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 - Panet, I. A1 - Chambodut, Aude A1 - Diament, M. A1 - Holschneider, Matthias A1 - Jamet, O. T1 - New insights on intraplate volcanism in French Polynesia from wavelet analysis of GRACE, CHAMP, and sea surface data JF - Journal of geophysical research : Solid earth N2 - [ 1] In this paper, we discuss the origin of superswell volcanism on the basis of representation and analysis of recent gravity and magnetic satellite data with wavelets in spherical geometry. We computed a refined gravity field in the south central Pacific based on the GRACE satellite GGM02S global gravity field and the KMS02 altimetric grid, and a magnetic anomaly field based on CHAMP data. The magnetic anomalies are marked by the magnetic lineation of the seafloor spreading and by a strong anomaly in the Tuamotu region, which we interpret as evidence for crustal thickening. We interpret our gravity field through a continuous wavelet analysis that allows to get a first idea of the internal density distribution. We also compute the continuous wavelet analysis of the bathymetric contribution to discriminate between deep and superficial sources. According to the gravity signature of the different chains as revealed by our analysis, various processes are at the origin of the volcanism in French Polynesia. As evidence, we show a large-scale anomaly over the Society Islands that we interpret as the gravity signature of a deeply anchored mantle plume. The gravity signature of the Cook-Austral chain indicates a complex origin which may involve deep processes. Finally, we discuss the particular location of the Marquesas chain as suggesting that the origin of the volcanism may interfere with secondary convection rolls or may be controlled by lithospheric weakness due to the regional stress field, or else related to the presence of the nearby Tuamotu plateau. Y1 - 2006 U6 - https://doi.org/10.1029/2005JB004141 SN - 0148-0227 VL - 111 PB - Union CY - Washington 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 - 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 -