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Quick-Look Tool for Gravity Field Accuracy Investigation

This tool explores the trade-offs in achievable gravity field accuracy by tuning parameters such as observation types, orbit height, inclination, and sensor/system accuracy. It provides a quick assessment of formal error estimations and assessments in terms of global spherical harmonic functions.

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Quick-Look Tool for Gravity Field Accuracy Investigation

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  1. On the Quick-look-tool and formations T. Reubelt, N. Sneeuw Institute of GeodesyUniversity of Stuttgart

  2. Quick-look-tool • Capabilities • investigation of trade-offs wrt. achievable gravity field accuracy (tunable parameters): • observation types (ll-SST, SGG, orbit perturbations, potential, accelerations) and combinations of them • orbit height • inclination • sensor/system accuracy (white noise, coloured noise, frequency dependent, …) • duration of observation-interval • ll-SST intersatellite-separation

  3. Quick-look-tool • Limitations • formal error estimations only, assessments only in terms of global spherical harmonic functions • no inclusion of aliasing (spatial and temporal) and/or omission errors • idealized circular repeat orbits • limited complexity of ll-SST observations (only along-track ll-SST, difficult or impossible to establish for pendulum or cartwheel)

  4. Quick-look-tool Test-Cases investigation of trade-offs for requirements review (Task 1 Report): → basic scenario: GRACE-like-formation ● σρ_dot= 1 μm/s, ● h = 450 km, ● I = 89°, ● T = 30 days, ● ρ = 200 km

  5. Quick-look-tool

  6. Quick-look-tool

  7. Quick-look-tool

  8. Quick-look-tool

  9. Quick-look-tool

  10. Quick-look-tool • Results • larger spatial resolution with • lower orbit • higher sensor accuracy • larger intersatellite-separation (@ same sensor noise) • longer observation period • but: lower orbit doesn’t scale the accuracy of the solution, it only improves higher degrees l • too large intersatellite separation leads to common-mode effects in lower degree harmonics • for lower degrees (here: l < 100) ll-SST is more accurate than SGG • combination of ll-SST and SGG improves resolution • largest combination effect: two ll-SST sensors on different inclinations

  11. Space-time-sampling / repeat orbit •  revolutions in  nodal days •  and  relative primes (no common divisor) • repeat period • orbit period •  space-time scales of a single (/) repeat orbit: • - minimum spatial scale: • - minimum temporal scale:

  12. Space-time-sampling sampling theorems • Nyquist • Heisenberg

  13. /-repeat multi-groundtrack Interleaved ground-track -shift Space-time-sampling (Heisenberg)

  14. Space-time-sampling how many “sensors” ? Given spatial samling Dspace and temporal sampling Dtime • different (/)-repeat-modes possible to reach aim • single groundtrack-strategy (t-shift) • interleaved groundtrack-strategy (-shift) • minimum number of „sensors“ N : • worst case scenario, though

  15. Formations • Simulations • duration: 1 month • sampling: Δt = 10 s, • orbit height: h = 450 km (non-repeat), • static field EIGEN-GRACE02S, degree/order 50/50 • acceleration approach, σrhoddot = 10-8 m/s² (no other error sources)

  16. Formations GRACE PENDULUM CARTWHEEL LISA

  17. Formations GRACE PENDULUM CARTWHEEL LISA

  18. Formations

  19. Formations

  20. Formations (perigee drift of Cartwheel) behaviour of Cartwheel due to perigee drift (≈ 4° for a polar orbit) situation 23 days later : radial ll-SST over poles situation at time t0: radial ll-SST over equator

  21. Formations (perigee drift of Cartwheel) radial ll-SST over equatorial regions (-16° < φ < 16°) radial ll-SST over polar regions (φ > 74°) (results from 8-day solutions)

  22. Formations • Results • advanced formation types improve the isotropy and sensitivity of measurements and thus lead to higher gravity field accuracy • The technical realisation of advanced formations are more difficult and expensive (formation control, Doppler effects, laser pointing, …) • GRACE, PENDULUM, CARTWHEEL are stable in Hill-frame, LISA changes in Hill-frame (→ changing sensitivity and isotropy?) • CARTWHEEL-behaviour (radial vs. along-track signal) changes due to perigee-drift (4° per day): • good for static gravity field • undesired for time-variable gravity field (changing isotropy, GRACE-like striping pattern for certain points of time) • for I = = 63.4349° / 116.5651° no perigee-drift, • homogeneous CARTWHEEL, useful in Bender formation ?

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