Rene Forsberg, Arne V. Olesen Dept of Geodynamics DTU-Space, Technical University of Denmark GOCE and airborne gravimetry - A perfect match for geoid determination -

Airborne Gravimetry Basic principle:  g = y - h´´ -  g eotvos -  g tilt - y 0 + g 0 -  (h - N) y: measured acceleration h´´: acceleration from GPS y 0 : airport base reading g 0 : airport reference gravity h : GPS ellipsoidal height  g eotvos : Eotvos correction  g tilt : Gravimeter tilt correction Current accuracy approx: km along-track filtering

Airborne Gravimetry – DTU-Space gravimeters Chekan-AM - GPS slaved platform - Dual quartz pendulums in viscous damping fluid Lacoste&Romberg S - Simple damped platform - Zero-length spring overdamped

Airborne gravimetry - IMU Auxillary strapdown IMU’s can reach the 1 mGal level Chile 2013 gravityflt elevations iMAR IMU Green, LCR blue (D. Becker, TU Darmstadt)

Airborne Gravimetry – error sources Filtering – lack of resolution Gravimeter scale errors – large difference on E- and W-heading flts Turbulence – unlinear effects in spring sensors Platform tilt correction – serious source of unlinear errors Base tie accuracy – absolute g-station information uncertainty Cross-over adjustment – source of aliasing … dont use GOCE can rescue biased airborne (and marine) data!

Chekan-AM test results - Denmark S-N and N-S flights Chekan accuracy: ~ 1 mGall Salt dome

Geoid – use of GOCE and airborne data Remove-restore principle: collocation + spherical FFT: The anomalous gravity potential T split into 3 parts – 3D fields (Molodensky formulation) T = T EGM/GOCE + T RTM + T res T EGM – spherical harmonic model EGM08 augmented with GOCE below ca. deg 200 (linear transition) T RTM – residual terrain effect (RTM) by prism integration T res – residual (i.e. unmodelled) local gravity effect Gridded data on surface transformed to residual geoid by Stokes/Molodensky integration - spherical FFT with Wong-Gore modified kernel

Analytical downward continuation and terrain effects - Least-squares collocation (planar or spherical self-consistent models) - Allows easy merging of surface and airborne data, time efficient in blocks - Alternate: Fourier methods (if survey flown at constant level..) - Use of remove-restore terrain reductions stabilize solution (terrain effects have to be filtered with the airborne data filter)

Examples of aerogravity results Mongolia nm line spacing + helicopter border survey (MonMap/NGA) Purpose of survey: National geoid + EGM08 Accuracy estimate from x-overs: 2.3 mgal rms

Comparison to GOCE as a function of max degree N (R5 direct) Unit: mGal NMeanStddev Data Airborne GOCE

Arctic Ocean 2009 LOMGRAV2009 – Ken Borek C-FMKB Ops from Eureka, Alert and Station Nord Nord Alert Eureka DC3 aircraft Joint with NRCan LCR S99 and SL1 Magnetometers 256 flight-hr in 6 weeks (down to -40 C) 1.7 mgal rms error [210 x-ings]

LOMGRAV09 – Denmark/Canada UNCLOS project Gravity anomalies on top of Arc GP NP Greenland Comparison to GOCE as a function of max degree N (R5 direct) Unit: mGal – atm.corr. applied NMeanStddev Data

SE-Asia Comparison to GOCE as a function of max degree N (R5 direct) Unit: mGal NMeanStddev Data R.m.s. error mGal Philippines Malaysia Indonesia

East Africa Comparison to GOCE as a function of max degree N (R5 direct) Unit: mGal NMeanStddev Data Ethiopia Tanzania

Surface data GOCE data Surface – GOCE data Direct Time-wise Zoom-In Spectral analysis - Indonesia region Method: - Fill-in by EGM08 (mainly marine) - 2D PSD estimation with FFT - Isotropic averaging of PSD - Conversion to degree variance 

Zoom-In Spectral analysis - Mongolia Surface data GOCE data

Nepal survey Dec 2010 – LCR S-38 and Chekan DTU Airborne gravity survey of Nepal 2010 – Beech King Air 200 Geoid project – Nepal Department of Survey + NGA Base GPS and gravity ties at Kathmandu Airport LaCoste and Romberg gravimeter, Chekan-AM Auxillary: Honeywell IMU, numerous GPS’s Flight elevations

Nepal SRTM terrain model meter Kathmandu Everest Annapurna

Nepal airborne and GOCE

Difference between EGM2008 and EGM2008/GOCE model Geoid domain

Terrain- and GOCE- reduced airborne and surface gravity Reduced gravity data showing contribution from airborne + surface data (and errors) Many errors in terrestrial gravity data … airborne have advantage of uniform quality DataMeanStd. dev. Airborne data Airborne – GOCE (360) Reduced airborne data Surface data Surface – GOCE Reduced surface data Statistics of data reductions

Geoid determination (final classical geoid) Geoid model MeanR.m.s. (m) Geoid model GOCE EGM Fit to GPS levelling Kathmandu Valley (offset due to Nepal datum)

Other geoids … Philippines Geoid 5 m contours + GOCE + DTU10 + SRTM DEM GPS user software

Other geoids … Philippines, validation Difference to GPS/Lev Difference MDT = MSS - N

Conclusions: Succesful airborne gravity surveys of challenging regions mGal accuracy Airborne data nearly bias-free relative to GOCE when tied and processed properly (no cross-over adjustment needed) Geoid models of 5-10 cm accuracy Complements and improve GOCE and EGM08.. basis for new vertical datums GOCE/airborne geoid accuracy many places not possible to validate … errors in levelling networks and geodynamics GOCE data contain information to degree 260, but R5 information decays from around degree 210. Aerogravity flight, Mt Everest Dec 2010 Aerogravity flight, Aconcagua, Feb 2010

Thanks for your attention Raja Ampat, Papua Indonesia, 2011