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Swarm ASM-VFM meeting 9-10 Apr 2015 ESTEC (NL)
Ideas for improving the disturbance model or
Welcome to the Null-Space!
Nils Olsen, Lars Tøffner-Clausen, Chris C. Finlay, Jonas NielsenDTU Space
Swarm ASM-VFM meeting 9-10 Apr 2015 ESTEC (NL)
Vector Disturbance Maps
These results (LTC model) are obtained by describing the dependence of the disturbance field on sun position using spherical harmonics, and using TSVD to regularize the model
Use of localized basis functions instead ?
Other regularisation method?
Swarm ASM-VFM meeting 9-10 Apr 2015 ESTEC (NL)
Disturbance field modeled by point-sources (monopoles)
• 1280 point sources distributed
on icosahedron grid at depth 0.9
• Mean horizontal separation: 0.056
Swarm ASM-VFM meeting 9-10 Apr 2015 ESTEC (NL)
Model Parametrisation
• Data set: 0403 data set without disturbance field correction(fully calibrated, but uncorrected data)
• Preliminary data screening: removal of 0.5% outliers (> 5s wrt to preliminary disturbance field model)
• Data subsampling: 10 minute values (615 000 vector triplets)
Swarm ASM-VFM meeting 9-10 Apr 2015 ESTEC (NL)
Disturbance field modeled by point-sources (monopoles)
Model regularisation: minimizing ||m|| (quadratic regularisation)
l = 5 x 105
larger l(smoother model)
smaller l
Swarm ASM-VFM meeting 9-10 Apr 2015 ESTEC (NL)
Vector Disturbance MapsLTC model (spherical harmonics) point sources
Swarm ASM-VFM meeting 9-10 Apr 2015 ESTEC (NL)
Why modeling using point sources instead of spherical harmonics?
• Disturbance model is overparameterized• d/o 25 in case of LTC model, corresponding to 3 x 25*27 = 3 x 675 = 2025
coefficients• 3 x 1280 point sources
• Model regularisation is needed• Quadratic regularisation (Tikhonov, TSVD, …) minimizes the
mean energy• ”smoothed peaks”, possible spurious features in ”weak field” regions
• Maximim Entropy Regularisation• Sharp(er) boundaries
Swarm ASM-VFM meeting 9-10 Apr 2015 ESTEC (NL)
Experience with crustal field modeling
Kother et al (GJI, in review)
Swarm ASM-VFM meeting 9-10 Apr 2015 ESTEC (NL)
Experience with crustal field modeling
Kother et al (GJI, in review)
Swarm ASM-VFM meeting 9-10 Apr 2015 ESTEC (NL)
First resultsQuadratic regularisation Maximum Entropy
regularisation
rms misfit: 169 pT
Swarm ASM-VFM meeting 9-10 Apr 2015 ESTEC (NL)
Preliminary Conclusion
• Disturbance field modeling using localized basis function (point sources) results in almost identical ruesults compared to use of spherical harmonics
• Maximum Entropy instead of quadratic regularisation leads to minimal changes• … difference to crustal field situation because disturbance field is basically
large-scale?
Swarm ASM-VFM meeting 9-10 Apr 2015 ESTEC (NL)
Assumption: disturbance depends on Sun position (a,b) wrt S/C
First challenge: VFM disturbance
Swarm Alpha
nT
Swarm ASM-VFM meeting 9-10 Apr 2015 ESTEC (NL)
Second Challenge: Calibration of VFM on Charlie
• ”Mapping” of FASM(A) F(C)
• Use of F(C) (instead of missing FASM(C)) to calibrate BVFM(C)
Assessment of these two approaches: Difference DFASM(A) –D|BVFM(C)|
no ASM available
230 pT rms 410 pT rms
This value includes contributions from
remaining VFM disturbance field
Ionospheric contributions (dawn-dusk orbit)
Data from night side regions
Swarm ASM-VFM meeting 9-10 Apr 2015 ESTEC (NL)
Assessment of VFM disturbance correction, VFM calibration and alignment
Difference of vector components DB(A) – DB(C)Difference in vector components between Alpha and Charlie provides independent check of
• VFM calibration• VFM disturbance correction• VFM – STR alignment
(Euler angle determination)
for both satellites …
• … and of the geomagnetic field model that has been used for the mapping A C
• 1 nT noise spec on field measurements appears to be met with margins - as far as one can tell
440 pT rms
380 pT rms
360 pT rms
Swarm ASM-VFM meeting 9-10 Apr 2015 ESTEC (NL)
SIFM+: Model using Vector Gradient Data
SIFMno gradient:no gradient data
SIFM:with scalar gradient datano vector gradient data
SIFM+:with scalar gradient datawith vector gradient data
Model from 2 years of CHAMP satellite data at 320 km altitude (10 x more crustal field power at n=70)
Degree correlation rn
Swarm ASM-VFM meeting 9-10 Apr 2015 ESTEC (NL)
SIFM+: Model using Vector Gradient Data
Difference to MF7Br at surface, n = 16 - 65
SIFM:no vector gradient dataSIFM+:with vector gradient data
Inclusion of vector gradient data alleviates Backus effect