The European geomagnetic secular variation and acceleration over the last four decades

1. The European geomagnetic secular variation and acceleration over the last four decades Mioara MANDEA GiulianaVerbanac, Monika Korte Helmholtz-Zentrum Potsdam Deutsches GeoForschungsZentrum - GFZ, Telegrafenberg, 14473, Potsdam, Germany Faculty of Science, University of Zagreb, Department of Geophysic, Horvatovac bb, Zagreb, Croatia.

2. Outline • We have taken advantage of the comparatively high density of geomagnetic observatories in Europe and, improving and regularizing the Spherical cap harmonic analyses, derived a regional model for the detailed study of secular variation and acceleration over the past four decades. • Times of zero acceleration in general do not occur simultaneously in all magnetic field components. Secular variation and acceleration show very dynamic patterns indicating rapid and complex causal processes in the Earth’s fluid core. • Data • Modeling and parametrization • Results • Animations

3. Data Geomagnetic observatories (full circles) and synthetic ones (triangles) for which synthetic data sets are computed from CM4 model. The large circle shows the border of the spherical cap (35°) used in the SCHA. The dashed boundary indicates the region of interest, over which all maps and animations are produced.

4. Modeling and parametrization The potential is a function of radius, co-latitude and longitude, is developed into a series of associated Legendre functions (Pm, nk) with non-integer degrees nk and integer orders m. The integer index k is used to order the functions and the SCHA coefficients, (gmk, hmk ). The values of n have to be non-integer in order to satisfy certain boundary conditions for the spherical cap instead of a whole sphere.

5. Modeling and parametrization y - data vector A - operator mapping model vector on to the data vector m, Ce - data error covariance matrix Λ - damping matrix λ - Lagrange multiplier The SCHA coefficients is expanded in time as a linear combination of cubic B-splines Bj(t)

6. Modeling and parametrization Following this approach, we minimize the functional: to find the best spatial (λ) and temporal (σ) damping constants λ =5x10−1, σ = 5x10−3.

7. Modeling and parametrization Trade-off curve of the spatial norm vs. misfit for EU_MIX model. (Logarithmic scale).

8. Results Maps of the X (left), Y (center) and Z (right) secular variation components at epoch 1980.5 obtained by SCHA (43 observatory locations – model EU_OBS).

9. Results Maps of the X (left), Y (center) and Z (right) secular variation components at epoch 1980.5 obtained by SCHA (43 observatory locations + 11 synthetic observatories - model EU_MIX).

10. Results Maps of the X (left), Y (center) and Z (right) differences between EU_MIX and EU_OBS. Triangles show the observatory locations.

11. Results The Xrmsmisfit at each observatory locations from the regional, EU_MIX model (green)and the global, CM4 model (yellow).

12. Results The Yrmsmisfit at each observatory locations from the regional, EU_MIX model (green)and the global, CM4 model (yellow).

13. Results The Zrmsmisfit at each observatory locations from the regional, EU_MIX model (green)and the global, CM4 model (yellow).

14. Results The overall rmsmisfit at each observatory locations from the regional, EU_MIX model (green)and the global, CM4 model (yellow).

15. Results Time-series for X, Y and Z SV components in TRO: corrected data (red), values from the EU_MIX (green) and CM4 (blue).

16. Results Time-series for X, Y and Z SV components in NGK: corrected data (red), values from the EU_MIX (green) and CM4 (blue).

17. Results Time-series for X, Y and Z SV components in COI: corrected data (red), values from the EU_MIX (green) and CM4 (blue).

18. Results Maps of the X (left), Y (center) and Z (right) secular acceleration components around 1970 obtained from EU_MIX model, with the largest areas of zero SA: 1969.3 for Y 1970.3 for X 1970.1 for Z

19. Results ANIMATIONS Maps of the X (left), Y (center) and Z (right) secular variation secular acceleration