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  • 1.
    Bagherbandi, Mohammad
    et al.
    Royal Institute of Technology (KTH), Division of Geodesy and Geoinformatics.
    Eshagh, Mehdi
    Department of Surveying, Islamic Azad University, Shahr-e-Rey Branch, Tehran, Iran.
    Recovery of Moho's undulations based on the Vening Meinesz-Moritz theory from satellite gravity gradiometry data: A simulation study2012Ingår i: Advances in Space Research, ISSN 0273-1177, E-ISSN 1879-1948, Vol. 49, nr 6, s. 1097-1111Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In the gravimetric approach to determine the Moho depth an isostatic hypothesis can be used. The Vening Meinesz–Moritz isostatic hypothesis is the recent theory for such a purpose. Here, this theory is further developed so that the satellite gravity gradiometry (SGG) data are used for recovering the Moho depth through a nonlinear integral inversion procedure. The kernels of its forward and inverse problems show that the inversion should be done in a larger area by 5° than the desired one to reduce the effect of the spatial truncation error of the integral formula. Our numerical study shows that the effect of this error on the recovered Moho depths can reach 6 km in Persia and it is very significant. The iterative Tikhonov regularization in a combination with either generalized cross validation or quasi-optimal criterion of estimating the regularization parameter seems to be suitable and the solution is semi-convergent up to the third iteration. Also the Moho depth recovered from the simulated SGG data will be more or less the same as that obtained from the terrestrial gravimetric data with a root mean square error of 2 km and they are statistically consistent.

  • 2.
    Eshagh, Mehdi
    Royal Institute of Technology (KTH), Division of Geodesy and Geoinformatics.
    The effect of spatial truncation error on integral inversion of satellite gravity gradiometry data2011Ingår i: Advances in Space Research, ISSN 0273-1177, E-ISSN 1879-1948, ISSN 0273-1177, Vol. 47, nr 7, s. 1238-1247Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    The satellite gravity gradiometry (SGG) data can be used for local modelling of the Earth's gravity field. In this study, the SGG data in the local north-oriented and orbital frames are inverted to the gravity anomaly at sea level using the second-order partial derivatives of the extended Stokes formula. The emphasis is on the spatial truncation error and the kernel behaviour of the integral formulas in the aforementioned frames. The paper will show that only the diagonal elements of gravitational tensor at satellite level are suitable for recovering the gravity anomaly at sea level. Numerical studies show that the gravity anomaly can be recovered in Fennoscandia with an accuracy of about 6 mGal directly from on-orbit SGG data.

  • 3.
    Eshagh, Mehdi
    et al.
    Högskolan Väst, Institutionen för ingenjörsvetenskap, Avd för elektro, lantmäteri och naturvetenskap.
    Ghorbannia, Morteza
    K.N. Toosi University of Technology, Department of Geodesy, Tehran.
    The effect of spatial truncation error on the variance of gravity anomalies derived from inversion of satellite orbital and gradiometric data2014Ingår i: Advances in Space Research, ISSN 0273-1177, E-ISSN 1879-1948, Vol. 54, nr 2, s. 261-271Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    The spatial truncation error (STE) is a significant systematic error in the integral inversion of satellite gradiometric and orbital data to gravity anomalies at sea level. In order to reduce the effect of STE, a larger area than the desired one is considered in the inversion process, but the anomalies located in its central part are selected as the final results. The STE influences the variance of the results as well because the residual vector, which is contaminated with STE, is used for its estimation. The situation is even more complicated in variance component estimation because of its iterative nature. In this paper, we present a strategy to reduce the effect of STE on the a posteriori variance factor and the variance components for inversion of satellite orbital and gradiometric data to gravity anomalies at sea level. The idea is to define two windowing matrices for reducing this error from the estimated residuals and anomalies. Our simulation studies over Fennoscandia show that the differences between the 0.5°×0.5°0.5°×0.5° gravity anomalies obtained from orbital data and an existing gravity model have standard deviation (STD) and root mean squared error (RMSE) of 10.9 and 12.1 mGal, respectively, and those obtained from gradiometric data have 7.9 and 10.1 in the same units. In the case that they are combined using windowed variance components the STD and RMSE become 6.1 and 8.4 mGal. Also, the mean value of the estimated RMSE after using the windowed variances is in agreement with the RMSE of the differences between the estimated anomalies and those obtained from the gravity model.

  • 4.
    Eshagh, Mehdi
    et al.
    Högskolan Väst, Institutionen för ingenjörsvetenskap, Avd för elektro, lantmäteri och naturvetenskap.
    Ghorbannia, Morteza
    Department of Geodesy, K.N.Toosi University of Technology.
    The use of Gaussian equations of motions of a satellite for local gravity anomaly recovery2013Ingår i: Advances in Space Research, ISSN 0273-1177, E-ISSN 1879-1948, Vol. 52, nr 1, s. 30-38Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    The orbital elements of a low Earth orbiting satellite and their velocities can be used for local determination of gravity anomaly. The important issue is to find direct relations among the anomalies and these parameters. Here, a primary theoretical study is presented for this purpose. The Gaussian equations of motion of a satellite are used to develop integral formulas for recovering the gravity anomalies. The behaviour of kernels of the integrals are investigated for a two-month simulated orbit similar to that of the Gravity field and steady-state ocean circulation explorer (GOCE) mission over Fennoscandia. Numerical investigations show that the integral formulas have neither isotropic nor well-behaved kernels. In such a case, gravity anomaly recovery is not successful due to large spatial truncation error of the integral formulas. Reformulation of the problem by combining the orbital elements and their velocities leads to an integral with a well-behaved kernel which is suitable for our purpose. Also based on these combinations some general relations among the orbital elements and their velocities are obtained which can be used for validation of orbital parameters and their velocities

  • 5.
    Eshagh, Mehdi
    et al.
    Royal Institute of Technology (KTH), Division of Geodesy and Geoinformatics, .
    Romeshkani, Mohsen
    Department of Geodesy, K.N. Toosi University of Technology, 470 Mirdamad Ave. West, Box 15875-4416, 19697 Tehran, Iran.
    Generation of vertical-horizontal and horizontal-horizontal gravity gradients using stochastically modified integral estimators2011Ingår i: Advances in Space Research, ISSN 0273-1177, E-ISSN 1879-1948, Vol. 48, nr 8, s. 1341-1358Artikel i tidskrift (Refereegranskat)
    Abstract [sv]

    The Earth's gravity field modelling is an ill-posed problem having a sensitive solution to the error of data. Satellite gravity gradiometry (SGG) is a space technique to measure the second-order derivatives of geopotential for modelling this field, but the measurements should be validated prior to use. The existing terrestrial gravity anomalies and Earth gravity models can be used for this purpose. In this paper, the second-order vertical–horizontal (VH) and horizontal–horizontal (HH) derivatives of the extended Stokes formula in the local north-oriented frame are modified using biased, unbiased and optimum types of least-squares modification. These modified integral estimators are used to generate the VH and HH gradients at 250 km level for validation purpose of the SGG data. It is shown that, unlike the integral estimator for generating the second-order radial derivative of geopotential, the system of equations from which the modification parameters are obtained is unstable for all types of modification, with large cap size and high degree, and regularization is strongly required for solving the system. Numerical studies in Fennoscandia show that the SGG data can be estimated with an accuracy of 1 mE using an integral estimator modified by a biased type least-squares modification. In this case an integration cap size of 2.5° and a degree of modification of 100 for integrating 30′ × 30′ gravity anomalies are required.

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