1 / 20

Satellite geophysics. Basic concepts. I1.1a

Satellite geophysics. Basic concepts. I1.1a. Z. Meridian plane. h. r. = geocentric latitude φ = geodetic latitude r = radial distance, h = ellipsoidal height a = semi-major axis, b = semi-minor axis z = axis of rotation, 1900. flattening = (a-b)/a. b. φ. X-Y. a.

fordon
Download Presentation

Satellite geophysics. Basic concepts. I1.1a

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Satellite geophysics. Basic concepts.I1.1a Z Meridian plane h r = geocentric latitude φ = geodetic latitude r = radial distance, h = ellipsoidal height a = semi-major axis, b = semi-minor axis z = axis of rotation, 1900. flattening = (a-b)/a. b φ X-Y a C.C.Tscherning, University of Copenhagen, 2013-10-25 1

  2. Coordinate-systems Example: Frederiksværk φ=560, λ=120, h= 50 m C.C.Tscherning, 2013-10-25.

  3. Geoid and mean sea level Earth surface H Geoid: gravity potential constant h=H+N=Orthometric height + geoid height along plumb-line =HN+ζ=Normal height + height anomaly, along plumb-line of gravity normal field N Ellipsoid C.C.Tscherning, 2013-10-25.

  4. GEOID

  5. Coordinate-systems and time. Z NON INERTIAL SYSTEM Mean-rotationaxis 1900. Gravity-centre Y- Rotates with the Earth CTS: Conventional Terrestrial System Greenwich X

  6. POLAR MOTION • Approximatively circular • Period 430 days (Chandler period) • Main reason: Axis of Inertia does not co-inside with axis of rotation. • Rigid Earth: 305 days: Euler-period.

  7. POLBEVÆGELSEN • . http://aiuws.unibe.ch/code/erp_pp.gif

  8. Ch. 3, Transformation CIS - CTS • Precession • Nutation • Rotation+ • Polar movement Sun+Moon

  9. Gravity potential, Kaula Chap. 1. • Attraction (force): • Direction from gravity center of m to M. • With m = 1 (unitless), then acceleration C.C.Tscherning, 2013-10-25.

  10. Gradient of scalar potential, V, C.C.Tscherning, 2013-10-25.

  11. Volume distribution, ρ(x,y,z) • V fulfills Laplace equation C.C.Tscherning, 2013-10-25.

  12. Spherical coordinates • Geocentric latitude • Longitude, λ, r = distance to origin. C.C.Tscherning, 2013-10-25.

  13. Laplace in spherical coordinates C.C.Tscherning, 2013-10-25.

  14. Spherical harmonics • Define: C.C.Tscherning, 2013-10-25.

  15. Orthogonal basis functions • Generalizes Fourier-series from the plane C.C.Tscherning, 2013-10-25.

  16. Gravity model database. Spherical harmonic coefficients: http://icgem.gfz-potsdam.de/ICGEM/ CCT, Nov. 2013. (CCT)

  17. Centrifugal potential • On the surface of the Earth we also measure the centrifugál acceleration, r C.C.Tscherning, 2013-10-25.

  18. Normal potential, U • Good approximation to potential of ideal Earth • Reference ellipsoid is equipotential surface, U=U0, ideal geoid. • It has correct total mass, M. • It has correct centrifugal potential • Knowledge of the series development of the gravity potential can be used to derive the flattening of the Earth ! C.C.Tscherning, 2013-10-25.

  19. Anomalous potential,T • T=W-U, • same mass and gravity center. • Makes all quantities small,gives base for linearisation. C.C.Tscherning, 2013-10-25.

  20. Gravity. Source: DTU-Space. Ole Andersen. CCT, Nov. 2013. (CCT)

More Related