| 1. |
- Eshagh, Mehdi
(författare)
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On the reliability and error calibration of some recent Earth's gravity models of GOCE with respect to EGM08
- 2013
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Ingår i: ACTA GEOD GEOPHYS. - : Springer Science and Business Media LLC. - 2213-5812 .- 2213-5820 .- 1217-8977 .- 1587-1037. ; 48:2, s. 199-208
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Tidskriftsartikel (refereegranskat)abstract
- The Gravity field and steady-state Ocean Circulation Explorer (GOCE) mission is dedicated to recover spherical harmonic coefficients of the Earth's gravity field to degree and order of about 250 using its satellite gradiometric data. Since these data are contaminated with coloured noise, therefore, their inversion will not be straightforward. Unsuccessful modelling of this noise will lead to biases in the harmonic coefficients presented in the Earth's gravity models (EGMs). In this study, five of the recent EGMs of GOCE such as two direct, two time-wise and one space-wise solution are used to degree and order 240 and their reliability is investigated with respect to EGM08 which is assumed as a reliable EGM. The detected unreliable coefficients and their errors are replaced by the corresponding ones from EGM08 as a combination strategy. A condition adjustment model is organised for each two corresponding coefficients of GOCE EGMs and EGM08; and errors of the GOCE EGMs are calibrated based on a scaling factor, obtained from a posteriori variance factor. When the factor is less than 2.5 it will be multiplied to the error otherwise the error of EGM08 coefficient will be considered as the calibrated one. At the end, a simple geoid estimator is presented which considers the EGMs and their errors and its outcomes are compared with the corresponding geoid heights derived from the Global Positioning System (GPS) and the levelling data (GPS/levelling data), over Fennoscandia. This comparison shows that some of the combined-calibrated GOCE EGMs are closer to the GPS/levelling data than the original ones.
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| 2. |
- Sjöberg, Lars E., et al.
(författare)
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A study on the Fennoscandian post-glacial rebound as observed by present-day uplift rates and gravity field model GOCO02S
- 2013
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Ingår i: Acta Geodaetica et Geophysica. - : Springer Science and Business Media LLC. - 2213-5812 .- 2213-5820 .- 1217-8977 .- 1587-1037. ; 48:3, s. 317-331
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Tidskriftsartikel (refereegranskat)abstract
- Repeated absolute gravity measurements in Fennoscandia have revealed that the on-going post-glacial rebound can be regarded as a pure viscous flow of mantle mass of density 3390 kg/m(3) towards the central part of the region caused by a gravity/uplift rate of -0.167 mu Gal/mm. Our model estimates the rebound induced rates of changes of surface gravity and geoid height to have peaks of -1.9 mu Gal/yr and 1.6 mm/yr, respectively, the former being consistent with absolute gravity observations. The correlation coefficient of the spherical harmonic representations of the geoid height and uplift rate for the spectral windows between degrees 10 and 70 is estimated to -0.99 +/- 0.006, and the maximum remaining land uplift is estimated to the order of 80 m. Both the (almost) linear increase of relaxation time with degree and the linear relation between geoid height and uplift rate support a model with mass flow in the major part of the mantle and disqualify the model with a flow in a thin channel below the crust. The mean viscosity of the flow in the central uplift region is estimated to 4x10(21) Pa s.
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| 3. |
- Sjöberg, Lars, et al.
(författare)
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The observed geoid height versus Airy's and Pratt's isostatic models using matched asymptotic expansions
- 2014
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Ingår i: Acta Geodaetica et Geophysica Hungarica. - : Springer Netherlands. - 1217-8977 .- 1587-1037 .- 2213-5812 .- 2213-5820. ; 49:4, s. 473-490
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Tidskriftsartikel (refereegranskat)abstract
- Isostasy is a key concept in geodesy and geophysics. The classical isostatic models of Airy/Heiskanen and Pratt/Hayford imply that the topographic mass surplus and ocean mass deficit are balanced by mountain roots and anti-roots in the former model and by density variations in the topography and the compensation layer below sea bottom in the latter model. In geophysics gravity inversion is an essential topic where isostasy comes to play. The main objective of this study is to compare the prediction of geoid heights from the above isostatic models based on matched asymptotic expansion with geoid heights observed by the Earth Gravitational Model 2008. Numerical computations were carried out both globally and in several regions, showing poor agreements between the theoretical and observed geoid heights. As an alternative, multiple regression analysis including several non-isostatic terms in addition to the isostatic terms was tested providing only slightly better success rates. Our main conclusion is that the geoid height cannot generally be represented by the simple formulas based on matched asymptotic expansions. This is because (a) both the geoid and isostatic compensation of the topography have regional to global contributions in addition to the pure local signal considered in the classical isostatic models, and (b) geodynamic phenomena are still likely to significantly blur the results despite that all spherical harmonic low-degree (below degree 11) gravity signals were excluded from the study.
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| 4. |
- Bagherbandi, Mohammad
(författare)
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Impact of compensating mass on the topographic mass-A study using isostatic and non-isostatic Earth crustal models
- 2012
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Ingår i: Acta Geodaetica et Geophysica Hungarica. - 1217-8977 .- 1587-1037. ; 47:1, s. 29-51
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Tidskriftsartikel (refereegranskat)abstract
- The Earth topographic masses are compensated by an isostatic adjustment. According to the isostatic hypothesis a mountain is compensated by mass deficiency beneath it, where the crust is floating on the viscous mantle. For study of the impact of the compensating mass on the topographic mass a crustal thickness (Moho boundary) model is needed. A new gravimetric-isostatic model to estimate the Moho depth, Vening Meinesz-Moritz model, and two well-known Moho models (CRUST2.0 and Airy-Heiskanen) are used in this study. All topographic masses cannot be compensated by simple isostatic assumption then other compensation mechanism should be considered. In fact small topographic masses can be supported by elasticity of the larger masses and deeper Earth's layers. We discuss this issue applying spatial and spectral analyses in this study. Here we are going to investigate influence of the crustal thickness and its density in compensating the topographic potential. This study shows that the compensating potential is larger than the topographic potential in low-frequencies vs. in high-frequencies which are smaller. The study also illustrates that the Vening Meinesz-Moritz model compensates the topographic potential better than other models, which is more suitable for interpolation of the gravity field in comparison with two other models. In this study, two methods are presented to determine the percentage of the compensation of the topographic potential by the isostatic model. Numerical studies show that about 75% and 57% of the topographic potentials are compensated by the potential beneath it in Iran and Tibet. In addition, correlation analysis shows that there is linear relation between the topographic above the sea level and underlying topographic masses in the low-frequencies in the crustal models. Our investigation shows that about 580 +/- 7.4 metre (in average) of the topographic heights are not compensated by variable the crustal root and density.
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| 5. |
- Eshagh, Mehdi
(författare)
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ON THE ESTIMATION OF VARIANCE IN UNSTABLE CONDITION ADJUSTMENT MODELS
- 2011
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Ingår i: ACTA GEOD GEOPHYS HUNG. - Budapest. - 1217-8977 .- 1587-1037. ; 46:1, s. 71-83
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Tidskriftsartikel (refereegranskat)abstract
- Estimation of variance in an ordinary adjustment model is straightforward, but if the model becomes unstable or ill-conditioned its solution and the variance of the solution will be very sensitive to the errors of observations. This sensitivity can be controlled by stabilizing methods but the results will be distorted due to stabilization. In this paper, stabilizing an unstable condition model using Tikhonov regularization, the estimations of variance of unit weight and variance components are investigated. It will be theoretically proved that the estimator of variance or variance components has not the minimum variance property when the model is stabilized, but unbiased estimation of variance is possible. A simple numerical example is provided to show the performance of the theory.
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| 6. |
- Eshagh, Mehdi, 1977-, et al.
(författare)
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Quality description for gravimetric and seismic Moho models of Fennoscandia through a combined adjustment
- 2012
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Ingår i: Acta Geodaetica et Geophysica Hungarica. - : Akademiai Kiado. - 1217-8977 .- 1587-1037. ; 47:4, s. 388-401
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Tidskriftsartikel (refereegranskat)abstract
- The gravimetric model of the Moho discontinuity is usually derived based on isostatic adjustment theories considering floating crust on the viscous mantle. In computation of such a model some a priori information about the density contrast between the crust and mantle and the mean Moho depth are required. Due to our poor knowledge about them they are assumed unrealistically constant. In this paper, our idea is to improve a computed gravimetric Moho model, by the Vening Meinesz-Moritz theory, using the seismic model in Fennoscandia and estimate the error of each model through a combined adjustment with variance component estimation process. Corrective surfaces of bi-linear, bi-quadratic, bi-cubic and multi-quadric radial based function are used to model the discrepancies between the models and estimating the errors of the models. Numerical studies show that in the case of using the bi-linear surface negative variance components were come out, the bi-quadratic can model the difference better and delivers errors of 2.7 km and 1.5 km for the gravimetric and seismic models, respectively. These errors are 2.1 km and 1.6 km in the case of using the bi-cubic surface and 1 km and 1.5 km when the multi-quadric radial base function is used. The combined gravimetric models will be computed based on the estimated errors and each corrective surface.
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| 7. |
- Shirazian, Masoud, et al.
(författare)
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A remark on the GNSS differenced phase ambiguity parameters
- 2011
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Ingår i: Acta Geodaetica et Geophysica Hungarica. - Budapest : Akadémiai Kiadó. - 1217-8977 .- 1587-1037. ; 46:4, s. 431-440
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Tidskriftsartikel (refereegranskat)abstract
- In the global navigation satellite system (GNSS) carrier phase data processing, cycle slips are limiting factors and affect the quality of the estimators in general. When differencing phase observations, a problem in phase ambiguity parameterization may arise, namely linear relations between some of the parameters. These linear relations must be considered as additional constraints in the system of observation equations. Neglecting these constraints, results in poorer estimators. This becomes significant when ambiguity resolution is in demand. As a clue to detect the problem in GNSS processing, we focused on the equivalence of using undifferenced and differenced observation equations. With differenced observables this equivalence is preserved only if we add certain constraints, which formulate the linear relations between some of the ambiguity parameters, to the differenced observation equations. To show the necessity of the additional constraints, an example is made using real data of a permanent station from the network of the international GNSS service (IGS). The achieved results are notable to the GNSS software developers.
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| 8. |
- Sjöberg, Lars E., et al.
(författare)
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A theory on geoid modelling by spectral combination of data from satellite gravity gradiometry, terrestrial gravity and an Earth Gravitational Model
- 2012
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Ingår i: Acta Geodaetica et Geophysica Hungarica. - 1217-8977 .- 1587-1037. ; 47:1, s. 13-28
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Tidskriftsartikel (refereegranskat)abstract
- In precise geoid modelling the combination of terrestrial gravity data and an Earth Gravitational Model (EGM) is standard. The proper combination of these data sets is of great importance, and spectral combination is one alternative utilized here. In this method data from satellite gravity gradiometry (SGG), terrestrial gravity and an EGM are combined in a least squares sense by minimizing the expected global mean square error. The spectral filtering process also allows the SGG data to be downward continued to the Earth's surface without solving a system of equations, which is likely to be ill-conditioned. Each practical formula is presented as a combination of one or two integral formulas and the harmonic series of the EGM. Numerical studies show that the kernels of the integral part of the geoid and gravity anomaly estimators approach zero at a spherical distance of about 5 degrees. Also shown (by the expected root mean square errors) is the necessity to combine EGM08 with local data, such as terrestrial gravimetric data, and/or SGG data to attain the 1-cm accuracy in local geoid determination.
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| 9. |
- Eshagh, Mehdi, et al.
(författare)
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A COMBINED GLOBAL MOHO MODEL BASED ON SEISMIC AND GRAVIMETRIC DATA
- 2011
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Ingår i: ACTA GEOD GEOPHYS HUNG. - 1217-8977. ; 46:1, s. 25-38
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Tidskriftsartikel (refereegranskat)abstract
- The Moho depth can be determined using seismic and/or gravimetric methods. These methods will not yield the same result as they are based on different hypotheses as well as different types, qualities and distributions of data. Here we present a new global model for the Moho computed based on a stochastic combination of seismic and gravimetric Moho models. This method employs condition equations in the spectral domain for the seismic and gravimetric models as well as degree-order variance component estimation to optimally weight the corresponding harmonics in the combination. The preliminary data for the modelling are the seismic model CRUST2.0 and a new gravimetric Moho model based on the inverse solution of the Vening Meinez-Moritz isostatic hypothesis and the global Earth Gravitational Model EGM08. Numerical results show that this method of stochastic combination agrees better with the seismic Moho model (3.6 km rms difference) than the gravimetric one. The model should be a candidate for dandifying the frequently sparsely data CRUST2.0. We expect that this way of combining seismic and gravimetric data would be even more fruitful in a regional study.
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| 10. |
- Eshagh, Medhi
(författare)
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INVERSION OF GRAVITY GRADIENTS FOR DETERMINATION OF GRAVITY ANOMALY IN THE POLAR GAPS
- 2010
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Ingår i: ACTA GEOD GEOPHYS HUNG. - 1217-8977. ; 45:4, s. 440-451
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Tidskriftsartikel (refereegranskat)abstract
- The Polar Regions are not covered by satellite gravity gradiometry data if the orbital inclination of the satellite is not equal to 90 degrees. This paper investigates the feasibility of determining gravity anomaly (at sea level) by inversion of satellite gravity gradiometry data in these regions. Inversion of each element of tensor of gravitation as well as their joint inversion are investigated. Numerical studies show that gravity anomaly can be recovered with an error of 3 mGal in the north polar gap and 5 mGal in south polar gaps in the presence of 1 mE white noise in the satellite data. These errors can be reduced to 1 mGal and 3 mGal, respectively, by removing the regularization bias from the recovered gravity anomalies.
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