ALBERT

Description: SUMMARY For the time stationary global geomagnetic field, a new modelling concept is presented. A Bayesian non-parametric approach provides realistic location dependent uncertainty estimates. Modelling related variabilities are dealt with systematically by making little subjective a priori assumptions. Rather than parametrizing the model by Gauss coefficients, a functional analytic approach is applied. The geomagnetic potential is assumed a Gaussian process to describe a distribution over functions. A priori correlations are given by an explicit kernel function with non-informative dipole contribution. A refined modelling strategy is proposed that accommodates non-linearities of archeomagnetic observables: First, a rough field estimate is obtained considering only sites that provide full field vector records. Subsequently, this estimate supports the linearization that incorporates the remaining incomplete records. The comparison of results for the archeomagnetic field over the past 1000 yr is in general agreement with previous models while improved model uncertainty estimates are provided.

Description: In a previous study, a new snapshot modeling concept for the archeomagnetic field was introduced (Mauerberger et al., 2020, https://doi.org/10.1093/gji/ggaa336). By assuming a Gaussian process for the geomagnetic potential, a correlation‐based algorithm was presented, which incorporates a closed‐form spatial correlation function. This work extends the suggested modeling strategy to the temporal domain. A space‐time correlation kernel is constructed from the tensor product of the closed‐form spatial correlation kernel with a squared exponential kernel in time. Dating uncertainties are incorporated into the modeling concept using a noisy input Gaussian process. All but one modeling hyperparameters are marginalized, to reduce their influence on the outcome and to translate their variability to the posterior variance. The resulting distribution incorporates uncertainties related to dating, measurement and modeling process. Results from application to archeomagnetic data show less variation in the dipole than comparable models, but are in general agreement with previous findings.

Description: Plain Language Summary: Global reconstructions of the past geomagnetic field are useful tools to study the geodynamo process that generates the Earth's magnetic field in the outer core. Data‐based field reconstructions are traditionally represented by a fixed number of coefficients in space and time. In a previous study, a new modeling concept for individual epochs of the magnetic field was introduced, which is better adapted to inhomogeneous data distributions as found in archeomagnetic data, and which provides more realistic uncertainty estimates. This new modeling concept effectively has one coefficient per data point. Here, the new method is expanded to also consider the time evolution and build continuous models of the past geomagnetic field. Uncertainties in archeomagnetic input data and in their ages are taken into account and contribute to estimating reasonable uncertainties for the resulting model. The application of the new method to archeomagnetic data over the past 1,200 years gives general agreement with previous findings with less variation in the dipole field contribution than seen in comparable models.

Description: Key Points: Extension of a previous study on spatial correlation based archeomagnetic modeling to the temporal domain. Dating uncertainties are incorporated by the noisy input Gaussian process formalism. Results show general agreement with comparable models with less variation in the dipole field contribution.

Description: Deutsche Forschungsgemeinschaft (DFG) http://dx.doi.org/10.13039/501100001659

Description: For the time stationary global geomagnetic field, a new modelling concept is presented. A Bayesian non-parametric approach provides realistic location dependent uncertainty estimates. Modelling related variabilities are dealt with systematically by making little subjective a priori assumptions. Rather than parametrizing the model by Gauss coefficients, a functional analytic approach is applied. The geomagnetic potential is assumed a Gaussian process to describe a distribution over functions. A priori correlations are given by an explicit kernel function with non-informative dipole contribution. A refined modelling strategy is proposed that accommodates non-linearities of archeomagnetic observables: First, a rough field estimate is obtained considering only sites that provide full field vector records. Subsequently, this estimate supports the linearization that incorporates the remaining incomplete records. The comparison of results for the archeomagnetic field over the past 1000 yr is in general agreement with previous models while improved model uncertainty estimates are provided.

Description: In a previous study, a new snapshot modeling concept for the archeomagnetic field was introduced (Mauerberger et al., 2020). By assuming a Gaussian process for the geomagnetic potential, a correlation based algorithm was presented, which incorporates a closed form spatial correlation function. This work extends the suggested modeling strategy to the temporal domain. A space-time correlation kernel is constructed from the tensor product of the closed form spatial correlation kernel with a squared exponential kernel in time. Dating uncertainties are incorporated into the modeling concept using a noisy input Gaussian process. All but one modeling hyperparameters are marginalized, to reduce their influence on the outcome and to translate their variability to the posterior variance. The resulting distribution incorporates uncertainties related to dating, measurement and modeling process. Results from application to archeomagnetic data show less variation in the dipole than comparable models, but are in general agreement with previous findings.

Description: The geomagnetic main field is vital for live on Earth, as it shields our habitat against the solar wind and cosmic rays. It is generated by the geodynamo in the Earth’s outer core and has a rich dynamic on various timescales. Global models of the field are used to study the interaction of the field and incoming charged particles, but also to infer core dynamics and to feed numerical simulations of the geodynamo. Modern satellite missions, such as the SWARM or the CHAMP mission, support high resolution reconstructions of the global field. From the 19th century on, a global network of magnetic bservatories has been established. It is growing ever since and global models can be constructed from the data it provides. Geomagnetic field models that extend further back in time rely on indirect observations of the field, i.e. thermoremanent records such as burnt clay or volcanic rocks and sediment records from lakes and seas. These indirect records come with (partially very large) uncertainties, introduced by the complex measurement methods and the dating procedure. Focusing on thermoremanent records only, the aim of this thesis is the development of a new modeling strategy for the global geomagnetic field during the Holocene, which takes the uncertainties into account and produces realistic estimates of the reliability of the model. This aim is approached by first considering snapshot models, in order to address the irregular spatial distribution of the records and the non-linear relation of the indirect observations to the field itself. In a Bayesian setting, a modeling algorithm based on Gaussian process egression is developed and applied to binned data. The modeling algorithm is then extended to the temporal domain and expanded to incorporate dating uncertainties. Finally, the algorithm is sequentialized to deal with numerical challenges arising from the size of the Holocene dataset. The central result of this thesis, including all of the aspects mentioned, is a new global geomagnetic field model. It covers the whole Holocene, back until 12000 BCE, and we call it ArchKalmag14k. When considering the uncertainties that are produced together with the model, it is evident that before 6000 BCE the thermoremanent database is not sufficient to support global models. For times more recent, ArchKalmag14k can be used to analyze features of the field under consideration of osterior uncertainties. The algorithm for generating ArchKalmag14k can be applied to different datasets and is provided to the community ss an open source python package.

Description: Das geomagnetische Hauptfeld ist essenziell für das Leben auf der Erde, da es unseren Lebensraum gegen den Sonnenwind und kosmische Strahlung abschirmt. Es wird vom Geodynamo im Erdkern erzeugt und zeigt eine komplexe Dynamik auf unterschiedlichen Zeitskalen. Globale Modelle des Magnetfelds werden zur Studie der Wechselwirkung von einströmenden geladenen Teilchen genutzt, aber auch um Kerndynamiken zu untersuchen und um sie in numerische Simulationen des Geodynamos einzuspeisen. Moderne Satellitenmissionen, wie SWARM und CHAMP, stützen hochauflösende Rekonstruktionen des globalen Felds. Seit dem 19. Jahrhundert wird ein globales Netzwerk von magnetischen Observatorien aufgebaut. Es wächst stetig und globale Modelle können aus den Daten, die es liefert, konstruiert werden. Geomagnetische Feldmodelle, die weiter in der Zeit zurückreichen, basieren auf indirekten Beobachtungen des Felds, d.h. auf thermoremanenten Daten, wie gebrannten Tonen oder vulkanischen Gesteinen, und auf Sedimentdaten aus Seen und Meeren. Diese indirekten Beobachtungen werden mit (teilweise sehr hohen) Unsicherheiten geliefert, die aus den komplexen Datierungs- und Messmethoden resultieren. Ziel dieser Arbeit ist die Entwicklung einer neuen Modellierungsmethode für das globale geomagnetische Feld während des Holozäns, welche die Unsicherheiten berücksichtigt und realistische Schätzungen für die Verlässlichkeit des Modells liefert. Dabei werden lediglich thermoremanente Daten betrachtet. Diesem Ziel wird sich zunächst genähert, indem ein Schnappschuss-Modell konstruiert wird, um die unregelmäßige räumliche Verteilung der Daten und die nichtlineare Beziehung zwischen Daten und Magnetfeld zu untersuchen. In einem Bayesianischen Rahmen wird ein auf Gaussprozessen basierender Algorithmus entwickelt und zunächst auf diskretisierte Daten angewendet. Dieser Algorithmus wird dann um eine zeitabhängige Komponente ergänzt und erweitert, um Datierungsfehler zu berücksichtigen. Zuletzt wird der Algorithmus sequenzialisiert, um mit numerischen Herausforderungen umzugehen, die aufgrund der Größe des Holozän-Datensatzes bestehen. Das zentrale Ergebnis dieser Arbeit, welches alle genannten Aspekte beinhaltet, ist ein neues globales geomagnetisches Feldmodell. Es deckt das gesamte Holozän ab, bis ins Jahr 12000 BCE, und wir nennen es ArchKalmag14k. Bei Betrachtung der Unsicherheiten, die gemeinsam mit dem Modell ermittelt werden, wird deutlich, dass die thermoremanente Datenbasis nicht ausreicht, um globale Modelle vor dem Jahr 6000 BCE zu stützen. Für jüngere Zeiträume kann ArchKalmag14k genutzt werden, um Merkmale des Erdmagnetfelds unter Berücksichtigung der a posteriori Unsicherheiten zu analysieren. Der Algorithmus, mit dem ArchKalmag14k erzeugt wurde, kann auf weitere Datensätze angewendet werden und wird als quelloffenes python-Paket zur Verfügung gestellt.

Description: pymagglobal serves the purpose of replacing some Fortran scripts, which are used in the geomagnetism community to evaluate global field models. It can be applied to all cubic-spline based geomagnetic field models stored in the same file format as gufm1 or the CALSxk model series. pymagglobal is provided as a python package. Install files for nix are included. This way pymagglobal can be easily set up under various system dependencies. The gitlab page provides installation instructions and can be found under "Related Work" in the left panel of this page. Documentation is provided using sphinx. A link can be found in the panel on the left.

Description: Due to poor global data coverage and large data uncertainties, Holocene magnetic field models are of limited resolution. The most commonly used modeling approach is based on an inversion strategy based on truncated spherical harmonics and does not provide uncertainty estimates. Focusing on snapshots of the magnetic field, the CORBASS (CORrelation Based Archeomagnetic SnapShot model) algorithm breaks with the tradition of truncated models by implementing a field model based on Gaussian processes (GP). This way regions covered well by data can be modeled with higher resolution, while areas of poor coverage remain uncertain. The GP approach provides a posterior covariance, together with the (mean) field model, which naturally serves as model uncertainty estimate. A full description of the model can be found in 〈TODO: reference to our upcoming paper〉. CORBASS is provided as a collection of python scripts together with an install file for a conda environment. This way CORBASS can be easily set up under various system dependencies. The gitlab page provides installation instructions, documentation and example notebooks and can be found under "Externe Ressourcen" in the left panel of this page.

Description: CORBAM (CORrelation Based Archeomagnetic Modeling) is a python package for Gaussian process based modeling of the archeomagnic field. Due to poor global data coverage and large data uncertainties, Holocene magnetic field models are of limited resolution. The most commonly used modeling approach is based on an inversion strategy based on truncated spherical harmonics and does not provide uncertainty estimates. CORBAM extends the previously published CORBASS algorithm to the temporal domain and thus again breaks with the tradition of truncated models. The feature of recovering regions with better data coverage with higher resolution translates to the temporal domain. Naturally, the Gaussian process based regression scheme provides uncertainties together with the most likely field model. A full description can be found in the preprint at the CORBAM website. CORBAM is provided as a python package. Install files for nix and conda are included. This way CORBAM can be easily set up under various system dependencies. The gitlab page provides installation instructions and can be found under "Related Work" in the left panel of this page. Additionally, the CORBAM website showcases example notebooks. Documentation is provided using sphinx. A link can be found in the panel on the left and on the CORBAM website.