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 - JOUR A1 - Zaourar, Naima A1 - Hamoudi, Mohamed A1 - Holschneider, Matthias A1 - Mandea, Mioara T1 - Fractal dynamics of geomagnetic storms JF - Arabian journal of geosciences N2 - We explore fluctuations of the horizontal component of the Earth's magnetic field to identify scaling behaviour of the temporal variability in geomagnetic data recorded by the Intermagnet observatories during the solar cycle 23 (years 1996 to 2005). In this work, we use the remarkable ability of scaling wavelet exponents to highlight the singularities associated with discontinuities present in the magnetograms obtained at two magnetic observatories for six intense magnetic storms, including the sudden storm commencements of 14 July 2000, 29-31 October and 20-21 November 2003. In the active intervals that occurred during geomagnetic storms, we observe a rapid and unidirectional change in the spectral scaling exponent at the time of storm onset. The corresponding fractal features suggest that the dynamics of the whole time series is similar to that of a fractional Brownian motion. Our findings point to an evident relatively sudden change related to the emergence of persistency of the fractal power exponent fluctuations precedes an intense magnetic storm. These first results could be useful in the framework of extreme events prediction studies. KW - Geomagnetic field KW - Magnetosphere KW - Geomagnetic storm KW - Multiscale analysis KW - Spectral exponent Y1 - 2013 U6 - https://doi.org/10.1007/s12517-011-0487-0 SN - 1866-7511 VL - 6 IS - 6 SP - 1693 EP - 1702 PB - Springer CY - Heidelberg 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 - 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 - 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 - Hayn, Michael A1 - Panet, I. A1 - Diament, M. A1 - Holschneider, Matthias A1 - Mandea, Mioara A1 - Davaille, A. T1 - Wavelet-based directional analysis of the gravity field evidence for large-scale undulations JF - Geophysical journal international N2 - In the eighties, the analysis of satellite altimetry data leads to the major discovery of gravity lineations in the oceans, with wavelengths between 200 and 1400 km. While the existence of the 200 km scale undulations is widely accepted, undulations at scales larger than 400 km are still a matter of debate. In this paper, we revisit the topic of the large-scale geoid undulations over the oceans in the light of the satellite gravity data provided by the GRACE mission, considerably more precise than the altimetry data at wavelengths larger than 400 km. First, we develop a dedicated method of directional Poisson wavelet analysis on the sphere with significance testing, in order to detect and characterize directional structures in geophysical data on the sphere at different spatial scales. This method is particularly well suited for potential field analysis. We validate it on a series of synthetic tests, and then apply it to analyze recent gravity models, as well as a bathymetry data set independent from gravity. Our analysis confirms the existence of gravity undulations at large scale in the oceans, with characteristic scales between 600 and 2000 km. Their direction correlates well with present-day plate motion over the Pacific ocean, where they are particularly clear, and associated with a conjugate direction at 1500 km scale. A major finding is that the 2000 km scale geoid undulations dominate and had never been so clearly observed previously. This is due to the great precision of GRACE data at those wavelengths. Given the large scale of these undulations, they are most likely related to mantle processes. Taking into account observations and models from other geophysical information, as seismological tomography, convection and geochemical models and electrical conductivity in the mantle, we conceive that all these inputs indicate a directional fabric of the mantle flows at depth, reflecting how the history of subduction influences the organization of lower mantle upwellings. KW - Wavelet transform KW - Satellite geodesy KW - Gravity anomalies and Earth structure KW - Pacific Ocean Y1 - 2012 U6 - https://doi.org/10.1111/j.1365-246X.2012.05455.x SN - 0956-540X SN - 1365-246X VL - 189 IS - 3 SP - 1430 EP - 1456 PB - Oxford Univ. Press CY - Oxford 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 - 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 - TY - JOUR A1 - Chambodut, Aude A1 - Mandea, Mioara T1 - Evidence for geomagnetic jerks in comprehensive models N2 - The rate of secular variation occasionally undergoes a sudden, sharp change, called a geomagnetic jerk. Such jerks have been detected in geomagnetic time series, centered-over the last four decades-around 1971, 1980, 1991, and 1999; others have been inferred from historical records. The geomagnetic jerks represent a reorganization of the secular variation, implying an internal origin, as established through spherical harmonic and wavelet analysis. However, some characteristics of jerks are not well understood. Here we estimate the occurrence dates for geomagnetic jerks, as they can be detected from a global geomagnetic model. This choice makes the present study novel, for two reasons. First, utilizing the comprehensive modelling approach allows for the use of a secular variation signal free of time-varying external fields and their corresponding induced counterpart, and observatory biases. Second, the model utilizes satellite data when available, in addition to observatory data. Indeed, POGO (1967 to 1971), MAGSAT (1979 to 1980), Orsted (1999 to present time) and CHAMP (2000 to present time) satellite measurements help to separate the different magnetic sources. In this study the CM4 comprehensive model is used for a global search of geomagnetic jerks and their occurrence dates. Our first result indicates that found geomagnetic jerks might not have been worldwide in occurrence. Moreover, the obtained dates suggest that jerks detected in the CM4 model over the last four decades occurred not simultaneously but at slightly different times around 1971, 1980 and 1991 Y1 - 2005 SN - 1343-8832 ER -