Papers by Matthias Holschneider
Journal of Geophysical Research: Space Physics, 2014
The magnetosphere-ionosphere-thermosphere (MIT) dynamic system significantly depends on the highl... more The magnetosphere-ionosphere-thermosphere (MIT) dynamic system significantly depends on the highly variable solar wind conditions, in particular, on changes of the strength and orientation of the interplanetary magnetic field (IMF). The solar wind and IMF interactions with the magnetosphere drive the MIT system via the magnetospheric field-aligned currents (FACs). The global modeling helps us to understand the physical background of this complex system. With the present study, we test the recently developed high-resolution empirical model of field-aligned currents MFACE (a high-resolution Model of Field-Aligned Currents through Empirical orthogonal functions analysis). These FAC distributions were used as input of the time-dependent, fully self-consistent global Upper Atmosphere Model (UAM) for different seasons and various solar wind and IMF conditions. The modeling results for neutral mass density and thermospheric wind are directly compared with the CHAMP satellite measurements. In addition, we perform comparisons with the global empirical models: the thermospheric wind model (HWM07) and the atmosphere density model (Naval Research Laboratory Mass Spectrometer and Incoherent Scatter Extended 2000). The theoretical model shows a good agreement with the satellite observations and an improved behavior compared with the empirical models at high latitudes. Using the MFACE model as input parameter of the UAM model, we obtain a realistic distribution of the upper atmosphere parameters for the Northern and Southern Hemispheres during stable IMF orientation as well as during dynamic situations. This variant of the UAM can therefore be used for modeling the MIT system and space weather predictions. A further step was using an IMF-dependent field-aligned current (FAC) model as input parameter for calculating the distribution of electric field patterns. Förster et al. [2012] and Namgaladze et al. [2013] used the empirical FAC model of Papitashvili et al. [2002], which is based on magnetic field observations from the satellites Magsat and Ørsted. These modeling simulations were done with the UAM model for various solar wind/IMF PROKHOROV ET AL.
La conference Perspectives in Mathematical Physics, International conference in honor of Alex Gro... more La conference Perspectives in Mathematical Physics, International conference in honor of Alex Grossmann, s'est tenue au CIRM, Campus de Luminy Marseille, France du 28 juillet au 1 Aout 1997. Editeurs: G. Saracco & M. Holschenider CNRS-CPT-98/P3748 Organisateurs Scientiques: G. Saracco, M. Holschneider, B. Torresani Comite Scientifique: 1- Mathematical Physics : JP Antoine (BE), Y. Avron (IL), R. Seiler (DE) 2- Wavelet Analysis : I. Daubechies (USA), Y. Meyer (FR) 3- Mathematics in Biology : JL Risler (FR) La diversite des interets scientifiques d'Alex Grossmann se retrouve dans le large spectre des origines scientifiques des personnes presentes, ainsi que dans leurs conferences. Celles-ci se regroupent en trois sections: - La premiere se rapporte a la Physique Mathematique, champ d'activite le plus ancien d'Alex, et regroupe un fort potentiel de collaborateurs et amis de longue date, ainsi qu'une nouvelle generation de jeunes scientifiques. Les intervenants sont ...
to isolate its large scales by reducing the energy contained in its small scales, we then derived... more to isolate its large scales by reducing the energy contained in its small scales, we then derived the dynamical equation, referred as ltered frozen ux equation, describing the spatio-temporal evolution of the ltered part of the eld. In the second step, we proposed a statistical parametrization of the ltered magnetic eld in order to account for both its remaining unresolved scales and its large scale uncertainties. These two modelization techniques were then included in the Bayesian formulation of the inverse problem. To explore the complex posterior distribution of the velocity eld 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 on real data for the single epoch 2005:0. PACS numbers:
Seismological Research Letters, 2015
In the present study, we summarize and evaluate the endeavors from recent years to estimate the m... more In the present study, we summarize and evaluate the endeavors from recent years to estimate the maximum possible earthquake magnitude mmax from observed data. In particular, we use basic and physically motivated assumptions to identify best cases and worst cases in terms of lowest and highest degree of uncertainty of mmax. In a general framework, we demonstrate that earthquake data and earthquake proxy data recorded in a fault zone provide almost no information about mmax unless reliable and homogeneous data of a long time interval, including several earthquakes with magnitude close to mmax, are available. Even if detailed earthquake information from some centuries including historic and paleoearthquakes are given, only very few, namely the largest events, will contribute at all to the estimation of mmax, and this results in unacceptably high uncertainties. As a consequence, estimators of mmax in a fault zone, which are based solely on earthquake‐related information from this region, have to be dismissed.
Statistics and Computing, 2022
The spatio-temporal epidemic type aftershock sequence (ETAS) model is widely used to describe the... more The spatio-temporal epidemic type aftershock sequence (ETAS) model is widely used to describe the self-exciting nature of earthquake occurrences. While traditional inference methods provide only point estimates of the model parameters, we aim at a fully Bayesian treatment of model inference, allowing naturally to incorporate prior knowledge and uncertainty quantification of the resulting estimates. Therefore, we introduce a highly flexible, non-parametric representation for the spatially varying ETAS background intensity through a Gaussian process (GP) prior. Combined with classical triggering functions this results in a new model formulation, namely the GP-ETAS model. We enable tractable and efficient Gibbs sampling by deriving an augmented form of the GP-ETAS inference problem. This novel sampling approach allows us to assess the posterior model variables conditioned on observed earthquake catalogues, i.e., the spatial background intensity and the parameters of the triggering func...
Bulletin of the Seismological Society of America, 2018
Journal of Computational and Applied Mathematics, 2017
In this paper we present a Bayesian framework for interpolating data in a reproducing kernel Hilb... more In this paper we present a Bayesian framework for interpolating data in a reproducing kernel Hilbert space associated with a random subdivision scheme, where not only approximations of the values of a function at some missing points can be obtained, but also uncertainty estimates for such predicted values. This random scheme generalizes the usual subdivision by taking into account, at each level, some uncertainty given in terms of suitably scaled noise sequences of i.i.d. Gaussian random variables with zero mean and given variance, and generating, in the limit, a Gaussian process whose correlation structure is characterized and used for computing realizations of the conditional posterior distribution. The hierarchical nature of the procedure may be exploited to reduce the computational cost compared to standard techniques in the case where many prediction points need to be considered.
In this paper we want to show, that the finite impulse response quadratic mirror filters (QMF) as... more In this paper we want to show, that the finite impulse response quadratic mirror filters (QMF) associated to a tower of grids ⊂ H = Z Zn can be identified with a right coset of the subgroup Fix(T ⊥,Map(T n → U(N) : poly) of the group of polynomial loops Map(Tn → U(N) : poly) with N = |H/ |. The QMF with some vanishing moments can be identified with cosets of subgroups. The problem to parameterize all finite impulse response QMF in arbitrary space dimensions is now equivalent to factorize all polynomial loops.
Applied and Computational Harmonic Analysis, 2010
Bulletin of the Seismological Society of America, 2018
Earthquake rates are driven by tectonic stress buildup, earthquake-induced stress changes, and tr... more Earthquake rates are driven by tectonic stress buildup, earthquake-induced stress changes, and transient aseismic processes. Although the origin of the first two sources is known, transient aseismic processes are more difficult to detect. However, the knowledge of the associated changes of the earthquake activity is of great interest, because it might help identify natural aseismic deformation patterns such as slow-slip events, as well as the occurrence of induced seismicity related to human activities. For this goal, we develop a Bayesian approach to identify change-points in seismicity data automatically. Using the Bayes factor, we select a suitable model, estimate possible change-points, and we additionally use a likelihood ratio test to calculate the significance of the change of the intensity. The approach is extended to spatiotemporal data to detect the area in which the changes occur. The method is first applied to synthetic data showing its capability to detect real change-points. Finally, we apply this approach to observational data from Oklahoma and observe statistical significant changes of seismicity in space and time.
Comptes Rendus de l Académie des Sciences - Series I - Mathematics
We present a new model of the Geomagnetic field spanning the last 20 years and called Kalmag. Der... more 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 though 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].
Journal of Geophysical Research: Solid Earth, 2016
We introduce a technique for the modeling and separation of geomagnetic field components that is ... more 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.
Lecture Notes in Physics
Without Abstract
Kyushu Journal of Mathematics, 2013
In this paper we investigate irregular Gabor frames. It is shown that for any Schwartz function t... more In this paper we investigate irregular Gabor frames. It is shown that for any Schwartz function the family of its time-frequency shifts constitutes a weighted Gabor frame if only the lattice of sampling time-frequency values is dense enough. The proof uses classical analysis tools only and is based on the localization of the kernel of the Gabor transform. Further, the method allows us to find the density bound explicitly. A numerical example is presented.
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Papers by Matthias Holschneider