TY - JOUR A1 - Baerenzung, Julien A1 - Holschneider, Matthias A1 - Lesur, Vincent T1 - Bayesian inversion for the filtered flow at the Earth's core-mantle boundary JF - Journal of geophysical research : Solid earth N2 - The inverse problem of determining the flow at the Earth's core-mantle boundary according to an outer core magnetic field and secular variation model has been investigated through a Bayesian formalism. To circumvent the issue arising from the truncated nature of the available fields, we combined two modeling methods. In the first step, we applied a filter on the magnetic field to isolate its large scales by reducing the energy contained in its small scales, we then derived the dynamical equation, referred as filtered frozen flux equation, describing the spatiotemporal evolution of the filtered part of the field. In the second step, we proposed a statistical parametrization of the filtered magnetic field in order to account for both its remaining unresolved scales and its large-scale uncertainties. These two modeling techniques were then included in the Bayesian formulation of the inverse problem. To explore the complex posterior distribution of the velocity field resulting from this development, we numerically implemented an algorithm based on Markov chain Monte Carlo methods. After evaluating our approach on synthetic data and comparing it to previously introduced methods, we applied it to a magnetic field model derived from satellite data for the single epoch 2005.0. We could confirm the existence of specific features already observed in previous studies. In particular, we retrieved the planetary scale eccentric gyre characteristic of flow evaluated under the compressible quasi-geostrophy assumption although this hypothesis was not considered in our study. In addition, through the sampling of the velocity field posterior distribution, we could evaluate the reliability, at any spatial location and at any scale, of the flow we calculated. The flow uncertainties we determined are nevertheless conditioned by the choice of the prior constraints we applied to the velocity field. Y1 - 2014 U6 - https://doi.org/10.1002/2013JB010358 SN - 2169-9313 SN - 2169-9356 VL - 119 IS - 4 SP - 2695 EP - 2720 PB - American Geophysical Union CY - Washington ER - TY - JOUR A1 - Baerenzung, Julien A1 - Holschneider, Matthias A1 - Wicht, Johannes A1 - Lesur, Vincent A1 - Sanchez, Sabrina T1 - The Kalmag model as a candidate for IGRF-13 JF - Earth, planets and space N2 - We present a new model of the geomagnetic field spanning the last 20 years and called Kalmag. Deriving from the assimilation of CHAMP and Swarm vector field measurements, it separates the different contributions to the observable field through parameterized prior covariance matrices. To make the inverse problem numerically feasible, it has been sequentialized in time through the combination of a Kalman filter and a smoothing algorithm. The model provides reliable estimates of past, present and future mean fields and associated uncertainties. The version presented here is an update of our IGRF candidates; the amount of assimilated data has been doubled and the considered time window has been extended from [2000.5, 2019.74] to [2000.5, 2020.33]. KW - Geomagnetic field KW - Secular variation KW - Assimilation KW - Kalman filter KW - Machine learning Y1 - 2020 U6 - https://doi.org/10.1186/s40623-020-01295-y SN - 1880-5981 VL - 72 IS - 1 PB - Springer CY - New York ER - TY - JOUR A1 - Bärenzung, Julien A1 - Holschneider, Matthias A1 - Lesur, Vincent T1 - constraints JF - Journal of geophysical research : Solid earth N2 - Prior information in ill-posed inverse problem is of critical importance because it is conditioning the posterior solution and its associated variability. The problem of determining the flow evolving at the Earth's core-mantle boundary through magnetic field models derived from satellite or observatory data is no exception to the rule. This study aims to estimate what information can be extracted on the velocity field at the core-mantle boundary, when the frozen flux equation is inverted under very weakly informative, but realistic, prior constraints. Instead of imposing a converging spectrum to the flow, we simply assume that its poloidal and toroidal energy spectra are characterized by power laws. The parameters of the spectra, namely, their magnitudes, and slopes are unknown. The connection between the velocity field, its spectra parameters, and the magnetic field model is established through the Bayesian formulation of the problem. Working in two steps, we determined the time-averaged spectra of the flow within the 2001–2009.5 period, as well as the flow itself and its associated uncertainties in 2005.0. According to the spectra we obtained, we can conclude that the large-scale approximation of the velocity field is not an appropriate assumption within the time window we considered. For the flow itself, we show that although it is dominated by its equatorial symmetric component, it is very unlikely to be perfectly symmetric. We also demonstrate that its geostrophic state is questioned in different locations of the outer core. Y1 - 2016 U6 - https://doi.org/10.1002/2015JB012464 SN - 2169-9313 SN - 2169-9356 VL - 121 SP - 1343 EP - 1364 PB - American Geophysical Union CY - Washington ER - TY - JOUR A1 - Bärenzung, Julien A1 - Holschneider, Matthias A1 - Wicht, Johannes A1 - Sanchez, Sabrina A1 - Lesur, Vincent T1 - Modeling and predicting the short-term evolution of the geomagnetic field JF - Journal of geophysical research : Solid earth N2 - We propose a reduced dynamical system describing the coupled evolution of fluid flow and magnetic field at the top of the Earth's core between the years 1900 and 2014. The flow evolution is modeled with a first-order autoregressive process, while the magnetic field obeys the classical frozen flux equation. An ensemble Kalman filter algorithm serves to constrain the dynamics with the geomagnetic field and its secular variation given by the COV-OBS.x1 model. Using a large ensemble with 40,000 members provides meaningful statistics including reliable error estimates. The model highlights two distinct flow scales. Slowly varying large-scale elements include the already documented eccentric gyre. Localized short-lived structures include distinctly ageostophic features like the high-latitude polar jet on the Northern Hemisphere. Comparisons with independent observations of the length-of-day variations not only validate the flow estimates but also suggest an acceleration of the geostrophic flows over the last century. Hindcasting tests show that our model outperforms simpler predictions bases (linear extrapolation and stationary flow). The predictability limit, of about 2,000 years for the magnetic dipole component, is mostly determined by the random fast varying dynamics of the flow and much less by the geomagnetic data quality or lack of small-scale information. KW - core flow KW - assimilation KW - prediction KW - length of day Y1 - 2018 U6 - https://doi.org/10.1029/2017JB015115 SN - 2169-9313 SN - 2169-9356 VL - 123 IS - 6 SP - 4539 EP - 4560 PB - American Geophysical Union CY - Washington ER - TY - JOUR A1 - Geese, Anne A1 - Mandea, Mioara A1 - Lesur, Vincent A1 - Hayn, Michael T1 - Regional modelling of the Southern African geomagnetic field using harmonic splines N2 - Over the southern African region the geomagnetic field is weak and changes rapidly. For this area series of geomagnetic field measurements exist since the 1950s. We take advantage of the existing repeat station surveys and observatory annual means, and clean these data sets by eliminating jumps and minimizing external field contributions in the original time-series. This unique data set allows us to obtain a detailed view of the geomagnetic field behaviour in space and time by computing a regional model. For this, we use a system of representation similar to harmonic splines. Initially, the technique is systematically tested on synthetic data. After systematically testing the method on synthetic data, we derive a model for 1961-2001 that gives a detailed view of the fast changes of the geomagnetic field in this region. Y1 - 2010 UR - http://onlinelibrary.wiley.com/journal/10.1111/(ISSN)1365-246X U6 - https://doi.org/10.1111/j.1365-246X.2010.04575.x SN - 0956-540X ER - TY - JOUR A1 - Holschneider, Matthias A1 - Lesur, Vincent A1 - Mauerberger, Stefan A1 - Baerenzung, Julien T1 - Correlation-based modeling and separation of geomagnetic field components JF - Journal of geophysical research : Solid earth N2 - 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. Y1 - 2016 U6 - https://doi.org/10.1002/2015JB012629 SN - 2169-9313 SN - 2169-9356 VL - 121 SP - 3142 EP - 3160 PB - American Geophysical Union CY - Washington ER - TY - GEN A1 - Lesur, Vincent A1 - Wardinski, Ingo A1 - Asari, Seiki A1 - Minchev, Borislav A1 - Mandea, Mioara T1 - Modelling the Earth's core magnetic field under flow constraints T2 - Postprints der Universität Potsdam : Mathematisch Naturwissenschaftliche Reihe N2 - 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. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 844 KW - Geomagnetism KW - core field modeling KW - core flow modeling KW - frozen-flux Y1 - 2020 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-430369 SN - 1866-8372 IS - 844 SP - 503 EP - 516 ER - TY - JOUR A1 - Lesur, Vincent A1 - Wardinski, Ingo A1 - Bärenzung, Julien A1 - Holschneider, Matthias T1 - On the frequency spectra of the core magnetic field Gauss coefficients JF - Physics of the earth and planetary interiors N2 - 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. KW - Geomagnetism KW - Core field KW - Secular variation rate of change KW - Geomagnetic jerks KW - Correlation based modelling Y1 - 2017 U6 - https://doi.org/10.1016/j.pepi.2017.05.017 SN - 0031-9201 SN - 1872-7395 VL - 276 SP - 145 EP - 158 PB - Elsevier CY - Amsterdam ER - TY - JOUR A1 - Prokhorov, Boris E. A1 - Förster, Matthias A1 - Lesur, Vincent A1 - Namgaladze, Alexander A. A1 - Holschneider, Matthias A1 - Stolle, Claudia T1 - Modeling of the ionospheric current system and calculating its JF - Magnetic Fields in the Solar System: Planets, Moons and Solar Wind Interactions N2 - The additional magnetic field produced by the ionospheric current system is a part of the Earth’s magnetic field. This current system is a highly variable part of a global electric circuit. The solar wind and interplanetary magnetic field (IMF) interaction with the Earth’s magnetosphere is the external driver for the global electric circuit in the ionosphere. The energy is transferred via the field-aligned currents (FACs) to the Earth’s ionosphere. The interactions between the neutral and charged particles in the ionosphere lead to the so-called thermospheric neutral wind dynamo which represents the second important driver for the global current system. Both processes are components of the magnetosphere–ionosphere–thermosphere (MIT) system, which depends on solar and geomagnetic conditions, and have significant seasonal and UT variations. The modeling of the global dynamic Earth’s ionospheric current system is the first aim of this investigation. For our study, we use the Potsdam version of the Upper Atmosphere Model (UAM-P). The UAM is a first-principle, time-dependent, and fully self-consistent numerical global model. The model includes the thermosphere, ionosphere, plasmasphere, and inner magnetosphere as well as the electrodynamics of the coupled MIT system for the altitudinal range from 80 (60) km up to the 15 Earth radii. The UAM-P differs from the UAM by a new electric field block. For this study, the lower latitudinal and equatorial electrodynamics of the UAM-P model was improved. The calculation of the ionospheric current system’s contribution to the Earth’s magnetic field is the second aim of this study. We present the method, which allows computing the additional magnetic field inside and outside the current layer as generated by the space current density distribution using the Biot-Savart law. Additionally, we perform a comparison of the additional magnetic field calculation using 2D (equivalent currents) and 3D current distribution. Y1 - 2018 SN - 978-3-319-64292-5 SN - 978-3-319-64291-8 U6 - https://doi.org/10.1007/978-3-319-64292-5_10 SN - 0067-0057 SN - 2214-7985 VL - 448 SP - 263 EP - 292 PB - Springer CY - Dordrecht ER - TY - JOUR A1 - Quesnel, Yoann A1 - Weckmann, Ute A1 - Ritter, Oliver A1 - Stankiewicz, Jacek A1 - Lesur, Vincent A1 - Mandea, Mioara A1 - Langlais, Benoit A1 - Sotin, Christophe A1 - Galdéano, Armand T1 - Simple models for the Beattie Magnetic Anomaly in South Africa N2 - The origin of the approximately 1000 km-long Beattie Magnetic Anomaly (BMA) in South Africa remains unclear and contentious. Key issues include the width, depth and magnetization of its source. In this study, we use uniformly magnetized spheres, prisms and cylinders to provide the simplest possible models which predict the 1 km-altitude aeromagnetic measurements along a profile across the BMA. The source parameters are adjusted by forward modeling. In case of a sphere, an inversion technique is applied to refine the parameters. Our results Suggest that two similarly magnetized and adjacent sources. With a vertical offset, can explain the observed magnetic anomaly. The best fitting model corresponds to two highly-magnetized (>5 A m(-1)) sheet-like prisms, extending from 9 to 12 kill depth, and from 13 to 18 kill depth, respectively, and with a total width reaching 80 km. Other less-preferred models show thicker and deeper magnetized volumes. Associated magnetizations seem to be mostly induced, although a weak remanent component is required to improve the fit. We also compare our results With the interpretation of independent magnetotelluric and seismic experiments along the same profile. It suggests that the geological sources for the BMA are mostly located in the middle crust and may be displaced by a shear zone or a fault. Contrary to previous models suggesting a serpentinized sliver of paleo-oceanic crust within the Natal-Namaqua Mobile Belt, we propose that granulite-facies mid-crustal rocks within this belt may cause the BMA. Y1 - 2009 UR - http://www.sciencedirect.com/science/journal/00401951 U6 - https://doi.org/10.1016/j.tecto.2008.11.027 SN - 0040-1951 ER -