PDS_VERSION_ID = PDS3 RECORD_TYPE = FIXED_LENGTH RECORD_BYTES = 80 OBJECT = TEXT PUBLICATION_DATE = 1999-11-11 NOTE = "Software Interface Specification for the Spherical Harmonics Binary Data Record (SHBDR) file. Formatted for display or printing at 58 lines per page with up to 78 constant width characters per line." END_OBJECT = TEXT END SOFTWARE INTERFACE SPECIFICATION SPHERICAL HARMONICS BINARY DATA RECORD (SHBDR) prepared by Richard A. Simpson Packard Bldg - Room 332 Stanford University Stanford, CA 94305-9515 Version 2.0.3 11 November 1999 PREFACE |====================================================================| | | | DOCUMENT CHANGE LOG | | | |====================================================================| |REVISION|REVISION| SECTION | REMARKS | | NUMBER | DATE | AFFECTED | | |--------+--------+------------+-------------------------------------| | 2.0 |98/04/20| All |Adapted from SHADR SIS V2.0 | |--------+--------+------------+-------------------------------------| | 2.0.1 |98/12/16| 4.1.2 |Change MGS DATA_SET_ID to | | | | | MGS-M-RSS-5-SDP-V1.0 | |--------+--------+------------+-------------------------------------| | 2.0.1 |98/12/16| 4.2.1 |Add optional START_TIME and STOP_TIME| | | | Table 4-2-1| | |--------+--------+------------+-------------------------------------| | 2.0.2 |99/03/09| 2.3 |Swap first two characters in file | | | | 4.2.1 | naming algorithm; generalize use of | | | | Fig. 4-2-1 | "nnnnvv" string in file name. | |--------+--------+------------+-------------------------------------| | 2.0.2 |99/03/09| Fig. 4-2-1 |Corrected suffix typos in label | |--------+--------+------------+-------------------------------------| | 2.0.2 |99/03/09|Distribution|Update list of PDS recipients. | |--------+--------+------------+-------------------------------------| | 2.0.2 |99/03/09| 1.3 |Update version, date for [3]. | |--------+--------+------------+-------------------------------------| | 2.0.2 |99/03/09|Acr & Abbrev|Change "LPX" to "LP" for Lunar | | | | 1.2 | Prospector. | |--------+--------+------------+-------------------------------------| | 2.0.2 |99/03/09| 1.5.4.1 |Substituted 7-bit ASCII characters | | | | 1.5.4.2 | for 8-bit versions | |--------+--------+------------+-------------------------------------| | 2.0.3 |99/11/11| 4.2.2.3 |Removed non-printing ASCII character | | | | B.1 | | |--------+--------+------------+-------------------------------------| | 2.0.3 |99/11/11|Distribution|Add: Guinness, Joy, Huber, Wilf | | | | |Remove: Henderson, Oliver | | | | |Update: Simpson, Tyler, Twicken, | | | | | Rappaport, Priest. | |--------+--------+------------+-------------------------------------| | 2.0.3 |99/11/11| Cover |Update contact information for | | | | | Simpson and PDS Operator | |========|========|============|=====================================| |====================================================================| | | | ITEMS TO BE DETERMINED | | | |====================================================================| | REVISION | SECTION | ITEM DESCRIPTION | RESOLUTION | | NUMBER | AFFECTED | | | |----------+----------+------------------------+---------------------| | 2.0 | 5 |Add names, contact info | | | | | for scientists on | | | | | specific products. | | |==========|==========|========================|=====================| Distribution JPL/Gravity A.S. Konopliv............ 301-125J ask@krait.jpl.nasa.gov N. Rappaport............301-125L rappapor@jpl.nasa.gov W.L. Sjogren..............301-150 wls@kamel.jpl.nasa.gov R. Wimberly.............301-150 Ravenel.N.Wimberly@jpl.nasa.gov D-N Yuan.................301-125J dny@krait.jpl.nasa.gov JPL/Mars Global Surveyor P. Priest...............264-860 trish@rodan.jpl.nasa.gov T. Thorpe...............264-214 Thomas.E.Thorpe@jpl.nasa.gov JPL/PDS J. Wilf...................171-264 joel.wilf@jpl.nasa.gov Stanford University R. Simpson..........Packard 332 rsimpson@magellan.stanford.edu J. Twicken..........Packard 321 joe@neptune.stanford.edu L. Tyler............Packard 331 len@nova.stanford.edu Washington University R.E. Arvidson.....Campus Box 1169 arvidson@wunder.wustl.edu J. Alexopoulos..Campus Box 1169 jim@wuzzy.wustl.edu E. Guinness.....Campus Box 1169 guinness@wunder.wustl.edu Goddard Space Flight Center F. Lemoine.............Code 926 flemoine@olympus.gsfc.nasa.gov D. Rowlands............Code 926 dave@usgrant.gsfc.nasa.gov D.E. Smith...............Code 920 dsmith@tharsis.gsfc.nasa.gov Massachusetts Institute of Technology M. Zuber.................54-518 zuber@tharsis.gsfc.nasa.gov CNES G. Balmino.................GRGS balmino@pontos.cst.cnes.fr UCLA S. Joy........IGPP/6707 Geology sjoy@igpp.ucla.edu New Mexico State University L. Huber.........Dept Astronomy lhuber@nmsu.edu Contents Preface.............................................................ii Document Change Log...............................................ii Items to be Determined...........................................iii Distribution......................................................iv Contents...........................................................v Acronyms and Abbreviations.......................................vii 1. General Description...............................................1 1.1. Overview......................................................1 1.2. Scope.........................................................1 1.3. Applicable Documents..........................................1 1.4. System Siting.................................................2 1.4.1. Interface Location and Medium.............................2 1.4.2. Data Sources, Transfer Methods, and Destinations..........2 1.4.3. Generation Method and Frequency...........................2 1.5. Assumptions and Constraints...................................2 1.5.1. Usage Constraints.........................................2 1.5.2. Priority Phasing Constraints..............................2 1.5.3. Explicit and Derived Constraints..........................2 1.5.4. Documentation Conventions.................................2 1.5.4.1. Data Format Descriptions..............................2 1.5.4.2. Time Standards........................................3 1.5.4.3. Coordinate Systems....................................3 1.5.4.4. Limits of This Document...............................3 1.5.4.5. Typographic Conventions...............................3 2. Interface Characteristics.........................................4 2.1. Hardware Characteristics and Limitations......................4 2.1.1. Special Equipment and Device Interfaces...................4 2.1.2. Special Setup Requirements................................4 2.2. Volume and Size...............................................4 2.3. Labeling and Identification...................................4 2.4. Interface Medium Characteristics..............................5 2.5. Failure Protection, Detection, and Recovery Procedures........5 2.6. End-of-File Conventions.......................................5 3. Access............................................................6 3.1. Programs Using the Interface..................................6 3.2. Synchronization Considerations................................6 3.2.1. Timing and Sequencing Considerations......................6 3.2.2. Effective Duration........................................6 3.2.3. Priority Interrupts.......................................6 3.3. Input/Output Protocols, Calling Sequences.....................6 4. Detailed Interface Specifications.................................7 4.1. Structure and Organization Overview...........................7 4.2. Detached PDS Label............................................7 4.2.1. Label Header..............................................7 4.2.2. TABLE Object Definitions.................................10 4.2.2.1. SHBDR Header Object Definition.........................11 4.2.2.2. SHBDR Names Object Definition..........................13 4.2.2.3. SHBDR Coefficients Object Definition...................14 4.2.2.4. SHBDR Covariance Object Definition.....................15 4.3. Data File....................................................16 4.3.1. SHBDR Header Object/Block................................16 4.3.2. SHBDR Names Block........................................16 4.3.3. SHBDR Coefficients Block.................................17 4.3.4. SHBDR Covariances Block..................................17 5. Support Staff and Cognizant Personnel............................18 Appendix A. Binary Data Format.....................................19 A.1. IEEE Integer Fields..........................................19 A.2. IEEE Floating-Point Fields...................................19 A.3. VAX Integer Fields...........................................20 A.4. VAX Floating-Point Fields....................................21 Appendix B. Example Data Products..................................22 B.1. Example Label................................................22 B.2. Example Data Object..........................................26 Tables 4-3-1. SHBDR Header Block.........................................16 4-3-2. SHBDR Names Block..........................................16 4-3-3. SHBDR Coefficients Block...................................17 4-3-4. SHBDR Covariance Block.....................................17 Figures 4-2-1. SHBDR Label Header..........................................8 Acronyms and Abbreviations ANSI American National Standards Institute ARC Ames Research Center ARCDR Altimetry and Radiometry Composite Data Record ASCII American Standard Code for Information Interchange CCSDS Consultative Committee for Space Data Systems CD-WO Compact-disc write-once CNES Centre National d'Etudes Spatiales CR Carriage Return dB Decibel DEC Digital Equipment Corporation DSN Deep Space Network FEA Front End Assembly GSFC Goddard Space Flight Center IEEE Institute of Electrical and Electronic Engineers IAU International Astronomical Union JPL Jet Propulsion Laboratory J2000 IAU Official Time Epoch K Degrees Kelvin kB Kilobytes km Kilometers LF Line Feed LP Lunar Prospector (mission or spacecraft) MB Megabytes MGN Magellan MGS Mars Global Surveyor MO Mars Observer NAIF Navigation and Ancillary Information Facility NASA National Aeronautics and Space Administration NAV Navigation Subsystem/Team ODL Object Definition Language (PDS) PDB Project Data Base PDS Planetary Data System RS Radio Science RSS Radio Science Subsystem RST Radio Science Team SCET Space Craft Event Time SFDU Standard Formatted Data Unit SHADR Spherical Harmonics ASCII Data Record SHBDR Spherical Harmonics Binary Data Record SHM Spherical Harmonics Model SIS Software Interface Specification SOPC Science Operations Planning Computer SPARC Sun Scaleable Processor Architecture SPK Spacecraft and Planet Kernel Format, from NAIF TBD To Be Determined TDB Temps Dynamique Barycentrique - IAU Standard Ephemeris Time UTC Universal Time Coordinated 1. General Description 1.1. Overview This Software Interface Specification (SIS) describes Spherical Harmonics Binary Data Record (SHBDR) files. The SHBDR is intended to be general and may contain coefficients for spherical harmonic expansions of gravity, topography, magnetic, and other fields. 1.2. Scope The format and content specifications in this SIS apply to all phases of the project for which a SHBDR is produced. The SHBDR was defined initially for gravity models derived from Magellan (MGN) and Mars Observer (MO) radio tracking data [1], but the format is more generally useful; this document includes updates for the Mars Global Surveyor (MGS) and Lunar Prospector (LP) missions. Specifics of the various models are included in [2], which will be updated as data for new spherical harmonic models are incorporated within the SHBDR definition. A Spherical Harmonic ASCII Data Record is also defined [3], which may be more suitable for large models or when all covariances will be included in the final product. The Mars Global Surveyor Mission is managed by the Jet Propulsion Laboratory (JPL) for the National Aeronautics and Space Administration. The Lunar Prospector Mission is managed by the Ames Research Center (ARC) for NASA. 1.3. Applicable Documents [1] Tyler, G.L., G. Balmino, D.P. Hinson, W.L. Sjogren, D.E. Smith, R. Woo, S.W. Asmar, M.J. Connally, C.L. Hamilton, and R.A. Simpson, Radio Science Investigations with Mars Observer, J. Geophys. Res., 97, 7759-7779, 1992. [2] Simpson, R.A., Interpretation and Use of Spherical Harmonics ASCII Data Record (SHADR) and Spherical Harmonics Binary Data Record (SHBDR), Version 1.0, 1993. [3] Simpson, R.A., Software Interface Specification: Spherical Harmonics ASCII Data Record (SHADR), Version 2.0.2, 9 March 1999. [4] MGN 630-7, Rev. D, Magellan Planetary Constants and Models, D.T. Lyons, Mission Design, Jet Propulsion Laboratory, 9 January 1991. [5] MO 642-321, Mars Observer Planetary Constants and Models, JPL D- 3444, November 1990. [6] D-7116, Rev. D, Planetary Science Data Dictionary Document, Jet Propulsion Laboratory, 15 June 1996. [7] D-7669 Part 2, Planetary Data System Standards Reference, PDS Version 3.2, Jet Propulsion Laboratory, 24 July 1995. 1.4. System Siting 1.4.1. Interface Location and Medium SHBDR files are created at the institution conducting the science analysis. SHBDR files can be electronic files or can be stored on compact-disc write-once (CD-WO) media. 1.4.2. Data Sources, Transfer Methods, and Destinations SHBDR files are created from radio tracking, vertical sounding, in situ, and/or other measurements at the institution conducting the scientific data analysis. They are transferred to and deposited in a data system specified by the managing institution. 1.4.3. Generation Method and Frequency Spherical Harmonic Models are developed separately at each institution conducting scientific analyses on raw data; each model meets criteria specified by the investigators conducting the analysis. Each model requires data from a large number of latitudes and longitudes, so that SHBDR files will be issued infrequently and on schedules which cannot be predicted at this time. 1.5. Assumptions and Constraints 1.5.1. Usage Constraints None. 1.5.2. Priority Phasing Constraints None. 1.5.3. Explicit and Derived Constraints None. 1.5.4. Documentation Conventions 1.5.4.1. Data Format Descriptions The reference data unit is the byte. Data may be stored in fields with various sizes and formats, viz. one-, two-, and four-byte binary integers, four- and eight-byte binary floating-point numbers, and character strings. Data are identified throughout this document as char 8 bits character uchar 8 bits integer short 16 bits integer long 32 bits integer float 32 bits floating point (sign, exponent, and mantissa) double 64 bits floating point (sign, exponent, and mantissa) u (prefix) unsigned (as with ulong for unsigned 32-bit integer) other special data structures such as time, date, etc. which are described within this document If a field is described as containing n bytes of ASCII character string data, this implies that the leftmost (lowest numbered) byte contains the first character, the next lowest byte contains the second character, and so forth. An array of n elements is written as array[n]; the first element is array[0], and the last is array[n-1]. Array[n][m] describes an n x m element array, with first element array[0][0], second element array[0][1], and so forth. Floating point (real) numbers are represented as double precision character strings in the FORTRAN 1P1E23.16 format. Fixed point (integer) numbers are represented using the FORTRAN I5 format. 1.5.4.2. Time Standards SHBDR files use the January 1.5, 2000 epoch as the standard time. Within the data files, all times are reported in Universal Coordinated Time (UTC) as strings of 23 ASCII characters. The time format is "YYYY-MM-DDThh:mm:ss.fff", where "-", "T", ":", and "." are fixed delimiters; "YYYY" is the year "19nn" or "20nn"; "MM" is a two- digit month of year; "DD" is a two-digit day of month; "T" separates the date and time segments of the string; "hh" is hour of day; "mm" is the minutes of hour (00-59); "ss" is the seconds of minute (00-59); and "fff" is fractional seconds in milliseconds. The date format is "YYYY-MM-DD", where the components are defined as above. 1.5.4.3. Coordinate Systems The SHBDR uses the appropriate planetocentric fixed body coordinate system [4, 5]. 1.5.4.4. Limits of This Document This document applies only to SHBDR data files. 1.5.4.5. Typographic Conventions This document has been formatted for simple electronic file transfer and display. Line lengths are limited to 80 ASCII characters, including line delimiters. No special fonts or structures are included within the file. Constant width characters are assumed for display. 2. Interface Characteristics 2.1. Hardware Characteristics and Limitations 2.1.1. Special Equipment and Device Interfaces Users of the SHBDR product must have access to the data system (or to media) on which SHBDR files are stored. 2.1.2. Special Setup Requirements None. 2.2. Volume and Size SHBDR products have variable length, depending on the degree and order of the model, the number of coefficients used, the number of other parameters included, and the number of tables included. A gravity model of degree and order N will have approximately N**2 coefficients and approximately N**4 covariances; for 8-byte binary storage and N=50, the total SHBDR volume will be about 30 MB. Vector quantities (e.g., magnetic field) may be described by a single SHBDR (in which all components are represented) or by a separate SHBDR for each field component. If the single SHBDR includes covariances, the file size will be approximately 27 times larger than the combined volumes of the three component files because of the inter-component covariance terms. In general, the SHBDR is recommended over the SHADR [3] when the data include covariances because of the smaller data volume associated with binary formats. 2.3. Labeling and Identification Each file has a name which describes its contents. The name includes the following structure which uniquely identifies it among SHBDR products: GTnnnnvv.SHB where "G" denotes the generating institution "J" for the Jet Propulsion Laboratory "G" for Goddard Space Flight Center "C" for Centre National d'Etudes Spatiales "T" indicates the type of data represented "G" for gravity field "T" for topography "M" for magnetic field "nnnnvv" is a 6-character modifier specified by the data producer. Among other things, this modifier may be used to indicate the target body, whether the SHBDR contains primary data values as specified by "T" or uncertainties/errors, and/or the version number. "SHB" denotes that this is an binary file of Spherical Harmonic coefficients Each SHBDR file is accompanied by a detached PDS label; that label is a file in its own right, having the name GTnnnnvv.LBL. 2.4. Interface Medium Characteristics SHBDR products are electronic files. 2.5. Failure Protection, Detection, and Recovery Procedures None. 2.6. End-of-File Conventions End of file labeling complies with standards for the medium on which the files are stored. 3. Access 3.1. Programs Using the Interface Data contained in SHBDR files will be accessed by programs at the home institutions of science investigators. Those programs cannot be identified here. 3.2. Synchronization Considerations 3.2.1. Timing and Sequencing Considerations N/A 3.2.2. Effective Duration N/A 3.2.3. Priority Interrupts None. 3.3. Input/Output Protocols, Calling Sequences None. 4. Detailed Interface Specifications 4.1. Structure and Organization Overview The SHBDR is a file generated by software at the institution conducting scientific data analysis. Each SHBDR file is accompanied by a detached PDS label. 4.2. Detached PDS Label The detached PDS label is a file with two parts -- a header, and a set of one to four PDS TABLE object definitions. The header contains information about the origin of the file and its general characteristics such as record type and size. The TABLE object definitions describe the format and content of the tables that make up the SHBDR data file. The SHBDR Header Table Object definition is required. The SHBDR Names Object Definition is required if there is an SHBDR Names Object in the file. The SHBDR Coefficients Table Object definition is required if there is a SHBDR Coefficients Table in the file; the SHBDR Covariance Table Object definition is required if there is a SHBDR Covariance Table. Each detached PDS label is constructed of ASCII records; each record in the label contains exactly 80 characters. The last two characters in each record are the carriage-return (ASCII 13) and line-feed (ASCII 10) characters. An example of a complete label is given in Appendix B. 4.2.1 Label Header The structure of the label header is illustrated in Figure 4-2-1. Keyword definitions are given below. PDS_VERSION_ID = The version of the Planetary Data System for which these data have been prepared; set to PDS3 by agreement between the Mars Global Surveyor Project and PDS. RECORD_TYPE = The type of record. Set to "FIXED_LENGTH" to indicate that all logical records have the same length. RECORD_BYTES = The number of bytes per (fixed-length) record. FILE_RECORDS = The number of records in the SHBDR file; instance dependent. ^SHBDR_HEADER_TABLE= File name and record number at which SHBDR_HEADER_TABLE begins. Set to ("GTnnnnvv.SHB",1) where "GTnnnnvv.SHB" is the file name as described in Section 2.3, and 1 is the record number since this is the first record in the SHBDR file. |====================================================================| | | | Figure 4-2-1 SHBDR Label Header | | | |====================================================================| | | | PDS_VERSION_ID = PDS3 | | RECORD_TYPE = FIXED_LENGTH | | RECORD_BYTES = nnn | | FILE_RECORDS = nnn | | ^SHBDR_HEADER_TABLE = ("GTnnnnvv.SHB",1) | | ^SHBDR_NAMES_TABLE = ("GTnnnnvv.SHB",1) | | ^SHBDR_COEFFICIENTS_TABLE = ("GTnnnnvv.SHB",nn) | | ^SHBDR_COVARIANCE_TABLE = ("GTnnnnvv.SHB",nnn) | | INSTRUMENT_HOST_NAME = "cccccccccccccccccccc" | | TARGET_NAME = "cccc" | | INSTRUMENT_NAME = "ccccccccccccccccccccccc" | | DATA_SET_ID = "ccccccccccccccccccccccc" | | OBSERVATION_TYPE = "ccccccccccccc" | | ORIGINAL_PRODUCT_ID = "cccccccccccc" | | PRODUCT_ID = "GTnnnnvv.SHB" | | PRODUCT_RELEASE_DATE = YYYY-MM-DD | | DESCRIPTION = "cccccccccccccccccc" | | START_ORBIT_NUMBER = nnnn | | STOP_ORBIT_NUMBER = nnnn | | START_TIME = YYYY-MM-DDThh:mm:ss | | STOP_TIME = YYYY-MM-DDThh:mm:ss | | PRODUCT_CREATION_TIME = YYYY-MM-DDThh:mm:ss.fff | | PRODUCER_FULL_NAME = "cccccccccccc" | | PRODUCER_INSTITUTION_NAME = "ccccccccccc" | | PRODUCT_VERSION_TYPE = "cccccccccccc" | | PRODUCER_ID = "ccccccc" | | SOFTWARE_NAME = "ccccccc;Vn.m" | | | |====================================================================| ^SHBDR_NAMES_TABLE= File name and record number at which SHBDR_NAMES_TABLE begins. The Names Table is required if the Coefficients Table is included in the file. This pointer will not appear in the SHBDR label if there is no Coefficients Table. Set to ("GTnnnnvv.SHB",nn) where "GTnnnnvv.SHB" is the file name as described in Section 2.3, and "nn" is the record number in the file where the Names Table begins. ^SHBDR_COEFFICIENTS_TABLE= File name and record number at which SHBDR_COEFFICIENTS_TABLE begins. The Coefficients Table is optional; this pointer will not appear in the SHBDR label if there is no Coefficients Table. Set to ("GTnnnnvv.SHB",nn) where "GTnnnnvv.SHB" is the file name as described in Section 2.3, and "nn" is the record number in the file where the Coefficients Table begins. ^SHBDR_COVARIANCE_TABLE= File name and record number at which SHBDR_COVARIANCE_TABLE begins. The Covariance Table is optional; this pointer will not appear in the SHBDR label if there is no Covariance Table. Set to ("GTnnnnvv.SHB",nn) where "GTnnnnvv.SHB" is the file name as described in Section 2.3, and "nn" is the record number in the file where the Covariance Table begins. INSTRUMENT_HOST_NAME = Name of the spacecraft; acceptable names include "MARS GLOBAL SURVEYOR" and "LUNAR PROSPECTOR". TARGET_NAME = A character string which identifies the target body. For MGS SHBDR files, the character string "MARS". For Lunar Prospector SHBDR files, the character string "MOON". INSTRUMENT_NAME = Name of the instrument; set to "RADIO SCIENCE SUBSYSTEM" for products generated from radio science data, or set to other instrument names as appropriate. DATA_SET_ID = Identifier for the data set of which this SHBDR product is a member. Set to "MGS-M- RSS-5-SDP-Vn.m" for Mars Global Surveyor SHBDR products, where "Vn.m" indicates the version number of the data set. Set to other data set identifiers as appropriate. OBSERVATION_TYPE= A character string which identifies the data in the product. For the spherical harmonic model of a gravity field, the character string "GRAVITY FIELD". For a model of planet topography, the character string "TOPOGRAPHY". ORIGINAL_PRODUCT_ID = Optional. An identifier for the product provided by the producer. Generally a file name, different from PRODUCT_ID, which would be recognized at the producer's institution PRODUCT_ID = A unique identifier for the product within the collection identified by DATA_SET_ID. Generally, the file name used in pointers such as ^SHBDR_HEADER_TABLE. The naming convention is defined in Section 2.3. PRODUCT_RELEASE_DATE = The date on which the product was released to the Planetary Data System; entered in the format "YYYY-MM-DD", where components are defined in Section 1.5.4.2. DESCRIPTION = A short description of the SHBDR product. START_ORBIT_NUMBER = Optional. The first orbit represented in the SHBDR product. An integer. STOP_ORBIT_NUMBER = Optional. The last orbit represented in the SHBDR product. An integer. START_TIME = Optional. The date/time of the first data included in the model, expressed in the format "YYYY-MM-DDThh:mm:ss" where the components are defined in section 1.5.4.2. STOP_TIME = Optional. The date/time of the last data included in the model, expressed in the format "YYYY-MM-DDThh:mm:ss" where the components are defined in section 1.5.4.2. PRODUCT_CREATION_TIME = The time at which this SHBDR was created; expressed in the format "YYYY-MM- DDThh:mm:ss.fff" where the components are defined in Section 1.5.4.2. PRODUCER_FULL_NAME= The name of the person primarily responsible for production of this SHBDR file. Expressed as a character string, for example "LESLIE R. JONES". PRODUCER_INSTITUTION_NAME= The name of the institution primarily responsible for production of this SHBDR. Standard values include "STANFORD UNIVERSITY" "GODDARD SPACE FLIGHT CENTER" "JET PROPULSION LABORATORY" "CENTRE NATIONAL D'ETUDES SPATIALES" PRODUCT_VERSION_TYPE= The version of this SHBDR. Standard values include "PREDICT", "PRELIMINARY", and "FINAL". PRODUCER_ID = The entity responsible for creation of the SHBDR product; for products generated by the Mars Global Surveyor Radio Science Team set to "MGS RST". SOFTWARE_NAME = The name and version number of the program creating this SHBDR file; expressed as a character string in the format "PROGRAM_NAME;n.mm" where "PROGRAM_NAME" is the name of the software and "n.mm" is the version number. 4.2.2 TABLE Object Definitions TABLE object definitions completely define the TABLE objects for each SHBDR file. Minor tailoring of the definitions for different OBSERVATION_TYPES precludes specification of exact definitions here. DESCRIPTION values, for example, will likely be tailored for each product type. In no case should there be a need to change the structure of the file, however. Entries "*" are provided by the label generating program based on information supplied elsewhere. 4.2.2.1 SHBDR Header Object Definition Each SHBDR Header Object is completely defined by the Header Object Definition in its Label. The Definition which follows gives the structure of the Header Object; some of the DESCRIPTION values may vary from product to product. The SHBDR Header Object Definition is a required part of the SHBDR label file. It immediately follows the label header. OBJECT = SHBDR_HEADER_TABLE ROWS = 1 COLUMNS = 9 ROW_BYTES = 56 INTERCHANGE_FORMAT = BINARY DESCRIPTION = "The SHBDR Header includes descriptive information about the spherical harmonic coefficients which follow in SHBDR_COEFFICIENTS_TABLE. The header consists of a single record of nine data columns requiring 56 bytes. The Header is followed by a pad of binary integer zeroes to ensure alignment with RECORD_BYTES." OBJECT = COLUMN NAME = "REFERENCE RADIUS" DATA_TYPE = * START_BYTE = 1 BYTES = 8 UNIT = "KILOMETER" DESCRIPTION = "The assumed reference radius of the spherical planet." END_OBJECT = COLUMN OBJECT = COLUMN NAME = "CONSTANT" DATA_TYPE = * START_BYTE = 9 BYTES = 8 UNIT = "N/A" DESCRIPTION = "For a gravity field model the gravitational constant GM in kilometers cubed per seconds squared for the planet. For a topography model, set to 1" END_OBJECT = COLUMN OBJECT = COLUMN NAME = "UNCERTAINTY IN CONSTANT" DATA_TYPE = * START_BYTE = 17 BYTES = 8 UNIT = "N/A" DESCRIPTION = "For a gravity field model the uncertainty in the gravitational constant GM in kilometers cubed per seconds squared for the planet. For a topography model, set to 0." END_OBJECT = COLUMN OBJECT = COLUMN NAME = "DEGREE OF FIELD" DATA_TYPE = * START_BYTE = 25 BYTES = 4 UNIT = "N/A" DESCRIPTION = "Degree of the model field." END_OBJECT = COLUMN OBJECT = COLUMN NAME = "ORDER OF FIELD" DATA_TYPE = * START_BYTE = 29 BYTES = 4 UNIT = "N/A" DESCRIPTION = "Order of the model field." END_OBJECT = COLUMN OBJECT = COLUMN NAME = "NORMALIZATION STATE" DATA_TYPE = * START_BYTE = 33 BYTES = 4 UNIT = "N/A" DESCRIPTION = "The normalization indicator. For gravity field: 0 coefficients are unnormalized 1 coefficients are normalized 2 other." END_OBJECT = COLUMN OBJECT = COLUMN NAME = "NUMBER OF NAMES" DATA_TYPE = * START_BYTE = 37 BYTES = 4 UNIT = "N/A" DESCRIPTION = "Number of valid names in the SHBDR Names Table. Also, the number of valid coefficients in the SHBDR Coefficients Table." END_OBJECT = COLUMN OBJECT = COLUMN NAME = "REFERENCE LONGITUDE" POSITIVE_LONGITUDE_DIRECTION = * DATA_TYPE = * START_BYTE = 41 BYTES = 8 UNIT = "DEGREE" DESCRIPTION = "The reference longitude for the spherical harmonic expansion; normally 0." END_OBJECT = COLUMN OBJECT = COLUMN NAME = "REFERENCE LATITUDE" DATA_TYPE = * START_BYTE = 49 BYTES = 8 UNIT = "DEGREE" DESCRIPTION = "The reference latitude for the spherical harmonic expansion; normally 0." END_OBJECT = COLUMN END_OBJECT = SHBDR_HEADER_TABLE 4.2.2.2 SHBDR Names Object Definition The SHBDR Names Object is completely defined by the Names Object Definition in the label. The definition below illustrates general structural form. The SHBDR Names Object is an optional part of the SHBDR file. If the Names Object is not included, either the Names Object Definition will be omitted or the number of rows will be set to zero (ROWS = 0). If the Names Object is not included, the pointer ^SHBDR_NAMES_TABLE will not appear in the Standard Keywords and Values. If the Coefficients Object is included in the SHBDR file, the Names Object is required. OBJECT = SHBDR_NAMES_TABLE ROWS = * COLUMNS = 1 ROW_BYTES = 8 INTERCHANGE_FORMAT = BINARY DESCRIPTION = "The SHBDR Names Table contains names for the solution parameters (including gravity field coefficients) which will follow in SHBDR_COEFFICIENTS_TABLE. The order of the names in SHBDR_NAMES_TABLE corresponds identically to the order of the parameters in SHBDR_COEFFICIENTS_TABLE. Each coefficient name is of the form Cij or Sij where i is the degree of the coefficient and j is the order of the coefficient. Both indices are three- digit zero-filled right-justified ASCII character strings (for example, C010005 for the 10th degree 5th order C coefficient, or S002001 for the 2nd degree 1st order S coefficient). The eighth byte in the table is an ASCII blank used to ensure that the row length is equal to RECORD_BYTES. Names of other solution parameters are limited to 8 ASCII characters; if less than 8, they will be left-justified and padded with ASCII blanks. The Names Table itself will be padded with ASCII blanks, if necessary, so that its length is an integral multiple of RECORD_BYTES." OBJECT = COLUMN NAME = "PARAMETER NAME" DATA_TYPE = CHARACTER START_BYTE = 1 BYTES = 8 UNIT = "N/A" DESCRIPTION = "The name of the coefficient or other solution parameter, left- justified and padded with ASCII blanks (if needed) to 8 characters." END_OBJECT = COLUMN END_OBJECT = SHBDR_NAMES_TABLE 4.2.2.3 SHBDR Coefficients Object Definition The SHBDR Coefficients Object is completely defined by the Coefficients Object Definition in the label. Small differences in DESCRIPTION values should be expected from product to product. The structure outlined in the Definition below should not vary, however. The SHBDR Coefficients Object is an optional part of the SHBDR data file. This allows the SHBDR to be used for targets which are too small or too remote to have easily discerned coefficients, but for which estimates of mass have been obtained (e.g., satellites Phobos and Deimos). If the Covariance Object is included in the SHBDR, the Coefficients Object is required. If the Coefficients Object is not included in the SHBDR file, either the SHBDR Coefficients Object Definition will be omitted or the number of rows will be set to zero (ROWS = 0). If the SHBDR Coefficients Object is not included, the pointer ^SHBDR_COEFFICIENTS_TABLE will not appear in the label header. If the SHBDR Coefficients Object Definition is included in the label, it immediately follows the SHBDR Names Object Definition. The order in which coefficients appear in the Coefficients Object is defined by the Names Object [2]. OBJECT = SHBDR_COEFFICIENTS_TABLE ROWS = * COLUMNS = 1 ROW_BYTES = 8 INTERCHANGE_FORMAT = BINARY DESCRIPTION = "The SHBDR Coefficients Table contains the coefficients and other solution parameters for the spherical harmonic model. The order of the coefficients in this table corresponds exactly to the order of the coefficient and parameter names in SHBDR_NAMES_TABLE. The SHBDR Coefficients Table will be padded with double precision DATA_TYPE zeroes so that its total length is an integral multiple of RECORD_BYTES." OBJECT = COLUMN NAME = "COEFFICIENT VALUE" DATA_TYPE = * START_BYTE = 1 BYTES = 8 UNIT = "N/A" DESCRIPTION = "A coefficient Cij or Sij or other solution parameter as specified in the SHBDR Names Table." END_OBJECT = COLUMN END_OBJECT = SHBDR_COEFFICIENTS_TABLE 4.2.2.4 SHBDR Covariance Object Definition The SHBDR Covariance Object is completely defined by the Covariance Object Definition in the label. Small differences in DESCRIPTION values should be expected from product to product. The structure established by the Definition below should not change, however. The SHBDR Covariance Object is an optional part of the SHBDR data file. If the Covariance Object is not included, either the Covariance Object Definition will be omitted or the number of rows will be set to zero (ROWS = 0). If the SHBDR Covariance Object is not included, the pointer ^SHBDR_COVARIANCE_TABLE will not appear in the label header. If the SHBDR Covariance Object Definition is included in the label, it immediately follows the SHBDR Coefficients Object Definition. The order in which covariance terms appear in the Covariance Object is defined by the Names Object [2]. OBJECT = SHBDR_COVARIANCE_TABLE ROWS = * COLUMNS = 1 ROW_BYTES = 8 INTERCHANGE_FORMAT = BINARY DESCRIPTION = "The SHBDR Covariance Table contains the covariances for the spherical harmonic model coefficients and other solution parameters. The order of the covariances in this table is defined by the product of the SHBDR Names Table with its transpose, except that redundant terms are omitted on their second occurrence. The SHBDR Covariance Table will be padded with double precision DATA_TYPE zeroes so that its total length is an integral multiple of RECORD_BYTES. OBJECT = COLUMN NAME = "COVARIANCE VALUE" DATA_TYPE = * START_BYTE = 1 BYTES = 8 UNIT = "N/A" DESCRIPTION = "The covariance value for the coefficients and other solution parameters specified by the product of SHBDR_NAMES_TABLE with its transpose, after omitting redundant terms." END_OBJECT = COLUMN END_OBJECT = SHBDR_COVARIANCE_TABLE 4.3. Data File Each SHBDR data file comprises one or more data blocks. The data objects were defined in Section 4.2. The data blocks are illustrated below. The Header Object is required in each SHBDR file; the Names Object, the Coefficients Object, and the Covariance Object are optional. If the Covariance Object is included, both the Coefficients Object and the Names Object are required; if the Coefficients Object is included, the Names Object is required. 4.3.1. SHBDR Header Object/Block The SHBDR Header Object contains the parameters necessary to interpret the data in the SHBDR file. The structure and content of the SHBDR Header Object are defined in Section 4.2.2.1. The SHBDR Header Object is a one-row table; hence the Header Object and the Header Block are logically synonymous. The structure of the Header Block is shown in Table 4-3-1. |====================================================================| | | | Table 4-3-1. SHBDR Header Block | | | |====================================================================| | Col No | Offset | Length | Format | Column Name | |--------|--------|--------|--------|--------------------------------| | 1 | +0 | 8 | double |Planetary Radius | |--------|--------|--------|--------|--------------------------------| | 2 | 8 | 8 | double |Constant | |--------|--------|--------|--------|--------------------------------| | 3 | 16 | 8 | double |Uncertainty in Constant | |--------|--------|--------|--------|--------------------------------| | 4 | 24 | 4 | long |Degree of Field | |--------|--------|--------|--------|--------------------------------| | 5 | 28 | 4 | long |Order of Field | |--------|--------|--------|--------|--------------------------------| | 6 | 32 | 4 | long |Normalization State | |--------|--------|--------|--------|--------------------------------| | 7 | 36 | 4 | long |Number of Names | |--------|--------|--------|--------|--------------------------------| | 8 | 40 | 8 | double |Reference Longitude | |--------|--------|--------|--------|--------------------------------| | 9 | 48 | 8 | double |Reference Latitude | |--------|--------|--------|--------|--------------------------------| | | +56 | | |========|========|========|========|================================| |====================================================================| | | | Table 4-3-2. SHBDR Names Block | | | |====================================================================| | Col No | Offset | Length | Format | Column Name | |--------|--------|--------|--------|--------------------------------| | 1 | +0 | 8 | A8 |Coefficient or Solution | | | | | |Parameter Name | |--------|--------|--------|--------|--------------------------------| | | +8 | | |========|========|========|========|================================| 4.3.2. SHBDR Names Block The SHBDR Names Object is comprised of one or more SHBDR Names Blocks. Each block contains the name of one coefficient or solution parameter in the Spherical Harmonic Model. The structure and content of the SHBDR Names Object are defined in Section 4.2.2.2. The structure of an individual block is shown in Table 4-3-2. 4.3.3. SHBDR Coefficients Block The SHBDR Coefficients Object comprises one or more SHBDR Coefficients Blocks. Each block contains the value of one coefficient or other solution parameter for the overall model defined by the SHBDR product. The structure and content of the SHBDR Coefficients Object are defined in Section 4.2.2.3. The structure of an individual block is shown in Table 4-3-3. |====================================================================| | | | Table 4-3-3. SHBDR Coefficients Block | | | |====================================================================| | Col No | Offset | Length | Format | Column Name | |--------|--------|--------|--------|--------------------------------| | 1 | +0 | 8 | double |Coefficient Cij or Sij or | | | | | |other solution parameter | |--------|--------|--------|--------|--------------------------------| | | +8 | | |========|========|========|========|================================| 4.3.4. SHBDR Covariance Block The SHBDR Covariance Object comprises one or more SHBDR Covariance Blocks. Each SHBDR Covariance Block contains one covariance for the overall model defined by the SHBDR product. The structure and content of the SHBDR Covariance Object are defined in Section 4.2.2.4. The structure of an individual block is shown in Table 4-3-4. The SHBDR Covariance Object is an optional component of the SHBDR file. |====================================================================| | | | Table 4-3-4. SHBDR Covariance Block | | | |====================================================================| | Col No | Offset | Length | Format | Column Name | |--------|--------|--------|--------|--------------------------------| | 1 | +0 | 8 | double |Covariance Value | |--------|--------|--------|--------|--------------------------------| | | +8 | | |========|========|========|========|================================| 5. Support Staff and Cognizant Personnel The following persons may be contacted for information. Mars Global Surveyor Radio Science Team: Richard A. Simpson Packard Building - Room 332 Center for Radar Astronomy Stanford University Stanford, CA 94305-9515 Phone: 650-723-3525 FAX: 650-723-9251 Electronic mail: rsimpson@magellan.stanford.edu Planetary Data System: PDS Operator Planetary Data System MS 171-264 Jet Propulsion Laboratory 4800 Oak Grove Drive Pasadena, CA 91109-8099 Phone: 626-744-5414 Electronic Mail: pds_operator@jpl.nasa.gov Appendix A. Binary Data Format A.1. IEEE Integer Fields 0 7 1-byte (char; uchar) --------- | [0] | --------- 0 15 2-byte (short; ushort) --------- --------- | [0] | [1] | --------- --------- 0 31 4-byte (long; ulong) --------- --------- --------- --------- | [0] | [1] | [2] | [3] | --------- --------- --------- --------- IEEE binary integers are stored in one, two, or four consecutive 8-bit bytes. Unsigned integers uchar, ushort, ulong, which always represent positive values, contain 8, 16, or 32 binary bits, respectively. As illustrated above, the significance increases from the rightmost bit to the leftmost (bit 0). Signed integers (char, short, long) are stored in the same way, except that negative values are formed by taking the corresponding positive value, complementing each bit, then adding unity -- known as "two's complement" format. As a consequence, a negative value always has bit 0 set "on". Integers are written externally in increasing byte-number order, i.e. [0], [1], etc., so that more significant bits always precede less significant ones. For example, the short value -2 is stored as a pair of bytes valued 0xff, 0xfe. A.2. IEEE Floating-Point Fields 0 1 8 9 31 4-byte (float) --------- --------- --------- --------- | | [0] | | [1] | [2] | [3] | --------- --------- --------- --------- 0 1 8 9 31 8-byte (double) --------- --------- --------- --------- | | [0] | | [1] | [2] | [3] | --------- --------- --------- --------- 32 63 --------- --------- --------- --------- | [4] | [5] | [6] | [7] | --------- --------- --------- --------- IEEE single- (double-) precision floating point numbers (known to IEEE enthusiasts as E-type floating-point formats, respectively) are stored in four (eight) consecutive bytes. Bit number 0 contains a sign indicator, S. Bits 1 through 8 (11) contain a binary exponent, E. The significance increases from bit 8 (11) through bit 1. Bits 9 (12) through 31 (63) contain a mantissa M, a 23-bit (52-bit) binary fraction whose binary point lies immediately to the left of bit 9 (12). The significance increases from bit 31 (63) through bit 9 (11). The value of the single-precision field is given by S E-127 (-1) *2 *(1+M) The value of the double-precision field is given by S E-1023 (-1) *2 *(1+M) The numbers are stored externally in increasing byte-number order, i.e. [0], [1], etc. For example, the maximum single-precision float value +3.40282347E+38 is stored as four bytes valued 0x7f, 0x7f, 0xff, 0xff. Special single-precision float values are represented as +Infinity (0x7f800000), -Infinity (0xff800000), quiet NaN (not a number) (0xffffffff), and signaling NaN (0x7f800001). A.3. VAX Integer Fields 0 7 1-byte (char; uchar) --------- | [0] | --------- 0 15 2-byte (short; ushort) --------- --------- | [1] | [0] | --------- --------- 0 31 4-byte (long; ulong) --------- --------- --------- --------- | [3] | [2] | [1] | [0] | --------- --------- --------- --------- VAX binary integers are stored in one, two, or four consecutive 8-bit bytes. Unsigned integers uchar, ushort, and ulong (which always represent positive values) contain 8, 16, or 32 binary bits, respectively. As illustrated above, the significance increases from the rightmost bit to the leftmost (bit 0). Signed integers (char, short, long) are stored in the same way, except that negative values are formed by taking the corresponding positive value, complementing each bit, then adding unity -- known as "two's complement" format. As a consequence, a negative value always has bit 0 set or "on." Integers are written externally in increasing byte-number order, i.e. [0], [1], etc., so that less significant bits always precede more significant ones. For example, the short value -2 is stored as a pair of bytes valued 0xfe, 0xff. (This section has been adapted from a description by P.G. Ford in the Magellan ARCDR SIS). A.4. VAX Floating-Point Fields 0 1 8 9 31 4-byte (float) --------- --------- --------- --------- | | [1] | | [0] | [3] | [2] | --------- --------- --------- --------- 0 1 8 9 31 8-byte (double) --------- --------- --------- --------- | | [1] | | [0] | [3] | [2] | --------- --------- --------- --------- 32 63 --------- --------- --------- --------- | [5] | [4] | [7] | [6] | --------- --------- --------- --------- VAX single- (double-) precision floating point numbers (known to VAX enthusiasts as F-type and D-type floating-point formats, respectively) are stored in four (eight) consecutive bytes. Bit number 0 contains a sign indicator, S. Bits 1 through 8 contain a binary exponent, E. The significance increases from bit 8 through bit 1. Bits 9 through 31 (63) contain a mantissa M, a 23-bit (55-bit) binary fraction whose binary point lies immediately to the left of bit 9. The significance increases from bit 31 (63) through bit 9. The value of the field is given by S E-129 (-1) *2 *(1+M) The numbers are stored externally in increasing byte-number order, i.e. [0], [1], etc. For example, the float value +1.0 is stored as four bytes valued 0x80, 0x40, 0x00, 0x00. (This section has been adapted from a description by P.G. Ford in the Magellan ARCDR SIS). Appendix B. Example SHBDR Label and Data Object B.1 Example Label The following is an example Label for a Spherical Harmonic Model (SHBDR) Coefficients File. In the next section, an example data object is shown PDS_VERSION_ID = PDS3 FILE_NAME = "JGNNNN01.SHB" RECORD_TYPE = FIXED_LENGTH RECORD_BYTES = 512 FILE_RECORDS = 5 ^SHBDR_HEADER_TABLE = ("JGNNNN01.SHB",1) ^SHBDR_NAMES_TABLE = ("JGNNNN01.SHB",2) ^SHBDR_COEFFICIENTS_TABLE = ("JGNNNN01.SHB",3) ^SHBDR_COVARIANCE_TABLE = ("JGNNNN01.SHB",4) INSTRUMENT_HOST_NAME = "MAGELLAN" TARGET_NAME = "VENUS" INSTRUMENT_NAME = "RADIO SCIENCE SUBSYSTEM" DATA_SET_ID = "MGN-V-RSS-5-SHGBDR-L2-V1.0" OBSERVATION_TYPE = "GRAVITY FIELD" PRODUCT_ID = "JGNNNN01.SHB"" PRODUCT_RELEASE_DATE = 1993-05-15 DESCRIPTION = "This file contains coefficients and related data for a spherical harmonic model of the Venus gravity field. Input data are from radio tracking of the Magellan spacecraft. This product is a set of binary tables: a header table, a names table, a coefficients table, and an optional covariance table. Definitions of the tables follow. This Magellan Venus gravity model is in the form of a Spherical Harmonics Binary Data Record (SHBDR). It has been produced by the Magellan Gravity Science Team at JPL under the direction of W.L. Sjogren." START_ORBIT_NUMBER = 4830 STOP_ORBIT_NUMBER = 4831 PRODUCT_CREATION_TIME = 1993-01-15T12:43:55.129 PRODUCER_FULL_NAME = "JODY MARSHALL" PRODUCER_INSTITUTION_NAME = "JET PROPULSION LABORATORY" PRODUCT_VERSION_TYPE = "PRELIMINARY" PRODUCER_ID = "MGN GRAVSCI TEAM" SOFTWARE_NAME = "SHGJ;V4.57" OBJECT = SHBDR_HEADER_TABLE ROWS = 1 COLUMNS = 9 ROW_BYTES = 56 INTERCHANGE_FORMAT = BINARY DESCRIPTION = "The SHBDR Header includes descriptive information about the spherical harmonic coefficients which follow in SHBDR_COEFFICIENTS_TABLE. The header consists of a single record of nine data columns requiring 56 bytes. The Header is followed by a pad of binary integer zeroes to ensure alignment with RECORD_BYTES." OBJECT = COLUMN NAME = "REFERENCE RADIUS" DATA_TYPE = IEEE_DOUBLE START_BYTE = 1 BYTES = 8 UNIT = "KILOMETER" DESCRIPTION = "The assumed reference radius of the spherical planet." END_OBJECT = COLUMN OBJECT = COLUMN NAME = "CONSTANT" DATA_TYPE = IEEE_DOUBLE START_BYTE = 9 BYTES = 8 UNIT = "N/A" DESCRIPTION = "For a gravity field model the gravitational constant GM in kilometers cubed per seconds squared for the planet. For a topography model, set to 1" END_OBJECT = COLUMN OBJECT = COLUMN NAME = "UNCERTAINTY IN CONSTANT" DATA_TYPE = IEEE_DOUBLE START_BYTE = 17 BYTES = 8 UNIT = "N/A" DESCRIPTION = "For a gravity field model the uncertainty in the gravitational constant GM in kilometers cubed per seconds squared for the planet. For a topography model, set to 0." END_OBJECT = COLUMN OBJECT = COLUMN NAME = "DEGREE OF FIELD" DATA_TYPE = IEEE_INTEGER START_BYTE = 25 BYTES = 4 UNIT = "N/A" DESCRIPTION = "Degree of the model field." END_OBJECT = COLUMN OBJECT = COLUMN NAME = "ORDER OF FIELD" DATA_TYPE = IEEE_INTEGER START_BYTE = 29 BYTES = 4 UNIT = "N/A" DESCRIPTION = "Order of the model field." END_OBJECT = COLUMN OBJECT = COLUMN NAME = "NORMALIZATION STATE" DATA_TYPE = IEEE_INTEGER START_BYTE = 33 BYTES = 4 UNIT = "N/A" DESCRIPTION = "The normalization indicator. For gravity field: 0 coefficients are unnormalized 1 coefficients are normalized 2 other." END_OBJECT = COLUMN OBJECT = COLUMN NAME = "NUMBER OF NAMES" DATA_TYPE = IEEE_INTEGER START_BYTE = 37 BYTES = 4 UNIT = "N/A" DESCRIPTION = "Number of valid names in the SHBDR Names Table. Also, the number of valid coefficients in the SHBDR Coefficients Table." END_OBJECT = COLUMN OBJECT = COLUMN NAME = "REFERENCE LONGITUDE" POSITIVE_LONGITUDE_DIRECTION = "EAST" DATA_TYPE = IEEE_DOUBLE START_BYTE = 41 BYTES = 8 UNIT = "DEGREE" DESCRIPTION = "The reference longitude for the spherical harmonic expansion; normally 0." END_OBJECT = COLUMN OBJECT = COLUMN NAME = "REFERENCE LATITUDE" DATA_TYPE = IEEE_DOUBLE START_BYTE = 49 BYTES = 8 UNIT = "DEGREE" DESCRIPTION = "The reference latitude for the spherical harmonic expansion; normally 0." END_OBJECT = COLUMN END_OBJECT = SHBDR_HEADER_TABLE OBJECT = SHBDR_NAMES_TABLE ROWS = 13 COLUMNS = 1 ROW_BYTES = 8 INTERCHANGE_FORMAT = BINARY DESCRIPTION = "The SHBDR Names Table contains names for the solution parameters (including gravity field coefficients) which will follow in SHBDR_COEFFICIENTS_TABLE. The order of the names in SHBDR_NAMES_TABLE corresponds identically to the order of the parameters in SHBDR_COEFFICIENTS_TABLE. Each coefficient name is of the form Cij or Sij where i is the degree of the coefficient and j is the order of the coefficient. Both indices are three- digit zero-filled right-justified ASCII character strings (for example, C010005 for the 10th degree 5th order C coefficient, or S002001 for the 2nd degree 1st order S coefficient). The eighth byte in the table is an ASCII blank used to ensure that the row length is equal to RECORD_BYTES. Names of other solution parameters are limited to 8 ASCII characters; if less than 8, they will be left-justified and padded with ASCII blanks. The Names Table itself will be padded with ASCII blanks, if necessary, so that its length is an integral multiple of RECORD_BYTES." OBJECT = COLUMN NAME = "PARAMETER NAME" DATA_TYPE = CHARACTER START_BYTE = 1 BYTES = 8 UNIT = "N/A" DESCRIPTION = "The name of the coefficient or other solution parameter, left- justified and padded with ASCII blanks (if needed) to 8 characters." END_OBJECT = COLUMN END_OBJECT = SHBDR_NAMES_TABLE OBJECT = SHBDR_COEFFICIENTS_TABLE ROWS = 13 COLUMNS = 1 ROW_BYTES = 8 INTERCHANGE_FORMAT = BINARY DESCRIPTION = "The SHBDR Coefficients Table contains the coefficients and other solution parameters for the spherical harmonic model. The order of the coefficients in this table corresponds exactly to the order of the coefficient and parameter names in SHBDR_NAMES_TABLE. The SHBDR Coefficients Table will be padded with double precision DATA_TYPE zeroes so that its total length is an integral multiple of RECORD_BYTES." OBJECT = COLUMN NAME = "COEFFICIENT VALUE" DATA_TYPE = IEEE_DOUBLE START_BYTE = 1 BYTES = 8 UNIT = "N/A" DESCRIPTION = "A coefficient Cij or Sij or other solution parameter as specified in the SHBDR Names Table." END_OBJECT = COLUMN END_OBJECT = SHBDR_COEFFICIENTS_TABLE OBJECT = SHBDR_COVARIANCE_TABLE ROWS = 91 COLUMNS = 1 ROW_BYTES = 8 INTERCHANGE_FORMAT = BINARY DESCRIPTION = "The SHBDR Covariance Table contains the covariances for the spherical harmonic model coefficients and other solution parameters. The order of the covariances in this table is defined by the product of the SHBDR Names Table with its transpose, except that redundant terms are omitted on their second occurrence. The SHBDR Covariance Table will be padded with double precision DATA_TYPE zeroes so that its total length is an integral multiple of RECORD_BYTES. OBJECT = COLUMN NAME = "COVARIANCE VALUE" DATA_TYPE = IEEE_DOUBLE START_BYTE = 1 BYTES = 8 UNIT = "N/A" DESCRIPTION = "The covariance value for the coefficients and other solution parameters specified by the product of SHBDR_NAMES_TABLE with its transpose, after omitting redundant terms." END_OBJECT = COLUMN END_OBJECT = SHBDR_COVARIANCE_TABLE END B.2 Example Data Object An example SHBDR data object corresponding to the label example in Section B.1 is shown in hexadecimal format below. Binary floating- point and integer values are represented using IEEE conventions. 0000000 40b7 a300 0000 0000 4113 d3ea 6666 6666 0000020 3ff0 0000 0000 0000 0000 0003 0000 0003 0000040 0000 0000 0000 000d 4066 8000 0000 0000 0000060 0000 0000 0000 0000 0000 0000 0000 0000 * 0001000 4330 3032 3030 3020 4330 3032 3030 3120 0001020 4330 3032 3030 3220 4330 3033 3030 3020 0001040 4330 3033 3030 3120 4330 3033 3030 3220 0001060 4330 3033 3030 3320 5330 3032 3030 3120 0001100 5330 3032 3030 3220 5330 3033 3030 3120 0001120 5330 3033 3030 3220 5330 3033 3030 3320 0001140 474d 2020 2020 2020 2020 2020 2020 2020 0001160 2020 2020 2020 2020 2020 2020 2020 2020 * 0002000 3ff0 0000 0000 0000 4000 0000 0000 0000 0002020 4008 0000 0000 0000 4010 0000 0000 0000 0002040 4014 0000 0000 0000 4018 0000 0000 0000 0002060 401c 0000 0000 0000 4020 0000 0000 0000 0002100 4022 0000 0000 0000 4024 0000 0000 0000 0002120 4026 0000 0000 0000 4028 0000 0000 0000 0002140 402a 0000 0000 0000 0000 0000 0000 0000 0002160 0000 0000 0000 0000 0000 0000 0000 0000 * 0003000 3ff0 0000 0000 0000 4000 0000 0000 0000 0003020 4008 0000 0000 0000 4010 0000 0000 0000 0003040 4014 0000 0000 0000 4018 0000 0000 0000 0003060 401c 0000 0000 0000 4020 0000 0000 0000 0003100 4022 0000 0000 0000 4024 0000 0000 0000 0003120 4026 0000 0000 0000 4028 0000 0000 0000 0003140 402a 0000 0000 0000 402c 0000 0000 0000 0003160 402e 0000 0000 0000 4030 0000 0000 0000 0003200 4031 0000 0000 0000 4032 0000 0000 0000 0003220 4033 0000 0000 0000 4034 0000 0000 0000 0003240 4035 0000 0000 0000 4036 0000 0000 0000 0003260 4037 0000 0000 0000 4038 0000 0000 0000 0003300 4039 0000 0000 0000 403a 0000 0000 0000 0003320 403b 0000 0000 0000 403c 0000 0000 0000 0003340 403d 0000 0000 0000 403e 0000 0000 0000 0003360 403f 0000 0000 0000 4040 0000 0000 0000 0003400 4040 8000 0000 0000 4041 0000 0000 0000 0003420 4041 8000 0000 0000 4042 0000 0000 0000 0003440 4042 8000 0000 0000 4043 0000 0000 0000 0003460 4043 8000 0000 0000 4044 0000 0000 0000 0003500 4044 8000 0000 0000 4045 0000 0000 0000 0003520 4045 8000 0000 0000 4046 0000 0000 0000 0003540 4046 8000 0000 0000 4047 0000 0000 0000 0003560 4047 8000 0000 0000 4048 0000 0000 0000 0003600 4048 8000 0000 0000 4049 0000 0000 0000 0003620 4049 8000 0000 0000 404a 0000 0000 0000 0003640 404a 8000 0000 0000 404b 0000 0000 0000 0003660 404b 8000 0000 0000 404c 0000 0000 0000 0003700 404c 8000 0000 0000 404d 0000 0000 0000 0003720 404d 8000 0000 0000 404e 0000 0000 0000 0003740 404e 8000 0000 0000 404f 0000 0000 0000 0003760 404f 8000 0000 0000 4050 0000 0000 0000 0004000 4050 4000 0000 0000 4050 8000 0000 0000 0004020 4050 c000 0000 0000 4051 0000 0000 0000 0004040 4051 4000 0000 0000 4051 8000 0000 0000 0004060 4051 c000 0000 0000 4052 0000 0000 0000 0004100 4052 4000 0000 0000 4052 8000 0000 0000 0004120 4052 c000 0000 0000 4053 0000 0000 0000 0004140 4053 4000 0000 0000 4053 8000 0000 0000 0004160 4053 c000 0000 0000 4054 0000 0000 0000 0004200 4054 4000 0000 0000 4054 8000 0000 0000 0004220 4054 c000 0000 0000 4055 0000 0000 0000 0004240 4055 4000 0000 0000 4055 8000 0000 0000 0004260 4055 c000 0000 0000 4056 0000 0000 0000 0004300 4056 4000 0000 0000 4056 8000 0000 0000 0004320 4056 c000 0000 0000 0000 0000 0000 0000 0004340 0000 0000 0000 0000 0000 0000 0000 0000 * 0005000