Geocenter motion estimatesfrom the IGS Analysis Center

solutions

P. Rebischung, X. Collilieux, Z. AltamimiIGN/LAREG & GRGS

1EGU General Assembly, Vienna, 26 April 2012

Background

• Global GNSS solutions are sensitive to geocenter motion in two different ways:

2

Through orbit dynamics Through loading deformations

Background

• Main limitation of « orbit dynamics »:

• The non-gravitational forces acting on GNSS satellites are not modeled accurately enough.

→ ACs have to estimate empirical accelerations which correlate with the CM location (origin).

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Example of accelerations that would be felt by a satellite if CM was shifted by 1 mm in the Z direction. Accelerations are shown in the « DYB » frame:

― D: Satellite-Sun axis

― Y: Rotation axis of solar panels

― B: Third axis

Correlations with some parameters of the CODE model are obvious (constant along D; once-per-rev along B).

Methodology

• Data:• Weekly solutions from 7 ACs (COD, EMR, ESA, GFZ, JPL, MIT, NGS)• 1998.0 – 2008.0 : reprocessed solutions• 2008.0 – 2011.3 : operational solutions

• Stacking:• For each AC, stack weekly solutions into a long-term piecewise linear

frame.

• Geocenter motion estimation:• Pseudo-Observations = weekly minus regularized position differences• Three possible models

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Methodology

5

Network shift approach

CF approachaka degree-1 deformation approach

(Blewitt et al., 2001)

CM approach(Lavallée et al., 2006)

nmnnn1

nmCFii

max

σARXTδX

ii RXTδX

with degree-1 Love numbers in CF frame with degree-1 Love numbers in CM frame

Estim

ates

of r

CM-C

F

from

orb

it dy

nam

ics

from

load

ing

defo

rmati

ons

1,0

11,

1,1

σ2σ2σ

loadCFT

TshiftCFTTshiftT

In the CM approach,both information contribute to the same estimate

(because degree-1 deformations have a translational part in the CM frame).

nmnnn1

nmCMii

max

σARXδX

1,0

11,

1,1

σ2σ2σ

CMT

In the following, use:

• well-d

istributed sub-network

• identity weight m

atrix

In the following, use n max=5

In the following, use n max=5

• Sub-annual frequencies corrupted by (odd) draconitic harmonics

Z: network shift approach

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All ACs a

ffected

Z: network shift approach• Low frequencies well explained by

annual + 1st draconitic:

→ Progressive phase shift wrt SLR• Similar patterns for ACs using the CODE model• Different pattern for JPL (and EMR?)

• Underlying annual signal unreliable:

7

Z: CF approach

8

• Draconitics smaller than in the network shift approach:

Z: CF approach

9

• Annual signal in phase with SLR for all ACs, over the whole time period

• But amplitude over-estimated:

• Also found with simulations (see Collilieux et al., JoG 2012)

• Aliasing of >5-degree deformations?

Note on the CM approach

• CM approach ≈ weighted mean of orbit dynamics and loading deformations

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≈ 0.65 for X≈ 0.60 for Y≈ 0.45 for Z

≈ 0.35 for X≈ 0.40 for Y≈ 0.55 for Z

with nmax=5

Z: CM approach

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)0.550.45( loadCFshiftCM ZZZ

• Some draconitics averaged; other cancelled (depending on their relative phases in Zshift and ZCF)

• ZCM alternately:• In good agreement with SLR;• ≈ 0;• Out-of-phase (recently, except JPL).

→ Is it really reasonable to make this weighted mean?

Z: CM approach

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)0.550.45( loadCFshiftCM ZZZ

X

• Network shift approach:• Draconitics up to 2 mm• Annual signal partly detected

• CF approach:• Draconitics as large as in net. shift• Annual signal in phase with SLR• Amplitude over-estimated

• CM approach:• Sometimes in good agreement

with SLR• But not always

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Y

• Network shift approach:• Draconitics up to 2 mm• Rather good annual signal

• CF approach:• Draconitics as large as in net. shift• Rather good annual signal• But slight phase shift for some ACs

• CM approach:• Strikingly good agreement with SLR• Net. shift & CF errors cancel out.

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Conclusions (1/2)

• Network shift (orbit dynamics):• All ACs affected by draconitics as large as « true » annual signal

• Effect of draconitics different for JPL (and EMR?) than for other ACs in Z(JPL’s first draconitic not in phase with other ACs)

• Underlying annual signals:• Unreliable in Z• Partly detected in X• Agrees well with SLR in Y

• CF approach (loading deformations):• Also corrupted by draconitics

• As large as in network shift in X & Y• But ~twice smaller in Z

• Annual signals in phase with SLR• But amplitudes over-estimated in X & Z

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Conclusions (2/2)

• CM approach (≈ weighted average):

• In X & Z, network shift and CF errors cancel sometimes out,but not always.

→ Isn’t the unification of orbit dynamics and loading deformations questionable?

• Strikingly good results in Y: network shift and CF errors cancel out.→ Why?

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Additional slides

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Note on the network shift approach

• Using raw cov. matrices gives unrealistic results:

• Shift estimates are perturbedby correlations with degree-1deformations.

•

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≈ 0.5 for X & Y≈ 0.8 for Z

X

19

Y

20

Z

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X: draconitic harmonicsRadius = 2 mm

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Network shift

CF

CM

1st 2nd 3rd 4th 5th 6th 7th

23

Network shift

CF

CM

Y: draconitic harmonicsRadius = 2 mm

1st 2nd 3rd 4th 5th 6th 7th

24

Network shift

CF

CM

Z: draconitic harmonicsRadius = 5 mm

Radius = 10 mm1st 2nd 3rd 4th 5th 6th 7th