Geomagnetic field models covering past millennia rely on two main data sources: archaeomagnetic data, that provide snapshots of the geomagnetic field at specific locations, and sediment records, that deliver time series of the geomagnetic field from individual drill cores. The limited temporal and spatial global coverage with archaeomagnetic data necessitates use of sediment data, especially when models go further back in time. However, the accurate preprocessing and interpretation of sediment data is crucial. Unlike archaeomagnetic data, sediment data does not provide absolute values for intensities and declinations; instead, it represents relative variations. The detrital remanent magnetization (DRM) of sediment records is influenced by various depositional (dDRM) effects that can result in inclination shallowing, as well as post-depositional (pDRM) processes that cause a delayed and smoothed signal. To address the distortion associated with the pDRM effects, a novel class of flexible parameterized lock-in functions has been proposed. These lock-in functions involve four parameters, which are estimated using a Bayesian modeling technique and archaeomagnetic data. By extending the space of hyperparameters to include the calibration factor for intensities, the declination offsets and the inclination shallowing factor, we present a fully Bayesian preprocessing method for sediment records in form of a Python package, called extit{sedprep}. By applying the estimated parameters to the raw sediment data extit{sedprep} is able to provide a calibrated and preprocessed palaeomagnetic record.

A document by Lukas Bohsung. Click on the document to view its contents.

A document by Yosuke Yamazaki. Click on the document to view its contents.

Space-based measurements of the Earth's magnetic field with a good spatiotemporal coverage are needed to understand the complex system of our surrounding geomagnetic field. High-precision magnetic field satellite missions form the backbone for sophisticated research, but they are limited in their coverage. Many satellites carry so-called platform magnetometers that are part of their attitude and orbit control systems. These can be re-calibrated by considering different behaviors of the satellite system, hence reducing their relatively high initial noise originating from their rough calibration. These platform magnetometer data obtained from non-dedicated satellite missions complement the high-precision data by additional coverage in space, time, and magnetic local times. In this work, we present an extension to our previous Machine Learning approach for the automatic in-situ calibration of platform magnetometers. We introduce a new physics-informed layer incorporating the Biot-Savart formula for dipoles that can efficiently correct artificial disturbances due to electric current-induced magnetic fields evoked by the satellite itself. We demonstrate how magnetic dipoles can be co-estimated in a neural network for the calibration of platform magnetometers and thus enhance the Machine Learning-based approach to follow known physical principles. Here we describe the derivation and assessment of re-calibrated datasets for two satellite missions, GOCE and GRACE-FO, which are made publicly available. We achieved a mean residual of about 7 nT and 4 nT for low- and mid-latitudes, respectively.

The primary data sources for reconstructing the geomagnetic field of the past millennia are archaeomagnetic and sedimentary paleomagnetic data. Sediment records, in particular, are crucial in extending the temporal and spatial coverage of global geomagnetic field models, especially when archaeomagnetic data is sparse. However, the post-depositional detrital remanent magnetization (pDRM) process is still poorly understood and can cause smoothing of the magnetic signal and offsets with respect to the sediment age. To make effective use of sedimentary data, it is essential to understand the lock-in process and its impact on the magnetic signal. In this study, we investigate the lock-in process theoretically and derive a parameterized lock-in function that can approximate possible lock-in behaviors. Additionally, we demonstrate that a lock-in function that is independent of absolute parameters can only be applied to the magnetic direction components (declination and inclination), but not to the relative intensity. Integrating this lock-in function into the ArchKalmag14k modeling procedure \cite{schanner2022archkalmag14k} allows including data from sediment records. The parameters of the lock-in function are estimated by the maximum likelihood method using archaeomagnetic data as a reference. The effectiveness of the proposed method is evaluated through synthetic tests. Additionally, we apply our technique to sediment records from two lakes in Sweden (Kälksjön and Gyltigesjön) as first case studies. Our results demonstrate that the proposed method is capable of effectively correcting the distortion caused by the lock-in process, making data from sedimentary records a more reliable and informative source for geomagnetic field reconstructions.

We propose a global geomagnetic field model for the last fourteen thousand years, based on thermoremanent records. We call the model ArchKalMag14k. ArchKalMag14k is constructed by modifying recently proposed algorithms, based on space-time correlations. Due to the amount of data and complexity of the model, the full Bayesian posterior is numerically intractable. To tackle this, we sequentialize the inversion by implementing a Kalman-filter with a fixed time step. Every step consists of a prediction, based on a degree dependent temporal covariance, and a correction via Gaussian process regression. Dating errors are treated via a noisy input formulation. Cross-correlations are re-introduced by a smoothing algorithm and model parameters are inferred from the data. Due to the specific statistical nature of the proposed algorithms, the model comes with space and time dependent uncertainty estimates. The new model ArchKalMag14k shows less variation in the large scale degrees than comparable models. Local predictions represent the underlying data and agree with comparable models, if the location is sampled well. Uncertainties are bigger for earlier times and in regions of sparse data coverage. We also use ArchKalMag14k to analyze the appearance and evolution of the South Atlantic anomaly together with reverse flux patches at the core mantel boundary, considering the model uncertainties. While we find good agreement with earlier models for recent times, our model suggests a different evolution of intensity minima prior to 1650 CE. In general, our results suggest that prior to 6000 BCE the database is not strong enough to support global models.

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.