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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 CERN. Mark Jones ENMEF-SU. Outline. Introduction CERN Coordinate System (CCS) Altitudes Geoid Models CERN Geodetic reference frames Z  H Transformation Conclusions. The Survey Team.

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Des Éléments Importants des Systèmes de Référence et de la Géodésie au CERN

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  1. Des Éléments Importants des Systèmes de Référence et de la Géodésie au CERN Mark Jones EN\MEF-SU

  2. Outline • Introduction • CERN Coordinate System (CCS) • Altitudes • Geoid Models • CERN Geodetic reference frames • Z  H Transformation • Conclusions

  3. The Survey Team • Large Scale Metrology Section • Metrology • Measurement • Alignment • Monitoring • As-built surveys • First Surveyors at CERN in1954 • Our 60th Anniversary thisyear too! • Surveying is the application of Geodesy

  4. Alexandrie Distance Aswan 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)

  5. 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! Pt3 q3 b a q1 q2 Pt1 Pt2 c

  6. 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

  7. 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

  8. Mapping

  9. 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

  10. CERN Reference System -1955 P0 d q P1

  11. CERN Reference System -1959 X P3 P0 P1 Y

  12. CERN Reference System -1962 Y P2 P1 X (X, Y) = (1000, 1000)

  13. CERN Reference System -1966 Y P2 P1 X (X, Y) = (2000, 2000)

  14. 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

  15. 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!

  16. CERN Vertical Reference –1954-1969 • PS • Horizontal Plane • Altitude433.660 m • ISR • Horizontal Plane • Altitude445.460 m

  17. 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 Y P0 P2 P1 X (X, Y) = (2000, 2000)

  18. CCS –Principal Point • Z-coordinate of PS Ring 2433.66000 m • P0 • XY-Coordinates (m) (2000.00000, 2097.79265) • Z-coordinate 2433.66000 m

  19. Vertical Reference –a Sphere • Sphere more complicated than a plane • Higher accuracy over larger areas, • Still easily defined mathematically

  20. Z-Coordinates and Altitudes ZCCS = H + 2000

  21. Z-Coordinates and Altitudes ZCCS ≠ H + 2000

  22. Z-Coordinates and Altitudes • Z-coordinate of PS Ring 2433.66000 m • Z-coordinate of P0 2433.66000 m ZCCS ≠ H + 2000 • Altitude (H) of PS Ring 433.66000 m • Altitude (H) of P0 433.65921 m

  23. Z H = 10 000 m Z = 10 000 m XY-Plane H = 10 000 m Z = 0 m Altitude

  24. CERN Reference System -1983 • CERN Coordinate System (CCS) • Unchanged • New Vertical Reference Surface • Increase in area covered by LEP (LHC) • Higher precision model required

  25. 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

  26. Topography of the Earth • The ellipsoiddoesn’ttakeintoaccount the topography • The Earthisirregular in shape • The gravityfieldisaffected by theseirregularities Mark Jones EST/SU -Séminaire Technique

  27. Mountainsaffect the Gravity Field Direction of the gravityvector Mass An equipotential surface of the gravityfield Geoid Mark Jones EST/SU -Séminaire Technique

  28. Geoid Model –CERN Geoid 1985 • Calculated differences between an ellipsoidand the Mean Sea Level equipotential of the gravity field • Geoidal Undulations • Institutd’Astronomie,BERN University • A grid of data points • Modelled by a polynomial surface • Hyperbolic Paraboloid • CG1985

  29. 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

  30. Geoid Model –CERN Geoid 2000 • Calculated differences between an ellipsoidand 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

  31. 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

  32. 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

  33. Geodeticreferenceellipsoid • Parameters: 2 radii Geodeticreferenceellipsoidestablishedlocally to better model the geoid Position and orientation established by 7 parameters : f0, l0 latitude, longitude h0geodeticheight a0azimuth h0, x0deflections of the vertical N0geoidalundulation Mark Jones EST/SU -Séminaire Technique

  34. 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

  35. Geodetic Coordinates • Latitude, f, Longitude, l, geodetic height, h ZG Geodetic reference frame P h YG f l Geodetic reference ellipsoid XG

  36. Geodetic Coordinates –P0 • Fix • Latitude, f0 = 51.3692 grad • Longitude, l0 = 6.72124 grad • geodetic height, h0 = 433.66000 m ZG h0 P0 YG f0 l0 XG

  37. Geoid • Fix • a0 = 0.0000 grad • N0 = 0.00000 m P0 h0 Geoid Horizontal plane ZG p0 f0 Plan XYG Mark Jones EST/SU -Séminaire Technique

  38. CCS and Geodetic Reference Frame Vertical CCS Z-Axis P0 CCS XY-plane h0 Horizontal plane ZG p0 f0 Plan XYG • Fix • h0 = 0.0000 grad • x0 = 0.0000 grad Mark Jones EST/SU -Séminaire Technique

  39. CCS and Geodetic Reference Frame • aCCS = 37.77864 Grad ZG aCCS YCCS ZCCS XCCS h0 P0 YG f0 l0 XG

  40. 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

  41. Z and H CCS Z-Axis P P0 ZP HP CCS XY-plane h0 NP ZG p0 f0 Plan XYG Mark Jones EST/SU -Séminaire Technique

  42. Conclusions • ZCCS≠ H + 2000 • Three different vertical reference surfaces • Implies three Z H Transformations • Care is needed to use the right transformation!

  43. 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

  44. Conclusions • Fortunately we no longer calculate things by hand! • We have developed a database and various software applications to help

  45. Thank you for your attention!

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