des Éléments importants des systèmes de référence et de la géodésie au cern
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Des Éléments Importants des Systèmes de Référence et de la Géodésie au CERN. Mark Jones EN\MEF-SU. Outline. Introduction CERN Coordinate System (CCS) Altitudes Geoid Models CERN Geodetic reference frames Z H Transformation Conclusions. The Survey Team. - PowerPoint PPT PresentationTRANSCRIPT
Des Éléments Importants des Systèmes de Référence et de la Géodésie au CERNMark Jones EN\MEF-SU
Outline• Introduction• CERN Coordinate System (CCS)• Altitudes• Geoid Models• CERN Geodetic reference frames• Z H Transformation• Conclusions
The Survey Team• Large Scale Metrology Section
• Metrology• Measurement• Alignment• Monitoring• As-built surveys
• First Surveyors at CERN in1954• Our 60th Anniversary this
year too!• Surveying is the application of Geodesy
Geodesy• Geodesy is the science concerned with the
Shape, Size, and the Gravity Field of the Earth (International Association of Geodesy)
• One of the oldest sciences• Includes temporal variations
• 1st Geodesist• Eratosthenes, 200 BC
~5950 km
(6371 km)
Aswan
Alexandrie
Distance
Surveying• Determine point positions• Different types of Observations
• Directions / Angles / Azimuths• Distances
• Redundant Observations• Identify errors• Optimisation algorithms (Least Squares)
• Simplify calculations as much as possible• Done by hand for many
hundreds of years!
ab
c
q1
q3
q2Pt1
Pt3
Pt2
Surveying• Different types of instruments
• Directions (and distances)• Theodolite / Camera /
Total Station / Laser Tracker /Laser Scanner
• Distances• Invar wires / EDM /
Digital Scales
• Height differences• Levels
Measured positions• 2D + 1 Reference system
• Horizontal / Planimetric positions• Latitude, f, and Longitude, l• Eastings, E, and Northings, N, (or X, Y)
in a mapping plane
• Altitudes, H• Heights above Mean Sea Level
Mapping
CERN Reference System• A Reference System covering the whole of
the CERN site• First version established at the start of the
PS Ring construction at CERN• Defines the relative location all things at
CERN• Sites• Buildings• Tunnels• Accelerators• Experiments
CERN Reference System -1955
P0
P1
d
q
CERN Reference System -1959
X
Y
P1
P0P3
CERN Reference System -1962
X
Y
P2
P1
(X, Y) = (1000, 1000)
CERN Reference System -1966
P2
P1
(X, Y) = (2000, 2000)
X
Y
Altitude (Orthometric Height)• Height above Mean Sea Level• Mean Sea Level
• Represents 70% of the Earth’s surface!• Traditionally determined by Tide Gauges• An equipotential surface of the gravity field
• Equipotential Surface is modelled by a reference surface, Geoid• The surface we choose depends on the
accuracy required• The accuracy required will also define the
area over which a given surface is valid
CERN Vertical Reference –1954-1970• A horizontal plane (or different planes)
• OK for a small area• Larger area means lower accuracy
• Easy for surveyors
• A Flat Earth• Challenging for
physicists!
CERN Vertical Reference –1954-1969• PS
• Horizontal Plane• Altitude
433.660 m
• ISR• Horizontal Plane• Altitude
445.460 m
CERN Reference System -1970• CERN Coordinate System (CCS)
• A Reference Frame with a 3D Cartesian Coordinate System
• Principal Point, pillar P0
• X and Y-axes directions unchanged
• Z-axis coincident with local vertical
P2
P1
(X, Y) = (2000, 2000)
X
Y
P0
CCS –Principal Point• Z-coordinate of PS Ring
2433.66000 m
• P0
• XY-Coordinates (m)
(2000.00000, 2097.79265)
• Z-coordinate
2433.66000 m
Vertical Reference –a Sphere• Sphere more complicated than a plane• Higher accuracy over larger areas, • Still easily defined mathematically
Z-Coordinates and Altitudes
ZCCS = H + 2000
Z-Coordinates and Altitudes
ZCCS ≠ H + 2000
Z-Coordinates and Altitudes
• Z-coordinate of PS Ring
2433.66000 m
• Z-coordinate of P0
2433.66000 m
• Altitude (H) of PS Ring
433.66000 m
• Altitude (H) of P0
433.65921 m
ZCCS ≠ H + 2000
Z
XY-Plane
Altitude
H = 10 000 mZ = 10 000 m
H = 10 000 mZ = 0 m
0 2000 4000 6000 8000 10000 120000.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
9.0
Distance between Sphere and Tangential Plane
Distance to Tangent Point / m
Dis
tan
ce b
etw
een
Sp
her
e an
d P
lan
e /
m
CERN Reference System -1983• CERN Coordinate System (CCS)
• Unchanged
• New Vertical Reference Surface• Increase in area covered by LEP (LHC)• Higher precision model required
Biaxial Ellipsoid Model• Ellipsoid of Revolution
• Ellipse rotated around one of its axes• Mathematics not too complicated• Closer match to the
Earth’s shape andgravity field
• Positioned locallyfor an even better match
• Geodetic Reference Ellipsoid, GRS-80
Mark Jones EST/SU -Séminaire Technique23/Mai/2001
Topography of the Earth
• The ellipsoid doesn’t take into account the topography
• The Earth is irregular in shape
• The gravity field is affected by these irregularities
Mark Jones EST/SU -Séminaire Technique23/Mai/2001
Mountains affect the Gravity Field
An equipotentialsurface of the gravity field
Direction of the gravity vector
Geoid
Mas
s
Geoid Model –CERN Geoid 1985• Calculated differences between an ellipsoid
and the Mean Sea Level equipotential of the gravity field• Geoidal Undulations• Institut d’Astronomie,
BERN University • A grid of data points
• Modelled by a polynomial surface
• Hyperbolic Paraboloid• CG1985
CERN Reference System -2000• CERN Coordinate System (CCS)
• Unchanged• Geodetic Reference Ellipsoid
• Unchanged• New Geoid Model
• Assure direction of CNGS beamline• Best recent model required
Geoid Model –CERN Geoid 2000• Calculated differences between an ellipsoid
and the Mean Sea Level equipotential of the gravity field• Geoidal Undulations• Office Fédéral de
Topographie, CH • A grid of data points
• Interpolated between grid points
• CG2000
Vertical Reference Surfaces at CERN• Geoid model, CG2000
• Grid of points (1 km spacing)• Cubic spline interpolation
• Geoid Model, CG1985• Hyperbolic paraboloid
• Spherical Model• Cartesian Z-coordinate
but how do we transform Z H
Z H Transformation• Need to determine the relationship
between the CCS Cartesian system and the Geoid Model
• Geoid model is tied to the Geodetic Reference Ellipsoid
• Need to establish the local position and orientation of the Reference Ellipsoid with respect to the CCS
Mark Jones EST/SU -Séminaire Technique
Geodetic reference ellipsoid
23/Mai/2001
• Parameters: 2 radiiGeodetic reference ellipsoid established locally to better model the geoid
Position and orientation established by 7 parameters :
f0, l0 latitude, longitudeh0 geodetic height a0 azimuthh0, x0 deflections of the verticalN0 geoidal undulation
CERN Reference Ellipsoids• Sphere
• Both radii equal• Mean Earth Radius defined by the IUGG
(International Union of Geodesy and Geophysics)
• R = 6371 km• Reference Ellipsoid
• GRS-80 adopted by the IUGG• a = 6 378 137 m, equatorial radius• b = 6 356 752 m, polar radius
Geodetic Coordinates• Latitude, f, Longitude, l, geodetic height, h
P
Geodetic reference ellipsoid
Geodetic reference frame
f
l
h
ZG
XG
YG
Geodetic Coordinates –P0
• Fix
• Latitude, f0 = 51.3692 grad
• Longitude, l0 = 6.72124 grad
• geodetic height, h0 = 433.66000 m
f0
l0
h0
ZG
XG
YG
P0
Mark Jones EST/SU -Séminaire Technique
• Fix
• a0 = 0.0000 grad
• N0 = 0.00000 m
Geoid
23/Mai/2001
h0
P0
p0
Horizontal plane
Plan XY G
ZG
f0
Geoid
Mark Jones EST/SU -Séminaire Technique
CCS and Geodetic Reference Frame
23/Mai/2001
h0
P0
p0
CCS XY-plane
Plan XY G
ZG
f0
Horizontal plane
CCS Z-AxisVertical
• Fix
• h0 = 0.0000 grad
• x0 = 0.0000 grad
CCS and Geodetic Reference Frame
f0
l0
h0
ZG
XG
YG
P0
• aCCS = 37.77864 Grad
XCCS
YCCS
ZCCS
aCCS
CERN Geodetic Reference Frame• Provides the link between different
coordinate systems (1D, 2D & 3D)• CCS (3D)• Altitudes (1D)• Latitude and Longitude (2D)• Mapping Planes (2D)• Global Geocentric Reference Frames
• Relies upon a model for the shape of the Earth and the Gravity Field
Mark Jones EST/SU -Séminaire Technique
Z and H
23/Mai/2001
h0
P0
p0
CCS XY-plane
Plan XY G
ZG
f0
P
HPZP
CCS Z-Axis
NP
Conclusions
• ZCCS ≠ H + 2000 • Three different vertical reference surfaces
• Implies three Z H Transformations• Care is needed to use the right
transformation!
Conclusions• Things aren’t quite as simple as they used
to be …• … and things get more complicated as the
required precision increases• Changes in the gravity field
• Tides, atmospheric pressure, water tables, plate tectonics …
• More precise determination of the gravity field
Conclusions• Fortunately we no longer calculate things
by hand!• We have developed a database and
various software applications to help
Thank you for your attention!