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 - Bailey, Iain W. A1 - Ben-Zion, Yehuda A1 - Becker, Thorsten W. A1 - Holschneider, Matthias T1 - Quantifying focal mechanism heterogeneity for fault zones in central and southern California N2 - P>We present a statistical analysis of focal mechanism orientations for nine California fault zones with the goal of quantifying variations of fault zone heterogeneity at seismogenic depths. The focal mechanism data are generated from first motion polarities for earthquakes in the time period 1983-2004, magnitude range 0-5, and depth range 0-15 km. Only mechanisms with good quality solutions are used. We define fault zones using 20 km wide rectangles and use summations of normalized potency tensors to describe the distribution of double-couple orientations for each fault zone. Focal mechanism heterogeneity is quantified using two measures computed from the tensors that relate to the scatter in orientations and rotational asymmetry or skewness of the distribution. We illustrate the use of these quantities by showing relative differences in the focal mechanism heterogeneity characteristics for different fault zones. These differences are shown to relate to properties of the fault zone surface traces such that increased scatter correlates with fault trace complexity and rotational asymmetry correlates with the dominant fault trace azimuth. These correlations indicate a link between the long-term evolution of a fault zone over many earthquake cycles and its seismic behaviour over a 20 yr time period. Analysis of the partitioning of San Jacinto fault zone focal mechanisms into different faulting styles further indicates that heterogeneity is dominantly controlled by structural properties of the fault zone, rather than time or magnitude related properties of the seismicity. Y1 - 2010 UR - http://onlinelibrary.wiley.com/journal/10.1111/(ISSN)1365-246X U6 - https://doi.org/10.1111/j.1365-246X.2010.04745.x SN - 0956-540X ER - TY - JOUR A1 - Benmehdi, Sabah A1 - Makarava, Natallia A1 - Benhamidouche, N. A1 - Holschneider, Matthias T1 - Bayesian estimation of the self-similarity exponent of the Nile River fluctuation JF - Nonlinear processes in geophysics N2 - The aim of this paper is to estimate the Hurst parameter of Fractional Gaussian Noise (FGN) using Bayesian inference. We propose an estimation technique that takes into account the full correlation structure of this process. Instead of using the integrated time series and then applying an estimator for its Hurst exponent, we propose to use the noise signal directly. As an application we analyze the time series of the Nile River, where we find a posterior distribution which is compatible with previous findings. In addition, our technique provides natural error bars for the Hurst exponent. Y1 - 2011 U6 - https://doi.org/10.5194/npg-18-441-2011 SN - 1023-5809 VL - 18 IS - 3 SP - 441 EP - 446 PB - Copernicus CY - Göttingen ER - TY - JOUR A1 - Berner, Nadine A1 - Trauth, Martin H. A1 - Holschneider, Matthias T1 - Bayesian inference about Plio-Pleistocene climate transitions in Africa JF - Quaternary science reviews : the international multidisciplinary research and review journal N2 - During the last 5 Ma the Earth's ocean-atmosphere system passed through several major transitions, many of which are discussed as possible triggers for human evolution. A classic in this context is the possible influence of the closure of the Panama Strait, the intensification of Northern Hemisphere Glaciation, a stepwise increase in aridity in Africa, and the first appearance of the genus Homo about 2.5 - 2.7 Ma ago. Apart from the fact that the correlation between these events does not necessarily imply causality, many attempts to establish a relationship between climate and evolution fail due to the challenge of precisely localizing an a priori unknown number of changes potentially underlying complex climate records. The kernel-based Bayesian inference approach applied here allows inferring the location, generic shape, and temporal scale of multiple transitions in established records of Plio-Pleistocene African climate. By defining a transparent probabilistic analysis strategy, we are able to identify conjoint changes occurring across the investigated terrigenous dust records from Ocean Drilling Programme (ODP) sites in the Atlantic Ocean (ODP 659), Arabian (ODP 721/722) and Mediterranean Sea (ODP 967). The study indicates a two-step transition in the African climate proxy records at (2.35-2.10) Ma and (1.70 - 1.50) Ma, that may be associated with the reorganization of the Hadley-Walker Circulation. . KW - Plio-Pleistocene KW - Hadley-Walker Circulation KW - climate transition KW - Bayesian inference KW - time series analysis KW - ODP 659 KW - ODP 721/722 KW - ODP 967 Y1 - 2022 U6 - https://doi.org/10.1016/j.quascirev.2021.107287 SN - 0277-3791 SN - 1873-457X VL - 277 PB - Elsevier CY - Oxford ER - TY - JOUR A1 - Bettenbühl, Mario A1 - Rusconi, Marco A1 - Engbert, Ralf A1 - Holschneider, Matthias T1 - Bayesian selection of Markov Models for symbol sequences application to microsaccadic eye movements JF - PLoS one N2 - Complex biological dynamics often generate sequences of discrete events which can be described as a Markov process. The order of the underlying Markovian stochastic process is fundamental for characterizing statistical dependencies within sequences. As an example for this class of biological systems, we investigate the Markov order of sequences of microsaccadic eye movements from human observers. We calculate the integrated likelihood of a given sequence for various orders of the Markov process and use this in a Bayesian framework for statistical inference on the Markov order. Our analysis shows that data from most participants are best explained by a first-order Markov process. This is compatible with recent findings of a statistical coupling of subsequent microsaccade orientations. Our method might prove to be useful for a broad class of biological systems. Y1 - 2012 U6 - https://doi.org/10.1371/journal.pone.0043388 SN - 1932-6203 VL - 7 IS - 9 PB - PLoS CY - San Fransisco ER - TY - JOUR A1 - Boehm, Thorsten A1 - Holschneider, Matthias A1 - Lignieres, Frederic A1 - Petit, Pascal A1 - Rainer, Monica A1 - Paletou, Francois A1 - Wade, Gregg A1 - Alecian, Evelyne A1 - Carfantan, Herve A1 - Blazere, Aurore A1 - Mirouh, Giovanni M. T1 - Discovery of starspots on Vega First spectroscopic detection of surface structures on a normal A-type star JF - Astronomy and astrophysics : an international weekly journal N2 - Context. The theoretically studied impact of rapid rotation on stellar evolution needs to be compared with these results of high-resolution spectroscopy-velocimetry observations. Early-type stars present a perfect laboratory for these studies. The prototype A0 star Vega has been extensively monitored in recent years in spectropolarimetry. A weak surface magnetic field was detected, implying that there might be a (still undetected) structured surface. First indications of the presence of small amplitude stellar radial velocity variations have been reported recently, but the confirmation and in-depth study with the highly stabilized spectrograph SOPHIE/OHP was required. Aims. The goal of this article is to present a thorough analysis of the line profile variations and associated estimators in the early-type standard star Vega (A0) in order to reveal potential activity tracers, exoplanet companions, and stellar oscillations. Methods. Vega was monitored in quasi-continuous high-resolution echelle spectroscopy with the highly stabilized velocimeter SOPHIE/OHP. A total of 2588 high signal-to-noise spectra was obtained during 34.7 h on five nights (2 to 6 of August 2012) in high-resolution mode at R = 75 000 and covering the visible domain from 3895 6270 angstrom. For each reduced spectrum, least square deconvolved equivalent photospheric profiles were calculated with a T-eff = 9500 and log g = 4.0 spectral line mask. Several methods were applied to study the dynamic behaviour of the profile variations (evolution of radial velocity, bisectors, vspan, 2D profiles, amongst others). Results. We present the discovery of a spotted stellar surface on an A-type standard star (Vega) with very faint spot amplitudes Delta F/Fc similar to 5 x 10(-4). A rotational modulation of spectral lines with a period of rotation P = 0.68 d has clearly been exhibited, unambiguously confirming the results of previous spectropolarimetric studies. Most of these brightness inhomogeneities seem to be located in lower equatorial latitudes. Either a very thin convective layer can be responsible for magnetic field generation at small amplitudes, or a new mechanism has to be invoked to explain the existence of activity tracing starspots. At this stage it is difficult to disentangle a rotational from a stellar pulsational origin for the existing higher frequency periodic variations. Conclusions. This first strong evidence that standard A-type stars can show surface structures opens a new field of research and ask about a potential link with the recently discovered weak magnetic field discoveries in this category of stars. KW - starspots KW - stars: early-type KW - stars: rotation KW - stars: oscillations KW - stars: individual: Vega KW - asteroseismology Y1 - 2015 U6 - https://doi.org/10.1051/0004-6361/201425425 SN - 0004-6361 SN - 1432-0746 VL - 577 PB - EDP Sciences CY - Les Ulis 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 - Chambodut, Aude A1 - Panet, I. A1 - Mandea, Mioara A1 - Diament, M. A1 - Holschneider, Matthias A1 - Jamet, O. T1 - Wavelet frames : an alternative to spherical harmonic representation of potential fields N2 - Potential fields are classically represented on the sphere using spherical harmonics. However, this decomposition leads to numerical difficulties when data to be modelled are irregularly distributed or cover a regional zone. To overcome this drawback, we develop a new representation of the magnetic and the gravity fields based on wavelet frames. In this paper, we first describe how to build wavelet frames on the sphere. The chosen frames are based on the Poisson multipole wavelets, which are of special interest for geophysical modelling, since their scaling parameter is linked to the multipole depth (Holschneider et al.). The implementation of wavelet frames results from a discretization of the continuous wavelet transform in space and scale. We also build different frames using two kinds of spherical meshes and various scale sequences. We then validate the mathematical method through simple fits of scalar functions on the sphere, named 'scalar models'. Moreover, we propose magnetic and gravity models, referred to as 'vectorial models', taking into account geophysical constraints. We then discuss the representation of the Earth's magnetic and gravity fields from data regularly or irregularly distributed. Comparisons of the obtained wavelet models with the initial spherical harmonic models point out the advantages of wavelet modelling when the used magnetic or gravity data are sparsely distributed or cover just a very local zone Y1 - 2005 SN - 0956-540X ER -