, since only the topmost surfaces of these
      rocks were exposed.  While the horizontal dimensions of
      the buried rocks are probably under-estimates, the average
      width-to-length ratio is about 0.7, regardless of depth.
      The vertical rock dimension is the most uncertain measurement;
      even perched rocks likely have settled into the regolith
      somewhat.  On average, the height-to-length ratio is about
      0.48 for perched rocks and 0.42 for partially buried rocks
      at VL1, with a relatively high variance in each case.
      From these values, one can calculate that the vertical
      exposure of partially buried rocks is about 85 percent,
      assuming that partially buried rocks have the same average
      axial ratios and relative orientations as perched rocks.
      However, since a partially buried rock may be exposed on
      one side (allowing estimation of the vertical dimension)
      and buried on the other side, the average burial depth is
      difficult to estimate.  Both  W/L  and  H/L  remain
      approximately constant as a function of rock size.
 
      A sophisticated analysis of measurement errors was beyond the
      scope of the original research [MOORE&KELLER1990]
      [MOORE&KELLER1991] and of this archiving effort.  It would also
      have exceeded the needs of most investigators interested in
      Mars rock distributions.  To carry out such an analysis a
      photogrammetrist would measure each of 500 or so 'points' three
      to five times, arriving at a distribution of errors which is
      related to base-height ratio (or range).  From that point, one
      must consider errors in differences in ranges and then
      elevations and differences in elevation.  The interested reader
      is referred to Figure 10 in [LIEBES&SCHWARTZ1977] for estimates
      of errors as a function of range and azimuth in the Viking
      Lander image data set.
 
      Mapping and analyses also improve understanding of the types
      and amounts of materials at the Lander sites.  Of particular
      importance is the fraction of area covered by
      uniform-appearing bright fine materials.  Casual inspection
      of images and mosaics suggests that such deposits are small
      and scarce, but the fraction of area covered by these fine
      materials at VL2 is 0.298.  The fraction of area covered by
      rocks at VL2 is 0.159 -- not significantly different from the
      0.14 obtained by [MOOREETAL1979][MOOREETAL1987] or the 0.188
      obtained by [MOORE&JAKOSKY1989].  All values are in agreement
      with the rock abundance 0.20+/-0.10 obtained from IRTM data
      [CHRISTENSEN1986].