TY - GEN A1 - Zaourar, Naima A1 - Hamoudi, Mohamed A1 - Mandea, Mioara A1 - Balasis, Georgios A1 - Holschneider, Matthias T1 - Wavelet-based multiscale analysis of geomagnetic disturbance T2 - Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe N2 - The dynamics of external contributions to the geomagnetic field is investigated by applying time-frequency methods to magnetic observatory data. Fractal models and multiscale analysis enable obtaining maximum quantitative information related to the short-term dynamics of the geomagnetic field activity. The stochastic properties of the horizontal component of the transient external field are determined by searching for scaling laws in the power spectra. The spectrum fits a power law with a scaling exponent β, a typical characteristic of self-affine time-series. Local variations in the power-law exponent are investigated by applying wavelet analysis to the same time-series. These analyses highlight the self-affine properties of geomagnetic perturbations and their persistence. Moreover, they show that the main phases of sudden storm disturbances are uniquely characterized by a scaling exponent varying between 1 and 3, possibly related to the energy contained in the external field. These new findings suggest the existence of a long-range dependence, the scaling exponent being an efficient indicator of geomagnetic activity and singularity detection. These results show that by using magnetogram regularity to reflect the magnetosphere activity, a theoretical analysis of the external geomagnetic field based on local power-law exponents is possible. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 947 KW - geomagnetic field KW - magnetosphere KW - geomagnetic storm KW - multiscale analysis KW - spectral exponent Y1 - 2020 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-436912 SN - 1866-8372 VL - 65 IS - 12 SP - 1525 EP - 1540 ER - TY - GEN A1 - Minchev, Borislav A1 - Chambodut, Aude A1 - Holschneider, Matthias A1 - Panet, Isabelle A1 - Schöll, Eckehard A1 - Mandea, Mioara A1 - Ramillien, Guillaume T1 - Local multi-polar expansions in potential field modeling T2 - Postprints der Universität Potsdam : Mathematisch Naturwissenschaftliche Reihe N2 - The satellite era brings new challenges in the development and the implementation of potential field models. Major aspects are, therefore, the exploitation of existing space- and ground-based gravity and magnetic data for the long-term. Moreover, a continuous and near real-time global monitoring of the Earth system, allows for a consistent integration and assimilation of these data into complex models of the Earth’s gravity and magnetic fields, which have to consider the constantly increasing amount of available data. In this paper we propose how to speed up the computation of the normal equation in potential filed modeling by using local multi-polar approximations of the modeling functions. The basic idea is to take advantage of the rather smooth behavior of the internal fields at the satellite altitude and to replace the full available gravity or magnetic data by a collection of local moments. We also investigate what are the optimal values for the free parameters of our method. Results from numerical experiments with spherical harmonic models based on both scalar gravity potential and magnetic vector data are presented and discussed. The new developed method clearly shows that very large datasets can be used in potential field modeling in a fast and more economic manner. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 845 KW - potential fields (gravity, geomagnetism) KW - inverse problem KW - spherical harmonics KW - satellite data KW - size reduction Y1 - 2020 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-428990 SN - 1866-8372 IS - 845 SP - 1127 EP - 1141 ER - TY - GEN A1 - Matuschek, Hannes A1 - Kliegl, Reinhold A1 - Holschneider, Matthias T1 - Smoothing Spline ANOVA decomposition of arbitrary Splines BT - an application to eye movements in reading T2 - Postprints der Universität Potsdam Mathematisch-Naturwissenschaftliche Reihe N2 - The Smoothing Spline ANOVA (SS-ANOVA) requires a specialized construction of basis and penalty terms in order to incorporate prior knowledge about the data to be fitted. Typically, one resorts to the most general approach using tensor product splines. This implies severe constraints on the correlation structure, i.e. the assumption of isotropy of smoothness can not be incorporated in general. This may increase the variance of the spline fit, especially if only a relatively small set of observations are given. In this article, we propose an alternative method that allows to incorporate prior knowledge without the need to construct specialized bases and penalties, allowing the researcher to choose the spline basis and penalty according to the prior knowledge of the observations rather than choosing them according to the analysis to be done. The two approaches are compared with an artificial example and with analyses of fixation durations during reading. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 537 Y1 - 2019 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-409788 SN - 1866-8372 IS - 537 ER -