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Schmidt M.,Deutsches Geodatisches Forschungsinstitut DGFI
International Association of Geodesy Symposia | Year: 2012

For analyzing and representing a one-dimensional signal wavelet methods are used for a long time. The basic feature of wavelet analysis is the localization property, i.e. it is - depending on the chosen wavelet - possible to study a signal just in a finite interval. Nowadays a large number of satellite missions allows to monitor various geophysical phenomena. Since often regional phenomena have to be studied, multi-dimensional wavelet methods come into question. In this paper the basic principles of a multi-scale representation of multi-dimensional signals using B-spline wavelets are presented. Finally the procedure is applied to an example of ionosphere research. © Springer-Verlag Berlin Heidelberg 2012. Source

Bouman J.,Deutsches Geodatisches Forschungsinstitut DGFI | Ebbing J.,Geological Survey of Norway | Fuchs M.,Deutsches Geodatisches Forschungsinstitut DGFI
Journal of Geophysical Research: Solid Earth | Year: 2013

The Gravity field and steady state Ocean Circulation Explorer (GOCE) is the European Space Agency's mission that combines GPS tracking and gravity gradiometry to determine the Earth's mean gravity field with unprecedented, global accuracy with a spatial resolution down to 80 km. This resolution makes GOCE gravity gradient data in particular useful for lithospheric scale modeling. However, the relation between coordinates in a model frame and at satellite altitude is not straightforward, and most geophysical modeling programs require a planar approximation, which may not be appropriate for satellite data. We derive the exact relation between the model reference frame, in which gradients from lithospheric modeling are given, and the local north-oriented frame in which GOCE gradients at 255 km altitude are given. We generated gradients from a GOCE gravity field model and assessed whether the orientation differences between local north-oriented frame and model reference frame are relevant. In addition, we assessed the same for airborne gradiometry at an altitude of 5 km because these data are complementary to GOCE. We find that if the regional area has a longitude extension of 5°, the errors stay below 10%. For larger areas the standard deviation of the systematic errors may be 40% of the signal standard deviation. Comparing topographic mass reduction in planar and spherical approximation, one sees significant long wavelength differences in terms of gravity gradients or gradient-tensor invariants. The maximum error is up to 1 E at satellite altitude compared with maximum signal amplitude of 3 E. Planar approximation is therefore not accurate enough for topographic mass reduction of GOCE gravity gradients. ©2012. American Geophysical Union. All Rights Reserved. Source

Bouman J.,Deutsches Geodatisches Forschungsinstitut DGFI | Fuchs M.J.,Deutsches Geodatisches Forschungsinstitut DGFI
Geophysical Journal International | Year: 2012

The GOCE mission, a part of ESA's Living Planet Programme, aims at improved gravity field modelling at high spatial resolution. On-board GOCE a gradiometer, in combination with a scientific on-board GPS receiver, measures the earth's gravity field with unprecedented accuracy. These measurements have been used to compute GOCE gravity field solutions and combined GOCE/GRACE solutions. The main difference between the solutions is how they incorporate the required a priori information, which consists either of existing gravity field models or Kaula's rule for the signal variances of the gravity field. We assessed four series of models by comparing the gravity gradients they predict with the measured GOCE gradients. The analysis of the gravity gradients fits may reveal differences between the different solutions that can be attributed to the solution strategy, assuming that the measurement errors are homogeneous. We compared the GOCE gradients with existing state-of-the-art global gravity field models and conclude that the gradient errors are indeed globally homogeneous, with the exception of the cross-track gradient especially south of Australia. Furthermore, we find that the use of existing global gravity field models as a priori information should be avoided because this may increase the gradient residuals in spatial and spectral domain. Finally, we may conclude that the GOCE and GRACE data are compatible and complementary. © 2012 The Authors Geophysical Journal International © 2012 RAS. Source

Fuchs M.J.,Deutsches Geodatisches Forschungsinstitut DGFI | Bouman J.,Deutsches Geodatisches Forschungsinstitut DGFI
Geophysical Journal International | Year: 2011

ESA's GOCE mission aims at improved global and regional gravity field information with high spatial resolution by measuring gravity gradients. A local analysis of the GOCE gravity gradient tensor may benefit from a rotation from the gradiometer reference frame to local reference frames such as the local north oriented reference frame. As the GOCE gravity gradients include accurate and less accurate measured gradients, the point-wise tensor rotation of the GOCE-only measurements may suffer from the projection of the errors of the less accurate gravity gradients onto the accurate gravity gradients. In addition, the GOCE gravity gradients have high accuracy in the measurement bandwidth but low accuracy below, and tensor rotation may cause leakage of the large error below the measurement bandwidth to the measurement bandwidth. Degradation of the rotated gravity gradients is circumvented by replacing the less accurate tensor components, as well as the signal below the measurement bandwidth of the accurate gravity gradients, with model signal. The combination of GOCE and model gravity gradients is performed by determining the effective measurement bandwidth (EMB), that is, the bandwidth in which the integrated signal-to-noise ratio of the GOCE gravity gradients is maximized. We find that the determination of the EMB is relatively independent of the reference gravity field model that is used. The lower bound of the EMB is well below the pre-mission specifications for the four accurate gravity gradients. In addition, we assess how much GOCE contributes to the gravity gradient signal in local frames and how much the model. For the radial gravity gradient the relative GOCE contribution is 98 per cent on average, whereas this is 65-97 per cent for the other gravity gradients. These numbers strongly depend on the local frame under consideration and on the geographical position. © 2011 The Authors Geophysical Journal International © 2011 RAS. Source

Dettmering D.,Deutsches Geodatisches Forschungsinstitut DGFI | Bosch W.,Deutsches Geodatisches Forschungsinstitut DGFI
Marine Geodesy | Year: 2010

Multi-mission altimeter observations are successfully used for global cross calibration of altimeters. The approach utilizes a least squares adjustment minimizing single and dual satellite crossover differences as well as consecutive differences of the radial component of single satellites. The method is applied to obtain a characterization of the radial errors of the first year of OSTM/Jason-2 data. A mean relative range bias of about 7.5 ± 0.2 cm with respect to Jason-1 was computed. The radial errors show increased auto-correlation at the orbit revolution period, which is related to geographically correlated error pattern with up to about 2 cm amplitude. © 2010, Taylor & Francis Group, LLC. Source

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