A New Lithospheric Field Model based on CHAMP and Swarm Magnetic Satellite Data

Transcription

1 A New Lithospheric Field Model based on CHAMP and Swarm Magnetic Satellite Data Nils Olsen 1, Dhananjay Ravat 2, Christopher C Finlay 1, Livia K. Kother 1 1 DTU Space, Technical University of Denmark 2 University of Kentucky, U.S.A. Thanks to the CHAMP and Swarm teams Nils Olsen (DTU Space) New Lithospheric Field Model 1 / 19

2 Lithospheric signature at various altitudes n [km] at ground CHAMP in 2010 Swarm (presently) 10 0 Power [nt 2 ] 10-2 h = 450 km h = 300 km 10-1 Amplitude [nt] Lithospheric signal for n = 100 (λ = 400 km): 10-4 h = 350 km degree n km altitude km altitude km altitude Nils Olsen (DTU Space) New Lithospheric Field Model 2 / 19

3 LCS-1: A new Lithospheric Field Model CHAMP NS (alongtrack) gradient data ( B NS, F NS ), Swarm NS gradient data ( B NS, F NS ), Swarm EW (Swarm Alpha Charlie) gradient data ( B EW, F EW ), Nils Olsen (DTU Space) New Lithospheric Field Model 3 / 19

4 LCS-1: A new Lithospheric Field Model CHAMP NS (alongtrack) gradient data ( B NS, F NS ), Swarm NS gradient data ( B NS, F NS ), Swarm EW (Swarm Alpha Charlie) gradient data ( B EW, F EW ), sec sampling, geomagnetic quiet conditions, 6.2 mio. data locations removal of CHAOS-6 core field (n 15) and magnetospheric field no further data treatment (no orbit-by-orbit filtering, no line-levelling ) data errors depend on magnetic latitude Nils Olsen (DTU Space) New Lithospheric Field Model 3 / 19

5 LCS-1: A new Lithospheric Field Model CHAMP NS (alongtrack) gradient data ( B NS, F NS ), Swarm NS gradient data ( B NS, F NS ), Swarm EW (Swarm Alpha Charlie) gradient data ( B EW, F EW ), sec sampling, geomagnetic quiet conditions, 6.2 mio. data locations removal of CHAOS-6 core field (n 15) and magnetospheric field no further data treatment (no orbit-by-orbit filtering, no line-levelling ) data errors depend on magnetic latitude Model parametrized by 35,000 point sources (monopoles) located 100 km below surface Nils Olsen (DTU Space) New Lithospheric Field Model 3 / 19

6 LCS-1: A new Lithospheric Field Model CHAMP NS (alongtrack) gradient data ( B NS, F NS ), Swarm NS gradient data ( B NS, F NS ), Swarm EW (Swarm Alpha Charlie) gradient data ( B EW, F EW ), sec sampling, geomagnetic quiet conditions, 6.2 mio. data locations removal of CHAOS-6 core field (n 15) and magnetospheric field no further data treatment (no orbit-by-orbit filtering, no line-levelling ) data errors depend on magnetic latitude Model parametrized by 35,000 point sources (monopoles) located 100 km below surface Data misfit: minimize robust (Tukey-weighted) data misfit Model regularization: minimize B r 1 (i.e. L 1 -norm) at surface (ellipsoid) Nils Olsen (DTU Space) New Lithospheric Field Model 3 / 19

7 LCS-1: A new Lithospheric Field Model CHAMP NS (alongtrack) gradient data ( B NS, F NS ), Swarm NS gradient data ( B NS, F NS ), Swarm EW (Swarm Alpha Charlie) gradient data ( B EW, F EW ), sec sampling, geomagnetic quiet conditions, 6.2 mio. data locations removal of CHAOS-6 core field (n 15) and magnetospheric field no further data treatment (no orbit-by-orbit filtering, no line-levelling ) data errors depend on magnetic latitude Model parametrized by 35,000 point sources (monopoles) located 100 km below surface Data misfit: minimize robust (Tukey-weighted) data misfit Model regularization: minimize B r 1 (i.e. L 1 -norm) at surface (ellipsoid) Final step: Representation by spherical harmonics up to n = 185 ensuring B = 0 Nils Olsen (DTU Space) New Lithospheric Field Model 3 / 19

8 Satellite altitude vs. time altitude [km] CHAMP Swarm Alpha + Charlie solar flux F 10.7 [10-22 Wm -2 Hz -1 ] year Nils Olsen (DTU Space) New Lithospheric Field Model 4 / 19

9 Data distribution vs. time 10 5 Number of data points per 2 months bin B EW F EW,dark B NS F NS,sunlit F NS,dark year Nils Olsen (DTU Space) New Lithospheric Field Model 5 / 19

10 Assigned data errors 3 North-South (alongtrack) gradient B r 25 3 East-West gradient B r B θ 2.5 B θ standard deviation [nt] B φ F [pt/km] standard deviation [nt] B φ F [pt/km] o -60 o -30 o 0 o 30 o 60 o 90 o QD latitude o -60 o -30 o 0 o 30 o 60 o 90 o QD latitude Nils Olsen (DTU Space) New Lithospheric Field Model 6 / 19

11 Why L1 Model Regularisation? Example: 2-D vector x = [x 1, x 2 ] = [1, ɛ], ɛ 1 Interpretation: x 1 represents stronger field in continental regions, while x 2 x 1 represents weak field in oceanic regions x 1 1 e x 2 Nils Olsen (DTU Space) New Lithospheric Field Model 7 / 19

12 Why L1 Model Regularisation? Example: 2-D vector x = [x 1, x 2 ] = [1, ɛ], ɛ 1 Interpretation: x 1 represents stronger field in continental regions, while x 2 x 1 represents weak field in oceanic regions L1-norm: 1 + ɛ L2-norm: 1 + ɛ 2 x 1 1 e x 2 Nils Olsen (DTU Space) New Lithospheric Field Model 7 / 19

13 Why L1 Model Regularisation? Example: 2-D vector x = [x 1, x 2 ] = [1, ɛ], ɛ 1 Interpretation: x 1 represents stronger field in continental regions, while x 2 x 1 represents weak field in oceanic regions L1-norm: 1 + ɛ L2-norm: 1 + ɛ 2 Model regularisation implies modification of x 1 and/or x 2, by δ 1 Modification of x 1 x 1 δ = 1 δ x 1 d 1 Modification of x 2 x 2 δ = ɛ δ e d x 2 Nils Olsen (DTU Space) New Lithospheric Field Model 7 / 19

14 Why L1 Model Regularisation? Example: 2-D vector x = [x 1, x 2 ] = [1, ɛ], ɛ 1 d Interpretation: x 1 represents stronger field in continental regions, while x 2 x 1 represents weak field in oceanic regions x 1 L1-norm: 1 + ɛ L2-norm: 1 + ɛ 2 Model regularisation implies modification of x 1 and/or x 2, by δ 1 Modification of x 1 x 1 δ = 1 δ L1-norm: 1 δ + ɛ L2-norm: 1 2δ + δ 2 + ɛ 2 Modification of x 2 x 2 δ = ɛ δ L1-norm: 1 δ + ɛ L2-norm: 1 2δɛ + δ 2 + ɛ 2 1 e x 2 d Nils Olsen (DTU Space) New Lithospheric Field Model 7 / 19

15 Why L1 Model Regularisation? Example: 2-D vector x = [x 1, x 2 ] = [1, ɛ], ɛ 1 d Interpretation: x 1 represents stronger field in continental regions, while x 2 x 1 represents weak field in oceanic regions x 1 L1-norm: 1 + ɛ L2-norm: 1 + ɛ 2 Model regularisation implies modification of x 1 and/or x 2, by δ 1 Modification of x 1 x 1 δ = 1 δ L1-norm: 1 δ + ɛ L2-norm: 1 2δ + δ 2 + ɛ 2 Modification of x 2 x 2 δ = ɛ δ L1-norm: 1 δ + ɛ L2-norm: 1 2δɛ + δ 2 + ɛ 2 Change of large component x 1 has same impact on L1-norm as change of small component x 2, despite their different size L2-norm is more sensitive to change in large component of x ( strong field regions ) but less sensitive to change in small component x 2 ( weak field regions ) 1 e x 2 d Nils Olsen (DTU Space) New Lithospheric Field Model 7 / 19

16 Z at Earth s surface (n = ) L 1 regularized model < B 2 r >= (48.5 nt) 2 ocean/continent = (39.4/66.1 nt) 2 Nils Olsen (DTU Space) New Lithospheric Field Model 8 / 19

17 Z at Earth s surface (n = ) L 1 regularized model < B 2 r >= (48.5 nt) 2 ocean/continent = (39.4/66.1 nt) 2 L 2 regularized model < B 2 r >= (48.2 nt) 2 ocean/continent = (40.1/63.6 nt) 2 same global rms misfit as L1 model Nils Olsen (DTU Space) New Lithospheric Field Model 8 / 19

18 Z at Earth s surface (n = ) L 1 regularized model < B 2 r >= (48.5 nt) 2 ocean/continent = (39.4/66.1 nt) 2 L 2 regularized model < B 2 r >= (48.2 nt) 2 ocean/continent = (40.1/63.6 nt) 2 same global rms misfit as L1 model L1: weaker oceanic but stronger continental field Nils Olsen (DTU Space) New Lithospheric Field Model 8 / 19

19 Z at Earth s surface (n = ) L 1 regularized model < B 2 r >= (48.5 nt) 2 ocean/continent = (39.4/66.1 nt) 2 L 2 regularized model < B 2 r >= (48.2 nt) 2 ocean/continent = (40.1/63.6 nt) 2 same global rms misfit as L1 model MF7 (n = 1 133) < B 2 r >= (42.7 nt) 2 Nils Olsen (DTU Space) New Lithospheric Field Model 8 / 19

20 Z at Earth s surface (n = ) L 1 regularized model < B 2 r >= (48.5 nt) 2 ocean/continent = (39.4/66.1 nt) 2 L 2 regularized model < B 2 r >= (48.2 nt) 2 ocean/continent = (40.1/63.6 nt) 2 same global rms misfit as L1 model L 1 regularized model (n = 1 133) < B 2 r >= (42.6 nt) 2 Nils Olsen (DTU Space) New Lithospheric Field Model 8 / 19

21 Bangui Anomaly MF7 Lithospheric Model (Maus et al., 2010) Nils Olsen (DTU Space) New Lithospheric Field Model 9 / 19

22 Bangui Anomaly LCS-1 Lithospheric Model Nils Olsen (DTU Space) New Lithospheric Field Model 9 / 19

23 Kursk Anomaly MF7 Lithospheric Model (Maus et al., 2010) Nils Olsen (DTU Space) New Lithospheric Field Model 10 / 19

24 Kursk Anomaly LCS-1 Lithospheric Model Nils Olsen (DTU Space) New Lithospheric Field Model 10 / 19

25 Australia: Comparison with airborne data LCS-1 airborne MF7 225 km LP filtered nt Nils Olsen (DTU Space) New Lithospheric Field Model 11 / 19

26 North America: Comparison with EMM2015 Possible contamination of EMM2015 model in auroral zone due to Polar Electrojets? EMM km lowpass filtered Credit: Mike Purucker Nils Olsen (DTU Space) New Lithospheric Field Model 12 / 19

27 Spectra at Earth s surface n [km] LCS-1 MF7 CHAOS-6 EMM R n [nt 2 ] degree n Nils Olsen (DTU Space) New Lithospheric Field Model 13 / 19

28 Conclusions High-resolution map of lithospheric field determined from Swarm (450 km altitude) and CHAMP (350 km) gradient data Improvement on CHAMP-only model possible due to the unique East-West gradient information provided by Swarm, despite the high altitude of Swarm L1 model regularisation: strong and sharp magnetic anomalies on continents but weak fields in oceanic regions Good agreement with independent airborne data down to 250 km wavelength Nils Olsen (DTU Space) New Lithospheric Field Model 14 / 19

29 Conclusions High-resolution map of lithospheric field determined from Swarm (450 km altitude) and CHAMP (350 km) gradient data Improvement on CHAMP-only model possible due to the unique East-West gradient information provided by Swarm, despite the high altitude of Swarm L1 model regularisation: strong and sharp magnetic anomalies on continents but weak fields in oceanic regions Good agreement with independent airborne data down to 250 km wavelength This is possible with Swarm at 450 km altitude exciting new possibilities for future when Swarm measures at altitudes of 350 km! Nils Olsen (DTU Space) New Lithospheric Field Model 14 / 19

30 Spectra and Degree Correlation at Earth s surface 55 n [km] n [km] LCS-1 50 MF7 CHAOS-6 EMM R n [nt 2 ] degree correlation n degree n 0.55 LCS-1 / MF7 LCS-1 / CHAOS-6 LCS-1 / EMM degree n Nils Olsen (DTU Space) New Lithospheric Field Model 15 / 19