1. Estimates of the Elastic Thickness of Antarctica from GOCE Gravity Models
Dan McKenzie1, Weiyong Yi2 and Reiner Rummel2 1Department of Earth Sciences, Bullard Labs, Madingley Road, Cambridge CB3 0EZ, U.K. 2Institut für Astronomische und Physikalische Geodäsie (IAPG), Technische Universität München, Arcisstr. 21, Munich, Germany
Change of Title
GOCE provides the first detailed gravity model of Antarctica
So one can look into mass compensation
Geophysics by Dan McKenzie
5th GOCE User Workshop, Paris ,

2. „geodetic“ isostasy Talk dedicated to Christian Tscherning
Interest in topic in 1984
Tofether with Dick Rapp, Hans Sünkel, Christian Tscherning
Purely geodetic but 3rd order
Balmino, Lambeck, Kaula in 1074

3. elastic flexure of the lithosphere
See also:
Watt AB, 2001, eq.(5.1) on page 177
Airy = local mass compensation
More realisitcal hypothesis:
Topographic load on elastic lithospheric plate
Elasitc plate model from civil engineering
(see Vening Meinesz)
PDE with bi-harmonic operator
W (Wurzel)= vertical deflection of plate
Solution easy in 2D Fourier domain
D = flexural rigidity with Te elastic thicknerss
Te thick= longwavelegth bending
Te shallow= shor wavelength

4. elastic flexure of the lithosphere
Solution with periodic load in Fourier domain
Gravity anomaly - -Elevation -- deflection
Mass balance between W and E
Admittance
= „how much topography plus compensation enters gravity“
Long wavelengths: Z=>0 deltaG = 0 isostasy
Short wavelengths: Z= mGal/km Bouguer
Bouguer plate:
111.9mGal/km

5. elastic flexure of the lithosphere
When the topography is isostatically compensated there is (essentially) no gravity anomaly. This is the region I have marked as convective.  The elastic effects become important in the middle bit, which goes from being compensated at long wavelengths to uncompensated at short ones.
Here we deal with full wave length (and not with half wave length)
Admittance for Central and Southern Africa

6. gravity anomaly over a hot region in the upper mantle
Hot rising mantle plume
Two effects:
Lower density of hot material
Dynamic topography
McKenzie D, AB Watts, B Parsons, M Roufosse, nature, 1980

7. example Hawaii: volcanic load on Pacific plate
Classical Test Case: Hawaii
= volcanic load on Pacific plate (80 Ma)
Good gravity data, good bathymety data
Watts AB, SF Daly, 1981

8. example Hawaii: volcanic load on Pacific plate

9. example Hawaii: volcanic load on Pacific plate
Admittance (left: convective part): perfect fit
Te= 18.2 km
At minimum of Misfit

10. example Hawaii: volcanic load on Pacific plate
GOCE gravity

11. example Hawaii: volcanic load on Pacific plate
Comparison of the surface gravity determined from altimetry with that calculated
from various satellite gravity models for the region round Hawaii. In each case the admittance
is calculated using the altimetric gravity field as input and the surface gravity calculated from
the GOCE harmonic coefficients as output, and is unity if the agreement is perfect. The impact of the
data from GOCE on the accuracy of the short wavelength data is clear, as is the improvement
resulting from increasing the maximum degree from 230 to 300.

12. GOCE DIR5 versus EGM2008 (by regions)
Antarctica
Antarctica
Now Antarctica
Comparison of DIR5 and EGM2008
RMS differences in 10-SH-degree steps for various regions
GOCE DIR5 versus EGM2008 (by regions)

13. gravity anomaly map based on GOCE DIR5
Antarctica
Dronning Maud
Land
Trans
Antarctic
Mnts
Gamburtsev
Mtns
Palmer
Gravity Anomaly Field Antarctica
And tectonic features
gravity anomaly map based on GOCE DIR5

14. improved ice bed, surface and thickness datasets for Antarctica
Bedmap 2
Bedrock topography, ice thickness
Bedmap2:
improved ice bed, surface and thickness datasets for Antarctica
Fretwell P et al., The Cryosphere, 2013

15. selected areas: West Antarctica and East Antarctica
East Antarctica is a croton containing very old rocks, whereas W Antarctica is much younger.
selected areas: West Antarctica and East Antarctica

16. elastic thickness East Antarctica Te = 20.4 km
East Antarctica is a croton containing very old rocks, whereas W Antarctica is much younger
The glaciation in Antarctica started at about the same time that Australia separated.  There is also a difference in how well the sub-ice topography is known, and hence how much noise there is in the signals. I suspect W Antarctic data is largely noise free, whereas that is certainly not true for E Antarctica.  My reaction is quite the opposite of yours: I am really surprised the E Antarctic data is so good.
elastic thickness East Antarctica Te = 20.4 km

17. Antarctica
elastic thickness East Antarctica Te = 6.0 km

18. Antarctica
to show the plate thickness in Antarctica, from surface wave tomography.  It is not yet very accurate, because there are so few seismometers operating in Antarctica.  Keith Priestley has now got a lot more data from temporary stations, and we will have a much better map in the next month or two.  But the map clearly shows the difference between E and W Antarctica, and explains why we get such different values of T_e.

19. „The no man‘s land between the disciplines of
geology, geophysics and geodesy should be
conquered by cooperation and not by domination.“
NJ Vlaar
in: Vening Meinesz, a pioneer in earth sciences
GOCE only reliable data set
Soon results from gravity project Antarctica
Geodynamics hidden under ice
Method works well
GD Garland & JR Apel (eds.): Quo vadimus: Geophysics for the next generation,
Geophysical Monograph 60, IUGG volume 10, 1990

20. literature
Fowler CMR: The solid earth, second edition, ch.5, Cambridge, 2008
Fretwell P et al.: Bedmap2: improved ice bed, surface and thickness data
sets for Antarctica, The Cryosphere, 7, 375–393, 2013
Heiskanen WA, FA Vening Meinesz: The earth and its gravity field, Ch.10,
McGraw-Hill,1958
Jeffreys Sir H: The earth, Sixth Edition, sect.6.06, Cambridge 1970
McKenzie D, C Bowin: The relationship between bathymetry and gravity
in the Atlantic Ocean. JGR 81, , 1976
McKenzie D, AB Watts, B Parsons, M Roufosse: Planform of mantle convection
beneath the Pacific Ocean, nature 288, 1980
McKenzie D, W Yi & Rummel: Estimates of Te from GOCE data, Earth and
Planetary Science Letters 399, , 2014
Turcotte DL, G Schubert: Geodynamics, ch.3 & 5, Wiley, New York, 1982
Watts AB: Isostasy and flexure of the lithosphere, ch.5, Cambridge 2001
Watts AB, SF Daly: Long wavelength gravity and topography anomalies, Ann.
Rev. Earth Planet. Sci :415-4
Acknowledgement: Christian Hirt drew our attention to Bedmap2

22. Antarctica