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Geomagnetic field modeling using spherical harmonics requires the inversion for hundreds to thousands of parameters. This large-scale problem can always be formulated as an optimization problem, where a global minimum of a certain cost function has to be calculated. A variety of approaches is known in order to solve this inverse problem, e.g. derivative-based methods or least-squares methods and their variants. Each of these methods has its own advantages and disadvantages, which affect for example the applicability to non-differentiable functions or the runtime of the corresponding algorithm.
In this work, we pursue the goal to find an algorithm which is faster than the established methods and which is applicable to non-linear problems. Such non-linear problems occur for example when estimating Euler angles or when the more robust L_1 norm is applied. Therefore, we will investigate the usability of stochastic optimization methods from the CMAES family for modeling the geomagnetic field of Earth's core. On one hand, basics of core field modeling and their parameterization are discussed using some examples from the literature. On the other hand, the theoretical background of the stochastic methods are provided. A specific CMAES algorithm was successfully applied in order to invert data of the Swarm satellite mission and to derive the core field model EvoMag. The EvoMag model agrees well with established models and observatory data from Niemegk. Finally, we present some observed difficulties and discuss the results of our model.
From monthly mean observatory data spanning 1957-2014, geomagnetic field secular variation values were calculated by annual differences. Estimates of the spherical harmonic Gauss coefficients of the core field secular variation were then derived by applying a correlation based modelling. Finally, a Fourier transform was applied to the time series of the Gauss coefficients. This process led to reliable temporal spectra of the Gauss coefficients up to spherical harmonic degree 5 or 6, and down to periods as short as 1 or 2 years depending on the coefficient. We observed that a k(-2) slope, where k is the frequency, is an acceptable approximation for these spectra, with possibly an exception for the dipole field. The monthly estimates of the core field secular variation at the observatory sites also show that large and rapid variations of the latter happen. This is an indication that geomagnetic jerks are frequent phenomena and that significant secular variation signals at short time scales - i.e. less than 2 years, could still be extracted from data to reveal an unexplored part of the core dynamics.
The Gravity Recovery and Climate Experiment Follow-On (GRACE-FO) mission carries magnetometers that are dedicated to enhance the satellite's navigation. After appropriate calibration and characterisation of artificial magnetic disturbances, these observations are valuable assets to characterise the natural variability of Earth's magnetic field. We describe the data pre-processing, the calibration, and characterisation strategy against a high-precision magnetic field model applied to the GRACE-FO magnetic data. During times of geomagnetic quiet conditions, the mean residual to the magnetic model is around 1 nT with standard deviations below 10 nT. The mean difference to data of ESA's Swarm mission, which is dedicated to monitor the Earth's magnetic field, is mainly within +/- 10 nT during conjunctions. The performance of GRACE-FO magnetic data is further discussed on selected scientific examples. During a magnetic storm event in August 2018, GRACE-FO reveals the local time dependence of the magnetospheric ring current signature, which is in good agreement with results from a network of ground magnetic observations. Also, derived field-aligned currents (FACs) are applied to monitor auroral FACs that compare well in amplitude and statistical behaviour for local time, hemisphere, and solar wind conditions to approved earlier findings from other missions including Swarm. On a case event, it is demonstrated that the dual-satellite constellation of GRACE-FO is most suitable to derive the persistence of auroral FACs with scale lengths of 180 km or longer. Due to a relatively larger noise level compared to dedicated magnetic missions, GRACE-FO is especially suitable for high-amplitude event studies. However, GRACE-FO is also sensitive to ionospheric signatures even below the noise level within statistical approaches. The combination with data of dedicated magnetic field missions and other missions carrying non-dedicated magnetometers greatly enhances related scientific perspectives.
Two recent magnetic field models, GRIMM and xCHAOS, describe core field accelerations with similar behavior up to Spherical Harmonic (SH) degree 5, but which differ significantly for higher degrees. These discrepancies, due to different approaches in smoothing rapid time variations of the core field, have strong implications for the interpretation of the secular variation. Furthermore, the amount of smoothing applied to the highest SH degrees is essentially the modeler’s choice. We therefore investigate new ways of regularizing core magnetic field models. Here we propose to constrain field models to be consistent with the frozen flux induction equation by co-estimating a core magnetic field model and a flow model at the top of the outer core. The flow model is required to have smooth spatial and temporal behavior. The implementation of such constraints and their effects on a magnetic field model built from one year of CHAMP satellite and observatory data, are presented. In particular, it is shown that the chosen constraints are efficient and can be used to build reliable core magnetic field secular variation and acceleration model components.
Background: GEOMAGIA50.v3 for sediments is a comprehensive online database providing access to published paleomagnetic, rock magnetic, and chronological data obtained from lake and marine sediments deposited over the past 50 ka. Its objective is to catalogue data that will improve our understanding of changes in the geomagnetic field, physical environments, and climate.
Findings: GEOMAGIA50.v3 for sediments builds upon the structure of the pre-existing GEOMAGIA50 database for magnetic data from archeological and volcanic materials. A strong emphasis has been placed on the storage of geochronological data, and it is the first magnetic archive that includes comprehensive radiocarbon age data from sediments. The database will be updated as new sediment data become available.
Conclusions: The web-based interface for the sediment database is located at http://geomagia.gfz-potsdam.de/geomagiav3/SDquery.php. This paper is a companion to Brown et al. (Earth Planets Space doi:10.1186/s40623-015-0232-0,2015) and describes the data types, structure, and functionality of the sediment database.
GEOMAGIA50.v3
(2015)
Background: GEOMAGIA50.v3 for sediments is a comprehensive online database providing access to published paleomagnetic, rock magnetic, and chronological data obtained from lake and marine sediments deposited over the past 50 ka. Its objective is to catalogue data that will improve our understanding of changes in the geomagnetic field, physical environments, and climate.
Findings: GEOMAGIA50.v3 for sediments builds upon the structure of the pre-existing GEOMAGIA50 database for magnetic data from archeological and volcanic materials. A strong emphasis has been placed on the storage of geochronological data, and it is the first magnetic archive that includes comprehensive radiocarbon age data from sediments. The database will be updated as new sediment data become available.
Conclusions: The web-based interface for the sediment database is located at http://geomagia.gfz-potsdam.de/geomagiav3/SDquery.php. This paper is a companion to Brown et al. (Earth Planets Space doi:10.1186/s40623-015-0232-0,2015) and describes the data types, structure, and functionality of the sediment database.