CCSD3ZF0000100000001NJPL3IFOPDS200000001 = SFDU_LABEL RECORD_TYPE = STREAM DATASET_COLLECTION_NAME = Pre-Magellan Radar and Gravity Data INSTRUMENT_HOST_NAME = {"ARECIBO OBSERVATORY", "AIRSAR", "GOLDSTONE SOLAR SYSTEM RADAR", "HAYSTACK OBSERVATORY", "PIONEER VENUS", "VIKING ORBITER 2"} TARGET_NAME = {EARTH, MOON, MARS, MERCURY, VENUS} FILE_TITLE = "Pre-Magellan Radar and Gravity Data" END Archive of Pre-Magellan Radar and Gravity Data Raymond Arvidson, Edward Guinness, Susan Slavney Planetary Data System Geosciences Node Department of Earth and Planetary Sciences McDonnell Center for the Space Sciences Washington University St. Louis, Missouri David Acevedo, Jason Hyon, Michael Martin, R. S. Saunders, T. W. Thompson Jet Propulsion Laboratory Pasadena, California With Contributions From Bruce Bills, Lunar and Planetary Institute; Donald B. Campbell, Cornell University; Pamela Clark, Raymond Jurgens, and William L. Sjogren, Jet Propulsion Laboratory; Peter Ford, Massachusetts Institute of Technology; Jeffrey Plaut, Washington University; Stanley Zisk, University of Hawaii July 12, 1990 TABLE OF CONTENTS 1. Introduction .................................................... 2 2. Disk Directory Structure ........................................ 3 3. Data Set Labels ................................................. 5 4. Pre-Magellan Radar and Gravity Data Set Descriptions ............ 7 4.1 AIRSAR ..................................................... 8 4.2 Earth-based Mars ........................................... 9 4.2.1 Goldstone Altimetry ................................. 9 4.2.2 Arecibo and Goldstone Model Radar Unit Map .......... 9 4.3 Earth-based Mercury Altimetry .............................. 10 4.4 Earth-based Lunar .......................................... 10 4.4.1 Arecibo 12.6 and 70 cm Radar Backscatter ............ 10 4.4.2 Haystack Radar Backscatter .......................... 13 4.5 Earth-based Venus .......................................... 17 4.5.1 Arecibo Radar Backscatter ........................... 17 4.5.2 Goldstone Radar Backscatter and Altimetry ........... 18 4.6 Pioneer-Venus Radar ........................................ 18 4.7 Pioneer-Venus and Viking Gravity ........................... 20 4.7.1 Pioneer-Venus LOS Gravity Data ...................... 20 4.7.2 Viking LOS Gravity Data ............................. 21 5. Data Set Index Files ............................................ 21 6. References ..................................................... 22 Appendix A - CD-ROM Volume, Directory and File Structures ........... 25 A.1 Volume and Directory Structures ............................ 25 A.2 File Structure ............................................. 25 A.2.1 Fixed-Length Files .................................. 25 A.2.2 Stream Files ........................................ 25 A.2.3 Extended Attribute Records .......................... 26 Appendix B - Syntactic Rules of Keyword Assignment Statements ....... 27 B.1 Integer Numbers ............................................ 27 B.2 Real Numbers ............................................... 27 B.3 Dates and Times ............................................ 28 B.4 Literal Values ............................................. 28 B.5 Text Character Strings ..................................... 28 Appendix C - Keyword Definitions .................................... 29 Appendix D - Venus Coordinate Systems ............................... 34 D.1 Arecibo Radar Images ....................................... 34 D.2 Goldstone Radar Images ..................................... 34 D.3 Pioneer-Venus Radar Data ................................... 35 Appendix E - Map Projections ........................................ 37 E.1 Simple Cylindrical Projection .............................. 37 E.2 Mercator Projection ........................................ 38 E.3 Lambert Conformal Projection ............................... 38 ii Pre-Magellan Radar and Gravity Data July 12, 1990 1. Introduction The purpose of this file (VOLINFO.TXT) is to provide: (a) descriptions of the data sets on the Pre-Magellan Radar and Gravity Data CD-ROM, including references that provide detailed descriptions of acquisition and processing of the data; (b) a discussion of the directory structure used in organizing the data sets as files, associated labels and index tables, and (c) background information on the standards used in generating the data files, associated labels, and the CD-ROM structure proper. The data included on this CD-ROM were chosen to provide the user with a range of derived data sets that will be directly relevant to analyses of Magellan radar and gravity data of Venus. Thus, Earth- based radar data of Venus, Mercury, Moon, and Mars are on the CD-ROM, along with various data sets derived from the Pioneer-Venus Orbiter Radar Mapper Experiment. A number of radar images are also included of the Pisgah volcanic field and Kelso dunes, Mojave Desert, acquired at varying frequencies, incidence angles, and polarization states by the Jet Propulsion Laboratory's AIRSAR. Finally, line of sight acceleration data derived from tracking the Pioneer Venus Orbiter and the Viking Orbiter 2 spacecraft are also on this CD-ROM. Release of the Pre-Magellan radar and gravity data set collection on a CD-ROM is a way of ensuring that the data are distributed widely and in a documented fashion. The generation of the CD-ROM was done jointly by the Planetary Data System and the Magellan Project. The effort was led by the Geosciences Node at Washington University, with significant help from other components of the PDS and the science community. The data set collection has also been formally ingested by the PDS, including peer review of the data and documentation, to ensure that the archive is of the highest quality. The metadata describing the data set collection and individual sets are also included in the PDS Central Catalog. The review process and documentation are crucial; without them the utility of derived or processed data in the planetary community would be greatly compromised. The peer review committee included Donald B. Campbell and Steven Squyres, Cornell University; Eric Eliason, U.S. Geological Survey, Flagstaff, Arizona; Paul Fisher, Brown University; Peter Ford, Massachusetts Institute of Technology; Robert Grimm, Southern Methodist University; Jeffrey Plaut, Washington University; R. Stephen Saunders and Ellen Stofan, Jet Propulsion Laboratory; and Stanley Zisk, University of Hawaii. Sections 2, 3 and 5 of this document describe the organization of the CD-ROM and the structure of the data set files, associated labels, and tables that provide metadata about each of the data sets. Section 4 describes each data set on the CD-ROM. Appendices detail the ISO standards used on the CD-ROM, rules for label keyword assignments, and definitions of keywords. The definitions are based on the PDS Data Dictionary. Finally, data files on this CD-ROM have detached PDS labels, and some also have attached VICAR2 labels. The reason is that Magellan radar image mosaic data will be released on CD-ROMs with 2 Pre-Magellan Radar and Gravity Data July 12, 1990 attached VICAR2 labels and detached PDS labels. Thus, the Pre-Magellan CD-ROM will utilize the same structure and will allow users with either PDS or VICAR2 label readers to efficiently access labels. Latitude and longitude coordinates used on this CD-ROM are consistent with the IAU standards in that Venus, which rotates in a retrograde sense, has longitudes that go from 0 to 360 degrees east, whereas prograde objects are 0 to 360 degrees west. Because of tradition, longitudes for the Moon do not always conform to this definition. On this CD-ROM the Arecibo lunar data have west-positive longitudes, and the Haystack data have east-positive longitudes. Latitudes are positive for northern latitudes and negative for southern latitudes. In Appendix C we define minimum and maximum longitudes based on the PDS data dictionary definitions, and warn the reader to beware of subtleties in defining longitudes for search purposes. 2. Disk Directory Structure The volume and directory structure of this CD-ROM conforms to the level-1 standard specified by the International Standards Organization (ISO). The ISO standard was used so that the disks can be accessed on a wide variety of computer systems. Information on the ISO CD-ROM standard is provided in Appendix A of this document. The top level directory of this CD-ROM contains three text files. The first is a brief description of the structure and contents of the disk called AAREADME.TXT. The second is a file called TEMPLATE.TXT, which contains the PDS central node catalog information that describes the data sets on this disk. The third file is called VOLDESC.SFD, which is meant to be read via computer and which contains a broad description of the structure and contents of the disk, written using a structured Standard Data Format Unit convention. All other files on the disk are contained in subdirectories as discussed below. The DOCUMENT directory contains the file you are reading now, i.e., VOLINFO.TXT, and VICAR2.TXT, a description of the standard VICAR2 labels that are attached to some of the image files on the Pre-Magellan CD-ROM. The directories that contain files and detached PDS labels are organized by a combination of observatory or spacecraft, target body, and data type. The AIRSAR directory contains radar images acquired by the JPL airborne polarimetric SAR instrument. The EBMARS directory contains the Goldstone altimetry data and an image that depicts radar unit maps used to model Goldstone and Arecibo observations of Mars. The EBMERC directory contains Goldstone altimetry data for Mercury. The EBMOON directory contains both Haystack and Arecibo lunar radar images, where the files from the two observatories are under separate subdirectories. Because of their large number, the Haystack images are further divided into subdirectories based on the zenith-azimuth coordinate system (see section 4.4.2). The EBVENUS directory contains subdirectories for Arecibo and Goldstone observations of Venus. The Goldstone images are further divided into subdirectories based on the 3 Pre-Magellan Radar and Gravity Data July 12, 1990 year in which the images were acquired. The PVVENUS directory contains separate subdirectories for the Pioneer Venus Radar Mapper Experiment and the Radio Experiment data sets. Finally, the VIKGRAV directory contains line of sight acceleration data from the Viking Orbiter 2 Radio Experiment observations. The following approach was used to name files in ways that allow the user to infer the type of data in a reasonably straightforward manner, while maintaining the 8 character limit for file names. The convention uses codes for the spacecraft or ground-based observatory that acquired the data, the target body, a 3 character ID number, and a data type, in the order presented. The codes are shown below, followed by several examples: Spacecraft/ Observatory Target I.D. Data Type A=Arecibo ETH=Earth nnn A=Altimetry D=DC-8 AIRSAR LUN=Moon D=Circular polarization transmit; same sense receive G=Goldstone MAR-Mars F=Fresnel reflection coefficient H=Haystack MER=Mercury H=Horizontal transmit, P=Pioneer-Venus VEN=Venus horizontal receive cross sections V=Viking L=Line of sight accelerations N=Ancillary data P=Circular polarization transmit; opposite sense receive R=Quasispecular roughness estimate S=Time series data set (for Pioneer Venus Radar Mapper) T=Temperature U=Unit map (Mars radar) V=Horizontal transmit, vertical receive polarization Examples: a. Viking Mars Line of Sight Accelerations, File One = VMAR001L.DAT b. Goldstone Mercury Altimetry, File twenty-eight = GMER028A.DAT c. DC-8 SAR Earth SAR HV image, file two = DETH002V.DAT 4 Pre-Magellan Radar and Gravity Data July 12, 1990 3. Data Set Labels The Pre-Magellan data set collection on this CD-ROM uses detached PDS labels to describe and point to data files. In some cases the image files have embedded VICAR2 labels. The reader is referred to the file VICAR2.TXT in the DOCUMENT directory and to LaVoie et al. (1987) for discussion of VICAR2 labels. The remainder of this section describes the detached PDS labels. The PDS label contains descriptive information about the data file and objects within the file. The label consists of keyword statements that conform to the Object Description Language (ODL) developed by the PDS project. There are three types of ODL statements within a label: structural statements, keyword assignment statements, and pointer statements. Structural statements provide a shell around keyword assignment statements to delineate which data object the assignment statements are describing. The structural statements are: 1) OBJECT = object_name 2) END_OBJECT 3) END The OBJECT statement begins the description of a particular data object and the END_OBJECT statement signals the end of the object's description. All keyword assignment statements between an OBJECT and its corresponding END_OBJECT statement describe the particular object named in the OBJECT statement. The END statement terminates a label. It must appear as a single statement that contains only the word END. A keyword assignment statement contains the name of an attribute and the value of that attribute. Keyword assignment statements are described in more detail in Appendix B of this document. These statements have the following format: name = value Values of keyword assignment statements can be numeric values, literals, or text strings. Pointer statements are a special class of keyword assignment statements. These pointers are expressed in the ODL using the following notation: ^object_name = location If the object is in the same file as the label, the location of the object is given as an integer representing the starting record number of the object, measured from the beginning of the file. The first label record in a file is record 1. Pointers are useful for describing the location of individual components of a data object. Pointer statements 5 Pre-Magellan Radar and Gravity Data July 12, 1990 are also used for pointing to data or information stored in separate files. An example of a pointer to information stored in a separate file is shown below: ^DESCRIPTION = "logical_file_name" The value of "logical_file_name" is the name of the file containing the description. An example of a pointer to a record within a file is: ^IMAGE = ("logical_file_name",2) This indicates that image data begins at record 2 in file "logical_file_name". Each keyword assignment is stored as a single variable-length record. An example of a label is shown below. Appendix C of this document provides a detailed description of each keyword found in the labels. Example of a detached PDS image label CCSD3ZF0000100000001NJPL3IF0PDS200000001 = SFDU_LABEL /* Detached PDS label for a Goldstone Venus Radar */ /* backscatter cross-section image */ RECORD_TYPE = FIXED_LENGTH RECORD_BYTES = 290 FILE_RECORDS = 292 /* Pointers to image file and objects within it */ ^FOREIGN_LABEL = ("GVEN001P.IMG",1) ^IMAGE = ("GVEN001P.IMG",3) /* Image descriptive information */ DATA_SET_ID = "GSSR-V-RTLS-5-12.6-9CM-V1.0" TARGET_NAME = VENUS IMAGE_TIME = 1972-06-20 EARTH_BASE_NAME = "GOLDSTONE SOLAR SYSTEM RADAR" EARTH_BASE_INSTITUTION_NAME = "JET PROPULSION LABORATORY" DATA_SET_PARAMETER_NAME = "BACKSCATTER CROSS SECTION" PRODUCER_FULL_NAME = "RAYMOND F. JURGENS" MAP_PROJECTION_TYPE = MERCATOR MAP_SCALE = 20.00 MAXIMUM_LATITUDE = 9.05 MINIMUM_LATITUDE = -5.41 MAXIMUM_LONGITUDE = 332.61 MINIMUM_LONGITUDE = 318.11 SUB_EARTH_LATITUDE = 1.83 SUB_EARTH_LONGITUDE = 325.36 RECEIVED_POLARIZATION ="OPPOSITE SENSE CIRCULAR" WAVELENGTH = 12.6 NOTE = "Scaled echo strength image of Venus acquired by the Goldstone Solar System Radar. Data are scaled to fit within an 8 bit unsigned byte value (pre-1977 data are scaled 6 Pre-Magellan Radar and Gravity Data July 12, 1990 to fit a 6 bit unsigned byte). Pre-1977 data are normalized relative to the square root of the scattering properties for an annulus about the sub-Earth point that includes the data. Later data are normalized by the average for the annulus. Longitudes in the PDS label are in IAU 1985 coordinates. Note that VICAR2 labels have longitudes that are 3.66 degrees smaller than the IAU 1985 values. For reference, see Jurgens, R. F., R. M. Goldstein, H. R. Rumsey and R. R. Green, Images of Venus by three-station radar interferometry - 1977 results, J. Geophys. Res., 85, 8282- 8294, 1980." /* Object descriptions */ OBJECT = FOREIGN_LABEL TYPE = VICAR2 RECORDS = 2 BYTES = 580 ^DESCRIPTION = "VICAR2.TXT" END_OBJECT = FOREIGN_LABEL OBJECT = IMAGE LINES = 290 LINE_SAMPLES = 290 SAMPLE_BITS = 8 SAMPLE_BIT_MASK = 2#00111111# SAMPLE_TYPE = UNSIGNED_INTEGER END_OBJECT = IMAGE END 4. Pre-Magellan Radar and Gravity Data Set Descriptions The data sets on the Pre-Magellan Radar and Gravity CD-ROM consist of images and tabular data. The following data sets are in the form of tables: Goldstone Mars altimetry, Goldstone Mercury altimetry, Pioneer Venus radar altimetry/radiometry, Pioneer Venus line-of-sight gravity, and Viking line-of-sight gravity. The remaining data sets are images in either the VICAR2 file format, described by the file VICAR2.TXT in the DOCUMENT directory, or raster format. A raster format file contains one record for each line in the image, with no embedded label information. Table 4.1 lists each data set, its format, the number of files, and whether it has an index table. The images and data tables are stored on the CD-ROM in the same format in which they were delivered by the various data producers. This is the reason some images have embedded VICAR2 labels and others do not. The data sets were not processed or otherwise altered in any way in compiling this data collection. However, the index tables in the INDEX directory were generated by personnel at the Geosciences Node, in order to provide a convenient summary of the data sets that contain a large number of files. 7 Pre-Magellan Radar and Gravity Data July 12, 1990 Table 4.1 Data Sets on the Pre-Magellan CD-ROM Data set File Number Index format of files table ________________________________________________________________________ AIRSAR Raster image 24 yes Goldstone Mars Altimetry Table 1 no Mars Radar Model Unit Map VICAR2 image 1 no Goldstone Mercury Altimetry Table 28 yes Arecibo 12.6 cm Moon Radar Raster image 4 no Arecibo 70 cm Moon Radar VICAR2 image 4 no Arecibo 70 cm Moon Radar Mosaic VICAR2 image 2 no Haystack Moon Radar Raster image 382 yes Arecibo Venus Radar Raster image 26 yes Goldstone Venus Radar VICAR2 image 98 yes Pioneer Venus Radar Maps VICAR2 image 5 no Pioneer Venus Altimetry/Radiometry Table 1 no Pioneer Venus SAR VICAR2 image 1 no Pioneer Venus LOS Gravity Table 2 no Viking Orbiter LOS Gravity Table 2 no ________________________________________________________________________ 4.1 AIRSAR AIRSAR is the Jet Propulsion Laboratory's airborne polarimetric SAR that operates at C (5.66 cm), L (23.98 cm), and P (68.13 cm) band wavelengths in a polarimetric mode (Zebker and van Zyl, 1987). AIRSAR acquires data that can be processed to backscatter image formats with range and azimuth resolutions of approximately 20 m and a cross track image width of approximately 10 km. The pixel values are in units of backscatter cross section, i.e., cross section/unit area. AIRSAR flew on NASA's DC-8 in June 1988 and acquired data at multiple incidence angles and azimuths over selected geological targets in the southern Mojave Desert of California (Arvidson et al., in preparation). A number of corner reflectors were placed in the target areas to provide a means of calibrating the radar data (van Zyl, 1990). As part of his Ph.D. thesis at Washington University, Jeffrey J. Plaut used the corner reflector signatures to generate images in proportion to radar backscatter cross section for the Pisgah volcanic field, the adjacent Lavic Lake Playa, and for the Kelso Dune Field. The reader is referred to Greeley et al. (1988) for a geological discussion of the Pisgah site and to Sharp (1966) for the Kelso Dune Field. The AIRSAR data on this CD-ROM consist of radar images at C, L, and P band frequencies for the Pisgah-Lavic and Kelso sites, in both HH (horizontal (linear) wave transmit, horizontal receive) and HV (horizontal transmit, vertical receive) polarizations. Further, three incidence angle views are included for the Pisgah-Lavic site. Thus, there are 6 Kelso scenes and 18 Pisgah-Lavic scenes for a total of 24 AIRSAR backscatter images. The intent is to provide radar backscatter images for a variety of system 8 Pre-Magellan Radar and Gravity Data July 12, 1990 and observation parameters over sites that can be visited and that range from rough aa flows, mantled pahoehoe flows, alluvial fans, relatively smooth playa surfaces, to a complex dune field. Data are expressed as backscatter cross section / unit area. The images are in raster format (one image line per record, with no embedded labels). Each image has 750 lines and 1024 samples per line. Samples are 32-bit real numbers. 4.2 Earth-based Mars 4.2.1 Goldstone Altimetry This data set consists of data taken by the Goldstone Solar System Radar at S-band (2.388 GHz, 12.6 cm wavelength before 1977; 2.23 GHz, 12.9 cm wavelength during and after 1977) during the 1971 through 1982 perihelic oppositions of Mars (Downs et al., 1975). Observations were conducted approximately every 3-5 days for the duration of the experiment. During each observation, the subradar point (the point on the planet closest to Earth) traced out an arc of almost constant latitude. This arc is referred to as the scan or the track. The Goldstone 1971-73 data set contains a total of 68 scans. One observation period lasted usually 8 hours or less. Since the spin rate of Mars is approximately 15 degrees per hour, each single scan spans, on the average, about 100 degrees in longitude. The coverage is not always continuous within a scan. The Goldstone Altimetry data set is in tabular format and consists of latitude, longitude, planetary radius, and altitude (in meters) relative to a 6 mb reference surface. Each altimetric observation covers an area of about 0.16 degrees in longitude and approximately 1.30 degrees in latitude. The entire set contains 46,139 altimetric values, all within the band of latitudes from approximately 23 degrees north to -23 degrees south. The altitudes in the data set are subject to two types of error: (1) Errors in the measurements of the range to the planet. These range errors are less than 100 meters on the average. (2) Errors due to the differences between the assumed shape of the reference figure and the actual shape of the planet. This error will affect global topography but not local topography. The peak-to-peak magnitude of this error is estimated to be 1800 meters. See Downs et al. (1975) for further details. 4.2.2 Arecibo and Goldstone Model Radar Unit Map Thompson and Moore (1989) have produced a model for 12.6 cm Arecibo and 12.9 cm Goldstone depolarized radar echo power of Mars that (1) matches the observed variation of total radar backscatter cross section with longitude for the Goldstone 1986 observations and (2) produces model spectra that have the broad features of spectra published by Harmon et al. (1982, 1985) for the Arecibo 1980-1982 observations. The depolarized data are same sense circular polarization observations, as described in Harmon et al. (1982, 1985). The model assumes that different geologic units on Mars backscatter in a uniformly bright 9 Pre-Magellan Radar and Gravity Data July 12, 1990 manner, where echo power is modeled as varying by the cosine of the radar incidence angle: echo strength = A * cosine (incidence angle), where A varies across the planet. Different geologic units of the model have different values of A. The model assigns depolarized echo power on a degree-by-degree basis in latitude and longitude. Fits to the observations were done with a trial-and-error method. See Thompson and Moore (1989) for more details. This data set consists of a single VICAR2 image, with 181 lines and 361 samples per line. Samples are 32- bit integers, least significant byte first. 4.3 Earth-based Mercury Altimetry This data set consists of tables of altimetric profiles acquired by the 12.6 cm Goldstone Solar System Radar in 1972, 1973, and 1974. Data are given in the form of latitude, longitude and planetary radius. Delay-doppler techniques were used to derive the altimetry data (Clark et al., 1988; Jurgens, 1982). Latitude resolution of the data is approximately 65 km, longitude resolution varies from 10 to 20 km, and the altitude resolution is approximately 150 m, degrading away from the subradar point (Clark et al., 1988). The reader is referred to Jurgens (1982) for details on observations and processing. 4.4 Earth-based Lunar 4.4.1 Arecibo 12.6 and 70 cm Radar Backscatter The Arecibo lunar data sets are of three types: (a) high resolution images acquired at 12.6 cm in 1986-1987; (b) a mosaic generated from 70 cm (430 MHz) data acquired in 1981-1984; and (c) high- resolution 70 cm data acquired in 1986-1987, displayed in delay-Doppler coordinates. The 12.6 cm data consist of backscatter images for four small areas of the Moon. The images are in raster format (one image line per record, with no embedded labels). Image samples are 16-bit unsigned integers, most significant byte first. The Copernicus and Mare Imbrium (Carlini) images are the average of 11 radar looks. The Gruithuisen Domes and Alpine Valley images are the average of 4 looks. Latitude- longitude coordinates given in the label are accurate to the nearest degree, and a Mercator projection is used. Longitudes are west- positive, ranging from 0 to 360 degrees. The data have been divided by estimates of the theoretical shape of the antenna beam, but not corrected for radar scattering laws. Data values are given as scaled backscatter cross section; i.e., data have been scaled to occupy the dynamic range of the output values. The incidence angle variation across the scenes is about 6 degrees and average incidence angles vary from 29 deg. (Copernicus), 43 deg. (Carlini), 55 deg. (Alpine Valley), to 58 deg. (Gruithuisen Domes). The reader should contact Donald B. Campbell, Cornell University, for more details. The mosaic generated from 70 cm 1981-84 data has a resolution ranging from 2 to 5 kilometers. Data are presented for opposite sense 10 Pre-Magellan Radar and Gravity Data July 12, 1990 and like sense circular receive polarizations. Thus, there are two image files, both with embedded VICAR2 labels. Image samples are stored as unsigned bytes. The polarized data were normalized using the 69 cm table of Hagfors (1967, 1970), while the depolarized data were corrected for a uniformly bright (i.e., cosine) scattering law. Data consist of scaled echo power in a square array with a 0.1 degree spacing. Data normalization consisted of corrections for antenna beam, scattering area, and scattering law. These data cover the earth-side hemisphere and are a mosaic of some 20 or more separate observations. The reader is referred to Thompson (1987) for more details. The 70 cm 1986-87 data are presented as images with pixel values in proportion to echo power, and in delay-Doppler coordinates where echoes are isolated in both range (time delay) and in Doppler frequency. The observational parameters associated with this data set are given in Table 4.2. Some general characteristics of the 70 cm radar at the Arecibo Observatory as used for these observations are given in Table 4.3. General descriptions of the delay-Doppler technique as it is applied to lunar radar observations is given by Pettengill et al. (1974), Thompson and Zisk (1972) and by Thompson (1987). These are unsigned byte images in VICAR2 format. The 1986/87 70 cm Arecibo observations encountered a number of experimental difficulties. Some of the data, particularly in 1986, had time base jumps that have not been removed. The 1986 observations used the 300 meter telescope for both transmission and reception and thus have high signal-to-noise. The 1987 observations emphasized dual polarization observations where the 300 meter antenna was used only for transmission, and echoes were received at a smaller antenna located some 11.6 km from the main antenna. The 1987 data thus generally have poor signal-to-noise. Some eight beam positions were attempted in 1986 and 1987, but only three have yielded good data. These three had antenna beams centered on Delisle in central Imbrium, on crater Copernicus, and on crater Tycho in the southern highlands. The Delisle and Copernicus data sets are polarized (opposite-sense circular) only; the Tycho data set has simultaneous polarized and depolarized (same-sense circular) echoes. The 1986/87 70 cm data set consists of scaled "raw" data, i.e. echo power as sampled in delay (range) and Doppler frequency. The data have not been "corrected" for scattering laws, antenna beam, or scattering area. Another data reduction factor concerns the number of "looks". All data have 4096 frequency bins. The Copernicus and Tycho data were created from data records that had 8192 consecutive time samples that were Fourier transformed to 8192 frequency bins. Pairs of frequency bins were then averaged, producing "two-look" data. In contrast, the Delisle data set had only 4096 time samples. There was no averaging, and thus the data are "single-look" data. The spectra contain a large amount of self noise that tends to be "smoothed" out in the data displays. This self noise would be clearly evident in examination of individual pixels. 11 Pre-Magellan Radar and Gravity Data July 12, 1990 The reader should contact T. W. Thompson, Jet Propulsion Laboratory, for more details. Table 4.2 1986/87 Arecibo 70 cm Moon Observation Parameters _______________________________________________________________________ Site Delisle Copernicus Tycho Date 03 July 86 23 May 87 30 May 87 _______________________________________________________________________ Beam Center Longitude 35-30 W 21-00 W 11-00 W Beam Center Latitude 29-50 N 12-00 N 43-00 S Delay Resolution 4 micros. 2 micros. 4 micros. Beam Center Resolution 0.8 km 0.6 km 1.0 km Frequency Resolution 0.0024 Hz 0.0024 Hz 0.0024 Hz Limb-Limb Doppler Spread 13.4 Hz 12.9 Hz 12.8 Hz Beam Center Resolution 0.8 km 0.6 km 0.6 km Sub-Radar Longitude 2.1 deg 5.5 deg -0.3 deg Sub-Radar Latitude -3.7 deg -0.4 deg -6.7 deg Transmit Antenna Main Main Main Receive Antenna Main Main Aux. (300 m.) (300 m.) (300 m.) Polarization OC (Pol) OC (Pol) OC (Pol) SC (Dep) Number of Looks 1 2 2 Range Bins 1600 2000 1500 Frequency Bins 4096 4096 4096 _______________________________________________________________________ 12 Pre-Magellan Radar and Gravity Data July 12, 1990 Table 4.3 Observation Parameters _______________________________________________________________________ Site Latitude 18 deg 21 min North Site Longitude 60 deg 45 min West Transmitter Frequency 430 MHz Transmitter Power 1.5 Mwatt Wavelength 69.8 cm Antenna Beam Width 9 arc-min _______________________________________________________________________ 4.4.2 Haystack Radar Backscatter The purpose of the Haystack radar scaled echo power images was to obtain highly resolved maps of the surface scattering characteristics at a wavelength of 3.8 cm from the entire earthside hemisphere of the Moon. Both polarized and depolarized images, using circular polarization, are included in the data set. While the radar surface resolution of about 2 km is only slightly worse than the best obtainable at optical wavelengths with Earth-based telescopes, the scattering is associated with very different scales of surface structure as compared to the optical data. The radar resolution was obtained with coherent-pulse analysis (delay-doppler mapping) as described in Pettengill et al. (1974), using the Haystack radar system. Detailed descriptions of data acquisition, reduction, and analysis are found in Zisk et al. (1974). The parameters used in the observations are listed in Table 4.4. In order to ensure efficient coverage of the near side of the Moon, a system of sub-areas was set up whose boundaries were roughly parallel to the isopleths of the delay-doppler coordinates. The earthside hemisphere was divided into nine concentric ZAC (Zenith-Azimuthal Coordinate) zones, each 10 degrees across, and centered on the selenographic origin. A tenth zone accommodated areas that are occasionally in view as a result of libration. Each zone was further subdivided in azimuth to produce ZAC-areas covering roughly equal regions of the Moon's surface. The data set consists of 382 files covering each of the ZACs defined in Zisk et al. (1974). The files are images in raster format (one image line per record, with no embedded labels). Image samples are stored as unsigned bytes. Longitude values given in the image labels are east-positive, ranging from 0 to 360. The image data are formatted as six valid bits (hexadecimal mask 3F), with logarithmic scaling. The original raw data were converted by this equation: DN = 2 + 20 * log(power/250.0) 13 Pre-Magellan Radar and Gravity Data July 12, 1990 This means that each increment of +1 in DN value represents a 5% increase in calibrated echo power. To recover relative power from the image data, the following formula may be used. For DN = 0: Normalized power = 0.0 (== no data). For DN between 1 and 63: Normalized power = 250 * (10.0 ** ( (DN-2) / 20 ) ) During the data processing, the raw measured echo power was divided by (1) a planet-wide scattering law, (2) the antenna beam pattern, (3) the projected illuminated area of each pixel, and (4) the measured percentage deviation in transmitted power. A few images may have residual sloping flat-fields due to minor undetected atmospheric effects or physical mis-pointing of the antenna. During each observation, the radar receiver was adjusted continuously to follow the predicted values of delay and doppler shift for the center of the mapping unit under observation. This center point then became the reference for the remainder of the map. Any time- varying error in the prediction ephemerides would cause blurring of the map, whereas an error that remained constant during the 10 minute observation would only displace the map in the delay or doppler directions. The range and range-rate of the center of mass of the Moon were predicted as outlined in Pettengill, et al. (1974), from the Nautical Almanac (i.e., Brown's theory) and from Brown's theory as corrected by Eckert. No attempt was made in the reduction of the maps themselves to compensate for the lunar topography; in all cases, a radius of 1738.0 km was assumed for the location of the backscattering element. The total discrepancy in range between predictions and observations was less than 6 km, and all but 0.5 to 1.0 km later proved to be the result of a combination of small errors in the working ephemeris (as compared to currently best-known values), and topography near the subradar point. The final backscatter values appear to have an internal consistency of better than 20% over most of the observed lunar surface, but observations near the lunar equator occasionally appear to be miscalibrated and may be low by factors of as much as 3 or 4. Since the results are lower than expected, anomalous atmospheric attenuation may be a possible cause, since most of the equatorial areas were observed at low elevation angles to obtain a proper delay-doppler geometry. The reader is referred to Zisk et al. (1974) for more details. 14 Pre-Magellan Radar and Gravity Data July 12, 1990 Table 4.4 Radar parameters for lunar observations (From Zisk et al. 1974) ________________________________________________________________________ Wavelength (frequency) 3.83 cm (7840.0 GHz) Polarization Transmitted Right circular Received Left (polarized) and right (depolarized) circular, simultaneously Transmitter: Power 200 kW (peak) Pulse length 3,4,5,7,10, or 13 microseconds (selected for that range resolution corresponding to 2 km on the surface) Interpulse period 25-90 milliseconds (adjusted for that frequency resolution corresponding to 2 km on the surface) Frequency standard utilization Hydrogen maser or rubidium standard. All transmitter, receiver, and timing functions. Precision Better than a part in 10**12 Receiver: System temperature Polarized 45K (sky); 180K (Moon) Depolarized 75K (sky); 210K (Moon) Operating Frequency 7840.0 GHz+Doppler offset to center of mapped area Setting accuracy plus or minus 0.01 Hz Resetting interval 10 milliseconds Antenna: Gain 66 dB Effective area 460 m^2 Beamwidth (one way) 4.4 arc min (full width at half power (two way) 3.1 arc min (full width at half power Pointing plus or minus 20 arc sec Real-time processing: 15 Pre-Magellan Radar and Gravity Data July 12, 1990 Computer Control Data Corp. Model 3300 Samples per received pulse 190 Calibration samples per interpulse 26 (20 usable) Sample interval 3-13 microseconds (to match transmitter pulsewidth) Post-processing: Number of pulses coherently analyzed 256 Duration of Coherent Integration Period (CIP) 6 to 26 s (=256 X interpulse period) Number of CIP's (looks) per map 85 plus or minus 5 Fluctuation of backscatter values 11% rms Normalization parameters: Background noise level per received pulse As measured at 1.0 ms prior to first lunar echo Assumed scattering law Depolarized: Cross section varies with cosine (incidence angle) Polarized: experimentally determined Area of resolution cell Range-Doppler coordinates Rectangular = pulsewidth * frequency resolution Lunar surface coordinates Same projected onto spherical lunar surface Additional corrections Transmitted power; Earth-Moon distance; Background level; Receiver gain Mapping parameters Observed coordinates Delay-doppler Projected surface 1738.0 km sphere Final map projections Mercator, Lambert Conformal Error in absolute locations plus or minus 4 km (rms) plus or minus 20 km (maximum) 16 Pre-Magellan Radar and Gravity Data July 12, 1990 4.5 Earth-based Venus 4.5.1 Arecibo Radar Backscatter The Arecibo 12.6 cm radar data set for Venus consists of scaled radar backscatter cross section images generated from data obtained in 1983 and 1988. The images are in raster format (one image line per record, with no embedded labels). The original images are in 16-bit, unsigned integer, most-significant-byte-first format. Since the volume of the entire set of 16-bit images would have exceeded the capacity of the CD-ROM, some of the images have been scaled to 8-bit versions. Specifically, the entire set of 1988 images are in the scaled 8-bit format, while all the 1983 images are in the original 16-bit format. In addition, a subset of the 1988 data is also given in 16-bit format. Both the 16-bit and the 8-bit images were provided by Don Campbell, Cornell University. The 1983 data (acquired in August) cover parts of the northern hemisphere of Venus and consist of 4 files. The first is a mosaic in a Mercator projection with a pixel spacing of 0.12 degrees in longitude. A grid spaced at 10 degrees in both latitude and longitude is embedded in the data. The remaining three files are sections of the mosaic. The mosaic covers 18 to 80 degrees north latitude and 250 (leftmost) to 40 (rightmost) degrees east longitude. The three sections of the 1983 mosaic cover the following areas: (a) 18 to 70 north latitude, 320 to 40 east longitude; 0.02 degrees long pixel spacing; (b) 69 to 80 north latitude, 267 to 21 east longitude, 0.04 degrees long pixel spacing; (c) 18 to 70 north latitude, 250 to 331 east longitude, 0.02 degrees longitude pixel spacing. The data correspond to incidence angle ranges of 44 to 70 degrees, relative to the sub-Earth point. Polarization is circular, with opposite sense receive, so the data consist of polarized returns. For the mosaic, a theoretical antenna beam pattern has been removed and the echoes have been corrected for a diffuse scattering law by multiplying by the cosine of the incidence angle. Data have been scaled to fit within a 16 bit interval. The 1988 data consist of two groups of images that cover the northern and southern hemispheres. Twenty-five individual "looks" were averaged to make each northern hemisphere image, whereas 26 looks were averaged for the southern hemisphere images. Incidence angles for most of the coverage are between 20 and 60 degrees; the extreme range is from 8 to 67 degrees. Ground resolution is between 1.5 and 2 km. The range resolution varies from 1.7 km at 20 degrees incidence to 0.8 km at 50 degrees; the Doppler resolution (approximately east-west) is about 1.3 km. The reader is referred to Campbell and Burns (1980) and Campbell et al. (1984, 1989) for detailed discussions of the observing and processing histories. 17 Pre-Magellan Radar and Gravity Data July 12, 1990 4.5.2 Goldstone Radar Backscatter and Altimetry Beginning in 1972 and continuing until the present, the Goldstone radar system has been used during inferior conjunctions to acquire S- band (12.6 cm from 1972 to 1975 and 12.9 cm after then) backscatter images and altimetry data for the equatorial region located between approximately 260 (leftmost) and 30 degrees (rightmost) east longitude (e.g., Rumsey et al., 1974; Goldstein et al., 1978; Jurgens et al., 1980; Jurgens et al., 1988a, b; Arvidson et al., 1990). Goldstone data offer a unique view of the planet, since the regions observed are located to the south of Venera Orbiter 15, 16 radar coverage and occupy a latitudinal belt that is not completely accessible by the Arecibo radar system. Goldstone observations cover approximately 32 million square kilometers or the equivalent of about 30% of the total area covered by Venera Orbiter 15, 16 observations. All observations were made at wavelengths of 12.6 or 12.9 cm using circular polarization. The transmitter and receiver were set for opposite sense circular polarizations so the received echoes result primarily from reflections from surfaces directed normal to the line of sight. Such scattering is usually called quasi-specular and provides a large signal-to-noise ratio at small angles of incidence, where the probability of finding surfaces normal to the impinging wave is large. Most of the observations were made using three stations as a multiple interferometer. Data are presented as the ratio of echo power divided by the square root of the power for a given annulus surrounding the sub- earth point, for data prior to 1977, and to the average for the annulus for later data. The altimetry data represent relative altitudes on the planet. The zero altitude varies from image to image. Altimetry data prior to 1977 are averaged and quantized to 8 levels. The reader is referred to Jurgens et al. (1980; 1988a, b) for observational and processing details. Both backscatter and altimetry data are in the form of unsigned byte VICAR2 images. Note that the VICAR2 labels for the 1980 and 1982 images are split between the first and last record in the data file (see the file VICAR2.TXT in the DOCUMENT directory). 4.6 Pioneer-Venus Radar In this section descriptions of the Pioneer Venus Radar Mapper data sets are provided. The Pioneer Venus Radar Mapper obtained measurements of the Venus surface from December 5, 1978 through March 23, 1981. It operated at a wavelength of 17 cm, and transmitted 17 watts of peak power through a 38 cm diameter antenna. The instrument made a series of measurements during each 12 second spacecraft revolution period: (a) radiometer calibration with the antenna pointed to the zenith (i.e., "cold space"), (b) 1 or 4 sets of altimetric measurements, (c) radiometer measurement with the antenna pointed to the nadir, and (d) one or two side-looking imaging measurements. The reader is referred to Pettengill et al. (1980a, b; 1983, 1988), to Masursky et al. (1980), and to Ford and Pettengill (1983) for detailed acquisition, processing, and analysis discussions. 18 Pre-Magellan Radar and Gravity Data July 12, 1990 The two radiometer measurements yielded a value for the 17 cm brightness temperature of that part of the planet viewed by the antenna at that time. The resolution depended on the altitude of the spacecraft, i.e., the footprint varied from 90 km diameter at periapsis (17 N latitude), to 1500 km diameter at extremes of coverage (74 N and 65 degrees S). The altimeter measurements were processed on board into profiles of echo power versus time delay. Subsequent ground processing matched these echoes against a suite of theoretical templates computed for scattering from a spherical planet whose surface obeys Hagfors' law of quasi-specular scattering. Each altimetry measurement yielded values of range, RMS surface slope, and Fresnel reflectivity. The imaging measurements were made when the antenna pointed to the side of the spacecraft nadir. Each 12 second spacecraft revolution yielded one or two maps of radar backscatter, each resolved into 64 pixels. The pixel size varied with spacecraft altitude, from 20x20 km at periapsis (17 degrees N) to 40x40 km at the extremes of the imaging mode (50 N and 15 S). An important correction was applied to the reflectivity measurements to allow for that fraction of the incident radar energy that was scattered over large angles by small-scale surface roughness and was therefore not sampled by the nadir-pointing altimeter. This correction used imaging-mode data to estimate the small-scale roughness in the vicinity of each altimeter footprint, and was therefore restricted to the region of the planet that was observed in both radar modes, i.e., 45 N latitude to 15 S. The method is described by Pettengill et al. (1988). The radar results have been collected into 7 files: a) PVEN001S.DAT A table containing the results from all altimeter and radiometer measurements, including the derived planet brightness temperature, radius, RMS surface slope, and reflectivity for over 150,000 footprints scattered over the Venus surface. The data span the range between 74 N latitude and 65 S. b) PVEN001A.IMG A VICAR2 image of planetary radius derived from the altimeter measurements. The data span the range between 74 N latitude and 65 S. Image samples are 32-bit real numbers. c) PVEN002T.IMG A VICAR2 image of 17 cm brightness temperature derived from the zenith- and nadir-pointing radiometric calibrations. The data span the range between 74 N latitude and 65 S. Image samples are 32-bit real numbers. d) PVEN003F.IMG 19 Pre-Magellan Radar and Gravity Data July 12, 1990 A VICAR2 image of the Fresnel reflectivity of the surface, derived from the altimeter measurements. The data span the range between 74 N latitude and 65 S. Image samples are 32-bit real numbers. e) PVEN004F.IMG A VICAR2 image of corrected Fresnel reflectivity of the surface, derived from the altimeter and side-looking backscatter measurements. The data span the range between 45 N latitude and 15 S. Image samples are 32-bit real numbers. f) PVEN005H.IMG A VICAR2 image of 17 cm radar backscatter cross section of the surface, derived from the side-looking imaging mode. The data have been normalized to 45 degrees incidence angle using the model of Muhleman (1964). The data span the range between 45 N latitude and 15 S. Image samples are 32-bit real numbers. g) PVEN006R.IMG A VICAR2 image of the rms slope of the surface, derived from radar altimeter measurements. The data span the range between 74 N and 65 S. Image samples are 32-bit real numbers. 4.7 Pioneer-Venus and Viking Gravity 4.7.1 Pioneer-Venus LOS Gravity Data Line of sight (LOS) gravity data were obtained as part of the Radio Science Experiment by tracking the Pioneer Venus Orbiter (Sjogren et al., 1980). The data set consists of a table with the following columns: spacecraft latitude, longitude (degrees), accelerations, and altitude (km). The acceleration data were determined from differentiation of raw Doppler residuals and are expressed as units of mm/s^2. To obtain LOS (line of sight) gravity in milligals, accelerations need to be multiplied by 100. An acceleration of 1.20 mm/s^2, therefore, corresponds to 120 mgal, a large gravity anomaly. The LOS data correspond to vertical gravity measurements for LOS acceleration vectors normal to the planet's surface. For other geometries, particularly those where the vector is off the normal, the determination is a mixture of the vertical and horizontal components. Consider that an acceleration towards the Earth (negative) near the planet's limb could arise from either a large mass between the Earth and the spacecraft, or a negative (less than average) local mass beyond the spacecraft. Also note that the direction of motion of the spacecraft (towards or away from Earth) determines the sign of the acceleration and, therefore, the sign of the corresponding gravity anomaly. This can be determined by noting the direction of motion in the data tables. Thus, care should be exercised in the interpretation of LOS gravity acceleration anomalies. 20 Pre-Magellan Radar and Gravity Data July 12, 1990 The acceleration data are at the altitude of the spacecraft. A fair rule-of-thumb is that the resolution is roughly equal to spacecraft altitude. The reader is referred to Sjogren et al. (1980) for more details. 4.7.2 Viking LOS Gravity Data Line of sight (LOS) gravity data were obtained as part of the Radio Science Experiment by tracking the Viking Orbiter 2 (Sjogren, 1979). The data set consists of a table with the following columns: spacecraft latitude, longitude (degrees), accelerations, and altitude (km). The acceleration data were determined from differentiation of raw Doppler residuals and are expressed as units of mm/s^2. To obtain LOS (line of sight) gravity in milligals, accelerations need to be multiplied by 100. An acceleration of 1.20 mm/s^2, therefore, corresponds to 120 mgal, a large gravity anomaly. LOS data correspond to vertical gravity measurements for LOS acceleration vectors normal to the planet's surface. For other geometries, particularly those where the vector is off the normal, the determination is a mixture of the vertical and horizontal components. Consider that an acceleration towards the Earth (negative) near the planet's limb could arise from either a large mass between the Earth and the spacecraft, or a negative (less than average) local mass beyond the spacecraft. Also note that the direction of motion of the spacecraft (towards or away from Earth) determines the sign of the acceleration and, therefore, the sign of the corresponding gravity anomaly. This can be determined by noting the direction of motion in the data tables. Thus, care should be exercised in the interpretation of LOS gravity acceleration anomalies. The acceleration data are at the altitude of the spacecraft. A fair rule-of-thumb is that the resolution is roughly equal to spacecraft altitude. The reader is referred to Sjogren (1979) and references contained within that paper for more details. 5. Data Set Index Files For those data sets that include many files, index tables have been created to allow the user to search for subsets of the data more efficiently. An index table lists the important label parameters for each file in a data set in a format that can be read by humans and also loaded into a data base management system. Each index table is accompanied by a detached PDS label that describes the columns in the table. The index tables and labels are in the directory INDEX. Table 4.1 shows which data sets have index tables. 21 Pre-Magellan Radar and Gravity Data July 12, 1990 6. References Arvidson, R.E., D. Evans, T. Farr, L. Gaddis, R. Greeley, E. Guinness, N. Lancaster, S. Petroy, J. Plaut, J. van Zyl, Mojave Remote Sensing Experiment, Bull. Geol. Soc. Am., in preparation. Arvidson, R.E., J.J. Plaut, R.F. Jurgens, R.S. Saunders, M.A. Slade, 1990, Geology of Southern Guinevere Planitia, Venus, based on analyses of Goldstone Radar Data, Proc. 20th Lunar and Planet. Sci. Conf., 557-572. Campbell, D.B. and B.A. Burns, 1980, Earth-based radar imagery of Venus, J. Geophys. Res., 85, 8271-8281. Campbell, D.B., J.W. Head, J.H. Harmon, and A.A. Hine, 1984, Venus: Volcanism and rift formation in Beta Regio, Science, 226, 167-170. Campbell, D.B., J.W. Head, A.A. Hine, J.K. Harmon, D.A. Senske, and P.C. Fisher, 1989, Styles of volcanism on Venus: New Arecibo high resolution radar data, Science, 246, 373-377. Clark, P.E., M.A. Leake, R.F. Jurgens, 1988, Goldstone Radar Observations of Mercury, in Mercury, Vilas, F., C.R. Chapman, M.S. Matthews, eds., 77-100. Downs, G.S., P.E. Reichley, R.R. Green, 1975, Radar Measurements of Martian Topography and Surface Properties: The 1971 and 1973 Oppositions, Icarus, 26, 273-312. Ford, P.G., and G.H. Pettengill, 1983, Venus: global surface radio emissivity, Science, 220, 1379-1381. Goldstein, R.M., R.R. Green, H.C. Rumsey, 1978, Venus radar brightness and altimetry images, Icarus, 36, 334-352. Greeley, R., N. Lancaster, R. Sullivan, R.S. Saunders, E. Theileg, S. Wall, A. Dobrovolskis, 1988, A relationship between radar backscatter and aerodynamic roughness--Preliminary results, Geophys. Res. Lett., 15, 565-568. Hagfors, T. 1967, A study of the depolarization of lunar radar echoes, Radio Science, 2, 445-465. Hagfors, T. 1970, Remote probing of the Moon by infrared and microwave emissions and by radar, Radio Science, 5, 189-227. Harmon, J.K., D.B. Campbell, S.J. Ostro, 1982, Dual polarization radar observations of Mars: Tharsis and environs, Icarus, 52, 171-187. Harmon, J.K. and S.J. Ostro, 1985, Mars: Dual polarization radar observations with coverage, Icarus, 62, 110-128. 22 Pre-Magellan Radar and Gravity Data July 12, 1990 Jurgens, R.F., R.M. Goldstein, H.C. Rumsey, R.R. Green, 1980, Images of Venus by three-station radar interferometry--1977 results, J. Geophys. Res., 85, 8282-8294. Jurgens, R.F., 1982, Earth-based radar studies of planetary surfaces and atmospheres, IEEE Trans., GE-28, 293. Jurgens, R.F., M.A. Slade, L. Robinett, S. Brokl, G.S. Downs, C. Frank, G.A. Morris, K.H. Farazian, F.P. Chan, 1988a, High resolution images of Venus from ground-based radar, Geophys. Res. Lett., 15, 577-580. Jurgens, R.F., M.A. Slade, R.S. Saunders, 1988b, Evidence for highly reflecting materials on the surface and subsurface of Venus, Science, 240, 1021-1023. LaVoie, S., C. Avis, H. Mortensen, C. Stanley, L. Wainio, 1987, VICAR - User's Guide, JPL Document D-4186, Jet Propulsion Laboratory, Pasadena, Ca. Martin, T. Z., M. D. Martin, and M. J. Braun, 1988, Standards for the Preparation and Interchange of Data Sets, JPL Document D-4683, Jet Propulsion Laboratory, Pasadena, Ca. Masursky, H., E. Eliason, P.G. Ford, G.E. McGill, G.H. Pettengill, G.G. Schaber, and G. Schubert, Pioneer Venus radar results: Geology from images and altimetry, J. Geophys. Res., 85, 8232-8260, 1980. Muhleman, D. O., 1964, Radar scattering from Venus and the Moon, Astron. J., 69, 34-41. Planetary Data System Catalog Design Document, JPL Document D-1152, V2.0, February 13, 1990, Jet Propulsion Laboratory, Pasadena, Ca. Pettengill, G.H., S.H. Zisk, T.W. Thompson, 1974, The mapping of lunar radar scattering characteristics, The Moon, 10, 3-16. Pettengill, G.H., D.F. Horwood, and C.H. Keller, 1980a, Pioneer Venus Orbiter Radar Mapper: Design and operation, IEEE Trans. Geosci. Remote Sens., GE-18, 28-32. Pettengill, G.H., E. Eliason, P.G. Ford, G.B. Loriot, H. Masursky, and G.E. McGill, 1980b, Pioneer Venus radar results: Altimetry and surface properties, J. Geophys. Res., 85, 8261-8270. Pettengill, G.H., P.G. Ford, and S. Nozette, 1983, Venus: Global surface radio reflectivity, Science, 217, 640-642. Pettengill, G.H., P.G. Ford, and B.D. Chapman, 1988, Venus: surface electromagnetic properties, J. Geophys. Res., 93, 14881-14892. Rumsey, H.C., G.A. Morris, R.R. Green, R.M. Goldstein, 1974, A radar brightness and altitude image of a portion of Venus, Icarus, 23, 1-7. 23 Pre-Magellan Radar and Gravity Data July 12, 1990 Sharp, R.P., 1966, Kelso Dunes, Mojave Desert, California, Bull. Geol. Soc. Am., 77, 1045-1074. Sjogren, W.L., R.J. Phillips, P.W. Birkeland, R.N. Wimberly, 1980, Gravity anomalies on Venus, J. Geophys. Res., 85, 8295-8302. Sjogren, W.L., 1979, Mars gravity: High resolution results from Viking Orbiter 2, Science, 1006-1010. Snyder, J.P., 1987, Map projections -- a working manual, U.S. Geological Survey Professional Paper 1395, United States Government Printing Office, Washington, 383p. Thompson, T.W., 1987, High-resolution lunar radar map at 70-cm wavelength, Earth, Moon, and Planets, 37, 59-70. Thompson, T.W., and H.J. Moore, 1989, A Model for Depolarized Radar Echoes from Mars, Proc. 19th Lunar and Planet. Sci. Conf., 409-422. Thompson, T.W., and S.H. Zisk, 1972, Radar mapping of lunar surface roughness, Chapter 1c in Thermal Characteristics of the Moon, Progress in Astronomics and Aeronautics, vol. 28, J. Lucas (ed). van Zyl, J.J., 1990, Calibration of polarimetric radar images using only image parameters and trihedral corner reflector responses, IEEE Trans. Geosci. and Remote Sens., submitted. Zebker, H.H., J.J. van Zyl, D.N. Held, 1987, Imaging polarimetry from wave synthesis, J. Geophys. Res., 92, 683-701. Zisk, S.H., G.H. Pettengill, G.W. Catuna, 1974, High-resolution radar maps of the lunar surface at 3.8-cm wavelength, The Moon, 10, 17-50. 24 Pre-Magellan Radar and Gravity Data July 12, 1990 Appendix A - CD-ROM Volume, Directory and File Structures A.1 Volume and Directory Structures The volume and directory structures of this CD-ROM conform to the standard specified by the International Organization for Standardization (ISO) [Information processing -- Volume and file structure of CD-ROM for information interchange, 1987, ISO/DIS document number 9660, International Organization for Standardization, 1 Rue de Varembe, Case Postale 56, CH-1121 Geneva 20, Switzerland.]. This CD-ROM disk conforms to the first level of interchange, level-1. A.2 File Structure The files on this CD-ROM are of two types: fixed-length files and stream files. The characteristics of each type are described in the following sections. A.2.1 Fixed-Length Files The records in a fixed-length file are all the same length, and there is no embedded information to indicate the beginning or end of a record. Fixed-length records allow any part of a file to be accessed directly without the need to pass through the file sequentially. The starting byte of any record can be calculated as follows: offset = (record-1)*length where: offset = offset byte position of record from start of file record = number of desired record length = length of record in bytes On this CD-ROM, images and table files are fixed-length. Image file names have the extension ".IMG", and table file names have the extensions ".DAT" (for data tables) and ".TAB" (for index tables). Image files contain binary data with no carriage-control information in them. Table files, however, contain ASCII text that can be printed or displayed on a terminal. Each record in a table file has the ASCII characters for carriage return and line feed (hex 0D and 0A) in the last two bytes. A.2.2 Stream Files Stream files are used to store ASCII text such as documentation and source code. A stream file may have records of varying lengths. The end of a record is marked by two bytes containing the ASCII carriage return and line feed characters (hex 0D and 0A). Stream files are different from variable-length files, which store the record size in the first two bytes of each record. This CD-ROM contains no variable-length files. 25 Pre-Magellan Radar and Gravity Data July 12, 1990 On this CD-ROM, documentation files and detached label files are in stream format. They may be printed or displayed on a terminal. Their file names have the extensions ".TXT" and ".LBL". Also, the file VOLDESC.SFD in the top-level directory is a stream file. A.2.3 Extended Attribute Records An extended attribute record (XAR) contains information about a file's record format, record attributes, and record length. The extended attribute record is not considered part of the file and is not seen by programs accessing a file with high-level I/O routines. Not all computer operating systems support extended attribute records. Those that do not will simply bypass the XAR when accessing a file. On this CD-ROM, fixed-length files have XARs, but stream files do not. 26 Pre-Magellan Radar and Gravity Data July 12, 1990 Appendix B - Syntactic Rules of Keyword Assignment Statements A keyword assignment statement, made up of a string of ASCII characters, contains the name of an attribute and the value of that attribute. A keyword assignment statement has the general form shown below: name = value [/* comment */] The format of each keyword assignment statement is free-form; blanks and tabs are ignored by a parsing routine. An attribute name is separated from its value by the equal symbol (=). Each keyword assignment statement may be followed by a comment that more completely describes the entry. The comment begins with a slash character followed by an asterisk character (/*), and terminates with an asterisk character followed by a slash character (*/). Comments may also exist on a line without a keyword assignment statement. Note that the brackets indicate that the comment and its delimiters are optional. Values associated with an attribute can be integers, real numbers, unitized real numbers, literals, times, or text strings. B.1 - Integer Numbers An integer value consists of a string of digits preceded optionally by a sign (+ or -). Non-decimal based integers are expressed according to the Ada language convention: b#nnnnnnn#, where 'b' represents the base of the number, and '#' delimits the number 'nnnnnnnn'. For example, the number expressed as 2#111# represents the binary number 111, which is 7 in base 10. B.2 - Real Numbers A real number has the form: [s]f.d[En] where: s = optional sign (+ or -) f = one or more digits that specify the integral portion of the number. d = one or more digits that specify the fraction portion of the number. n = an optional exponent expressed as a power of 10. A unitized real number is a real number with an associated unit of measurement. The units for a real number value are enclosed in angle brackets (< >). For example, 1.234 indicates a value of 1.234 seconds. 27 Pre-Magellan Radar and Gravity Data July 12, 1990 B.3 - Dates and Times A special form of a numeric field is a time value. The following format of date/time representations is used: yyyy-mm-ddThh:mm:ss.fffZ where: yyyy = year mm = month dd = day of month hh = hour mm = minute ss = seconds fff = fraction of a second Z = The Z qualifier indicates the time is expressed as Universal Time Coordinated (UTC). B.4 - Literal Values A literal value is an alphanumeric string that is a member of a set of finite values. It can also contain underscore character (_). A literal value must be delimited by single quote (') characters if it does not begin with a letter (A-Z). If the literal begins with a letter, it does not have to be enclosed in single quotes. If a literal appears within single quotes, the literal may contain any printable ASCII character. For example, the literal value '1:1' is legal as long as the single quoted format is used. A keyword assignment statement using a literal value might look like the examples shown below: FILTER_NAME = CLEAR IMAGE_ID = '122S01' These statements say that the CLEAR filter was used to acquire an image and that the image_id was 122S01. B.5 - Text Character Strings Text strings can be any length and can consist of any sequence of printable ASCII characters including tabs, blanks, carriage-control, or line-feed characters. Text strings are enclosed in double quote characters. If the text string comprises several lines, it continues until a double quote character is encountered and includes the carriage- control and line-feed characters. 28 Pre-Magellan Radar and Gravity Data July 12, 1990 Appendix C - Keyword Definitions The definitions of the keywords used in the detached PDS labels on the Pre-Magellan Radar and Gravity Data CD-ROM are given below. Where applicable the definitions are taken from the PDS data dictionary (PDS Catalog Design Document, 1990) or the PDS Standards for the Preparation and Interchange of Data Sets (SPIDS) document (Martin et al., 1988). There are some differences from the PDS data dictionary in the definitions used on this CD-ROM, since the definitions of some keywords in the current PDS data dictionary do not describe radar data. In addition, some keywords for radar derived data do not exist in the current PDS data dictionary. AIRCRAFT_ALTITUDE The altitude of the aircraft during data collection. AIRCRAFT_HEADING The direction of flight clockwise relative to geodetic north of the aircraft during data collection. ALONG_TRACK_SAMPLE_SIZE The size of a radar pixel in the direction parallel to the ground track of the radar instrument. BYTES The number of bytes containing a data item. COLUMNS The number of items of information in each row of a data table. CROSS_TRACK_SAMPLE_SIZE The size of a radar pixel in the direction perpendicular to the ground track of the radar instrument. DATA_SET_ID A unique alphanumeric identifier for a data set. It is used as a primary key in the PDS catalog. DATA_SET_PARAMETER_NAME The name of the physical parameter represented in an image. Note this definition differs from the PDS data dictionary definition. DATA_SET_PARAMETER_UNIT The units of measure for the physical parameter represented in an image. DATA_TYPE The data type of a data item. Valid values are INTEGER, REAL, DATE, TIME, and CHARACTER. 29 Pre-Magellan Radar and Gravity Data July 12, 1990 DESCRIPTION Text describing an object. Sometimes this is expressed as a pointer to another file containing the descriptive text; e.g., ^DESCRIPTION = "VICAR2.TXT" indicates that the file VICAR2.TXT contains a description of the object. EARTH_BASE_INSTITUTION_NAME The university, research center, NASA center, or other institution associated with an Earth-based laboratory or observatory. EARTH_BASE_NAME The name of an Earth-based laboratory or observatory. END_OBJECT This keyword is used by ODL to indicate the end of a data object definition. EVENT_START_TIME The date and time of the beginning of an event, such as data collection, in PDS standard (UTC) format. EVENT_STOP_TIME The date and time of the end of an event, such as data collection, in PDS standard (UTC) format. FEATURE_NAME The name of a feature. For planets, it is the IAU approved name. For the Earth, it can be the common name of a geographic feature. FILE_RECORDS The number of physical records in a data file. FORMAT The Fortran 77 representation of the format statement needed to read a data item. HEADER The embedded label information at the beginning of a data file, expressed as a pointer to the record in the file where the header begins; e.g., ^HEADER = ("filename",1) indicates that a header begins in record 1 of file "filename". IMAGE The data in an image file, expressed as a pointer to the record where the data begins. For example, ^IMAGE = ("filename",3) indicates that image data begins in record 3 of file "filename". IMAGE_TIME The time of the image acquisition in PDS standard (UTC) format. INCIDENCE_ANGLE 30 Pre-Magellan Radar and Gravity Data July 12, 1990 The angle of the incoming radar beam relative to the local surface normal. Note this definition is different from the PDS data dictionary definition, which is specific to optical images. INSTRUMENT_NAME The full name of an instrument. INTERCHANGE_FORMAT The type of data stored in a data table, such as ASCII or BINARY. LATITUDE The value of the planetographic latitude of a point of interest. Latitude is defined in terms of the IAU convention that identifies the north pole as that pole of rotation that lies on the north side of the invariable plane of the solar system. Latitude values range from -90 degrees at the south pole to +90 degrees at the north pole. LINES The number of lines in an image. LINE_PREFIX_BYTES The number of bytes of data that precede the image data in each image line. LINE_SAMPLES The number of samples contained in each image line. LONGITUDE The value of the planetographic longitude of a point of interest. Values are positive in the direction opposite to the rotation. For example, east longitudes are positive for Venus and west longitudes are positive for Mars and Mercury. Values of longitude given in labels on this CD-ROM range from 0 to 360 degrees. MAP_PROJECTION_TYPE The type of map projection used to project image data. MAP_SCALE The scale of a map. The units of map scale are dependent on the particular map projection. MAXIMUM_LATITUDE The northernmost latitude of a spatial area. MAXIMUM_LONGITUDE The value of the largest longitude within a spatial area. See the definition of longitude for more detail. Note that the value of maximum longitude will be less than the value of minimum longitude for areas that cross the prime meridian. MINIMUM_LATITUDE The southernmost latitude of a spatial area. 31 Pre-Magellan Radar and Gravity Data July 12, 1990 MINIMUM_LONGITUDE The value of the smallest longitude within a spatial area. See the definition of longitude for more detail. Note that the value of minimum longitude will be greater than the value of maximum longitude for areas that cross the prime meridian. NAME The name of a column in a table. NOTE Descriptive text about a data file, often including a reference. OBJECT This keyword specifies the name of a data object. It is used by ODL to indicate the start of a data object definition. PRODUCER_FULL_NAME The full name of the individual mainly responsible for production of a data set. RECEIVED_POLARIZATION The polarization of the received radar wave. RECORDS The number of records in the object being described; for example, the number of records in a header object. RECORD_BYTES The number of bytes in each record of a data file. RECORD_TYPE The record structure type of a data file. Valid values are FIXED_LENGTH, VARIABLE_LENGTH, and STREAM. Images and data tables usually have fixed-length records, whereas text files have stream format records. REGION_ID An identifier for a region on a planetary surface. Regions are divisions of a planetary surface into areas that serve as the basis for systematic mapping activities. ROWS The number of logical records in a data table. ROW_BYTES The number of bytes in each row (i.e., logical record) of a data table. SAMPLE_BITS The number of bits of data comprising one sample or pixel in an image. Common values are 8, 16, and 32. SAMPLE_TYPE 32 Pre-Magellan Radar and Gravity Data July 12, 1990 The data type of an image sample or pixel. The table below lists the values used on this CD-ROM: UNSIGNED_INTEGER An unsigned integer value. Samples with a length of 16 bits are in most-significant-byte first order. VAX_INTEGER A signed integer value in least-significant- byte first order. VAX_REAL A real (floating point) value in VAX format. SOURCE_TAPE_ID The tape identifier that archives the data source of a derived data product. SPACECRAFT_NAME The commonly used name associated with a spacecraft. START_BYTE The byte position of the beginning of a data item within a row of data. SUB_EARTH_LATITUDE The latitude on a planetary surface closest to an Earth-based observatory. SUB_EARTH_LONGITUDE The longitude on a planetary surface closest to an Earth-based observatory. TARGET_NAME The name of a planetary body, such as a planet or satellite. TRANSMITTED_POLARIZATION The polarization of the transmitted radar wave. TYPE The type of header in a data file, such as a VICAR2 label embedded in the image file. UNIT The units of measure of a data item. WAVELENGTH The value of the wavelength used by a particular radar system. 33 Pre-Magellan Radar and Gravity Data July 12, 1990 Appendix D - Venus Coordinate Systems The Venus data sets included on the Pre-Magellan CD-ROM have been produced by different research groups at various times. Thus, the latitude-longitude coordinate systems used vary from data set to data set. This means that a given feature on Venus may have different latitude-longitude values in the various data sets. It is beyond the scope of producing this CD-ROM to provide detailed conversions for each data set to a common coordinate system. However, to provide the user with enough information to extract latitude and longitude values from the data, this appendix outlines coordinate system information that was provided by the data producers. If further information on Venus coordinate systems is needed, the user is encouraged to contact the data producer. D.1 Arecibo Radar Images The coordinate system used in generating the images acquired in 1983 had the Venus pole direction with a right ascension of 92.8 degrees and a declination of -67.2 degrees at epoch 1950. The radius used for Venus was 6051.4 km. Longitude coordinates were based on a rotation period of 243.018 days, and the origin was defined by having the subradar point at longitude -39.36 degrees on 20 June 1964 (JD 2438566.5) at 0 hour UT. The coordinate system used in generating the images acquired in 1988 had the Venus pole direction with a right ascension of 92.710 degrees and a declination of -67.157 degrees at epoch 1950. The radius used for Venus was also 6051.4 km. Longitude coordinates were based on a rotation period of 243.025 days, and the origin was defined by having the subradar point at longitude -39.256 degrees on 20 June 1964 (JD 2438566.5) at 0 hour UT. In this coordinate system, the prime meridian will cross the central feature of the crater Ariadne, located at latitude 44 degrees north. Contact Donald Campbell, Cornell University, for more information. D.2 Goldstone Radar Images The coordinate system used in generating the Goldstone radar and altimetry images of Venus is as follows. The Venus north pole direction was at a right ascension of 272.200 degrees and a declination of 66.845 degrees in 1950.0 coordinates. The rotation period used for Venus was 243.0084 days. The prime meridian was defined by a Cartesian unit vector in the equatorial plane and passing through the prime meridian with a value of (-0.56629100, -0.76121813, -0.31600864) at Julian date 2440319.5, which is near the time of the 1969 inferior conjunction of Venus. This system was used to generate the original latitudes and longitudes. In order to make the Goldstone coordinates roughly consistent with the IAU 1985 standard, a value of 3.66 degrees has been 34 Pre-Magellan Radar and Gravity Data July 12, 1990 added to the longitude values. Contact Raymond Jurgens at the Jet Propulsion Laboratory for further details. D.3 Pioneer-Venus Radar Data The following information was provided by Peter Ford at the Massachusetts Institute of Technology regarding the coordinate systems for the Pioneer-Venus Radar Data. The latitudes and longitudes in the Pioneer Venus data sets on this CD-ROM are expressed in the Venus body fixed system adopted by the IAU in 1985 and used by the Magellan Project. It is related to other coordinate systems via a series of time-dependent rotation matrices. These coordinate systems are as follows: PVO80 Venus body fixed (Pioneer Venus) VME50 Venus equator of 1950 EMO50 Earth ecliptic of 1950 EME50 Earth equator of 1950 EME00 Earth equator of J2000 EMO00 Earth ecliptic of J2000 VME00 Venus equator of J2000 (JPL/IAU) VBF85 Venus body fixed (Magellan) (IAU of 1985) [1] The Pioneer Venus Coordinate System (PVO80) Latitude of Venus pole . . . . . . . . . 88.50737 deg Longitude of Venus pole . . . . . . . . . 31.48165 deg Rotation period . . . . . . . . . . . . .243.0 days Latitude of Venus ascending node. . . . . -1.39873 deg Longitude of Venus ascending node . . . . 51.91788 deg Longitude of prime meridian in 1964.0 . .164.6089 deg The angles and ascending node are defined in the EMO50 coordinate system. The following transformation matrices operate on right-handed cartesian 3-vectors. [2] PVO80 -> VME50 Rotation | cos(d) -sin(d) 0 | V(VME50) = E * V(PVO80) = | sin(d) cos(d) 0 | * V(PVO80) | 0 0 1 | d = 164.6089 - (JD-1950)*360/243.0 [3] VME50 -> EMO50 Rotation V(EMO50) = F * V(VME50) | 0.616606488128 -0.786958046198 0.0222142369303 | F = | 0.78689300063 0.616939511419 0.0136031176373 | 35 Pre-Magellan Radar and Gravity Data July 12, 1990 | -0.0244099233564 0.00909245696085 0.999660683866 | [4] EMO50 -> EME50 Rotation V(EME50) = B**-1 * V(EMO50) | 1.0 0.0 0.0 | B**-1 = | 0.0 0.9174369451139180 -0.3978812030494049 | | 0.0 0.3978812030494049 0.9174369451139180 | [5] EME50 -> EME00 Rotation V(EME00) = A * V(EME50) | 0.9999256794956877 -0.0111814832204662 -0.0048590038153592 | A = | 0.0111814832391717 0.9999374848933135 -0.0000271625947142 | | 0.0048590037723143 -0.0000271702937440 0.9999881946023742 | [6] EME00 -> VME00 Rotation V(VME00) = C**-1 * V(EME00) | 0.99889808 0.04693211 0.0 | C**-1 = | -0.04325546 0.92064453 0.38799822 | | 0.01820958 -0.38757068 0.92166012 | [7] VME00 -> VBF85 Rotation | cos(w) sin(w) 0 | V(VBF85) = D**-1 * V(VME00) = | -sin(w) cos(w) 0 | * V(VME00) | 0 0 1 | w = 160.39-1.4813291*(JD-2000) [8] Resulting PVO80 -> VBF85 Rotation Cartesian 3-vectors are transformed by the product of the individual rotation matrices, i.e. D**-1(w) * C**-1 * A * B**-1 * F * E(d) which depends on time through (w) and (d). At the epoch of 1980.0, i.e. approximately in the middle of the Pioneer Venus data taking period, | 0.999990805 0.001520115 -0.004009573 | V(VBF85) = | -0.001530001 0.999995801 -0.002462105 | * V(PVO80) | 0.004005809 0.002468222 0.999988929 | 36 Pre-Magellan Radar and Gravity Data July 12, 1990 Appendix E - Map Projections Most images on this CD-ROM are displayed in simple cylindrical or Mercator map projections. In addition, some of the Haystack radar images of the Moon are displayed in Lambert conformal map projections. The following equations provide descriptions of these map projections. See Snyder (1987) for further details. The equations can be used to compute the latitude and longitude of any location in an image. The image coordinate system used in the mapping equations is defined as having line 1 and sample 1 in the upper left corner of the image. Lines increase from top to bottom and samples increase from left to right. The mapping equations assume that the pixel coordinates are for the center of the pixel and that the corresponding latitude and longitude values are also for the center of the pixel. This convention may not apply to all images on this CD-ROM since the data were submitted by several different groups. Thus, computations using these equations may have small errors if different conventions were used. E.1 Simple Cylindrical Projection The latitude of a pixel in a simple cylindrical projection can be computed using: LAT = MAXLAT - (X-1)/S where: LAT is latitude, MAXLAT is the maximum latitude of the image, X is the line number, and S is the map scale in pixels/degree. Computation of the longitude of a pixel in a simple cylindrical projection depends on the positive longitude direction. For planets where west longitude is positive, the longitude of a pixel is given by: LON = MAXLON - (Y-1)/S where: LON is longitude, MAXLON is the maximum longitude, and Y is the sample number. For planets where east longitude is positive, longitude is computed as follows: LON = MINLON + (Y-1)/S where MINLON is the minimum longitude. In both cases, if the longitude is outside the range of 0 to 360 degrees then add or subtract 360 so that the longitude will be within the proper range. 37 Pre-Magellan Radar and Gravity Data July 12, 1990 E.2 Mercator Projection Computation of longitude for a Mercator projection is the same as just described for the simple cylindrical projection. The latitude calculation is based on a spherical planet, which is normally used for the Moon and Venus. There are no Mercator maps of Mars or the Earth on this CD-ROM, where formulas for an ellipsoid would be used. The latitude of a given pixel in a Mercator map can be computed using: LAT = 2 arctan (V * W) - 90 where V and W are computed as: V = exp { [-Pi * (X-1)] / [180 * S] } W = tan (45 + MAXLAT/2) Pi = 3.14159 Note that degrees are used for the trigonometric functions. E.3 Lambert Conformal Projection A Lambert conformal projection can be constructed by projecting latitude and longitude positions onto a cone that intersects the planet at two latitudes. The latitudes of intersection are known as standard parallels. The Haystack radar images of the Moon use two different Lambert conformal projections for images outside the equatorial region (equatorial images are displayed in Mercator projections). Those images with center latitudes between 16 and 48 degrees use a Lambert conformal projection with standard parallels of 21.33333 and 42.66667 degrees. Those images with center latitudes greater than 48 degrees use standard parallels of 53.33333 and 74.66667 degrees. Note that for the southern hemisphere the same projections are used, but with negative values for the standard parallels. Also, a spherical planet is assumed in the equations. The following four constants are required in computing the latitude and longitude of a given pixel. Their values need to be computed once for the entire image. U = ln [cos(B1) / cos(B2)] / ln [tan(45 + B2/2) / tan(45 + B1/2)] where: B1 is the first standard parallel (i.e., closest to the equator) and B2 is the second standard parallel. Note that arguments to the trigonometric functions are in degrees. The constant U can be thought of as the longitude scale factor for the projection. T = (cos(B1) / U) * (tan (45 + B1/2)) ** U The constant T can be thought of as the latitude scale factor for the projection. 38 Pre-Magellan Radar and Gravity Data July 12, 1990 K = (S * 180) / Pi where S is the map scale in pixels/degree. The scale for the Haystack images is given as 0.0012838507 radians of arc per pixel, which is equal to 13.59449 pixels/degree. RA = (K * T) / (tan (45 + CENLAT/2)) ** U where: CENLAT is the center latitude of the projection. RA is the distance on the map from the pole to the map origin. Center latitudes and longitudes for the Haystack images are listed in the file HLUNINDX.TAB in the INDEX directory. The pixel value must be translated relative to the center of the image in order to compute a latitude and longitude. In addition, the direction of the map projection's X axis is reversed from the line direction because of the convention that line numbers increase towards the bottom of the image. Thus, translated pixel values would be: XD = XC - X YD = Y - YC where: XD and YD are the translated line and sample values, respectively; and XC and YC are the center line and center sample values. Latitude and longitude are computed with: LAT = 2 * arctan [(K * T / PL)) ** (1/U)] - 90 LON = (PA / U) + CENLON where CENLON is the center longitude of the image and: PL = sqrt [YD*YD + (RA-XD) * (RA-XD)] PA = arctan [YD/(RA-XD)] The parameter PL takes the same sign as U, which is negative for maps of the southern hemisphere. 39