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  • 1.
    Bagherbandi, Mohammad
    et al.
    KTH, School of Architecture and the Built Environment (ABE), Urban Planning and Environment, Geodesy and Geoinformatics. University of Gävle, Sweden.
    Tenzer, Robert
    Sjöberg, Lars E.
    KTH, School of Architecture and the Built Environment (ABE), Urban Planning and Environment, Geodesy and Geoinformatics.
    Abrehdary, Majid
    KTH, School of Architecture and the Built Environment (ABE), Urban Planning and Environment, Geodesy and Geoinformatics.
    On the residual isostatic topography effect in the gravimetric Moho determination2015In: Journal of Geodynamics, ISSN 0264-3707, E-ISSN 1879-1670, Vol. 83, p. 28-36Article in journal (Refereed)
    Abstract [en]

    In classical isostatic models, a uniform crustal density is typically assumed, while disregarding the crustal density heterogeneities. This assumption, however, yields large errors in the Moho geometry determined from gravity data, because the actual topography is not fully isostatically compensated. Moreover, the sub-crustal density structures and additional geodynamic processes contribute to the overall isostatic balance. In this study we investigate the effects of unmodelled density structures and geodynamic processes on the gravity anomaly and the Moho geometry. For this purpose, we define the residual isostatic topography as the difference between actual topography and isostatic topography, which is computed based on utilizing the Vening Meinesz-Moritz isostatic theory. We show that the isostatic gravity bias due to disagreement between the actual and isostatically compensated topography varies between 382 and 596 mGal. This gravity bias corresponds to the Moho correction term of 16 to 25 km. Numerical results reveal that the application of this Moho correction to the gravimetrically determined Moho depths significantly improves the RMS fit of our result with some published global seismic and gravimetric Moho models. We also demonstrate that the isostatic equilibrium at long-to-medium wavelengths (up to degree of about 40) is mainly controlled by a variable Moho depth, while the topographic mass balance at a higher-frequency spectrum is mainly attained by a variable crustal density.

  • 2.
    Bagherbandi, Mohammad
    et al.
    KTH, School of Architecture and the Built Environment (ABE), Urban Planning and Environment, Geodesy and Geoinformatics.
    Tenzer, Robert
    Sjöberg, Lars E.
    KTH, School of Architecture and the Built Environment (ABE), Urban Planning and Environment, Geodesy and Geoinformatics.
    Novak, Pavel
    Improved global crustal thickness modeling based on the VMM isostatic model and non-isostatic gravity correction2013In: Journal of Geodynamics, ISSN 0264-3707, E-ISSN 1879-1670, Vol. 66, p. 25-37Article in journal (Refereed)
    Abstract [en]

    In classical isostatic models for a gravimetric recovery of the Moho parameters (i.e., Moho depths and density contrast) the isostatic gravity anomalies are usually defined based on the assumption that the topographic mass surplus and the ocean mass deficiency are compensated within the Earth's crust. As acquired in this study, this assumption yields large disagreements between isostatic and seismic Moho models. To assess the effects not accounted for in classical isostatic models, we conduct a number of numerical experiments using available global gravity and crustal structure models. First, we compute the gravitational contributions of mass density contrasts due to ice and sediments, and subsequently evaluate respective changes in the Moho geometry. Residual differences between the gravimetric and seismic Moho models are then used to predict a remaining non-isostatic gravity signal, which is mainly attributed to unmodeled density structures and other geophysical phenomena. We utilize three recently developed computational schemes in our numerical studies. The apparatus of spherical harmonic analysis and synthesis is applied in forward modeling of the isostatic gravity disturbances. The Moho depths are estimated globally on a 1 arc-deg equiangular grid by solving the Vening-Meinesz Moritz inverse problem of isostasy. The same estimation model is applied to evaluate the differences between the isostatic and seismic models. We demonstrate that the application of the ice and sediment density contrasts stripping gravity corrections is essential for a more accurate determination of the Moho geometry. We also show that the application of the additional non-isostatic correction further improves the agreement between the Moho models derived based on gravity and seismic data. Our conclusions are based on comparing the gravimetric results with the CRUST2.0 global crustal model compiled using results of seismic surveys.

  • 3.
    Eshagh, Mehdi
    KTH, School of Architecture and the Built Environment (ABE), Urban Planning and Environment, Geodesy and Geoinformatics. Department of Engineering Science, University West, Trollhättan, Sweden .
    An integral approach to regional gravity field refinement using earth gravity models2013In: Journal of Geodynamics, ISSN 0264-3707, E-ISSN 1879-1670, Vol. 68, p. 18-28Article in journal (Refereed)
    Abstract [en]

    The idea of this paper is to refine the terrestrial gravimetric data with the Earth's gravity models (EGMs) and produce a high quality source of gravity data. For this purpose, biased and unbiased integral estimators are presented. These estimators are used to refine gravimetric data over Fennoscandia with the ITG-GRACE2010s and GO_CONS_GCF_2_DIR_R2 EGMs, which are the recent products of the gravity field and climate experiment (GRACE) and the gravity field and steady-state ocean circulation explorer (GOCE) satellite missions. Numerical results show that the biased integral estimator has smaller global root mean square error (RMSE) than the unbiased one. Also a simple strategy is presented to down-weight the low-frequencies the terrestrial data in spectral combination. The gravity anomalies, computed by EGM08, are compared to the refined anomalies for evaluation purpose. In the case of using a cap size of 1 degrees for integration the EGM08 gravity anomalies are more correlated with the refined ones. Also the band-limited kernels can simply be generated to maximum degree of the used EGMs for both estimators. Comparisons of the combined anomalies and those of EGM08 show insignificant differences between the biased and unbiased estimators in practice. However, the biased estimator seems to be proper one for gravity data refinement due to its smaller global RMSE.

  • 4.
    Eshagh, Mehdi
    KTH, School of Architecture and the Built Environment (ABE), Transport and Economics, Geodesy.
    Least-squares modification of extended Stokes' formula and its second-order radial derivative for validation of satellite gravity gradiometry data2010In: Journal of Geodynamics, ISSN 0264-3707, E-ISSN 1879-1670, Vol. 49, no 2, p. 92-104Article in journal (Refereed)
    Abstract [en]

    The gravity anomalies at sea level can be used to validate the satellite gravity gradiometry data. Validation of such a data is important prior to downward continuation because of amplification of the data errors through this process. In this paper the second-order radial derivative of the extended Stokes' formula is employed and the emphasis is on least-squares modification of this formula to generate the second-order radial gradient at satellite level. Two methods in this respect are proposed: (a) modifying the second-order radial derivative of extended Stokes' formula directly, and (b) modifying extended Stokes' formula prior to taking the second-order radial derivative. Numerical studies show that the former method works well but the latter is very sensitive to the proper choice of the cap size of integration and degree of modification.

  • 5.
    Eshagh, Mehdi
    et al.
    KTH, School of Architecture and the Built Environment (ABE), Transport and Economics, Geodesy.
    Sjöberg, Lars Erik
    KTH, School of Architecture and the Built Environment (ABE), Transport and Economics, Geodesy.
    Atmospheric effects on satellite gravity gradiometry data2009In: Journal of Geodynamics, ISSN 0264-3707, E-ISSN 1879-1670, Vol. 47, no 1, p. 9-19Article in journal (Refereed)
    Abstract [en]

    Atmospheric masses play an important role in precise downward continuation and validation of satellite gravity gradiometry data. In this paper we present two alternative ways to formulate the atmospheric potential. Two density models for the atmosphere are proposed and used to formulate the external and internal atmospheric potentials in spherical harmonics. Based on the derived harmonic coefficients, the direct atmospheric effects oil the satellite gravity gradiometry data are investigated and presented ill the orbital frame over Fennoscandia. The formulas of the indirect atmospheric effects oil gravity anomaly and geoid (downward continued quantities) are also derived using the proposed density models. The numerical results show that the atmospheric effect can only be significant for precise validation or inversion of the GOCE gradiometric data at the mE level.

  • 6.
    Eshagh, Mehdi
    et al.
    KTH, School of Architecture and the Built Environment (ABE), Urban Planning and Environment, Geoinformatik och Geodesi.
    Sjöberg, Lars Erik
    KTH, School of Architecture and the Built Environment (ABE), Urban Planning and Environment, Geoinformatik och Geodesi.
    Determination of gravity anomaly at sea level from inversion of satellite gravity gradiometric data2011In: Journal of Geodynamics, ISSN 0264-3707, E-ISSN 1879-1670, Vol. 51, no 5, p. 366-377Article in journal (Refereed)
    Abstract [en]

    Gravity gradients can be used to determine the local gravity field of the Earth. This paper investigates downward continuation of all elements of the disturbing gravitational tensor at satellite level using the second-order partial derivatives of the extended Stokes formula in the local-north oriented frame to determine the gravity anomaly at sea level. It considers the inversion of each gradient separately as well as their joint inversion. Numerical studies show that the gradients T-zz, T-xx, T-yy and T-xz have similar capability of being continued downward to sea level in the presence of white noise, while the gradient T-yz is considerably worse than the others. The bias-corrected joint inversion process shows the possibility of recovering the gravity anomaly with 1 mGal accuracy. Variance component estimation is also tested to update the observation weights in the joint inversion.

  • 7.
    Kiamehr, Ramin
    et al.
    KTH, School of Architecture and the Built Environment (ABE), Transport and Economics.
    Sjöberg, Lars
    KTH, School of Architecture and the Built Environment (ABE), Transport and Economics, Geodesy.
    Impact of the precise geoid model in studying tectonic structures- a case study in Iran2006In: Journal of Geodynamics, ISSN 0264-3707, E-ISSN 1879-1670, J. Geodynamics, Vol. 42, no 1-3, p. 1-11Article in journal (Refereed)
    Abstract [en]

    Iran is one of the most active regions in the world with respect,to earthquakes and tectonic motions in the lithosphere. In order to study the impact of the geoid model in detecting plate tectonic boundaries and in the establishment of an accurate height datum for future geodynamic observations, a new combined gravimetric geoid model for Iran (IRG04C) was computed by the method of least squares modification of Stokes formula based on the most recent gravity anomaly database, SRTM high resolution Digital Elevation Model (DEM), GRACE GGM02 Global Geopotential Model and GPS/levelling data. The RMS fit of the new geoid model versus GPS/levelling data is 9 cm, which is a 10 times better fit compared to the most recent published gravimetric geoid model in the area. An integrated approach, combining gravity, geoid and seismology data as well as a digital elevation model, was used to find possible correlations between these parameters. Our investigation indicates that all earthquakes with magnitude over 6.0 in the Richter scale are located in areas with a geoid slope exceeding 7.5%. The study shows a significant correlation between the horizontal gradient of the geoid and plate tectonic activities.

  • 8. Pan, M.
    et al.
    Sjöberg, Lars Erik
    KTH, Superseded Departments, Infrastructure.
    Asfaw, L. M.
    Asenjo, E.
    Alemu, A.
    Hunegnaw, A.
    An analysis of the Ethiopian Rift Valley GPS campaigns in 1994 and 19992002In: Journal of Geodynamics, ISSN 0264-3707, E-ISSN 1879-1670, Vol. 33, no 3, p. 333-343Article in journal (Refereed)
    Abstract [en]

    In cooperation with the Geophysical Observatory, Addis Ababa University, the Department of Geodesy and Photogrammetry of the Royal Institute of Technology carried out GPS measurements at three deformation networks in the Ethiopian Rift Valley in 1994 and 1999. For these campaigns the session-to-session repeatabilities were about 5 and 4 mm in the horizontal components and 50 and 10 mm in the vertical components using the IGS precise orbits, respectively. The results show, that the stations of the E3 network in the Rift Valley moved with a magnitude of 2.5 +/- 1.3 mm/a to the SE, and a magnitude of 21.3 +/- 1.4 mm/a to the ENE in the northeast (close to Assab of the Red Sea) relative to the station Addis Ababa on the African plate. The direction of movement is consistent with the local spreading vector of the Red Sea Rift with the N84degreesE slip direction estimated from seismic data. The sites of the E1 network moved by a rate of about 1-2 mm/a to the SE relative also to the station Addis Ababa. Further to the south there is an indication from our GPS data that the stations on the Somalian plate of the E2 network move by a rate of about 2.5 mm/a to the E or SE relative to the African plate. This motion can also be confirmed by geological and geodynamic data.

  • 9. Pan, M.
    et al.
    Sjöberg, Lars Erik
    KTH, Superseded Departments, Infrastructure.
    Talbot, C. J.
    Crustal movements in Skane, Sweden, between 1992 and 1998 as observed by GPS2001In: Journal of Geodynamics, ISSN 0264-3707, E-ISSN 1879-1670, Vol. 31, no 3, p. 311-322Article in journal (Refereed)
    Abstract [en]

    We estimate a network of crustal deformations in Skane, southern Sweden, using observations of the Global Positioning System (GPS) from 1992, 1996 and 1998. The network straddles the Tornquist zone, potentially one of the most active fault zones in Sweden. In addition to two stations of the Swedish permanent GPS network (Onsala and Hassleholm), it includes seven GPS sites spaced approximately 80 km apart. The precisions of the relative horizontal components for these stations are described by repeatabilities with approximately 3 mm in the north-south direction and about 2 mm in the east-west direction in the campaigns in the reference frame ITRF96. About 70% of the GPS integer carrier phase ambiguities were resolved for the three campaigns. Three stations south of the Tornquist zone moved with a rate of 5+/-0.2 mm/a toward the SW-SE, and two other stations further to the east with a rate of 2+/-0.2 mm/a toward the SE, relative to station Onsala. The displacements mean that a lateral strike-slip transtensional fault exists within the Tornquist zone, and the relative motion between the two sides along the zone was about 2 mm/a. The old fault is still active, which is consistent with geological results. The station Stavershult closest to Onsala moved NE with about 1.5+/-0.8 mm/a relative to the station Onsala. This may imply a transtensional fault between Stavershult and Onsala. If we assume that Stavershult represents the Baltic shield, Onsala has moved 1.5 mm/a toward the southwest with respect to the Baltic shield, which was confirmed by data of Very Long Baseline Interferometry (VLBI) and Satellite Laser Ranging (SLR) from 1976 to 1997 (Argus, D.F., Peltier, W.R., Watkins, M.M. Glacial isostatic adjustment observed by Very Long Baseline Interferometry and Satellite Laser Ranging geodesy. JGR 1999;104(B12);29077-93).

  • 10.
    Sjöberg, Lars Erik
    et al.
    KTH, Superseded Departments, Geodesy and Photogrammetry.
    Pan, M.
    Asenjo, E.
    Erlingsson, S.
    Glacial rebound near Vatnajokull, Iceland, studied by GPS campaigns in 1992 and 19962000In: Journal of Geodynamics, ISSN 0264-3707, E-ISSN 1879-1670, Vol. 29, no 2-Jan, p. 63-70Article in journal (Refereed)
    Abstract [en]

    Since about 1920 the Vatnajokull ice cap in Iceland has experienced a significant retreat, corresponding to a volume reduction of more than 180 km(3). With two GPS campaigns in 1992 and 1996 along the southern border of the glacier preliminary results reveal land uplift rates of 1-6 mm/yr, after a one-parameter (bias) fit with recent earth rheology models. The best fit model suggests that the lithosphere in the area is about 30 km thick and the viscosity of the asthenosphere 5 x 10(18) Pa s. The rms fit of uplift rate at all GPS sites is +/-1.4 mm/yr. As the GPS data alone cannot provide the absolute uplift rates, the one-parameter fit to the theoretical modelling implies that the absolute rates were estimated by the matching of the GPS data and model. The resulting uplift rate at station Hofn (1 mm/yr) is not consistent with two independent sources, and we therefore conclude that further GPS epoch and permanent GPS site data are needed to confirm the present geodynamic processes near Vatnajokull.

  • 11. Sun, W. K.
    et al.
    Sjöberg, Lars Erik
    KTH, Superseded Departments, Infrastructure.
    Permanent components of the crust, geoid and ocean depth tides2001In: Journal of Geodynamics, ISSN 0264-3707, E-ISSN 1879-1670, Vol. 31, no 3, p. 323-339Article in journal (Refereed)
    Abstract [en]

    The tidal deformation caused by the luni-solar potential includes not only a periodic part, but also a time-independent part, called the permanent tide. How to deal with the tidal correction in gravimetric observations, especially the treatment of the permanent tide, has been discussed for a long time, since some practical and physical problems exist anyhow. A resolution adopted by IAG (1983) was that the permanent tidal attraction of the Moon and the Sun should be eliminated, but the permanent tidal deformation of the Earth be maintained. This is called zero gravity, and the geoid associated with it is the zero geoid. As to the crust deformation, Poutanen et al. (Poutanen, M., Vermeer, M., Makinen, J., 1996. The permanent tide in GPS positioning. Journal of Geodesy 70, 499-504.) suggested that co-ordinates should be reduced to the zero crust, i.e. the crust that includes the effect of the permanent tide. This research shows that horizontal components of the permanent earth tides, which are not considered in recent studies, are also important in GPS positioning and geoid determination. Since the tide-generating potential can be expanded into harmonics and divided into two parts (geodetic coefficients and the group of harmonic waves), the permanent earth tides can be easily obtained by multiplying the amplitude of the zero-frequency wavelength by the corresponding geoid geodetic coefficient. Formulas for both elastic and fluid cases are presented. Numerical results for the elastic case show that he vertical permanent crust (zero crust), geoid and ocean depth tides reach -12.0, -5.8 and 6.1 cm at the poles, and 5.9, 2.9 and -3.0 cm at the equator, respectively. The horizontal permanent crust, geoid and ocean depth tide components reach as much as 2.5, 8.7 and 6.3 cm, respectively. According to the solution of IAG (1983), the permanent vertical components are kept in GPS positioning and geoid computation. Thus, it is natural to include the horizontal components correspondingly.

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