Maximum entropy regularization of time-dependent geomagnetic field models

SUMMARY We present new dedicated core surface field models spanning the decade from 2000.0 to 2010.0. These models, called gufm‐sat, are based on CHAMP, Ørsted and SAC‐C satellite observations along with annual differences of processed observatory monthly means. A spatial parametrization of spherical harmonics up to degree and order 24 and a temporal parametrization of sixth‐order B‐splines with 0.25 yr knot spacing is employed. Models were constructed by minimizing an absolute deviation measure of misfit along with measures of spatial and temporal complexity at the core surface. We investigate traditional quadratic or maximum entropy regularization in space, and second or third time derivative regularization in time. Entropy regularization allows the construction of models with approximately constant spectral slope at the core surface, avoiding both the divergence characteristic of the crustal field and the unrealistic rapid decay typical of quadratic regularization at degrees above 12. We describe in detail aspects of the models that are relevant to core dynamics. Secular variation and secular acceleration are found to be of lower amplitude under the Pacific hemisphere where the core field is weaker. Rapid field evolution is observed under the eastern Indian Ocean associated with the growth and drift of an intense low latitude flux patch. We also find that the present axial dipole decay arises from a combination of subtle changes in the southern hemisphere field morphology.

Section: Core Field Modelling Methodologymentioning

confidence: 99%

“…To solve this non‐linear optimization problem we use a Newton type iteration scheme (e.g. Luenberger 1969; Tarantola 2005) as described in Gillet et al (2007). Iteration is carried out until the spatial and temporal norms of the differences between models at successive iterations change by less than 0.5 per cent.…”

Section: Core Field Modelling Methodologymentioning

confidence: 99%

Core surface magnetic field evolution 2000-2010

Finlay

Jackson

Gillet³

et al. 2012

“…Various choices of regularization norm in time and space have been explored by different authors (e.g. Bloxham & Jackson 1992;Jackson et al 2007;Gillet et al 2007;Korte & Holme 2010;Finlay et al 2012). In this study we used the Ohmic dissipation norm at the CMB (Gubbins & Bloxham 1985;Jackson et al 2000) for the spatial regularization:…”

Section: Inversion Proceduresmentioning

confidence: 99%

Limitations in paleomagnetic data and modelling techniques and their impact on Holocene geomagnetic field models

Panovska

Korte

Finlay

et al. 2015

S U M M A R YCharacterization of geomagnetic field behaviour on timescales of centuries to millennia is necessary to understand the mechanisms that sustain the geodynamo and drive its evolution. As Holocene paleomagnetic and archeomagnetic data have become more abundant, strategies for regularized inversion of modern field data have been adapted to produce numerous timevarying global field models. We evaluate the effectiveness of several approaches to inversion and data handling, by assessing both global and regional properties of the resulting models. Global Holocene field models cannot resolve Southern hemisphere regional field variations without the use of sediments. A standard data set is used to construct multiple models using two different strategies for relative paleointensity calibration and declination orientation and a selection of starting models in the inversion procedure. When data uncertainties are considered, the results are similar overall regardless of whether we use iterative calibration and reorientation, or co-estimation of the calibration and orientation parameters as part of the inversion procedure. In each case the quality of the starting model used for initial relative paleointensity calibration and declination orientation is crucial and must be based on the best absolute information available. Without adequate initial calibration the morphology of dipole moment variations can be recovered but its absolute value will be correlated with the initial intensity calibrations, an effect that might be mitigated by ensuring an appropriate fit to enough high quality absolute intensity data with low uncertainties. The declination reorientation mainly impacts regional field structure and in the presence of non-zonal fields will result in a non-zero local average. The importance of declination orientation is highlighted by inconsistencies in the West Pacific and Australian sediment records in CALS10k.1b model. Great care must also be taken to assess uncertainties associated with both paleomagnetic and age data and to evaluate the effects of poor data distribution. New consistently allocated uncertainty estimates for sediment paleomagnetic records highlight the importance of adequate uncertainties in the inversion process, as they determine the relative weighting among the data and overall normalized misfit levels which in turn influence the complexity of the inferred field models. Residual distributions suggest that the most appropriate misfit measure is the L 1 norm (minimum absolute deviation) rather than L 2 (least squares), but this seems to have relatively minor impact on the overall results. For future Holocene field modelling we see a need for comprehensive methods to assess uncertainty in individual archeomagnetic data so that these data or models derived from them can be used for reliable initial relative paleointensity calibration and declination orientation in sediments. More work will be needed to assess whether co-estimation or an iterative approach to inversion is more efficient overall...

“…This observation suggests that non‐minimum‐norm methods, for example, maximum entropy methods (e.g. Jackson 2003; Gillet et al 2007), which do not penalize sharp peaks, may be appropriate for modelling the SV in future. Overall, it is plausible that the map truncated to degree 13 may give a fair representation of the large‐scale structure of the SV at the CMB.…”

Section: Plotting the Truncated Secular Variationmentioning

confidence: 99%

Mapping geomagnetic secular variation at the core-mantle boundary

Holme

Olsen²,

Bairstow

2011

S U M M A R YData from recent satellite missions have vastly increased the resolution of models of the geomagnetic field, and its first and second time derivatives -secular variation (SV) and secular acceleration (SA). The spectra of both SV and SA are 'blue' at the core-mantle boundary, both well-fit by functions proportional to l(l + 1) where l is the spherical harmonic degree. The ratio of the two spectra defines a timescale for geomagnetic variations of approximately 10 yrs for all resolvable harmonic degrees. The blue spectra should prevent meaningful maps of the SV being generated; nevertheless, the coherence of the maps up to harmonic degree 13 suggests that it is possible to obtain useful insight from their examination. Low SV is confirmed under the Pacific, but also revealed under the North Atlantic and Antarctica. These features are more readily explained in terms of dynamo control through thermal core-mantle coupling than by electromagnetic screening. Comparison with maps from measurements prior to the recent satellites, using the 'Comprehensive Model', suggests that models back to at least 1970 are sufficiently good to enable direct comparison of the SV.