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  • 1.
    Abrehdary, Majid
    et al.
    KTH, School of Architecture and the Built Environment (ABE), Urban Planning and Environment, Geodesy and Satellite Positioning.
    Sjöberg, Lars E.
    KTH, School of Architecture and the Built Environment (ABE), Urban Planning and Environment, Geodesy and Satellite Positioning.
    Bagherbandi, Mohammad
    KTH, School of Architecture and the Built Environment (ABE), Urban Planning and Environment, Geodesy and Satellite Positioning.
    The spherical terrain correction and its effect on the gravimetric-isostatic Moho determination2016In: Geophysical Journal International, ISSN 0956-540X, E-ISSN 1365-246X, Vol. 204, no 1, 262-273 p.Article in journal (Refereed)
    Abstract [en]

    In this study, the Moho depth is estimated based on the refined spherical Bouguer gravity disturbance and DTM2006 topographic data using the Vening Meinesz-Moritz gravimetric-isostatic hypothesis. In this context, we compute the refined spherical Bouguer gravity disturbances in a set of 1 degrees x 1 degrees blocks. The spherical terrain correction, a residual correction to each Bouguer shell, is computed using rock heights and ice sheet thicknesses from the DTM2006 and Earth2014 models. The study illustrates that the defined simple Bouguer gravity disturbance corrected for the density variations of the oceans, ice sheets and sediment basins and also the non-isostatic effects needs a significant terrain correction to become the refined Bouguer gravity disturbance, and that the isostatic gravity disturbance is significantly better defined by the latter disturbance plus a compensation attraction. Our study shows that despite the fact that the lateral variation of the crustal depth is rather smooth, the terrain affects the result most significantly in many areas. The global numerical results show that the estimated Moho depths by the simple and refined spherical Bouguer gravity disturbances and the seismic CRUST1.0 model agree to 5.6 and 2.7 km in RMS, respectively. Also, the mean value differences are 1.7 and 0.2 km, respectively. Two regional numerical studies show that the RMS differences between the Moho depths estimated based on the simple and refined spherical Bouguer gravity disturbance and that using CRUST1.0 model yield fits of 4.9 and 3.2 km in South America and yield 3.2 and 3.4 km in Fennoscandia, respectively.

  • 2.
    Joud, Mehdi S. Shafiei
    et al.
    KTH, School of Architecture and the Built Environment (ABE), Urban Planning and Environment, Geodesy and Satellite Positioning.
    Sjöberg, Lars E.
    KTH, School of Architecture and the Built Environment (ABE), Urban Planning and Environment, Geodesy and Satellite Positioning.
    Bagherbandi, Mohammad
    KTH, School of Architecture and the Built Environment (ABE), Urban Planning and Environment, Geodesy and Satellite Positioning. University of Gävle, Sweden.
    Use of GRACE data to detect the present land uplift rate in Fennoscandia2017In: Geophysical Journal International, ISSN 0956-540X, E-ISSN 1365-246X, Vol. 209, no 2, 909-922 p.Article in journal (Refereed)
    Abstract [en]

    After more than 13 yr of GRACE monthly data, the determined secular trend of gravity field variation can be used to study the regions of glacial isostatic adjustment (GIA). Here we focus on Fennoscandia where long-term terrestrial and high-quality GPS data are available, and we study the monthly GRACE data from three analysis centres. We present a new approximate formula to convert the secular trend of the GRACE gravity change to the land uplift rate without making assumptions of the ice load history. The question is whether the GRACEderived land uplift rate by our method is related to GIA. A suitable post-processing method for the GRACE data is selected based on weighted RMS differences with the GPS data. The study reveals that none of the assumed periodic changes of the GRACE gravity field is significant in the estimation of the secular trend, and they can, therefore, be neglected. Finally, the GRACEderived land uplift rates are obtained using the selected post-processing method, and they are compared with GPS land uplift rate data. The GPS stations with significant differences were marked using a statistical significance test. The smallest rms difference (1.0 mm a-1) was obtained by using GRACE data from the University of Texas.

  • 3. Koci, L.
    et al.
    Belonoshko, Anatoly B.
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Condensed Matter Theory.
    Ahuja, Rajeev
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering.
    Molecular dynamics calculation of liquid iron properties and adiabatic temperature gradient in the Earth's outer core2007In: Geophysical Journal International, ISSN 0956-540X, E-ISSN 1365-246X, Vol. 168, no 2, 890-894 p.Article in journal (Refereed)
    Abstract [en]

    The knowledge of the temperature radial distribution in the Earth's core is important to understand the heat balance and conditions in the Earth's interior. Molecular dynamics (MD) simulations were applied to study the properties of liquid iron under the pressure-temperature conditions of the Earth's outer core. It is shown that the model used for the MD simulations can reproduce recent experimentally determined structure factor calculations to the highest pressure of 58 GPa. Applying this model for higher pressures, the calculated densities and diffusion parameters agree well with the results of first-principles. The MD calculations indicate that a reasonable estimate of the adiabatic temperature profile in the Earth's outer core could be evaluated.

  • 4.
    Sjöberg, Lars E.
    KTH, School of Architecture and the Built Environment (ABE), Urban Planning and Environment, Geodesy and Geoinformatics.
    On the isostatic gravity anomaly and disturbance and their applications to vening meinesz-moritz gravimetric inverse problem2013In: Geophysical Journal International, ISSN 0956-540X, E-ISSN 1365-246X, Vol. 193, no 3, 1277-1282 p.Article in journal (Refereed)
    Abstract [en]

    In this study,we showthat the traditionally defined Bouguer gravity anomaly needs a correction to become 'the no-topography gravity anomaly' and that the isostatic gravity anomaly is better defined by the latter anomaly plus a gravity anomaly compensation effect than by the Bouguer gravity anomaly plus a gravitational compensation effect. This is because only the newisostatic gravity anomaly completely removes and compensates for the topographic effect. F. A. Vening Meinesz' inverse problem in isostasy deals with solving for the Moho depth from the known external gravity field and mean Moho depth (known, e.g. from seismic reflection data) by a regional isostatic compensation using a flat Earth approximation. H. Moritz generalized the problem to that of a global compensation with a spherical mean Earth approximation. The problem can be formulated mathematically as that of solving a non-linear Fredholm integral equation. The solutions to these problems are based on the condition of isostatic balance of the isostatic gravity anomaly, and, theoretically, this assumption cannot be met by the old definition of the isostatic gravity anomaly. We show how the Moho geometry can be solved for the gravity anomaly, gravity disturbance and disturbing potential, etc., and, from a theoretical point of view, all these solutions are the same.

  • 5.
    Sjöberg, Lars Erik
    KTH, School of Architecture and the Built Environment (ABE), Transport and Economics, Geodesy.
    Solving Vening Meinesz-Moritz inverse problem in isostasy2009In: Geophysical Journal International, ISSN 0956-540X, E-ISSN 1365-246X, Vol. 179, no 3, 1527-1536 p.Article in journal (Refereed)
    Abstract [en]

    Vening Meinesz' inverse problem in isostasy deals with solving for the Moho depth from known Bouguer gravity anomalies and "normal" Moho depth (T-0, known, e. g. from seismic reflection data) using a flat Earth approximation. Moritz generalized the problem to the global case by assuming a spherical approximation of the Earth's surface, and this problem is also treated here. We show that T-0 has an exact physical meaning. The problem can be formulated mathematically as that of solving a non-linear Fredholm integral equation of the first kind, and we present an iterative procedure for its solution. Moreover, we prove the uniqueness of the solution. Second, the integral equation is modified to a more suitable form, and an iterative solution is presented also for this. Also, a second-order approximate formula is derived, which determines the Moho depth to first/linear order by an earth gravitational model (EGM), and the remaining short-wavelength/non-linear part, of the order of 2 km, can be determined by iteration. A direct, second-order formula, in principle accurate to the order of 25 m, combines the first-order solution from an EGM with a second-order term, which may include terrestrial Bouguer gravity anomalies around the computation point.

  • 6.
    Sjöberg, Lars Erik
    KTH, School of Architecture and the Built Environment (ABE), Transport and Economics, Geodesy.
    The terrain correction in gravimetric geoid computation-is it needed?2009In: Geophysical Journal International, ISSN 0956-540X, E-ISSN 1365-246X, Vol. 176, no 1, 14-18 p.Article in journal (Refereed)
    Abstract [en]

    It is well known among geodesists that the gravitational effect of the topography must be removed (direct topographic effect) prior to geoid computation, for example, by Stokes' formula, and restored afterward (indirect topographic effect). The direct effect is usually decomposed into the effects of the Bouguer shell (-V-B) and the terrain. While the computation of V-B is a simple matter, the detailed consideration of the terrain effect is more difficult. This study emphasizes, that, in principle, the geoid height can be determined by the remove restore technique in considering only V-B and the effect of an arbitrarily small area of the terrain along the radius vector at the computation point, and that the determination of VB requires only the density distribution be known along this radius. The method is justified by the approximation theorems of Runge-Krarup and Keldysh-Lavrentieff. The answer to the headline question is therefore no. A closely related question is how to find a candidate method for the analytical continuation of the external potential. The paper studies whether a Taylor series can take on this role. It is concluded that this series will converge, if the direct effects of the Bouguer potential and the mass of the terrain in a near-zone around the computation point (P) are applied prior to downward continuation. The radius of the near-zone is shown not to exceed that of the height of any mountain around P, which, in the worst case (with P located near the top of Mt Everest) yields a radius of convergence within 9 km. In most cases the radius is much smaller. Hence, only a very local part of the terrain potential must be removed to allow the determination of the geoid height by Taylor expansion. Importantly, if the height of P is at least twice that of any point of the near-zone topography (e.g. for airborne and satellite gravity), the Taylor series always converges without any reduction for terrain.

  • 7.
    Sjöberg, Lars Erik
    et al.
    KTH, Superseded Departments, Geodesy and Photogrammetry.
    Nahavandchi, H.
    The atmospheric geoid effects in Stokes' formula2000In: Geophysical Journal International, ISSN 0956-540X, E-ISSN 1365-246X, Vol. 140, no 1, 95-100 p.Article in journal (Refereed)
    Abstract [en]

    The application of Stokes' formula requires that the atmospheric effect on the gravity anomaly is removed. We show that this direct effect reaches about -40 cm over the Himalayas and Antarctica. The restoring of the atmospheric masses yields the indirect atmospheric effect, reaching about -20 cm for the same regions. Consequently, the total atmospheric effect on the geoid is of the order of - 60 cm. However, for most areas close to sea level, the correction is within a few centimetres. Furthermore, the total atmospheric geoid effect is derived for the truncated as well as the modified Stokes formula. It is emphasized that the traditional (IAG) approach to adding a direct atmospheric effect to gravity may lead to a serious geoid bias in the truncated Stokes formula. However, as all the parameters of the bias are known, it can easily be corrected. In contrast, we suggest that the total atmospheric effect on the geoid be determined separately. In this approach the bias is avoided.

  • 8.
    Sjöberg, Lars Erik
    et al.
    KTH, Superseded Departments, Infrastructure.
    Pan, Ming
    KTH, Superseded Departments, Infrastructure.
    Erlingsson, S.
    Asenjo, Erick
    KTH, Superseded Departments, Infrastructure.
    Arnason, K.
    Land uplift near Vatnajokull, Iceland, as observed by GPS in 1992, 1996 and 19992004In: Geophysical Journal International, ISSN 0956-540X, E-ISSN 1365-246X, Vol. 159, no 3, 943-948 p.Article in journal (Refereed)
    Abstract [en]

    Warming of the climate in the 20th century has been manifested by an ablation of Europe's largest ice cap, Vatnajokull in Iceland. The thin elastic lithosphere and the low-viscosity asthenosphere are responding to the reduction in mass by current land uplift in the vicinity of the ice cap suggested to be of the order of 5-10 mm yr(-1): lithosphere thickness and asthenosphere viscosities compatible with these values have been inferred. From our repeated GPS epoch campaigns in 1992, 1996 and 1999 uplift rates are estimated to be of the order of 5-19 mm yr(-1), and the uplift rate is decreasing by -0.11 +/- 0.01 mm yr(-1) km(-1) with radial distance from the centre of the ice cap. These results deviate from previous Earth rheology models estimated for the region. Our data indicate that the lithosphere thickness might be of the order of 10-20 km and the asthenosphere viscosity may be as low as 5 x 10(17) Pa s, but these parameters need a careful fitting to the estimated uplift rates.

  • 9. Vanicek, P.
    et al.
    Tenzer, R.
    Sjöberg, Lars Erik
    KTH, Superseded Departments, Infrastructure.
    Martinec, Z.
    Featherstone, W. E.
    New views of the spherical Bouguer gravity anomaly2004In: Geophysical Journal International, ISSN 0956-540X, E-ISSN 1365-246X, Vol. 159, no 2, 460-472 p.Article in journal (Refereed)
    Abstract [en]

    This paper presents a number of newconcepts concerning the gravity anomaly. First, it identifies a distinct difference between a surface (2-D) gravity anomaly (the difference between actual gravity on one surface and normal gravity on another surface) and a solid (3-D) gravity anomaly defined in the fundamental gravimetric equation. Second, it introduces the 'no topography' gravity anomaly (which turns out to be the complete spherical Bouguer anomaly) as a means to generate a quantity that is smooth, thus suitable for gridding, and harmonic, thus suitable for downward continuation. It is understood that the possibility of downward continuing a smooth gravity anomaly would simplify the task of computing an accurate geoid. It is also shown that the planar Bouguer anomaly is not harmonic, and thus cannot be downward continued.

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