des Éléments importants des systèmes de référence et de la géodésie au cern

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


X

Y

P1

P0P3


X

Y

P2

P1

(X, Y) = (1000, 1000)


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


ZCCS ≠ H + 2000


• 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


• 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


• 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


• Fix

• a0 = 0.0000 grad

• N0 = 0.00000 m

Geoid

23/Mai/2001

h0

P0

p0

Horizontal plane

Plan XY G

ZG

f0

Geoid


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


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!

des Éléments importants des systèmes de référence et de la géodésie au cern

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