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An application of FEM to the geodetic boundary value problem

An application of FEM to the geodetic boundary value problem. Z . F ašková, R. Čunderlík. Faculty of Civil Engineering Slovak University of Technology in Bratislava, Slovakia. Formulation of mixed geodetic BVP Potential theory Geodetic BVP Mixed geodetic BVP Numerical experiments in ANSYS

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An application of FEM to the geodetic boundary value problem

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  1. An application of FEM to the geodetic boundary value problem Z. Fašková, R. Čunderlík Faculty of Civil Engineering Slovak University of Technology in Bratislava, Slovakia

  2. Formulation of mixed geodetic BVP • Potential theory • Geodetic BVP • Mixed geodetic BVP Numerical experiments in ANSYS • Global Quasigeoid Model

  3. Potential theory - Gravity field • Gravity potential W(x): • Gravity (acceleration) g(x): The Earth

  4. Potential theory – Normal field Normal body (equipotential ellipsoid, spheroid) is given by :-major semi axes a - geopotential coefficient J2,0(flattening) - geocentric gravitational constant GM - spin velocity w • Normal potential U(x): • Normal gravity g(x) Ellipsoid

  5. Potential theory - Disturbing field • Disturbing potential T(x): • Gravity anomaly Dg(x): • Gravity disturbance dg(x) Ellipsoid

  6. Geodetic BVP • Stokes-Helmert concept (1849) • Molodenskij concept (1960) • Height anomaly and geoidal height

  7. Mixed geodetic BVP R2 G2 R1 G1 W The air

  8. Numerical experiments in ANSYS • 3D elements (15600 elements) with base 5° * 5° • G1 – 1221 nodes

  9. Surface gravity disturbances generated fromEGM-96 geopotentential coefficientsby using program f477b

  10. Potential solution Quasigeoidal heights

  11. Comparison of solution with BEM

  12. Differences between solutions

  13. Thanks for your attention

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