final presentation, swarm e2e study, june 18, 2004, estec, nio #1 1-nov-15 swarm end-to-end mission...

Final Presentation, Swarm E2E study, June 18, 2004, ESTEC, nio #1 Apr 20, 2023

Swarm End-To-End Mission Performance StudyFinal Presentation

The Swarm E2E Consortium

DSRI:Eigil Friis ChristensenFlemming Hansen Alexei KuvshinovNils OlsenPer Lundahl ThomsenSusanne Vennerstrøm

IPGP:Gauthier HulotMioara Mandea

BGS:Vincent LesurSusan MacmillanAlan Thomson

GFZ:Monika KorteHermann LührStefan MausChristoph ReigberPatricia RitterMartin Rother

GSFC:Michael PuruckerTerence Sabaka

IUEM:Pascal Tarits

G FZ Potsda m IPG P IU EM B G S G SFC

D SR IStudy C oordina tion


Outline of Presentations

• Overview, Achieved Milestones (NIO)

• Results: Comprehensive Inversion (TJS)

• Results: Lithospheric Field Recovery Using Gradient Method (HL)

• Results: Mapping of 3D Mantle Inhomogeneities (NIO)

• Assessment (NIO)

• General discussion


Study Logic

• Task 1: Industrial Module– to be used by industry for their system simulation– Output: software (Matlab) + documentation

• Task 2+3: Swarm mission simulation – Determination and evaluation of scientific benefit of different mission scenarios– Task 3: including s/c and payload errors (from models provided by industry)


The Magnetic Field Contributions Described by the three Modules

large scale


Contents of Industrial Package


Outline of Task 2+3Mission Performance Simulator


Forward Scheme: Production of Synthetic Data

• Design of constellations

• Orbit Calculation– full mission: 4 years– mission start on January 1, 1997 (one solar cycle before anticipated launch)

• Calculation of synthetic magnetic and electric field data – magnetic field generator– electric field generator– auxiliary data


Orbit Design Constellation #1

• Two pairs of satellites450 and 550 km initial altitude86.0° and 85.4° inclination

• lower satellites are close together separation a few hundred km

• upper satellites are at antipodal position 180° separation

• Different inclinations yields different drift rates0.44 min/day differential drift rate corresponding to 90° separation after 27 months


Orbit Design Constellation #2

• Pool of 6 (7) satellites

• Analysis of data from different combinations of up to 4 satellites

• Final name convention

• Swarm A (= 4)

• Swarm B (= 5)

• Swarm C (= 1)

• Swarm D (= 2)


Advantage of two satellites flying side-by-side

1

1 0

Re{grad }

, , ,

Crustal Field, quasi-complex SHA representation:

Difference of at two satellites separated

, Re{gr

by :

ad }

1

nN nm m imn n

n m

m m mn n n

m m in n

V

aV a P e

r

g ih

r r V

e

B

B

Β Β Β

m

1 2 1 cos

1.5

Filter Gain ime m

Strong attenuation of large-scale

magnetospheric terms

Amplificationof m»0 terms


Magnetic Field Gradient at 400 km altitude

Br B B

Mag

netic

fie

ldE

ast-

Wes

t G

radi

ent

of M

agne

tic f

ield


Magnetic Field Generation


Improved Forward Scheme for Constellation #2

• improved parameterization of magnetospheric sources: n=3, m=1 based on hour-by-hour analysis of world-wide distributed observatory data after removal of CM4

• induced contributions are considered using a 3D conductivity model (oceans, sediments + deep-located mantle inhomogeneities)

• ”boosted” secular variation• Noise added (based on CHAMP experience and Swarm specifications)


Power Spectral Density of Simulated Noise

In January 2004 (production of data of constellation #2), the Phase A System Simulator models produces time series of magnetic field that are off by several nT.

Therefore use of simple noise model, based on scaled CHAMP data

= (0.1, 0.07, 0.07) nT in agreement with Swarm performance requirements

simple noise model Phase A noise model


Data Products

For each constellation:

• 190 million satellite positions

• 10,950 data files

• 26.5 GB of data

Production of synthetic data for one constellation takes a couple of weeks


In-flight Calibration and Alignmentof the Vector Fluxgate Magnetometer (VFM)

Calibration: Determination of the instrument response (including time and temperature drifts) by comparison with the readings of the Absolute Scalar Magnetometer (ASM)

– methods developed for present single satellite missions Ørsted and CHAMP– Successful application to simulated Swarm data– exact timing of the instruments is essential (t < 5 sec, cf. SRD)

before in-flight calibration(using pre-flight values)

after in-flight calibration


In-flight Calibration and Alignmentof the Vector Fluxgate Magnetometer (VFM)

Alignment: Determination of the rotation between the VFM and the star imager (ASC)

– Single satellite methods work well provided that » the ”true” magnetic field is sufficiently well known

» the difference B has some special properties (distribution of B in VFM frame)

– Probably significantly relaxed conditions if constellation aspect (multi-satellite method) is considered

– The mechanical stability of the VFM/ASC assembly (optical bench) is very essential!– Development of multi-satellite methods for in-flight alignment is needed


Various Approaches for Field Recovery

• Comprehensive Inversion (cf. presentation by T. J. Sabaka)

• Core Field and Secular Variation - Method 1

• Core Field and Secular Variation - Method 2

• Lithospheric Field Recovery - Method 1 (cf. presentation by H. Lühr)

• Lithospheric Field Recovery - Method 2

• 3-D Mantle conductivity - Method 1 (cf. presentation by N. Olsen)

• 3-D Mantle conductivity - Method 2


Test Plan

• Closed-loop-simulation: Test of the forward and inversion approaches using noise-free data

– using data that only contain source fields for which we invert for

• Focus on field contributions that are main Swarm objectives– Core field and secular variation– Lithospheric field

• Test quantities: Difference between recovered and original model– Power spectrum of the model SH coefficients– Degree correlation n of coefficients– Sensitivity matrix– Global Maps (e.g., of Br) of the model difference

• Results:– successful recovery of the original model using clean, noise-free and noisy data

• Definition: noisy data data containing S/C and payload noise noise-free data data without S/C and payload noise clean data data that only contain source contribution

thatis inverted for


Example of Closed-Loop Analysis

Recovery of lithospheric field ...

... and of high-degree secular variation

using data from 4 Swarm satellites and 88 observatories

degree correlation n > 0.9

Achieved by Comprehensive Inversion; details will be given by T.J. Sabaka

original modelrecovered model

difference


Results: Mission Performance

• Recovery of all relevant source contributions by Comprehensive Inversion (T. J. Sabaka)

• Recovery of the lithospheric field (H. Lühr)• 3-D Conductivity of the Mantle (N. Olsen)


Comparison of Filter Method and CI

• CI superior at n<70, especially for terms m close to 0

• Filter method is superior for n > 70


Mapping of 3D Mantle Conductivity

Forward conductivity model contains• near-surface conductors

(oceans, sediments)

• local (small-scale) inhomogeneities(plumes, subduction zones)

• regional inhomogeneities(e.g., covering one plate)

Attempt to map 3D mantle conductivity structure


HH

z

yx

z

z

z

zz

z

BC

dydBdxdB

B

dzdB

BC

BCdz

dB

CzB

B

//

/

1

)/exp(

Transfer Function: C-response

• C from local Bz and BH , derived using a SHA

• Frequency dependence of C() (or of other transfer functions) provides information on conductivity-depth structure (z)

Electromagnetic Induction:Attenuation of B with depth z:

0 B


Mapping of 3D Mantle Structure

Real and imaginary part of the local C-response for a period of 7 days, reconstructed from time-series of spherical harmonic coefficients up to degree N.

N = 5 N = 9 N = 45 (all terms)


Assessment: Core Field and Secular Variation

Without Swarm: only ground station data

With Swarm: local time coverage and improved quality

Degree n

Wavelength [km]

8

5000

14

2850

Degree relative error % 4.4 82

Degree correlation 0.999 0.80

Total relative error % 4


Assessment: Lithospheric Field

A: 4-5 times more accurate than CHAMP

Lower pair A+B (gradient) for detail

Higher C separates external sources

Combination A+B+C: optimal recovery up to n=130


Assessment: Lithospheric Field (cont.) Br at ground

Degree n

Wavelength [km]

60

667

110

364

Degree relative error % 4.1 47

Degree correlation 0.996 0.88

Total relative error % 7.9

degree n up to 60 degree n up to 130

nT


True Model Swarm A+B+C Swarm A km

Mission Performance: 3-D Mantle Conductivity

Period 7 days

Detection of inhomogenities of mantle conductivity is possible with Swarm constellation #2

Data from one satellite is sufficient to resolve inhomogeneities


Conclusions and Recommendations

• Full mission simulation performed for two constellations– Production of synthetic data of all relevant contributions to Earth’ smagnetic

field

– Recovery of the various field contributions using different approachComprehensive Inversion was chosen as the primary approach

• Evaluation of Swarm constellations ... and of the methods for field analysis

• Modified 3-satellite constellation (one pair of lower satellites, one higher satellite) fulfills the primary Swarm science objectives


Recommendations for Future Studies

• Develop methods for pre-flight determination and test of VFM / ASC rotation

• Develop multi-satellite tools for in-flight alignment• More sophisticated methods for utilizing the magnetic field gradient in

geomagnetic field modelling• Develop methods for imaging (mapping) of 3-D mantle inhomogeneities

final presentation, swarm e2e study, june 18, 2004, estec, nio #1 1-nov-15 swarm end-to-end mission...

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