@article{HolschneiderLesurMauerbergeretal.2016,
  author    = {Holschneider, Matthias and Lesur, Vincent and Mauerberger, Stefan and Baerenzung, Julien},
  title     = {Correlation-based modeling and separation of geomagnetic field components},
  series = {Journal of geophysical research : Solid earth},
  volume    = {121},
  journal   = {Journal of geophysical research : Solid earth},
  publisher = {American Geophysical Union},
  address   = {Washington},
  issn      = {2169-9313},
  doi       = {10.1002/2015JB012629},
  pages     = {3142 -- 3160},
  year      = {2016},
  abstract  = {We introduce a technique for the modeling and separation of geomagnetic field components that is based on an analysis of their correlation structures alone. The inversion is based on a Bayesian formulation, which allows the computation of uncertainties. The technique allows the incorporation of complex measurement geometries like observatory data in a simple way. We show how our technique is linked to other well-known inversion techniques. A case study based on observational data is given.},
  language  = {en}
}
@article{SchannerMauerbergerKorteetal.2021,
  author    = {Schanner, Maximilian Arthus and Mauerberger, Stefan and Korte, Monika and Holschneider, Matthias},
  title     = {Correlation based time evolution of the archeomagnetic field},
  series = {Journal of geophysical research : JGR ; an international quarterly. B, Solid earth},
  volume    = {126},
  journal   = {Journal of geophysical research : JGR ; an international quarterly. B, Solid earth},
  number    = {7},
  publisher = {American Geophysical Union},
  address   = {Washington},
  issn      = {2169-9313},
  doi       = {10.1029/2020JB021548},
  pages     = {22},
  year      = {2021},
  abstract  = {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.},
  language  = {en}
}
@article{MauerbergerSchannerKorteetal.2020,
  author    = {Mauerberger, Stefan and Schanner, Maximilian Arthus and Korte, Monika and Holschneider, Matthias},
  title     = {Correlation based snapshot models of the archeomagnetic field},
  series = {Geophysical journal international},
  volume    = {223},
  journal   = {Geophysical journal international},
  number    = {1},
  publisher = {Oxford Univ. Press},
  address   = {Oxford},
  issn      = {0956-540X},
  doi       = {10.1093/gji/ggaa336},
  pages     = {648 -- 665},
  year      = {2020},
  abstract  = {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 apriori 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. Apriori 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.},
  language  = {en}
}