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  • 1
    Publication Date: 2019-04-05
    Description: Various types of heterogeneous observations can be combined within a parameter estimation process using spherical radial basis functions (SRBF) for regional gravity field refinement. However, this process is in most cases ill-posed, and thus, regularization is indispensable. We discuss two frequently used methods for choosing the regularization parameter which are the L-curve method and variance component estimation (VCE). Based on these two methods, we propose two new approaches for the regularization parameter determination, which combine the L-curve method and VCE. The first approach, denoted as ‘VCE + L-curve method’, starts with the calculation of the relative weights between the observation techniques by means of VCE. Based on these weights the L-curve method is applied to determine the regularization parameter. In the second approach, called ‘L-curve method + VCE’, the L-curve method determines first the regularization parameter and it is set to be fixed during the calculation of the relative weights between the observation techniques from VCE. These methods are investigated based on two different estimation concepts for combining various observation techniques. All the methods are applied and compared in six study cases using four types of observations in Europe. The results show that the ‘VCE + L-curve method’ delivers the best results in all the six cases, no matter using SRBFs with smoothing or non-smoothing features. The ‘L-curve method + VCE’ also gives rather good results, generally outperforming the cases just using the L-curve method or VCE. Therefore, we conclude that the newly proposed methods are decent and stable for regularization parameter determination when different data sets are combined and can be recommended regardless of the type of SRBFs used.
    Electronic ISSN: 1869-9537
    Topics: Geosciences
    Published by Copernicus on behalf of European Geosciences Union.
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  • 2
    Publication Date: 2019-07-16
    Print ISSN: 0949-7714
    Electronic ISSN: 1432-1394
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
    Published by Springer
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  • 3
    Publication Date: 2016-07-29
    Print ISSN: 0949-7714
    Electronic ISSN: 1432-1394
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
    Published by Springer
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  • 4
    Publication Date: 2021-09-02
    Description: Abstract
    Description: TIM_R6e is an extended version of the satellity-only global gravity field model TIM_R6 (Brockmann et al., 2019) which includes additional terrestrial gravity field observations over GOCE's polar gap areas. The included terrestrial information consists of the PolarGap campaign data (Forsberg et al., 2017) augumented by the AntGG gravity data compilation (Scheinert et al., 2016) over the southern polar gap (〉83°S) and the ArcGP data (Forsberg et al. 2007) over the northern polar gap (〉83°N). The combination is performed on normal equation level, encompassing the terrestrial data as spectrally limited geographic 0.5°x0.5° grids over the polar gaps.
    Description: TechnicalInfo
    Description: Processing procedures: (extending TIM_R6)Gravity from orbits (SST): (identical to TIM_R6)- short-arc integral method applied to kinematic orbits, up to degree/order 150- orbit variance information included as part of the stochastic model, it is refined by empirical covariance functionsGravity from gradients (SGG): (identical to TIM_R6)- parameterization up to degree/order 300- observations used: Vxx, Vyy, Vzz and Vxz in the Gradiometer Reference Frame (GRF)- realistic stochastic modelling by applying digital decorrelation filters to the observation equations; estimated separately for individual data segments applying a robust procedureGravity from terrestrial observations (TER):- collocation of the original terrestrial data sources onto 30'x30' geographic gravity disturbance grids (in the polar gap areas above 83° southern/northern latitude, thus forming a pair of polar caps)- spectral limitation of the data to D/O 300 within the collocation process- the chosen grid is fully compatible with the grid of the zero observation constraints of the original TIM_R6 model. In its function it replaces the original constraints- from the collocated polar caps, a partial normal equation system, up to D/O 300 is derivedCombined solution:- addition of normal equations (SST D/O 150, SGG D/O 300, TER D/O 300)- Constraints: * Kaula-regularization applied to coefficients of degrees/orders 201 - 300 (constrained towards zero, fully compatible with TIM_R6)- weighting of SST and SGG is identical to TIM_R6. All TER observations are weighted with 5 mGal.Specific features of resulting gravity field:- Gravity field solution is (mostly) independent of any other gravity field information (outside the polar gap region)- Constraint towards zero starting from degree/order 201 to improve signal-to-noise ratio- Related variance-covariance information represents very well the true errors of the coefficients (outside the polar gap region)- Solution can be used for independent comparison and combination on normal equation level with other satellite-only models (e.g. GRACE), terrestrial gravity data, and altimetry (outside the polar gap region)- Since in the low degrees the solution is based solely on GOCE orbits, it is not competitive with a GRACE model in this spectral region (outside the polar gap region)- In comparison to TIM_R6, TIM_R6e should deliver more accurate results, especially towards the polar gaps. However, as it uses additional data sources it cannot be seen as totally independent anymore: even outside the polar gap regions correlations (introduced by the holistic nature of spherical harmonics) may be found.
    Keywords: global gravitational model ; ICGEM ; GOCE ; PolarGap ; geodesy ; EARTH SCIENCE 〉 SOLID EARTH 〉 GEODETICS 〉 GEOID CHARACTERISTICS ; EARTH SCIENCE 〉 SOLID EARTH 〉 GRAVITY/GRAVITATIONAL FIELD 〉 GRAVITY
    Language: English
    Type: Dataset , Dataset
    Format: 3 Files
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