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RECORD_BYTES = 80
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= TEXT
PUBLICATION_DATE = 2008-07-28
NOTE
= "Software Interface Specification for
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END
SOFTWARE INTERFACE SPECIFICATION
RADIO SCIENCE DIGITAL MAP (RSDMAP) PRODUCTS
prepared by
Richard A. Simpson
Packard Building - Room 332
Stanford University
Stanford, CA
94305
Peggy L. Jester
SGT, Inc / Code 614.1
NASA GSFC / Wallops Flight Facility
Wallops
Island, VA 23337 USA
Version 3.2
13 October 2010
PREFACE
|====================================================================|
|
|
|
DOCUMENT CHANGE LOG
|
|
|
|====================================================================|
|REVISION|REVISION| SECTION |
REMARKS
|
| NUMBER
| DATE | AFFECTED |
|
|--------+--------+------------+-------------------------------------|
| 2.0 |98/04/20| All |Adapted from V1.0.2 for MGS and Lunar|
|
| |
| Prospector.
|
|--------+--------+------------+-------------------------------------|
| 2.0.1 |98/12/16| 4.2.1 |Change MGS DATA_SET_ID to
|
|
| |
| MGS-M-RSS-5-SDP-V1.0
|
|--------+--------+------------+-------------------------------------|
| 2.0.1 |98/12/16| Appendix B |Added
examples in B.1 and B.2 |
|--------+--------+------------+-------------------------------------|
| 2.0.2 |99/03/09|Distribution|Update
list of PDS recipients |
|--------+--------+------------+-------------------------------------|
| 2.0.2 |99/03/09|Acr &
Abbrev|Changed "LPX" to "LP" for Lunar |
|
| | 1.2 | Prospector
|
|--------+--------+------------+-------------------------------------|
| 2.0.2 |99/03/09| 2.3 |Generalized use of
"nnnnvv" string in|
|
| |
| file naming.
|
|--------+--------+------------+-------------------------------------|
| 2.0.2 |99/03/09| Fig. 4-2-3
|Generalized value for pointer |
|
| |
| ^DATA_SET_MAP_PROJECTION
|
|--------+--------+------------+-------------------------------------|
| 2.0.2 |99/03/09| Fig. 4-2-2 |Removed
keyword UNIT from IMAGE |
|
| | B.1 | object definition
|
|--------+--------+------------+-------------------------------------|
| 2.0.2
|99/03/09| 1.5.4.1 |Substituted 7-bit ASCII
characters |
| |
| 1.5.4.2 | for 8-bit versions
|
|--------+--------+------------+-------------------------------------|
| 3.0 |06/03/15| All |Adapted from V2.0.2 for Messenger and|
|
| |
| MRO. Streamlined format,
omitting |
|
| |
| obsolete distribution list and table|
|
| |
| of Items to be
|
|--------+--------+------------+-------------------------------------|
| 3.1 |08/07/28| 2.3 |Updated file naming convention |
|
| |
| for MRO
|
|--------+--------+------------+-------------------------------------|
| 3.2 |10/13/10| 2.3 |Updated file naming convention |
|
| |
| to include more characters to |
|
| |
| describe solution of the field |
|========|========|============|=====================================|
Contents
Preface.............................................................ii
Document Change
Log...............................................ii
Contents.........................................................iii
Acronyms and
Abbreviations.........................................v
1.
General Description...............................................1
1.1. Overview......................................................1
1.2.
Scope.........................................................1
1.3. Applicable
Documents..........................................1
1.4. System
Siting.................................................1
1.4.1. Interface Location
and Medium.............................1
1.4.2. Data Sources,
Transfer Methods, and Destinations..........1
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. Image Object
Definition...................................9
4.2.3. Image Map Projection
Object Definition...................10
4.3. Data
File....................................................11
5. Support
Staff and Cognizant Personnel............................12
Appendix
A. Binary Data
Format.....................................13
A.1. IEEE Integer
Fields..........................................13
A.2. IEEE Floating-Point
Fields...................................13
A.3. VAX Integer
Fields...........................................14
A.4. VAX Floating-Point
Fields....................................15
Appendix
B. Example Data
Products..................................16
B.1. Example Label................................................16
B.2. Example Data
Object..........................................17
Figures
4-2-1. RSDMAP Label
Header.........................................7
4-2-2. RSDMAP Image Object
Definition..............................9
4-2-3. RSDMAP Image Map Projection
Definition.....................10
Acronyms and Abbreviations
ANSI American
National Standards Institute
APL Applied
Physics Laboratory
ARC Ames
Research Center
ARCDR MGN Altimetry and
Radiometry Composite Data Record
ASCII American Standard
Code for Information Interchange
ASU Arizona
State University
CD-WO compact-disc
write-once
CNES Centre National
d'Etudes Spatiales
CR
Carriage return (ASCII character)
dB
Decibel
DEC Digital
Equipment Corporation
DSN Deep
Space Network
DVD Digital Video Disc or Digital
Versatile Disc
EGM96 Earth Gravitational Model 1996
FEA Front End
Assembly
GSFC Goddard Space
Flight Center
IEEE Institute of
Electrical and Electronic Engineers
IAU
International Astronomical Union
JHU Johns Hopkins University
JPL Jet
Propulsion Laboratory
J2000 IAU Official Time
Epoch
K
Degrees Kelvin
kB
kilobytes
km
Kilometers
LAST Laser Altimeter Science Team
(Messenger)
LF Line feed (ASCII
character)
LP
Lunar Prospector (mission or spacecraft)
MESSENGER MErcury Surface Space
ENvironment, GEochemistry,
and Ranging (acronym for mission to Mercury)
MGN Magellan
(project or spacecraft)
MGS Mars
Global Surveyor
MIT Massachusetts Institute of
Technology
MLA MESSENGER Laser Altimeter
MO
Mars Observer
MRO Mars Reconnaissance Orbiter
NAIF Navigation and
Ancillary Information Facility
NASA National
Aeronautics and Space Administration
NAV
Navigation Subsystem/Team
ODL Object
Definition Language (PDS)
PDS Planetary
Data System
RS
Radio Science
RSDMAP Radio Science Digital Map
Product
RSS Radio
Science Subsystem
RST Radio
Science Team
SCET Space Craft
Event Time
SHADR Spherical Harmonic
ASCII Data Record
SHBDR Spherical Harmonic
Binary Data Record
SHM Spherical
Harmonic 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
TES Thermal
Emission Spectrometer
UTC Universal
Time Coordinated
1. General Description
1.1. Overview
This Software
Interface Specification (SIS) describes Radio
Science
Digital Map (RSDMAP) files. The
RSDMAP product was designed
for
geoid, isostatic anomaly, Bouguer anomaly, or other digital maps
derived
primarily from Radio Science data [1].
Use of the RSDMAP format
is not
limited to Radio Science data, however.
1.2. Scope
The format and
content specifications in this SIS apply to all
phases of
a project for which RSDMAP products are produced.
The RSDMAP
product was defined initially for free air gravity
maps
derived from Magellan (MGN) and Mars Observer (MO) radio tracking
data, but
the format is more generally useful.
It was adapted in 1999
for Mars
Global Surveyor (MGS) and Lunar Prospector (LP) radio data with options for MGS
Thermal Emission Spectrometer (TES) data.
In this revision it is adapted for Mars Reconnaissance Orbiter (MRO)
[6,7] and the MESSENGER [8,9] missions.
The Magellan,
Mars Observer, Mars Global Surveyor, and Mars Reconnaissance Orbiter missions
are or were managed by the Jet Propulsion Laboratory (JPL) for the National
Aeronautics and Space Administration (NASA). Lunar Prospector was managed by the Ames Research Center
(ARC) for NASA. MESSENGER is managed
by the Johns Hopkins University Applied Physics Laboratory (APL), in Laurel
Maryland.
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] MGN
630-7, Rev. D, Magellan Planetary Constants and Models, D.T.
Lyons, Mission
Design, Jet Propulsion Laboratory, 9 January 1991.
[3] MO
642-321, Mars Observer Planetary Constants and Models, JPL
D-3444, November
1990.
[4]
D-7116, Rev. D, Planetary Science Data Dictionary Document,
Jet Propulsion
Laboratory, 28 August 2002.
[5]
D-7669 Part 2, Planetary Data System Standards Reference, PDS
Version 3.6, Jet Propulsion Laboratory, 1 August 2003.
[6] Mars Reconnaissance Orbiter Mission
Plan, Revision C: July 2005,
prepared by Robert Lock Document JPL D-22239,
MRO-31-201.
[7] MRO-D-22685, Rev B., Planetary
Constants and Models, 05-15-2003.
[8] McAdams, J. V. (JHU/APL), MESSENGER
mission overview and trajectory
design, American Institute of Aeronautics and
Astronautics,
American
Astronautical Society (AIAA/AAS) Astrodynamics Specialist
Conference, Paper AAS 03-541, 20 pp., Big Sky,
MT, August 3-7, 2003.
[9] McAdams, J. V., D. W. Dunham, R. W.
Farquhar (all at JHU/APL),
A. H. Taylor, and B. G. Williams (both at KinetX, Inc.),
Trajectory
design and maneuver strategy for the MESSENGER
mission to Mercury,
15th American Astronautical Society
(AAS)/American Institute of
Aeronautics and Astronautics (AIAA) Space Flight
Mechanics Conf.,
Paper AAS 05-173, 21 pp., Copper Mountain, CO,
January 23-27, 2005.
[10] Wessel, P. and W. H. F. Smith, Free
software helps map and display data,
EOS Trans. AGU, 72, 441, 1991.
[11] Generic Mapping Tools website:
http://gmt.soest.hawaii.edu/.
1.4. System Siting
1.4.1. Interface Location and Medium
RSDMAP files
are created at the institution conducting the
science
analysis. RSDMAP files are
electronic files.
1.4.2. Data Sources, Transfer Methods,
and Destinations
RSDMAP 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.
RSDMAP files
will be delivered to users via electronic networks and
on
compact-disc write-once volumes (CD-WO).
1.4.3. Generation Method and Frequency
RSDMAP files
are developed separately at each institution
conducting
scientific analyses on raw data.
Each digital map meets
criteria
specified by the investigators conducting the analysis.
Each
digital map typically requires data from a large number of
latitudes
and longitudes, so that RSDMAP files will be issued
infrequently
and on schedules which cannot be predicted.
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
The
detailed formats of the numeric fields are defined in Appendix A.
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 by
m element
array, with first element array[0][0], second element
array[0][1],
and so forth.
1.5.4.2. Time Standards
RSDMAP 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 hour (00-59); and
"fff"
is in milliseconds.
The date format
is "YYYY-MM-DD", where the components are
defined
as above.
1.5.4.3. Coordinate Systems
Coordinate
systems for RSDMAP products are specified in the
IMAGE_MAP_PROJECTION
definition in the PDS label (see Section 4.2.3).
These may
be described more fully in other documents -- e.g. [2,3].
1.5.4.4. Limits of This Document
This document
applies only to RSDMAP 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
RSDMAP product must have access to the data system
(or to
backup media) on which RSDMAP files are stored.
2.1.2. Special Setup Requirements
None.
2.2. Volume and Size
RSDMAP products
have variable length depending on the resolution
of the
map, the number of quantities represented in the image, and the
format of
the individual data points. A
rectangular map of resolution
1 degree
in both latitude and longitude with a single parameter given
as a
double precision floating point number requires about 520 kB
total. The same map in one-byte integers would
require about 65 kB.
2.3. Labeling and Identification
The length of
file names is limited to 27 or less characters before the period delimeter and
3 characters after the period delimeter.
Each file has a
name which describes its contents. The name
includes
the following structure which uniquely identifies it among
RSDMAP
products. Beginning with the MRO
gravity products the following file naming convention is used:
GTsss_ffff_nnnn_cccc.IMG
where
"G" denotes the generating
institution
"A" for Arizona State University
"J" for the Jet Propulsion Laboratory
"G" for Goddard Space Flight Center
"C" for Centre
National d'Etudes Spatiales
"S" for Stanford University
"T" indicates the type of mission
data represented
"G" for gravity field
"T" for topography
"M" for magnetic field
"sss" is a 3-character
modifier specified by the data
producer. This modifier is used to indicate the source
spacecraft or project, such as MRO for the Mars
Reconnaisance Orbiter.
"_" the
underscore character is used to delimit information
in the file name for clarity.
"ddddff" is a 4- to 6-character modifier
specified by the data
producer to indicate the degree and order of the
solution for the gravity field, topography or magnetic
field.
"_" the
underscore character is used to delimit information
in the file name for clarity.
"nnnn" is a 4- to
8-character modifier indicating the type
of data represented
"ANOM" for free air gravity anomalies
"ANOMERR"
for free air gravity anomaly
errors
(1)
"GEOID" for geoid
"GEOIDERR" for
geoid errors (1)
"BOUG" for Bouguer anomaly
"ISOS" for isostatic anomaly
"TOPO" for topography
"MAGF" for magnetic field
(1) Geoid and gravity anomaly errors are computed
from a mapping of the error covariance matrix
of the gravity field solution.
"_" the underscore character is
used to delimit information
in the file name for clarity.
"cccc" is a 2- to 4-character
modifier specified by the data producer
to indicate
the degree and order to which the potential
solution (gravity,
topography or magnetic field) has
been
evaluated. In the case of the error maps for the
gravity
anomalies or geoid, this field indicates to
which
maximum degree and order the error covariance was '
used to
propagate the spatial errors
".IMG" indicates the data is stored as an image.
Each RSDMAP
file is accompanied by a detached PDS label; that label is a file in its own
right with name GTsss_ffff_nnnn_cccc.LBL
2.4. Interface Medium Characteristics
RSDMAP 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 of the data system
or medium
on which they are stored.
3. Access
3.1. Programs Using the Interface
Data contained
in RSDMAP 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 RSDMAP is a
file generated by software at the institution
conducting
scientific data analysis. Each
RSDMAP file is
accompanied
by a detached PDS label.
4.2.
Detached PDS Label
The detached
PDS label has three parts -- a header, an IMAGE
object
definition, and an IMAGE_MAP_PROJECTION definition. The header
contains
information about the origin of the file and its general
characteristics
such as record type and size. The
IMAGE object definition contains information about the image -- lines, pixels,
scaling of pixel values, etc. The
IMAGE_MAP_PROJECTION definition describes how one should display the image.
Each detached
PDS label is constructed of ASCII records;
each
record 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 file header is illustrated in
Figure
4-2-1. Keyword definitions are
given below.
|====================================================================|
|
|
| Figure
4-2-1 RSDMAP Label Header
|
|
|
|====================================================================|
|
|
| PDS_VERSION_ID = PDS3
|
| RECORD_TYPE = FIXED_LENGTH
|
| RECORD_BYTES = nnn
|
| FILE_RECORDS = nnn |
| ^IMAGE = "GTnnnnvv.IMG"
|
| INSTRUMENT_HOST_NAME =
"cccccccccccccccccccc"
|
| TARGET_NAME = "cccc"
|
| INSTRUMENT_NAME =
"ccccccccccccccccccccccc"
|
| DATA_SET_ID =
"ccccccccccccccccccccccc"
|
| ORIGINAL_PRODUCT_ID =
"ccccccccccccccc"
|
| PRODUCT_ID =
"GTnnnnvv.IMG" |
| PRODUCT_RELEASE_DATE = YYYY-MM-DD
|
| DESCRIPTION =
"cccccccccccccccccc"
|
| START_ORBIT_NUMBER = nnnn
|
| STOP_ORBIT_NUMBER = nnnn
|
| START_TIME =
YYYY-MM-DDThh:mm:ss.fff
|
| STOP_TIME =
YYYY-MM-DDThh:mm:ss.fff
|
| SOFTWARE_NAME =
"ccccccc;Vn.m"
|
| PRODUCT_CREATION_TIME =
YYYY-MM-DDThh:mm:ss.fff
|
| PRODUCER_ID = "ccccccc"
|
|
|
|====================================================================|
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 RSDMAP file;
instance dependent.
^IMAGE
=
File name of the RSDMAP file in the form
"GTnnnnvv.IMG", where the structure is
explained in Section 2.3.
INSTRUMENT_HOST_NAME
= Name of the
spacecraft; acceptable names
include "MARS GLOBAL SURVEYOR", "LUNAR
PROSPECTOR", "MARS RECONNAISSANCE ORBITER",
and "MESSENGER".
TARGET_NAME
=
A character string which identifies the
target body. For MGS and
MRO RSDMAP files,
the character string "MARS". For Lunar
Prospector RSDMAP files, the character
string "MOON". For
MESSENGER RSDMAP files,
the character string "MERCURY".
INSTRUMENT_NAME
= Name of the
instrument; set to "RADIO
SCIENCE SUBSYSTEM" for products generated
from radio science data, or to other
instrument names as appropriate.
DATA_SET_ID
=
Identifier for the data set of which this
RSDMAP product is a member.
Set to "MGS-M-
RSS-5-SDP-Vn.m" for Mars Global Surveyor
RSDMAP products, where "Vn.m" indicates the
version number of the data set. Set to
"MRO-M-RSS-5-SDP-Vn.m" for MRO. Set to
"MESS-H-RSS-5-SDP-Vn.m" for MESSENGER.
Set to "LP-L-RSS-5-SHGBDR-L2-Vn.m"
for Lunar Prospector;
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.
Usually the same as the value for ^IMAGE.
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 RSDMAP product.
START_ORBIT_NUMBER
=
Optional. The first orbit
represented in
the RSDMAP product. An
integer.
STOP_ORBIT_NUMBER
=
Optional. The last orbit
represented in
the RSDMAP product. An
integer.
START_TIME
=
The Earth Receive Time at which the first
sample was acquired, expressed in the format
"YYYY-MM-DDThh:mm:ss.fff" where the
components are defined in Section 1.5.4.2.
STOP_TIME
=
The Earth Receive Time at which the last
sample was acquired, expressed in the format
"YYYY-MM-DDThh:mm:ss.fff" where the
components are defined in
Section 1.5.4.2.
SOFTWARE_NAME
= The
name and version number of the program
creating this RSDMAP 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.
PRODUCT_CREATION_TIME
= The time at which this
RSDMAP was created;
expressed
in the format "YYYY-MM-
DDThh:mm:ss.fff" where
the components are
defined in Section 1.5.4.2.
PRODUCER_ID
=
The entity responsible for creation of the
RSDMAP
product; for products generated by the
Mars Global Surveyor Radio Science Team, set
to "MGS RST".
4.2.2. Image Object Definition
The Image
Object Definition in the label completely describes
the
accompanying Digital Map. It
immediately follows the label
header
and has the format shown in Figure 4-2-2.
Keywords
are defined in [4]. There is no
requirement within
this
document that there be any relationship among RECORD_BYTES,
LINE_SAMPLES,
and SAMPLE_BITS other than that the number of bytes
in an
image line be an integral multiple of RECORD_BYTES (Section
4.2.1). It is strongly recommended, however,
that producers of
RSDMAP
files make the line lengths identically equal to RECORD_BYTES
to ensure
maximum compatibility with existing image processing
software. For compatibility, producers are also
encouraged to use
8- or
16-bit integer pixels rather than longer formats.
|====================================================================|
|
|
|
Figure 4-2-2 RSDMAP Image
Object Definition
|
|
|
|====================================================================|
|
|
| OBJECT
= IMAGE
|
| LINES
= nnnn
|
| LINE_SAMPLES
= nnnn
|
| SAMPLE_TYPE
= nnnn
|
| SAMPLE_BITS
= nnnn
|
| OFFSET
= nnn.ff |
| SCALING_FACTOR
= nnn.ff
|
| DESCRIPTION
= "cccccccccccccc"
|
| END_OBJECT =
IMAGE
|
|
|
|====================================================================|
4.2.3.
Image Map Projection Object Definition
The Image Map
Projection Object Definition specifies the map
projection
for an RSDMAP product. It is used
for interpretation of
the
RSDMAP data; it is not required for understanding the structure
of the
file. It immediately follows the
Image Object Definition and
has the
form shown in Figure 4-2-3.
|====================================================================|
|
|
|
Figure 4-2-3 RSDMAP Image
Map Projection Definition |
|
|
|====================================================================|
|
|
| OBJECT
= IMAGE_MAP_PROJECTION
|
|
^DATA_SET_MAP_PROJECTION = "cccccccc.CAT"
|
| COORDINATE_SYSTEM_NAME =
ccccccccccccc
|
| COORDINATE_SYSTEM_TYPE =
ccccccccccccc
|
| MAP_PROJECTION_TYPE =
"ccccccccccc"
|
| A_AXIS_RADIUS
= nnn.ff <unit>
|
| B_AXIS_RADIUS
= nnn.ff <unit>
|
| C_AXIS_RADIUS
= nnn.ff <unit>
|
|
FIRST_STANDARD_PARALLEL = "N/A"
|
|
SECOND_STANDARD_PARALLEL = "N/A"
|
|
POSITIVE_LONGITUDE_DIRECTION = ccccccccccccc
|
| CENTER_LATITUDE
= nnn.ff <unit>
|
| CENTER_LONGITUDE = nnn.ff <unit>
|
| REFERENCE_LATITUDE =
"N/A"
|
| REFERENCE_LONGITUDE =
"N/A"
|
| LINE_FIRST_PIXEL
= nnn
|
| LINE_LAST_PIXEL
= nnn
|
| SAMPLE_FIRST_PIXEL =
nnn
|
| SAMPLE_LAST_PIXEL
= nnn
|
|
MAP_PROJECTION_ROTATION = nnn.ff <unit>
|
| MAP_RESOLUTION
= nnn.ff <unit>
|
| MAP_SCALE
= "N/A"
|
| MAXIMUM_LATITUDE
= nnn.ff <unit>
|
| MINIMUM_LATITUDE
= nnn.ff <unit>
|
| EASTERNMOST_LONGITUDE =
nnn.ff <unit>
|
| WESTERNMOST_LONGITUDE =
nnn.ff <unit>
|
| LINE_PROJECTION_OFFSET =
nnn.ff
|
|
SAMPLE_PROJECTION_OFFSET = nnn
|
| END_OBJECT =
IMAGE_MAP_PROJECTION
|
|
|
|====================================================================|
Keywords are
defined, and standard values are given, in [4].
For Mars
Global Surveyor, Mars Reconnaissance Orbiter, and Messenger RSDMAP
products,
the following are required:
COORDINATE_SYSTEM_NAME
=
"PLANETOCENTRIC"
COORDINATE_SYSTEM_TYPE = "BODY-FIXED
ROTATING"
POSITIVE_LONGITUDE_DIRECTION =
"EAST"
DSMP.CAT is a file stored elsewhere (in the
CATALOG directory); it specifies the map projection more explicitly.
4.3 Data File
The data file
is the Image Object, defined in 4.2.2 and
presumed
to contain the digital map.
Each map
comprises LINES rows of LINE_SAMPLES pixels; each
pixel
occupies SAMPLE_BITS bits.
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
Stanford University
Stanford,
CA 94305
Phone: 650-723-3525
FAX:
650-723-9251
Electronic mail:
rsimpson@magellan.stanford.edu
Mars Reconnaissance Orbiter Gravity
Science Team:
Frank G. Lemoine
Code 698, Planetary Geodynamics Laboratory
NASA Goddard Space Flight Center
Greenbelt, Maryland 20771 U.S.A.
Phone: 301-614-6109
FAX:
301-614-6522
Electronic mail:
Frank.Lemoine@gsfc.nasa.gov
Messenger Laser Altimeter Science
Team:
Maria T. Zuber
Department of Earth, Atmospheric, and Planetary
Sciences
Massachusetts Institute of Technology
54-918
Cambridge, MA 02139-4307
Phone: 617-253-0149
FAX: 617-253-8298
Planetary Data
System:
PDS Operator
Planetary Data System
MS 202-101
Jet Propulsion Laboratory
4800 Oak Grove Drive
Pasadena, CA 91109-8099
Phone: 818-354-4321
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 RSDMAP Label and
Data Object
B.1 Example Label
PDS_VERSION_ID
= PDS3
RECORD_TYPE =
FIXED_LENGTH
RECORD_BYTES
= 2880
FILE_RECORDS
= 180
^IMAGE
= "GG041A60.IMG"
INSTRUMENT_HOST_NAME
= "MARS RECONNAISSANCE ORBITER"
TARGET_NAME
= "MARS"
INSTRUMENT_NAME
= "RADIO SCIENCE SUBSYSTEM"
DATA_SET_ID
= "MRO-M-RSS-5-SDP-V1.0"
ORIGINAL_PRODUCT_ID = "MGM1041A.ANOMALY"
PRODUCT_ID
= "GG041A60.IMG"
PRODUCT_RELEASE_DATE
= 2006-02-23
DESCRIPTION
= "
This file contains a digital
map of the gravity anomalies derived from
the MGM1041A model of the Mars gravity field. Each point gives the
Mars gravity anomaly in milligals, which is the difference of
the
model gravity on the geoid from the normal gravity on a
reference
ellipsoid with
semi-major-axis =
3397.0 km,
GM
= 42828.37024 km**3/s**2,
1/flattening = 196.877360, and
rotation rate = 7.08821806630385e-5 rad/s.
The GG041A60 gravity anomaly map is computed from a truncated
MGM1041A
solution (from degree 2 up to
degree 60) where 'GD' in the file name
indicates it is Gravity anomaly data, '041A' indicates the
MGM1041A
solution is used, and '60' indicates the maximum degree of
the field
used to create the map.
The map was produced by the Mars Global Surveyor Gravity
Science Team
at GSFC under the direction of David E. Smith, by Frank G.
Lemoine.
This anomaly map contains 64800 values.
Location of minimum and maximum anomalies in this file:
Minimum: -507.752 mGals; Longitude = 313.50 E; Latitude 15.50 S
Maximum: 2977.960 mGals; Longitude = 226.50 E; Latitude 18.50 N
The binary data format are big endian (binary style on SUN OS type
workstations).
START_ORBIT_NUMBER =
"N/A"
STOP_ORBIT_NUMBER
= "N/A"
START_TIME
= 1997-10-13T00:00:00.000
STOP_TIME
= 2002-05-27T23:59:59.000
SOFTWARE_NAME
= "HIGEN;V9.0"
PRODUCT_CREATION_TIME =
2006-02-23T17:50:00.000
PRODUCER_ID
= "MRO GST"
/*
Structure Objects */
OBJECT
= IMAGE
LINES
= 180
LINE_SAMPLES
= 360
SAMPLE_TYPE
= "IEEE REAL"
SAMPLE_BITS
= 64
OFFSET
= 0.0E+00
SCALING_FACTOR
= 1.0E+00
DESCRIPTION
= "The Digital Map contains
values of the gravity anomaly. The values can be obtained
by multiplying the sample in the map by
SCALING_FACTOR
and then adding OFFSET. One milligal equals 0.01 mm/s/s."
END_OBJECT
= IMAGE
OBJECT =
IMAGE_MAP_PROJECTION
^DATA_SET_MAP_PROJECTION =
"DSMAP2.CAT"
COORDINATE_SYSTEM_TYPE =
"BODY-FIXED ROTATING"
COORDINATE_SYSTEM_NAME =
"PLANETOCENTRIC"
MAP_PROJECTION_TYPE =
"SIMPLE CYLINDRICAL"
A_AXIS_RADIUS
= 3397.00 <KM>
B_AXIS_RADIUS
= 3397.00 <KM>
C_AXIS_RADIUS
= 3379.75 <KM>
FIRST_STANDARD_PARALLEL =
"N/A"
SECOND_STANDARD_PARALLEL =
"N/A"
POSITIVE_LONGITUDE_DIRECTION =
"EAST"
CENTER_LATITUDE
= 0.0 <DEGREES>
CENTER_LONGITUDE
= 180.0 <DEGREES>
REFERENCE_LATITUDE = 0.0
<DEGREES>
REFERENCE_LONGITUDE = 0.0
<DEGREES>
LINE_FIRST_PIXEL
= 1
LINE_LAST_PIXEL = 180
SAMPLE_FIRST_PIXEL =
1
SAMPLE_LAST_PIXEL
= 360
MAP_PROJECTION_ROTATION = 0.0
<DEGREES>
MAP_RESOLUTION
= 1.0E+00
MAP_SCALE
= "N/A"
MAXIMUM_LATITUDE
= 89.5 <DEGREES>
MINIMUM_LATITUDE
= -89.5 <DEGREES>
EASTERNMOST_LONGITUDE =
359.5 <DEGREES>
WESTERNMOST_LONGITUDE =
0.5 <DEGREES>
LINE_PROJECTION_OFFSET =
89.5
SAMPLE_PROJECTION_OFFSET = -0.5
END_OBJECT
= IMAGE_MAP_PROJECTION
END
B.2 Example Data Object
The list below contains the ascii
dump of the first and last record
or the map file cited in B.1. The first
record consists of the map data
at the northernmost latitude (89.5
degrees), sequentially from longitude
0.5 to 359.5 degrees. The last record
contains the map data for the southern-
most latitude (-89.5 deg) from longitude
0.5 to 359.5 degrees.
A convenient way to read the image
data for the
example givien in Appendix B.1 is with a fortran program
that has the following statements:
......................................
implicit double
precision(a-h,o-z)
dimension rec(360)
dminlon = 0.5d0
dmaxlat = +89.5d0
open(10,file='gg041a60.img',recl=2880,access='direct')
line=1
do 5 line=1,180
10
read(10,rec=line)rec
do 20 i=1,360
dlon = dminlon +
dfloat(i-1)
dlat = dmaxlat -
dfloat(line-1)
write(6,30)dlon,dlat,rec(i)
20
continue
30
format(1x,2f15.5,e20.8)
5
continue
99
stop
end
........................................
The image file may also be read directly
into a GMT (Generic
Mapping Tools) [10,11] grd file using the following command:
(noting that the command wraps around onto
a second line in
this document).
xyz2grd gg041a60.img -ZTLd -Gmgm1041a.grd
-I1/1 -R0.5/359.5/-89.5/89.5
-Ddeg/d eg/milligals/1/0/" Gravity Anomaly to 60"
–V
A generic GMT script to plot the img file
is given below:
========================================================
set -x
rm –f mgm1041a.grd out.ps tmp.cpt
xyz2grd gg041a60.img -ZTLd -Gmgm1041a.grd -I1/1
-R0.5/359.5/-89.5/89.5
-Ddeg/d eg/milligals/1/0/" Gravity Anomaly to 60" –V
grd2cpt mgm1041a.grd –Chaxby –L-600/600
–S-600/600/100 –Z –V > tmp.cpt
grdimage
mgm1041a.grd –Ctmp.cpt –JM8.0i –R0/360/-70/70
–B30g30/30g30 –K > out.ps
grdinfo –M mgm1041a.grd
psscale –Ctmp.cpt –D11.0/14.0/16.0/0.3h
–B:.ÓGMM-2B Gravity Anomalies (60x60) (mGals)Ó: -O >>out.ps
ps2pdf out.ps
......
Sample records from gg041a60.img
rec = 1
39.426
39.303 39.186 39.074 38.968
38.867 38.772 38.683
38.599
38.521 38.448 38.381 38.319
38.264 38.213 38.169
38.129
38.096 38.068 38.045 38.028
38.017 38.011 38.010
38.016
38.026 38.042 38.064 38.091
38.123 38.161 38.204
38.252
38.306 38.365 38.430 38.500
38.575 38.655 38.741
38.832
38.928 39.029 39.136 39.247
39.364 39.485 39.612
39.743
39.880 40.022 40.168 40.319
40.476 40.637 40.802
40.973
41.148 41.328 41.512 41.701
41.894 42.092 42.294
42.501
42.712 42.927 43.147 43.371
43.598 43.830 44.066
44.306
44.549 44.797 45.048 45.303
45.562 45.824 46.089
46.358
46.631 46.907 47.186 47.468
47.753 48.041 48.332
48.626
48.923 49.223 49.525 49.830
50.137 50.447 50.759
51.073
51.389 51.708 52.028 52.350
52.674 53.000 53.328
53.657
53.987 54.319 54.652 54.987 55.322
55.659 55.996
56.334
56.673 57.013 57.353 57.694
58.035 58.377 58.718
59.060
59.402 59.744 60.085 60.426
60.767 61.107 61.447
61.787
62.125 62.463 62.799 63.135
63.470 63.803 64.135
64.466 64.795
65.122 65.448 65.772 66.094
66.414 66.733
67.048
67.362 67.673 67.982 68.289
68.592 68.893 69.191
69.487
69.779 70.068 70.354 70.636
70.915 71.191 71.463
71.732
71.996 72.257 72.514 72.767 73.016 73.261
73.501
73.737
73.969 74.196 74.418 74.636
74.849 75.057 75.260
75.458
75.651 75.839 76.021 76.199
76.371 76.537 76.698
76.853
77.003 77.147 77.285 77.417
77.544 77.664 77.779
77.887 77.989 78.086
78.175 78.259 78.336 78.407
78.472
78.530
78.581 78.626 78.665 78.697
78.722 78.741 78.753
78.758
78.757 78.749 78.734 78.713
78.685 78.650 78.608
78.559
78.504 78.442 78.373 78.297
78.215 78.126 78.030
77.927
77.818 77.702 77.580 77.450
77.315 77.172 77.023
76.868
76.706 76.538 76.364 76.183
75.996 75.803 75.603
75.398
75.186 74.969 74.746 74.517
74.282 74.041 73.795
73.543
73.286 73.024 72.757 72.484
72.206 71.923 71.636
71.343
71.046 70.745 70.439 70.128
69.814 69.495 69.173
68.846
68.516 68.182 67.845 67.504
67.160 66.813 66.464
66.111
65.755 65.397 65.037 64.674
64.309 63.943 63.574
63.204
62.832 62.458 62.084 61.708
61.331 60.953 60.575
60.196
59.817 59.438 59.058 58.679
58.299 57.920 57.542
57.164
56.787 56.410 56.035 55.661
55.288 54.917 54.547
54.179
53.813 53.449 53.087 52.727
52.370 52.015 51.663
51.313
50.966 50.622 50.282 49.944
49.610 49.279 48.951
48.627
48.307 47.990 47.678 47.369
47.064 46.764 46.468
46.176
45.888 45.605 45.326 45.052
44.782 44.517 44.257
44.002
43.751 43.506 43.265 43.029
42.799 42.573 42.353
42.138
41.928 41.724 41.524 41.330
41.142 40.958 40.780
40.608
40.441 40.279 40.123 39.973
39.828 39.688 39.554
rec = 180
137.311 137.340 137.364
137.382 137.395 137.402 137.404 137.401
137.392 137.378 137.359 137.334
137.303 137.268 137.227 137.181
137.129 137.073 137.011 136.944
136.872 136.795 136.713 136.625
136.533 136.436 136.334 136.227 136.116 136.000 135.879 135.753
135.623 135.488 135.349 135.206
135.058 134.905 134.749 134.588
134.424 134.255 134.082 133.906
133.725 133.541 133.353 133.161
132.966 132.767 132.565 132.359
132.150 131.938 131.723 131.505
131.283 131.059 130.832 130.602 130.369 130.134 129.896 129.656
129.413 129.168 128.920 128.671
128.419 128.165 127.910 127.652
127.393 127.132 126.869 126.604
126.339 126.071 125.803 125.533
125.261 124.989 124.716 124.441 124.166 123.890 123.613 123.336
123.058 122.779 122.500 122.221
121.941 121.661 121.381 121.101
120.821 120.541 120.261 119.981
119.701 119.422 119.143 118.865
118.587 118.310 118.034 117.759
117.484 117.210 116.937 116.666
116.395 116.126 115.858 115.591 115.326 115.062 114.799 114.539
114.280 114.022 113.767 113.513
113.262 113.012 112.765 112.519
112.276 112.035 111.797 111.561
111.327 111.096 110.867 110.641
110.418 110.198 109.980 109.766 109.554 109.345 109.140 108.938
108.738 108.542 108.350 108.161
107.975 107.793 107.614 107.439
107.267 107.100 106.936 106.776
106.619 106.467 106.319 106.174
106.034 105.898 105.766 105.638
105.515 105.395 105.281 105.170
105.064 104.963 104.865 104.773 104.685 104.602 104.523 104.449
104.380 104.315 104.255 104.200
104.150 104.105 104.065 104.029
103.998 103.973 103.952 103.936
103.925 103.919 103.919 103.923
103.932 103.946 103.965 103.990 104.019 104.053 104.093 104.137
104.186 104.241 104.300 104.364
104.434 104.508 104.587 104.671
104.760 104.854 104.953 105.057
105.165 105.278 105.396 105.519
105.646 105.778 105.914 106.056
106.201 106.351 106.506 106.665
106.828 106.996 107.168 107.344
107.524 107.709 107.897 108.090
108.286 108.487 108.691 108.899
109.110 109.326 109.545 109.767
109.993 110.222 110.455 110.690
110.929 111.172 111.417 111.665
111.916 112.169 112.426 112.685 112.947 113.211 113.478 113.747
114.018 114.291 114.567 114.845
115.124 115.405 115.688 115.973
116.260 116.547 116.837 117.127
117.419 117.712 118.006 118.301
118.596 118.893 119.190 119.488
119.786 120.085 120.384 120.683
120.982 121.282 121.581 121.880
122.179 122.477 122.775 123.073
123.369 123.665 123.961 124.255
124.548 124.840 125.131 125.420
125.708 125.995 126.280 126.563
126.844 127.124 127.401 127.677
127.950 128.221 128.489 128.756 129.019 129.280 129.538 129.793
130.046 130.295 130.541 130.785
131.025 131.261 131.494 131.724
131.950 132.172 132.391 132.606
132.816 133.023 133.226 133.425
133.620 133.810 133.996 134.177
134.355 134.527 134.695 134.859
135.018 135.172 135.321 135.465
135.605 135.739 135.869 135.994
136.113 136.228 136.337 136.441
136.540 136.633 136.722 136.805
136.883 136.955 137.022 137.084
137.140 137.191 137.236 137.276