Viking Lander Rock Dataset Description Extracted from the PDS dataset catalog file provided by R.A. Simpson. Minor updates have been made. Dataset Overview ================ The imaging system on each Viking Lander consisted of two identical cameras. These cameras operated throughout the mission, returning nearly 6600 images. This dataset catalogs rocks that were identified in the images, their locations and dimensions. Derived statistical distributions for the rocks were derived and are included in the dataset. This data set includes a table giving locations and dimensions of 425 rocks (plus 2 possible outcrops) located near VL1 (file vl1rocks.csv) and a second table of 499 rocks near VL2 (file vl2rocks.csv). It also includes derivative tables showing number density and areal coverage as a function of rock diameter (vl1norml.csv and vl2norml.csv, 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 and Keller, 1990; 1991]. 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.csv; tables of rock distribution by surface type have names of the form vl*surfs.csv. 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 [Moore et al., 1987]; (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 [Liebes, 1982]; (2) Lander camera mosaics with overlaid contours [Liebes, 1982]; 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 [Binder et al., 1977], but it is possible that they could be large rocks [Sharp and Malin, 1984] 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, because 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.csv; the contributions from the different surface types are tabulated in vl*surfs.csv. Data Products ============= Two tables contain basic rock population data derived from images, maps derived from images, and other data. Tables vl1rocks.csv and vl2rocks.csv 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 [Liebes, 1982], 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 [Liebes, 1982] 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; each row is terminated with an ASCII carriage-return line-feed pair. Each table is accompanied by a detached PDS4 label that fully describes its format and content. The file vl0rocks.csv is identical to vl1rocks.csv except that the two 'outcrops' have been omitted. It is accompanied by detached PDS4 label vl0rocks.xml. The file vl1axrat.csv is a table of binned results of calculations based on vl1rocks.csv. 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.csv 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. Because 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). The file vl1axrat.csv 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 that could not be binned (e.g., the computation required height for a buried rock), the next 17 are for bins in increasing average diameter, and the last is a summary for all diameters. vl1axrat.csv is accompanied by a detached PDS4 label that fully describes both its content and format (vl1axrat.xml). The file vl1surfs.csv 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.csv table below. The file vl1surfs.csv is accompanied by a detached PDS4 label that fully describes both its content and format (vl1surfs.xml). The file vl1norml.csv 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. The file vl1norml.csv replicates the results reported earlier by Moore and Keller, [1990; 1991], with minor corrections. The file vl1norml.csv is accompanied by a detached PDS4 label that fully describes both its content and format (vl1norml.csv). Files vl2axrat.csv, vl2surfs.csv, and vl2norml.csv are the respective files for the Viking Lander 2 site. Each is accompanied by a detached PDS4 label with an extension *.xml. Files vl0axrat.csv, vl0surfs.csv, and vl0norml.csv are the respective files for the Viking Lander 1 site but with the two 'outcrops' omitted. Each is accompanied by a detached PDS4 label with an extension *.xml. Coordinate Systems ================== The photogrammetric reference points of the two cameras on each Lander were separated by 0.822 m [Liebes and Schwartz, 1977]. 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 [Liebes, 1982]: '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 [Liebes, 1982]. Rock positions are given with respect to the Local Gravity-Normal (LGN) map grid defined in [Liebes, 1982]. Rock orientations indicate the direction of the long axis of the rock and are measured clockwise from the LGN Y-axis. The above information on the Viking Lander coordinate systems is what was known when the original rock dataset was archived. For current estimates of the Viking Lander locations on Mars and their orientation and tilt, check the data archived at the PDS NAIF node in their SPICE kernels. 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 VL1 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, because 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, because 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 and Keller, 1990; 1991] 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 that 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 and Schwartz [1977] 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 Moore et al. [1979] and Moore et al. [1987] or the 0.188 obtained by Moore and Jakosky [1989]. All values are in agreement with the rock abundance 0.20+/-0.10 obtained from IRTM data [Christensen, 1986]. Differences between the PDS3 and PDS4 Datasets ============================================== Differences between the PDS3 version of the VL rock dataset and the PDS4 version are documented and discussed in the pds4_processing_notes.pdf document. The main difference is that the data file format changed slightly to conform to PDS4 standards. The PDS4 data files are formatted as delimited tables and have file extensions of *.csv. Information in PDS4 labels conform to the PDS4 Information Model. PDS4 uses XML documents for its labels and they have extensions of *.xml. The software directory from the PDS3 dataset is not included in the PDS4 dataset because PDS does not archive software. The original fortran source code and operating instructions are included in the document collection, however. The source code file treated as a document. It is intended to help explain how the derived spatial and size-frequency distribution products were computed. Bin boundaries used to generate the derived files in this dataset start at 1/128 m and increase by factors of sqrt(2) [Moore and Keller, 1990; 1991]; results can be conveniently displayed on log-log plots. The software can be ported to other languages and modified for other bin definitions. At the time of release of the PDS4 dataset the original PDS3 dataset is still available at the Geosciences Node site. References Cited ================ Binder, A.B., R.E. Arvidson, E.A. Guinness, K.L. Jones, E.C. Morris, T.A. Mutch, D.C. Pieri, and C.E. Sagan, The geology of the Viking Lander 1 site, JGR, V. 82, p. 4439-4451, 1977; doi: https://doi.org/10.1029/JS082i028p04439. Christensen, P.R., The spatial distribution of rocks on Mars, Icarus, V. 68, p. 217-238, 1986; doi: https://doi.org/10.1016/0019-1035(86)90020-5. Liebes, S., Viking Lander Atlas of Mars, NASA Contractor Report 3568, 1982. Liebes, S., and A.A. Schwartz, Viking 1975 Mars lander interactive computerized video stereophotogrammetry, JGR, V. 82, p. 4421-4429, 1977; doi: https://doi.org/10.1029/JS082i028p04421. Moore, H.J., and B.M. Jakosky, Viking landing sites, remote sensing observations, and physical properties of Martian surface materials, Icarus, V. 81, p. 164-184, 1989; doi: https://doi.org/10.1016/0019-1035(89)90132-2. Moore, H.J., and J.M. Keller, Surface-material maps of the Viking landing sites on Mars, Reports Planet. Geol. Geophysics Program, NASA TM-4210, 533-535, 1990. Moore, H.J., and J.M. Keller, Surface-material maps of the Viking landing sites on Mars, Reports Planet. Geol. Geophysics Program, NASA TM-4300, 160-162, 1991. Moore, H.J., C.R. Spitzer, K.Z. Bradford, P.M. Cates, R.E. Hutton, and R.W. Shorthill, Sample fields of the Viking landers, physical properties, and aeolian processes, JGR, V. 84, p. 8365-8377, 1979. Moore, H.J., R.E. Hutton, G.D. Clow, and C.R. Spitzer, Physical properties of the surface materials at the Viking landings sites on Mars, USGS Professional Paper 1389, 1987. Sharp, R.P., and M.C. Malin, Surface geology from Viking landers on Mars: a second look, GSA Bull., V. 95, p. 1398-1412, 1984.