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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. Univ Karlstad, Sweden.
    Sjöberg, L. 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. Univ Gavle, Sweden.
    Sampietro, D.
    Towards the Moho depth and Moho density contrast along with their uncertainties from seismic and satellite gravity observations2017In: Journal of Applied Geodesy, ISSN 1862-9016, E-ISSN 1862-9024, Vol. 11, no 4, p. 231-247Article in journal (Refereed)
    Abstract [en]

    We present a combined method for estimating a new global Moho model named KTH15C, containing Moho depth and Moho density contrast (or shortly Moho parameters), from a combination of global models of gravity (GOCO05S), topography (DTM2006) and seismic information (CRUST1.0 and MDN07) to a resolution of 1 degrees x 1 degrees based on a solution of Vening Meinesz-Moritz' inverse problem of isostasy. This paper also aims modelling of the observation standard errors propagated from the Vening Meinesz-Moritz and CRUST1.0 models in estimating the uncertainty of the final Moho model. The numerical results yield Moho depths ranging from 6.5 to 70.3 km, and the estimated Moho density contrasts ranging from 21 to 650 kg/m(3), respectively. Moreover, test computations display that in most areas estimated uncertainties in the parameters are less than 3 km and 50 kg/m(3), respectively, but they reach to more significant values under Gulf of Mexico, Chile, Eastern Mediterranean, Timor sea and parts of polar regions. Comparing the Moho depths estimated by KTH15C and those derived by KTH11C, GEMMA2012C, CRUST1.0, KTH14C, CRUST14 and GEMMA1.0 models shows that KTH15C agree fairly well with CRUST1.0 but rather poor with other models. The Moho density contrasts estimated by KTH15C and those of the KTH11C, KTH14C and VMM model agree to 112, 31 and 61 kg/m(3) in RMS. The regional numerical studies show that the RMS differences between KTH15C and Moho depths from seismic information yields fits of 2 to 4 km in South and North America, Africa, Europe, Asia, Australia and Antarctica, respectively.

  • 2.
    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. Univ Gavle, Dept Ind Dev IT & Land Management, SE-80176 Gavle, Sweden.
    Combined Moho parameters determination using CRUST1.0 and Vening Meinesz-Moritz model2015In: Journal of Earth Science, ISSN 1674-487X, E-ISSN 1867-111X, Vol. 26, no 4, p. 607-616Article in journal (Refereed)
    Abstract [en]

    According to Vening Meinesz-Moritz (VMM) global inverse isostatic problem, either the Moho density contrast (crust-mantle density contrast) or the Moho geometry can be estimated by solving a non-linear Fredholm integral equation of the first kind. Here solutions to the two Moho parameters are presented by combining the global geopotential model (GOCO-03S), topography (DTM2006) and a seismic crust model, the latter being the recent digital global crustal model (CRUST1.0) with a resolution of 1A(0)x1A(0). The numerical results show that the estimated Moho density contrast varies from 21 to 637 kg/m(3), with a global average of 321 kg/m(3), and the estimated Moho depth varies from 6 to 86 km with a global average of 24 km. Comparing the Moho density contrasts estimated using our leastsquares method and those derived by the CRUST1.0, CRUST2.0, and PREM models shows that our estimate agrees fairly well with CRUST1.0 model and rather poor with other models. The estimated Moho depths by our least-squares method and the CRUST1.0 model agree to 4.8 km in RMS and with the GEMMA1.0 based model to 6.3 km.

  • 3.
    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.
    Modelling Moho depth in ocean areas based on satellite altimetry using Vening Meinesz–Moritz’ method2016In: Acta Geodaetica et Geophysica Hungarica, ISSN 1217-8977, E-ISSN 1587-1037, Vol. 51, no 2, p. 137-149Article in journal (Refereed)
    Abstract [en]

    An experiment for estimating Moho depth is carried out based on satellite altimetryand topographic information using the Vening Meinesz–Moritz gravimetric isostatichypothesis. In order to investigate the possibility and quality of satellite altimetry in Mohodetermination, the DNSC08GRA global marine gravity field model and the DTM2006 globaltopography model are used to obtain a global Moho depth model over the oceans with aresolution of 1 x 1 degree. The numerical results show that the estimated Bouguer gravity disturbancevaries from 86 to 767 mGal, with a global average of 747 mGal, and the estimatedMoho depth varies from 3 to 39 km with a global average of 19 km. Comparing the Bouguergravity disturbance estimated from satellite altimetry and that derived by the gravimetricsatellite-only model GOGRA04S shows that the two models agree to 13 mGal in root meansquare (RMS). Similarly, the estimated Moho depths from satellite altimetry andGOGRA04S agree to 0.69 km in RMS. It is also concluded that possible mean dynamictopography in the marine gravity model does not significantly affect the Moho determination.

  • 4.
    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, p. 262-273Article 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.

  • 5.
    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.
    Sampietro, Daniele
    Modelling Moho parameters and their uncertainties from the combination of the seismic and satellite gravity dataManuscript (preprint) (Other academic)
    Abstract [en]

    We present a method for estimating a new global Moho model (KTH15C), containing Moho depth and density contrast, from a combination of global models of gravity (GOCO05S), topography (DTM2006) and seismic information (CRUST1.0 and MDN07) to a resolution of 1°×1° based on a solution of Vening Meinesz-Moritz’ inverse problem of isostasy. Particularly, this article has its emphasis on the modelling of the observation standard errors propagated from the Vening Meinesz-Moritz and CRUST1.0 models in estimating the uncertainty of the final Moho model. The numerical results yield Moho depths ranging from 6.5 to 70.1 km, with a global average of 23.4 ± 13 km. The estimated Moho density contrasts range from 21 to 680 kg/m3, with a global average of 345.4 ± 112 kg/m3. Moreover, test computations display that in most areas estimated uncertainties in the parameters are less than 3 km and 50 kg/m3, respectively, but they reach to more significant values under Gulf of Mexico, Chile, Eeastern Mediterranean, Timor sea and parts of polar regions. Comparing the Moho depths estimated by KTH15C and those derived by KTH11C, GEMMA2012C, CRUST1.0, KTH14C, CRUST14 and GEMMA1.0 models shows that KTH15C agree fairly well with CRUST1.0 but rather poor with other models. The Moho density contrasts estimated by KTH15C and those of the KTH11C and KTH14C model agree to 120 and 80 kg/m3 in RMS. The regional numerical studies show that the RMS differences between KTH15C and Moho depths from seismic information yields fits of 2 to 4 km in South and North America, Africa, Europe, Asia, Australia and Antarctica, respectively.    

  • 6.
    Amin, Hadi
    et al.
    Faculty of Engineering and Sustainable Development, The University of Gävle.
    Sjöberg, Lars
    KTH, School of Architecture and the Built Environment (ABE), Real Estate and Construction Management, Geodesy and Satellite Positioning. Faculty of Engineering and Sustainable Development, University of Gävle.
    Bagherbandi, Mohammad
    KTH, School of Architecture and the Built Environment (ABE), Real Estate and Construction Management, Geodesy and Satellite Positioning. Faculty of Engineering and Sustainable Development, The University of Gävle.
    A global vertical datum defined by the conventional geoid potential and the Earth ellipsoid parameters2019In: Journal of Geodesy, ISSN 0949-7714, E-ISSN 1432-1394Article in journal (Refereed)
    Abstract [en]

    The geoid, according to the classical Gauss–Listing definition, is, among infinite equipotential surfaces of the Earth’s gravity field, the equipotential surface that in a least squares sense best fits the undisturbed mean sea level. This equipotential surface, except for its zero-degree harmonic, can be characterized using the Earth’s global gravity models (GGM). Although, nowadays, satellite altimetry technique provides the absolute geoid height over oceans that can be used to calibrate the unknown zero-degree harmonic of the gravimetric geoid models, this technique cannot be utilized to estimate the geometric parameters of the mean Earth ellipsoid (MEE). The main objective of this study is to perform a joint estimation of W0, which defines the zero datum of vertical coordinates, and the MEE parameters relying on a new approach and on the newest gravity field, mean sea surface and mean dynamic topography models. As our approach utilizes both satellite altimetry observations and a GGM model, we consider different aspects of the input data to evaluate the sensitivity of our estimations to the input data. Unlike previous studies, our results show that it is not sufficient to use only the satellite-component of a quasi-stationary GGM to estimate W0. In addition, our results confirm a high sensitivity of the applied approach to the altimetry-based geoid heights, i.e., mean sea surface and mean dynamic topography models. Moreover, as W0 should be considered a quasi-stationary parameter, we quantify the effect of time-dependent Earth’s gravity field changes as well as the time-dependent sea level changes on the estimation of W0. Our computations resulted in the geoid potential W0 = 62636848.102 ± 0.004 m2 s−2 and the semi-major and minor axes of the MEE, a = 6378137.678 ± 0.0003 m and b = 6356752.964 ± 0.0005 m, which are 0.678 and 0.650 m larger than those axes of GRS80 reference ellipsoid, respectively. Moreover, a new estimation for the geocentric gravitational constant was obtained as GM = (398600460.55 ± 0.03) × 106 m3 s−2.

  • 7.
    Bagherbandi, M.
    et al.
    KTH, School of Architecture and the Built Environment (ABE), Urban Planning and Environment, Geodesy and Geoinformatics.
    Eshagh, Mehdi
    KTH, School of Architecture and the Built Environment (ABE), Urban Planning and Environment, Geodesy and Geoinformatics.
    Crustal thickness recovery using an isostatic model and GOCE data2012In: Earth Planets and Space, ISSN 1343-8832, E-ISSN 1880-5981, Vol. 64, no 11, p. 1053-1057Article in journal (Refereed)
    Abstract [en]

    One of the GOCE satellite mission goals is to study the Earth's interior structure including its crustal thickness. A gravimetric-isostatic Moho model, based on the Vening Meinesz-Moritz (VMM) theory and GOCE gradiomet-ric data, is determined beneath Iran's continental shelf and surrounding seas. The terrestrial gravimetric data of Iran are also used in a nonlinear inversion for a recovering-Moho model applying the VMM model. The newly-computed Moho models are compared with the Moho data taken from CRUST2.0. The root-mean-square (RMS) of differences between the CRUST2.0 Moho model and the recovered model from GOCE and that from the terrestrial gravimetric data are 3.8 km and 4.6 km, respectively.

  • 8.
    Bagherbandi, Mohammad
    KTH, School of Architecture and the Built Environment (ABE), Urban Planning and Environment, Geoinformatik och Geodesi.
    A comparison of three gravity inversion methods for crustal thickness modelling in Tibet plateau2012In: Journal of Asian Earth Sciences, ISSN 1367-9120, E-ISSN 1878-5786, Vol. 43, no 1, p. 89-97Article in journal (Refereed)
    Abstract [en]

    Crustal thickness can be determined by gravimetric methods based on different assumptions, e.g. by isostatic hypotheses. Here we compare three gravimetric inversion methods to estimate the Moho depth. Two Moho models based on the Vening Meinesz-Moritz hypothesis and one by using Parker-Oldenburg's algorithm, which are investigated in Tibet plateau. The results are compared with CRUST2.0, and it will be presented that the estimated Moho depths from the Vening Meinesz-Moritz model will be better than the Parker-Oldenburg's algorithm.

  • 9.
    Bagherbandi, Mohammad
    KTH, School of Architecture and the Built Environment (ABE), Urban Planning and Environment, Geoinformatik och Geodesi.
    An Isostatic Earth Crustal Model: and Its Applications2011Doctoral thesis, monograph (Other academic)
    Abstract [en]

     The Mohorovičič discontinuity (Moho), which is the surface separating the Earth’s crust from the mantle, is of great interest among geoscientists. The Moho depth can be determined by seismic and gravimetric methods. The seismic methods are expensive, time-consuming and suffer from lack of global coverage of data, while the gravimetric methods use inexpensive and mostly already available global and regional data based on an isostatic model. The main reasons for studying an isostatic model are on one hand the gaps and uncertainties of the seismic models, and, on the other hand, the generous availability of gravity data from global models for the gravimetric-isostatic model. In this study, we present a new gravimetric-isostatic Moho model, called the Vening Meinesz-Moritz (VMM) model. Also, a combined Moho model based on seismic and gravimetric models is presented.

    Classical isostatic hypotheses assume that the topographic potential is fully compensated at all wavelengths, while is not the case in reality. We found that the maximum degree of compensation for the topographic potential based on the new Moho model is 60, corresponding to the resolution of about 330 km. Other (dynamic) isostatic effects (such as temporal compensation, plate tectonics, post-glacial rebound, etc) should be considered as well, which are disregarded in this thesis. Numerical results imply that the dynamic phenomena affect mostly the long-wavelengths.

    The VMM model is applied for different purposes. The Moho density contrast is an important parameter for estimating the Moho depth, and we present a technique to simultaneously estimate Moho depth and density contrast by the VMM and seismic models. Another application is the recovery of gravity anomaly from Satellite Gravity Gradiometry (SGG) data by a smoothing technique, and we show that the VMM model performs better than the Airy-Heiskanen isostatic model. We achieved an rms difference of 4 mGal for the gravity anomaly estimated from simulated GOCE data in comparison with EGM08, and this result is better than direct downward continuation of the data without smoothing. We also present a direct method to recover Moho depth from the SGG mission, and we show that the recovered Moho is more or less of the same quality as that obtained from terrestrial gravimetric data (with an rms error of 2 km). Moreover, a strategy is developed for creating substitutes for missing GOCE data in Antarctica, where there is a polar gap of such data.

    The VMM model is further used for constructing a Synthetic Earth Gravity Model (SEGM). The topographic-isostatic potential is simple to apply for the SEGM, and the latter can be an excellent tool to fill data gaps, extending the EGMs to higher degrees and validating a recovery technique of the gravity field from a satellite mission. Regional and global tests of the SEGM yield a relative error of less than 3 % vs. EGM08 to degree 2160.

     

  • 10.
    Bagherbandi, Mohammad
    KTH, School of Architecture and the Built Environment (ABE), Urban Planning and Environment, Geodesy and Geoinformatics.
    Combination of seismic and an isostatic crustal thickness models using Butterworth filter in a spectral approach2012In: Journal of Asian Earth Sciences, ISSN 1367-9120, E-ISSN 1878-5786, Vol. 59, no SI, p. 240-248Article in journal (Refereed)
    Abstract [en]

    In this study, using Butterworth filter a combined crustal thickness model based on seismic and isostatic-gravimetric models is presented in a spectral domain. Vening Meinesz-Moritz isostatic model and a seismic model which obtained from sparse seismic data are two models used in this study. The filter used helps to join two models without any jump in the overlap degree in the spectral domain. The main motivations of this study are (a) presenting a higher resolution for the crustal thickness and (b) removing non-isostatic effects from the isostatic model. The result obtained from the combined model is a synthetic Earth crustal model up to degree 180 (equivalent resolution 1° × 1°). In spite of the differences in the some parts of the Earth between the seismic and isostatic-gravimetric models, the test computations show a satisfactory agreement between the results provided. Numerical results show that this method of combination agrees with the seismic crustal thickness (about 2.0. km rms difference).

  • 11.
    Bagherbandi, Mohammad
    KTH, School of Architecture and the Built Environment (ABE), Urban Planning and Environment, Geodesy and Satellite Positioning. University of Gävle, Sweden.
    Deformation monitoring using different least squares adjustment methods: A simulated study2016In: KSCE Journal of Civil Engineering, ISSN 1226-7988, E-ISSN 1976-3808, Vol. 20, no 2, p. 855-862Article in journal (Refereed)
    Abstract [en]

    This study aims to investigate the ability of different least squares adjustment techniques for detecting deformation. A simulated geodetic netwo rk is used for this purpose. The observations are collected using the Total Station instrument in three epochs and different least squares adjustment methods are used to analyze the simulated network. The applied methods are adjustment-byelement, using variance-covariance components and Tikhonov regularization. For numerical computation, we utilized exist geodetic network around the simulated network and the deformation (changes in the simulated network) imposes to the object using a simulator in each epoch. The obtained results demonstrate that more accurate outcome for detection of small deformation is possible by estimating variance-covariance components. The difference of the estimated and the simulated deformations in the best scenario, i.e., applying variance-covariance components, is 0.2 and 0.1 mm in x and y directions. In comparison with adjustment by element and Tikhonov regularization methods the differences are 1.1 and 0.1 in x direction and 1.4 and 1.1 mm in y direction, respectively. In addition, it is also possible to model the deformation and therefore it can be seen that how the calculated displacement will affect the result of deformation modelling. It has been demonstrated that determining reasonable variance-covariance components is very important to estimate realistic deformation model and monitoring the geodetic networks.

  • 12.
    Bagherbandi, Mohammad
    KTH, School of Architecture and the Built Environment (ABE), Urban Planning and Environment, Geoinformatik och Geodesi.
    Global earth isostatic model using smoothed Airy-Heiskanen and Vening Meinesz hypotheses2012In: Earth Science Informatics, ISSN 1865-0473, Vol. 5, no 2, p. 93-104Article in journal (Refereed)
    Abstract [en]

    Isostatic hypotheses are used for different purposes in geophysics and geodesy. The Erath crustal thickness modelling is more complicated than the classical isostatic models. In this study we try to modify Airy-Hesiskanen model, utilizing a smoothing factor, to a model with regional or global isostatic model through a modern solution of the gravimetric-isostatic Vening Meinesz model and CRUST.0. In Airy-Hesiskanen's theory there is no correlation between neighbouring crustal columns, while this must be the case in reality due to the elasticity of the Earth. The idea is to keep the simplicity of the Airy-Heiskanen model, because it needs only the topographic data, and change the model which becomes to a model with regional/global isostatic model. The isostatic assumption for compensating the topographic potential is incomplete, as there are other geophysical phenomena which should be considered. Using the isostatic hypothesis for determining the depth of crust causes some disturbing signals in the gravity anomaly (approximately 285 mGal), which influence the crustal thickness determination. In this paper a simple method use for removing these effects. Spherical harmonic potential coefficients of the topographic compensation masses are used for modifying Airy-Heiskanen's model in a least-square adjustment procedure by estimating smoothing factor. The numerical analysis shows that below degree 10, the modified Airy-Hesiskanen and Vening Meinesz models are close together. Smoothing factors for modifying the Airy-Hesiskanen model vary from 0.75 to 0.64 between degrees 200 and 2159.

  • 13.
    Bagherbandi, Mohammad
    KTH, School of Architecture and the Built Environment (ABE), Urban Planning and Environment, Geoinformatik och Geodesi.
    Impact of compensating mass on the topographic mass-A study using isostatic and non-isostatic Earth crustal models2012In: Acta Geodaetica et Geophysica Hungarica, ISSN 1217-8977, E-ISSN 1587-1037, Vol. 47, no 1, p. 29-51Article in journal (Refereed)
    Abstract [en]

    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.

  • 14.
    Bagherbandi, Mohammad
    KTH, School of Architecture and the Built Environment (ABE), Urban Planning and Environment, Geoinformatik och Geodesi.
    Moholso: A MATLAB program to determine crustal thickness by an isostatic and a global gravitational model2012In: Computers & Geosciences, ISSN 0098-3004, E-ISSN 1873-7803, Vol. 44, p. 177-183Article in journal (Refereed)
    Abstract [en]

    This paper focuses on the modeling of the boundary between Earth's crust and upper mantle using a gravimetric-isostatic model. Here a MATLAB code is presented based on the gravimetric-isostatic model i.e. the Veiling Meinesz-Moritz model. Inverse problems in isostasy consist in making the isostatic anomalies to be zero under a certain isostatic hypothesis. The Vening Meinesz-Moritz problem is to determine the Moho depth such that the compensating attraction totally compensates the Bouguer gravity anomaly on the Earth's surface, implying that the isostatic anomaly vanishes on the Earth's surface. The main idea is easy but the theoretical analysis is somewhat difficult. Here a practical method to recover the Moho depth from the gravity data is used in the MATLAB code (Moholso.m) based on the Vening Meinesz-Moritz method. The code has been designed based on different sub-codes. The body of the main code works according to the vectorization technique, because this technique causes that the speed of code increases. One of the important possible limitations for the code is over-flow and under-flow for higher degrees in the fully normalized associated Legendre function. This problem occurs in the subroutine applied in this study, it limits the numerical study up to degrees 1800-2000.

  • 15.
    Bagherbandi, Mohammad
    et al.
    KTH, School of Architecture and the Built Environment (ABE), Urban Planning and Environment, Geodesy and Satellite Positioning.
    Bai, Y.
    Sjöberg, L. E.
    Tenzer, R.
    Abrehdary, Majid
    KTH, School of Architecture and the Built Environment (ABE), Urban Planning and Environment, Geodesy and Satellite Positioning.
    Miranda, S.
    Alcacer Sanchez, J. M.
    Effect of the lithospheric thermal state on the Moho interface: A case study in South America2017In: Journal of South American Earth Sciences, ISSN 0895-9811, E-ISSN 1873-0647, Vol. 76, p. 198-207Article in journal (Refereed)
    Abstract [en]

    Gravimetric methods applied for Moho recovery in areas with sparse and irregular distribution of seismic data often assume only a constant crustal density. Results of latest studies, however, indicate that corrections for crustal density heterogeneities could improve the gravimetric result, especially in regions with a complex geologic/tectonic structure. Moreover, the isostatic mass balance reflects also the density structure within the lithosphere. The gravimetric methods should therefore incorporate an additional correction for the lithospheric mantle as well as deeper mantle density heterogeneities. Following this principle, we solve the Vening Meinesz-Moritz (VMM) inverse problem of isostasy constrained by seismic data to determine the Moho depth of the South American tectonic plate including surrounding oceans, while taking into consideration the crustal and mantle density heterogeneities. Our numerical result confirms that contribution of sediments significantly modifies the estimation of the Moho geometry especially along the continental margins with large sediment deposits. To account for the mantle density heterogeneities we develop and apply a method in order to correct the Moho geometry for the contribution of the lithospheric thermal state (i.e., the lithospheric thermal-pressure correction). In addition, the misfit between the isostatic and seismic Moho models, attributed mainly to deep mantle density heterogeneities and other geophysical phenomena, is corrected for by applying the non-isostatic correction. The results reveal that the application of the lithospheric thermal-pressure correction improves the RMS fit of the VMM gravimetric Moho solution to the CRUST1.0 (improves ∼ 1.9 km) and GEMMA (∼1.1 km) models and the point-wise seismic data (∼0.7 km) in South America.

  • 16.
    Bagherbandi, Mohammad
    et al.
    KTH, School of Architecture and the Built Environment (ABE), Urban Planning and Environment, Geodesy and Satellite Positioning.
    Bai, Yongliang
    Key Laboratory of Marine Geology and Environment, Institute of Oceanology, Chinese Academy of Sciences No.7 Nanhai Rd, Qingdao 266071, China.
    Sjöberg, Lars E.
    KTH, School of Architecture and the Built Environment (ABE), Urban Planning and Environment, Geodesy and Satellite Positioning.
    Tenzer, Robert
    School of Geodesy and Geomatics, Wuhan University, 129 Luoyu Road, Wuhan, China..
    Abrehdary, Majid
    KTH, School of Architecture and the Built Environment (ABE), Urban Planning and Environment, Geodesy and Satellite Positioning.
    Miranda, Silvia
    Departamento de Geofísica y Astronomía, FCEFN. Universidad Nacional de San Juan, Meglioli 1160 Sur, 5400. Rivadavia, San Juan, Argentina.
    Sanchez, Juan
    Departamento de Geofísica y Astronomía, FCEFN. Universidad Nacional de San Juan, Meglioli 1160 Sur, 5400. Rivadavia, San Juan, Argentina..
    Effect of the lithospheric thermal state on the Moho geometryManuscript (preprint) (Other academic)
    Abstract [en]

    Gravimetric methods applied for a Moho recovery in areas with sparse and irregular distribution of seismic data often assume only a constant crustal density. Results of the latest studies, however, indicate that corrections for the crustal density heterogeneities could improve the gravimetric result especially in regions with a complex geologic/tectonic structure. Moreover, the isostatic mass balance reflects also the density structure within the mantle. The gravimetric methods should therefore incorporate an additional correction for the sub-crustal density heterogeneities. Following this principle, we solve the Vening Meinesz-Moritz (VMM) inverse problem of isostasy constrained on seismic data to determine the Moho depth of the South American tectonic plate including surrounding oceans, while taking into consideration the crustal and mantle density heterogeneities. Our numerical result confirms that the contribution of sediments significantly modifies the Moho geometry especially along the continental margins with large sediment deposits. To account for the mantle density heterogeneities we develop and apply a method of correcting the Moho geometry for the contribution of the lithospheric thermal state (i.e., the lithospheric thermal-pressure correction). In addition, the misfit between the isostatic and seismic Moho models, attributed mainly to deep mantle density heterogeneities and other geophysical phenomena, is corrected for by applying the non-isostatic correction. The results reveal that the application of the lithospheric thermal-pressure correction improves the RMS fit of the VMM gravimetric Moho solution to the CRUST1.0 seismic model and the point-wise seismic data in South America about 40% and 7% respectively.  

  • 17.
    Bagherbandi, Mohammad
    et al.
    KTH, School of Architecture and the Built Environment (ABE), Urban Planning and Environment, Geoinformatik och Geodesi.
    Eshagh, Mehdi
    Recovery of Moho's undulations based on the Vening Meinesz-Moritz theory from satellite gravity gradiometry data: A simulation study2012In: Advances in Space Research, ISSN 0273-1177, E-ISSN 1879-1948, Vol. 49, no 6, p. 1097-1111Article in journal (Refereed)
    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.

  • 18.
    Bagherbandi, Mohammad
    et al.
    KTH, School of Architecture and the Built Environment (ABE), Urban Planning and Environment, Geodesy and Geoinformatics.
    Eshagh, Mehdi
    KTH, School of Architecture and the Built Environment (ABE), Urban Planning and Environment, Geodesy and Geoinformatics.
    Sjöberg, Lars E.
    KTH, School of Architecture and the Built Environment (ABE), Urban Planning and Environment, Geodesy and Geoinformatics.
    Multi-objective versus single-objective models in geodetic network optimization2009In: Nordic Journal of Surveying and Real Estate Research, ISSN 1459-5877, E-ISSN 2341-6599, Vol. 6, no 1, p. 7-20Article in journal (Refereed)
  • 19.
    Bagherbandi, Mohammad
    et al.
    KTH, School of Architecture and the Built Environment (ABE), Urban Planning and Environment, Geoinformatik och Geodesi.
    Sjoberg, Lars E.
    KTH, School of Architecture and the Built Environment (ABE), Urban Planning and Environment, Geoinformatik och Geodesi.
    Comparison of crustal thickness from two gravimetric-isostatic models and CRUST2.02011In: Studia Geophysica et Geodaetica, ISSN 0039-3169, E-ISSN 1573-1626, Vol. 55, no 4, p. 641-666Article in journal (Refereed)
    Abstract [en]

    The MohoroviiA double dagger discontinuity is the boundary between the Earth's crust and mantle. Several isostatic hypotheses exist for estimating the crustal thickness and density variation of the Earth's crust from gravity anomalies. The goal of this article is to compare the Airy-Heiskanen and Vening Meinesz-Moritz (VMM) gravimetric models for determining Moho depth, with the seismic Moho (CRUST2.0 or SM) model. Numerical comparisons are performed globally as well as for some geophysically interesting areas, such as Fennoscandia, Persia, Tibet, Canada and Chile. These areas are most complicated areas in view of rough topography (Tibet, Persia and Peru and Chile), post-glacial rebound (Fennoscandia and Canada) and tectonic activities (Persia). The mean Moho depth provided by CRUST2.0 is 22.9 +/- 0.1 km. Using a constant Moho density contrast of 0.6 g/cm(3), the corresponding mean values for Airy-Heiskanen and VVM isostatic models become 25.0 +/- 0.04 km and 21.6 +/- 0.08 km, respectively. By assuming density contrasts of 0.5 g/cm(2) and 0.35 g/cm(3) for continental and oceanic regions, respectively, the VMM model yields the mean Moho depth 22.6 +/- 0.1 km. For this model the global rms difference to CRUST2.0 is 7.2 km, while the corresponding difference between Airy-Heiskanen model and CRUST2.0 is 11 km. Also for regional studies, Moho depths were estimated by selecting different density contrasts. Therefore, one conclusion from the study is that the global compensation by the VMM method significantly improves the agreement with the CRUST2.0 vs. the local compensation model of Airy-Heiskanen. Also, the last model cannot be correct in regions with ocean depth larger than 9 km (e.g., outside Chile), as it may yield negative Moho depths. This problem does not occur with the VMM model. A second conclusion is that a realistic variation of density contrast between continental and oceanic areas yields a better fit of the VMM model to CRUST2.0. The study suggests that the VMM model can primarily be used to densify the CRUST2.0 Moho model in many regions based on separate data by taking advantage of dense gravity data. Finally we have found also that the gravimetric terrain correction affects the determination of the Moho depth by less than 2 km in mean values for test regions, approximately. Hence, for most practical applications of the VMM model the simple Bouguer gravity anomaly is sufficient.

  • 20.
    Bagherbandi, Mohammad
    et al.
    KTH, School of Architecture and the Built Environment (ABE), Urban Planning and Environment, Geodesy and Geoinformatics.
    Sjöberg, Lars E.
    University of Gävle, Sweden.
    A synthetic Earth gravity model based on a topographic-isostatic model2012In: Studia Geophysica et Geodaetica, ISSN 0039-3169, E-ISSN 1573-1626, Vol. 56, no 4, p. 935-955Article in journal (Refereed)
    Abstract [en]

    The Earth's gravity field is related to the topographic potential in medium and higher degrees, which is isostatically compensated. Hence, the topographic-isostatic (TI) data are indispensable for extending an available Earth Gravitational Model (EGM) to higher degrees. Here we use TI harmonic coefficients to construct a Synthetic Earth Gravitational Model (SEGM) to extend the EGMs to higher degrees. To achieve a high-quality SEGM, a global geopotential model (EGM96) is used to describe the low degrees, whereas the medium and high degrees are obtained from the TI or topographic potential. This study differes from others in that it uses a new gravimetric-isostatic model for determining the TI potential. We test different alternatives based on TI or only topographic data to determine the SEGM. Although the topography is isostatically compensated only to about degree 40-60, our study shows that using a compensation model improves the SEGM in comparison with using only topographic data for higher degree harmonics. This is because the TI data better adjust the applied Butterworth filter, which bridges the known EGM and the new high-degree potential field than the topographic data alone.

  • 21.
    Bagherbandi, Mohammad
    et al.
    KTH, School of Architecture and the Built Environment (ABE), Urban Planning and Environment, Geoinformatik och Geodesi.
    Sjöberg, Lars E
    KTH, School of Architecture and the Built Environment (ABE), Urban Planning and Environment, Geoinformatik och Geodesi.
    Determination of crustal thickness by Vening Meinesz-Moritz hypothesis and its geodetic applications2010Conference paper (Other (popular science, discussion, etc.))
  • 22.
    Bagherbandi, Mohammad
    et al.
    KTH, School of Architecture and the Built Environment (ABE), Urban Planning and Environment, Geodesy and Geoinformatics.
    Sjöberg, Lars E.
    KTH, School of Architecture and the Built Environment (ABE), Urban Planning and Environment, Geodesy and Geoinformatics. University of Gävle, Sweden .
    Improving gravimetric-isostatic models of crustal depth by correcting for non-isostatic effects and using CRUST2.02013In: Earth-Science Reviews, ISSN 0012-8252, E-ISSN 1872-6828, Vol. 117, p. 29-39Article in journal (Refereed)
    Abstract [en]

    The principle of isostasy is important in different fields of geosciences. Using an isostatic hypothesis for estimating the crustal thickness suffers from the more or less incomplete isostatic model and that the observed gravity anomaly is not only generated by the topographic/isostatic signal but also by non-isostatic effects (NIEs). In most applications of isostatic models the NIEs are disregarded. In this paper, we study how some isostatic models related with Vening Meinez's isostatic hypothesis can be improved by considering the NIE. The isostatic gravity anomaly needs a correction for the NIEs, which varies from as much as 494 mGal to -308 mGal. The result shows that by adding this correction the global crustal thickness estimate improves about 50% with respect to the global model CRUST2.0, i.e. the root mean square differences of the crustal thickness of the best Vening Meinesz type and CRUST2.0 models are 6.9 and 3.2 km before and after improvement, respectively. As a result, a new global model of crustal thickness using Vening Meinesz and CRUST2.0 models is generated. A comparison with an independent African crustal depth model shows an improvement of the new model by 6.8 km vs. CRUST2.0 (i.e. rms differences of 3.0 and 9.8 km, respectively). A comparison between oceanic lithosphere age and the NIEs is discussed in this study, too. One application of this study can be to improve crustal depth in areas where CRUST2.0 data are sparse and bad and to densify the resolution vs. the CRUST2.0 model. Other applications can be used to infer the viscosity of the mantle from the NIEs signal to study various locations around the Earth for understanding complete, over- and under-compensations of the topography.

  • 23.
    Bagherbandi, Mohammad
    et al.
    KTH, School of Architecture and the Built Environment (ABE), Urban Planning and Environment, Geoinformatik och Geodesi.
    Sjöberg, Lars E.
    KTH, School of Architecture and the Built Environment (ABE), Urban Planning and Environment, Geoinformatik och Geodesi.
    Non-isostatic effects on crustal thickness: A study using CRUST2.0 in Fennoscandia2012In: Physics of the Earth and Planetary Interiors, ISSN 0031-9201, E-ISSN 1872-7395, Vol. 200, p. 37-44Article in journal (Refereed)
    Abstract [en]

    The crustal thickness can be determined based on gravimetric-isostatic and seismic models. Modelling crustal thickness by a gravimetric-isostatic model suffers from some problems. The isostatic assumption for compensating the topographic potential is incomplete, as there are other effects which should be considered. Using the isostatic hypothesis for determining the depth of crust causes some disturbing signals, non-isostatic effects, which influence the crustal thickness determination. Isostatic and non-isostatic compensations are the main issues in this paper. We present three methods to overcome the problem due to the disturbing signals, namely the approach by truncating the spherical harmonic approach, determination of non-isostatic correction using a seismic crustal thickness model (e.g., CRUST2.0) and combination of isostatic and seismic models by applying a least-squares adjustment method. The estimated results of the non-isostatic effects varies between 65.2 and 391.8 mGal in Fennoscandia. The root mean squares difference of the crustal thickness obtained from the gravimetric-isostatic model and CRUST2.0 is improved up to six times (from 6.15 to 0.97 km) when the non-isostatic effects are considered.

  • 24.
    Bagherbandi, Mohammad
    et al.
    KTH, School of Architecture and the Built Environment (ABE), Urban Planning and Environment, Geodesy and Satellite Positioning. University of Gävle, Sweden .
    Sjöberg, Lars E.
    KTH, School of Architecture and the Built Environment (ABE), Urban Planning and Environment, Geodesy and Satellite Positioning.
    Tenzer, Robert
    Abrehdary, Majid
    KTH, School of Architecture and the Built Environment (ABE), Urban Planning and Environment, Geodesy and Satellite Positioning.
    A new Fennoscandian crustal thickness model based on CRUST1. 0 and a gravimetric–isostatic approach2015In: Earth-Science Reviews, ISSN 0012-8252, E-ISSN 1872-6828, Vol. 145, p. 132-145Article, review/survey (Refereed)
    Abstract [en]

    In this paper a new gravimetric–isostatic crustal thickness model (VMM14_FEN) is estimated for Fennoscandia. The main motivation is to investigate the relations between geological and geophysical properties, the Moho depth and crust–mantle density contrast at the crust–mantle discontinuity. For this purpose the Bouguer gravity disturbance data is corrected in two main ways namely for the gravitational contributions of mass density variation due to the different layers of the Earth's crust such as ice and sediments, as well as for the gravitational contribution from deeper masses below the crust. This second correction (for non-isostatic effects) is necessary because in general the crust is not in complete isostatic equilibrium and the observed gravity data are not only generated by the topographic/isostatic masses but also from those in the deep Earth interior. The correction for non-isostatic effects is mainly attributed to unmodeled mantle and core boundary density heterogeneities. These corrections are determined using the recent seismic crustal thickness model CRUST1.0. We compare our modeling results with previous studies in the area and test the fitness. The comparison with the external Moho model EuCRUST-07 shows a 3.3 km RMS agreement for the Moho depth in Fennoscandia. We also illustrate how the above corrections improve the Moho depth estimation. Finally, the signatures of geological structures and isostatic equilibrium are studied using VMM14_FEN, showing how main geological unit structures attribute in isostatic balance by affecting the Moho geometry. The main geological features are also discussed in the context of the complete and incomplete isostatic equilibrium.

  • 25.
    Bagherbandi, Mohammad
    et al.
    KTH, School of Architecture and the Built Environment (ABE), Urban Planning and Environment, Geodesy and Geoinformatics.
    Tenzer, R.
    Geoid-to-quasigeoid separation computed using the GRACE/GOCE global geopotential model GOCO02S -A case study of Himalayas and Tibet2013In: Terrestrial, Atmospheric and Oceanic Science, ISSN 1017-0839, E-ISSN 2223-8964, Vol. 24, no 1, p. 59-68Article in journal (Refereed)
    Abstract [en]

    The geoid-to-quasigeoid correction has been traditionally computed approximately as a function of the planar Bouguer gravity anomaly and the topographic height. Recent numerical studies based on newly developed theoretical models, however, indicate that the computation of this correction using the approximate formula yields large errors especially in mountainous regions with computation points at high elevations. In this study we investigate these approximation errors at the study area which comprises Himalayas and Tibet where this correction reaches global maxima. Since the GPS-leveling and terrestrial gravity datasets in this part of the world are not (freely) available, global gravitational models (GGMs) are used to compute this correction utilizing the expressions for a spherical harmonic analysis of the gravity field. The computation of this correction can be done using the GGM coefficients taken from the Earth Gravitational Model 2008 (EGM08) complete to degree 2160 of spherical harmonics. The recent studies based on a regional accuracy assessment of GGMs have shown that the combined GRACE/GOCE solutions provide a substantial improvement of the Earth's gravity field at medium wavelengths of spherical harmonics compared to EGM08. We address this aspect in numerical analysis by comparing the gravity field quantities computed using the satellite-only combined GRACE/GOCE model GOCO02S against the EGM08 results. The numerical results reveal that errors in the geoid-to-quasigeoid correction computed using the approximate formula can reach as much as ~1.5 m. We also demonstrate that the expected improvement of the GOCO02S gravity field quantities at medium wavelengths (within the frequency band approximately between 100 and 250) compared to EGM08 is as much as ±60 mGal and ±0.2 m in terms of gravity anomalies and geoid/quasigeoid heights respectively.

  • 26.
    Bagherbandi, Mohammad
    et al.
    KTH, School of Architecture and the Built Environment (ABE), Urban Planning and Environment, Geodesy and Geoinformatics.
    Tenzer, Robert
    Comparative analysis of Vening-Meinesz Moritz isostatic models using the constant and variable crust-mantle density contrast - a case study of Zealandia2013In: Proceedings of the Indian Academy of Sciences, Earth and Planetary Sciences, ISSN 0253-4126, E-ISSN 0973-774X, Vol. 122, no 2, p. 339-348Article in journal (Refereed)
    Abstract [en]

    We compare three different numerical schemes of treating the Moho density contrast in gravimetric inverse problems for finding the Moho depths. The results are validated using the global crustal model CRUST2.0, which is determined based purely on seismic data. Firstly, the gravimetric recovery of the Moho depths is realized by solving Moritz's generalization of the Vening-Meinesz inverse problem of isostasy while the constant Moho density contrast is adopted. The Pratt-Hayford isostatic model is then facilitated to estimate the variable Moho density contrast. This variable Moho density contrast is subsequently used to determine the Moho depths. Finally, the combined least-squares approach is applied to estimate jointly the Moho depths and density contract based on a priori error model. The EGM2008 global gravity model and the DTM2006.0 global topographic/bathymetric model are used to generate the isostatic gravity anomalies. The comparison of numerical results reveals that the optimal isostatic inverse scheme should take into consideration both the variable depth and density of compensation. This is achieved by applying the combined least-squares approach for a simultaneous estimation of both Moho parameters. We demonstrate that the result obtained using this method has the best agreement with the CRUST2.0 Moho depths. The numerical experiments are conducted at the regional study area of New Zealand's continental shelf.

  • 27.
    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.
    Moho depth uncertainties in the Vening-Meinesz Moritz inverse problem of isostasy2014In: Studia Geophysica et Geodaetica, ISSN 0039-3169, E-ISSN 1573-1626, Vol. 58, no 2, p. 227-248Article in journal (Refereed)
    Abstract [en]

    We formulate an error propagation model based on solving the Vening Meinesz-Moritz (VMM) inverse problem of isostasy. The system of observation equations in the VMM model defines the relation between the isostatic gravity data and the Moho depth by means of a second-order Fredholm integral equation of the first kind. The corresponding error model (derived in a spectral domain) functionally relates the Moho depth errors with the commission errors of used gravity and topographic/bathymetric models. The error model also incorporates the non-isostatic bias which describes the disagreement, mainly of systematic nature, between the isostatic and seismic models. The error analysis is conducted at the study area of the Tibetan Plateau and Himalayas with the world largest crustal thickness. The Moho depth uncertainties due to errors of the currently available global gravity and topographic models are estimated to be typically up to 1-2 km, provided that the GOCE gravity gradient observables improved the medium-wavelength gravity spectra. The errors due to disregarding sedimentary basins can locally exceed similar to 2 km. The largest errors (which cause a systematic bias between isostatic and seismic models) are attributed to unmodeled mantle heterogeneities (including the core-mantle boundary) and other geophysical processes. These errors are mostly less than 2 km under significant orogens (Himalayas, Ural), but can reach up to similar to 10 km under the oceanic crust.

  • 28.
    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.

  • 29.
    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.

  • 30.
    Bagherlbandi, Mohammad
    et al.
    KTH, School of Architecture and the Built Environment (ABE), Urban Planning and Environment, Geoinformatik och Geodesi.
    Sjöberg, Lars E.
    KTH, School of Architecture and the Built Environment (ABE), Urban Planning and Environment, Geoinformatik och Geodesi.
    Modelling the density contrast and depth of the Moho discontinuity by seismic and gravimetric-isostatic methods with an application to Africa2012In: Journal of African Earth Sciences, ISSN 1464-343X, Vol. 68, p. 111-120Article in journal (Refereed)
    Abstract [en]

    The crustal thickness (Moho depth) is of interest in several geosciences applications, such as geography, geophysics and geodesy. Usually the crustal depth and density variations are estimated by seismic survey data. As such data collection is very time-consuming and expensive an attractive option could be to use a gravimetric/isostatic model. In this case, realistic estimates for the crustal density and Moho density contrast (MDC) are important. In this study, we first use the seismic crustal thickness of CRUST2.0 model as a known parameter in combination with gravimetric data in estimating the crust-mantle density contrast by the isostatic model of Vening Meinesz-Moritz. We present different models to estimate the MDC and its impact on the modelling of the gravimetric-isostatic Moho depth. The theory is applied to estimate the Moho depth of the African continental crust by using different models for the MDC: (a) constant value (0.6 g/cm(3)), (b) Pratt-Hayford's model, (c) CRUST2.0 as input to three gravimetric/isostatic models based on Vening Meinesz-Moritz theory. The isostatic models agree by 5.8-7.1 km in the rms with the regional seismic model at a resolution of 2 degrees x 2 degrees, and the smallest rms difference at a resolution of 1 degrees x 1 degrees is of 7.2 km. For comparison, the rms differences of CRUST2.0 and the regional seismic model are 8.8 and 9.1 km at the resolutions of 2 degrees (interpolated) and 1 degrees, respectively. The result suggests that the gravimetric/isostatic Moho model can be used in densification of the CRUST2.0 Moho geometry, and to improve it in areas with poor data.

  • 31.
    Baranov, Alexey
    et al.
    Russian Acad Sci, Schmidt Inst Phys Earth, Moscow 119991, Russia.;Russian Acad Sci, Inst Earthquake Predict Theory & Math Geophys, Moscow 119991, Russia..
    Bagherbandi, Mohammad
    KTH, School of Architecture and the Built Environment (ABE), Real Estate and Construction Management, Geodesy and Satellite Positioning.
    Tenzer, Robert
    Hong Kong Polytech Univ, Dept Land Surveying & Geoinformat, Hong Kong, Peoples R China..
    Combined Gravimetric-Seismic Moho Model of Tibet2018In: GEOSCIENCES, ISSN 2076-3263, Vol. 8, no 12, article id UNSP 461Article in journal (Refereed)
    Abstract [en]

    Substantial progress has been achieved over the last four decades to better understand a deep structure in the Himalayas and Tibet. Nevertheless, the remoteness of this part of the world still considerably limits the use of seismic data. A possible way to overcome this practical restriction partially is to use products from the Earth's satellite observation systems. Global topographic data are provided by the Shuttle Radar Topography Mission (SRTM). Global gravitational models have been derived from observables delivered by the gravity-dedicated satellite missions, such as the Gravity Recovery and Climate Experiment (GRACE) and the Gravity field and steady-state Ocean Circulation Explorer (GOCE). Optimally, the topographic and gravity data should be combined with available results from tomographic surveys to interpret the lithospheric structure, including also a Moho relief. In this study, we use seismic, gravity, and topographic data to estimate the Moho depth under orogenic structures of the Himalayas and Tibet. The combined Moho model is computed based on solving the Vening Meinesz-Moritz (VMM) inverse problem of isostasy, while incorporating seismic data to constrain the gravimetric solution. The result of the combined gravimetric-seismic data analysis exhibits an anticipated more detailed structure of the Moho geometry when compared to the solution obtained merely from seismic data. This is especially evident over regions with sparse seismic data coverage. The newly-determined combined Moho model of Tibet shows a typical contrast between a thick crustal structure of orogenic formations compared to a thinner crust of continental basins. The Moho depth under most of the Himalayas and the Tibetan Plateau is typically within 60-70 km. The maximum Moho deepening of similar to 76 km occurs to the south of the Bangong-Nujiang suture under the Lhasa terrane. Local maxima of the Moho depth to similar to 74 km are also found beneath Taksha at the Karakoram fault. This Moho pattern generally agrees with the findings from existing gravimetric and seismic studies, but some inconsistencies are also identified and discussed in this study.

  • 32. Baranov, Alexey
    et al.
    Tenzer, Robert
    Bagherbandi, Mohammad
    KTH, School of Architecture and the Built Environment (ABE), Urban Planning and Environment. University of Gävle, Sweden.
    Combined Gravimetric-Seismic Crustal Model for Antarctica2018In: Surveys in geophysics, ISSN 0169-3298, E-ISSN 1573-0956, Vol. 39, no 1, p. 23-56Article, review/survey (Refereed)
    Abstract [en]

    The latest seismic data and improved information about the subglacial bedrock relief are used in this study to estimate the sediment and crustal thickness under the Antarctic continent. Since large parts of Antarctica are not yet covered by seismic surveys, the gravity and crustal structure models are used to interpolate the Moho information where seismic data are missing. The gravity information is also extended offshore to detect the Moho under continental margins and neighboring oceanic crust. The processing strategy involves the solution to the Vening Meinesz-Moritz's inverse problem of isostasy constrained on seismic data. A comparison of our new results with existing studies indicates a substantial improvement in the sediment and crustal models. The seismic data analysis shows significant sediment accumulations in Antarctica, with broad sedimentary basins. According to our result, the maximum sediment thickness in Antarctica is about 15 km under Filchner-Ronne Ice Shelf. The Moho relief closely resembles major geological and tectonic features. A rather thick continental crust of East Antarctic Craton is separated from a complex geological/tectonic structure of West Antarctica by the Transantarctic Mountains. The average Moho depth of 34.1 km under the Antarctic continent slightly differs from previous estimates. A maximum Moho deepening of 58.2 km under the Gamburtsev Subglacial Mountains in East Antarctica confirmed the presence of deep and compact orogenic roots. Another large Moho depth in East Antarctica is detected under Dronning Maud Land with two orogenic roots under Wohlthat Massif (48-50 km) and the Kottas Mountains (48-50 km) that are separated by a relatively thin crust along Jutulstraumen Rift. The Moho depth under central parts of the Transantarctic Mountains reaches 46 km. The maximum Moho deepening (34-38 km) in West Antarctica is under the Antarctic Peninsula. The Moho depth minima in East Antarctica are found under the Lambert Trench (24-28 km), while in West Antarctica the Moho depth minima are along the West Antarctic Rift System under the Bentley depression (20-22 km) and Ross Sea Ice Shelf (16-24 km). The gravimetric result confirmed a maximum extension of the Antarctic continental margins under the Ross Sea Embayment and the Weddell Sea Embayment with an extremely thin continental crust (10-20 km).

  • 33.
    Eshagh, Mehdi
    et al.
    Department of Engineering Science, University West, Trollhättan, Sweden .
    Bagherbandi, Mohammad
    Faculty of Engineering and Sustainable Development University of Gävle.
    Combined Moho Estimators2014In: Geodynamics Research International Bulletin, E-ISSN 2345-4997, Vol. 1, no 3Article in journal (Refereed)
    Abstract [en]

    In this study, we develop three estimators to optimally combine seismic and gravimetric models of Moho surface. The first estimator combines them by their special harmonic coefficients; the second one uses the spherical harmonic coefficients of the seismic model and use integral formula for the gravimetric one. The kernel of the integral terms of this estimator shows that a cap size of 20◦ is required for the integration, but since this integral is presented to combine the low frequencies of the gravimetric model, a low resolution model is enough for the integration. The third estimator uses the gravity anomaly and converts its low frequencies to those of the gravimetric Moho model, meanwhile combining them with those of seismic one. This integral requires an integration domain of 30◦ for the gravity anomalies but since the maximum degree of this kernel is limited to a specific degree, the use of its spectral form is recommended. The kernel of the integral involving the gravity anomalies, developed for recovering high frequencies of Moho, is written in a closed-from formula and its singularity is investigated. This kernel is well-behaving and decreases fast, meaning that it is suitable for recovering the high frequencies of the Moho surface.

  • 34.
    Eshagh, Mehdi
    et al.
    KTH, School of Architecture and the Built Environment (ABE), Urban Planning and Environment, Geodesy and Geoinformatics.
    Bagherbandi, Mohammad
    KTH, School of Architecture and the Built Environment (ABE), Urban Planning and Environment, Geodesy and Geoinformatics.
    Quality Description For Gravimetric And Seismic Moho Models Of Fennoscandia Through A Combined Adjustment2012In: Acta Geodaetica et Geophysica Hungarica, ISSN 1217-8977, E-ISSN 1587-1037, Vol. 47, no 4, p. 388-401Article in journal (Refereed)
    Abstract [en]

    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.

  • 35. Eshagh, Mehdi
    et al.
    Bagherbandi, Mohammad
    KTH, School of Architecture and the Built Environment (ABE), Urban Planning and Environment, Geoinformatik och Geodesi.
    Smoothing impact of isostatic crustal thickness models on local integral inversion of satellite gravity gradiometry data2011In: ACTA GEOPHYSICA, ISSN 1895-6572, Vol. 59, no 5, p. 891-906Article in journal (Refereed)
    Abstract [en]

    The effects of topographic masses on satellite gradiometric data are large and in order to reduce the magnitude of these effects some compensation mechanisms should be considered. Here we use the isostatic hypotheses of Airy-Heiskanen and the recent Vening Meinesz-Moritz for compensating these effects and to smooth the data prior to their downward continuation to gravity anomaly. The second-order partial derivatives of extended Stokes' formula are used for the continuations over a topographically rough territory like Persia. The inversions are performed and compared based on two schemes of the remove-compute-restore technique and direct downward continuation. Numerical results show that the topographic-isostatic effect based on Vening Meinesz-Mortiz's hypothesis smoothes the data better than that based on Airy-Heiskanen's hypothesis. Also the quality of inversions of the smoothed data by this mechanism is twice better than that of the nonsmoothed ones.

  • 36.
    Eshagh, Mehdi
    et al.
    KTH, School of Architecture and the Built Environment (ABE), Urban Planning and Environment, Geoinformatik och Geodesi.
    Bagherbandi, Mohammad
    KTH, School of Architecture and the Built Environment (ABE), Urban Planning and Environment, Geoinformatik och Geodesi.
    Sjöberg, Lars E.
    KTH, School of Architecture and the Built Environment (ABE), Urban Planning and Environment, Geoinformatik och Geodesi.
    A COMBINED GLOBAL MOHO MODEL BASED ON SEISMIC AND GRAVIMETRIC DATA2011In: ACTA GEOD GEOPHYS HUNG, ISSN 1217-8977, Vol. 46, no 1, p. 25-38Article in journal (Refereed)
    Abstract [en]

    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.

  • 37.
    Gido, Nureldin A. A.
    et al.
    KTH, School of Architecture and the Built Environment (ABE), Real Estate and Construction Management, Geodesy and Satellite Positioning. Univ Gavle, Fac Engn & Sustainable Dev, SE-80176 Gavle, Sweden..
    Bagherbandi, Mohammad
    KTH, School of Architecture and the Built Environment (ABE), Real Estate and Construction Management, Geodesy and Satellite Positioning. Univ Gavle, Fac Engn & Sustainable Dev, SE-80176 Gavle, Sweden..
    Sjoberg, Lars E.
    KTH, School of Architecture and the Built Environment (ABE), Real Estate and Construction Management, Geodesy and Satellite Positioning. Univ Gavle, Fac Engn & Sustainable Dev, SE-80176 Gavle, Sweden..
    Tenzer, Robert
    Hong Kong Polytech Univ, Dept Land Surveying & Geoinformat, Kowloon, Hong Kong, Peoples R China..
    Studying permafrost by integrating satellite and in situ data in the northern high-latitude regions2019In: Acta Geophysica, ISSN 1895-6572, E-ISSN 1895-7455, Vol. 67, no 2, p. 721-734Article in journal (Refereed)
    Abstract [en]

    There is an exceptional opportunity of achieving simultaneous and complementary data from a multitude of geoscience and environmental near-earth orbiting artificial satellites to study phenomena related to the climate change. These satellite missions provide the information about the various phenomena, such as sea level change, ice melting, soil moisture variation, temperature changes and earth surface deformations. In this study, we focus on permafrost thawing and its associated gravity change (in terms of the groundwater storage), and organic material changes using the gravity recovery and climate experiment (GRACE) data and other satellite- and ground-based observations. The estimation of permafrost changes requires combining information from various sources, particularly using the gravity field change, surface temperature change, and glacial isostatic adjustment. The most significant factor for a careful monitoring of the permafrost thawing is the fact that this process could be responsible for releasing an additional enormous amount of greenhouse gases emitted to the atmosphere, most importantly to mention carbon dioxide (CO2) and methane that are currently stored in the frozen ground. The results of a preliminary numerical analysis reveal a possible existence of a high correlation between the secular trends of greenhouse gases (CO2), temperature and equivalent water thickness (in permafrost active layer) in the selected regions. Furthermore, according to our estimates based on processing the GRACE data, the groundwater storage attributed due to permafrost thawing increased at the annual rates of 3.4, 3.8, 4.4 and 4.0cm, respectively, in Siberia, North Alaska and Canada (Yukon and Hudson Bay). Despite a rather preliminary character of our results, these findings indicate that the methodology developed and applied in this study should be further improved by incorporating the in situ permafrost measurements.

  • 38.
    Gido, Nureldin A. A.
    et al.
    KTH, School of Architecture and the Built Environment (ABE), Real Estate and Construction Management, Geodesy and Satellite Positioning. Univ Gävle.
    Bagherbandi, Mohammad
    KTH, School of Architecture and the Built Environment (ABE), Real Estate and Construction Management, Geodesy and Satellite Positioning. Univ Gävle.
    Sjöberg, Lars E.
    KTH, School of Architecture and the Built Environment (ABE), Real Estate and Construction Management, Geodesy and Satellite Positioning. Univ Gävle.
    A gravimetric method to determine horizontal stress field due to flow in the mantle in Fennoscandia2019In: GEOSCIENCES JOURNAL, ISSN 1226-4806, Vol. 23, no 3, p. 377-389Article in journal (Refereed)
    Abstract [en]

    Mass changes and flow in the Earth's mantle causes the Earth's crust not only to move vertically, but also horizontally and to tilt, and produce a major stress in the lithosphere. Here we use a gravimetric approach to model sub-lithosphere horizontal stress in the Earth's mantle and its temporal changes caused by geodynamical movements like mantle convection in Fennoscandia. The flow in the mantle is inferred from tectonics and convection currents carrying heat from the interior of the Earth to the crust. The result is useful in studying how changes of the stress influence the stability of crust. The outcome of this study is an alternative approach to studying the stress and its change using forward modelling and the Earth's viscoelastic models. We show that the determined horizontal stress using a gravimetric method is consistent with tectonics and seismic activities. In addition, the secular rate of change of the horizontal stress, which is within 95 kPa/year, is larger outside the uplift dome than inside.

  • 39.
    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, p. 909-922Article 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.

  • 40. Novák, P.
    et al.
    Tenzer, R.
    Eshagh, Mehdi
    KTH, School of Architecture and the Built Environment (ABE), Urban Planning and Environment, Geodesy and Geoinformatics.
    Bagherbandi, Mohammad
    KTH, School of Architecture and the Built Environment (ABE), Urban Planning and Environment, Geodesy and Geoinformatics.
    Evaluation of gravitational gradients generated by Earth's crustal structures2013In: Computers & Geosciences, ISSN 0098-3004, E-ISSN 1873-7803, Vol. 51, p. 22-33Article in journal (Refereed)
    Abstract [en]

    Spectral formulas for the evaluation of gravitational gradients generated by upper Earth's mass components are presented in the manuscript. The spectral approach allows for numerical evaluation of global gravitational gradient fields that can be used to constrain gravitational gradients either synthesised from global gravitational models or directly measured by the spaceborne gradiometer on board of the GOCE satellite mission. Gravitational gradients generated by static atmospheric, topographic and continental ice masses are evaluated numerically based on available global models of Earth's topography, bathymetry and continental ice sheets. CRUST2.0 data are then applied for the numerical evaluation of gravitational gradients generated by mass density contrasts within soft and hard sediments, upper, middle and lower crust layers. Combined gravitational gradients are compared to disturbing gravitational gradients derived from a global gravitational model and an idealised Earth's model represented by the geocentric homogeneous biaxial ellipsoid GRS80. The methodology could be used for improved modelling of the Earth's inner structure.

  • 41.
    Sjoberg, Lars E.
    et al.
    KTH, School of Architecture and the Built Environment (ABE), Urban Planning and Environment, Geoinformatik och Geodesi.
    Bagherbandi, Mohammad
    KTH, School of Architecture and the Built Environment (ABE), Urban Planning and Environment, Geoinformatik och Geodesi.
    Quasigeoid-to-geoid determination by EGM082012In: Earth Science Informatics, ISSN 1865-0473, Vol. 5, no 2, p. 87-91Article in journal (Refereed)
    Abstract [en]

    We present a method to estimate the difference between quasigeoid and geoid heights globally from the Earth Gravitational Model EGM08 and a related topographic model. The numerical computations with the standard topographic density of 2.67 g/cm(3) show that the maximum and minimum of the separations are estimated to 5.47 m and -0.11 m on the Tibet plateau and in the Indian Ocean, respectively. These estimates do not consider possible topographic density variations, which result in topographic bias changes proportional to the topographic elevation squared. Assuming such density changes of 10% from the standard value, the separation may change up to 5 dm.

  • 42.
    Sjöberg, Lars
    et al.
    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.
    Bagherbandi, Mohammad
    KTH, School of Architecture and the Built Environment (ABE), Urban Planning and Environment, Geodesy and Geoinformatics.
    The observed geoid height versus Airy's and Pratt's isostatic models using matched asymptotic expansions2014In: Acta Geodaetica et Geophysica, ISSN 2213-5812, Vol. 49, no 4, p. 473-490Article in journal (Refereed)
    Abstract [en]

    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.

  • 43.
    Sjöberg, Lars
    et al.
    KTH, School of Architecture and the Built Environment (ABE), Urban Planning and Environment, Geoinformatik och Geodesi.
    Bagherbandi, Mohammad
    KTH, School of Architecture and the Built Environment (ABE), Urban Planning and Environment, Geoinformatik och Geodesi.
    A method of estimating the Moho density contrast with a tentative application of EGM08 and CRUST2.02011In: ACTA GEOPHYSICA, ISSN 1895-6572, Vol. 59, no 3, p. 502-525Article in journal (Refereed)
    Abstract [en]

    Based on Vening Meinez-Moritz global inverse isostatic problem, the Moho density contrast is formulated as that of finding a solution of a Fredholm integral equation of the first kind. We present solutions to this equation by combining global models of gravity (EGM08), topography (DTM2006) and seismic crust (CRUST2.0) to a resolution of 2A degrees x2A degrees. The test computations yielded Moho density contrasts ranging from 81.5 kg/m3 (in Pacific) to 988 kg/m(3) (Tibet), with averages of 678 +/- 78 and 334 +/- 108 kg/m(3) for continental and oceanic regions, respectively, and a global average of 448 +/- 187 kg/m(3). Estimated Moho depths range from 8 to 75 km with continental and oceanic averages of 36.6 +/- 5.3 km and 12.9 +/- 5.8 km, respectively, and a global average of 21 +/- 12.5 km. This article has its emphasis on the new theory, while significant corrections to computational results are expected in a forthcoming study, where the isostatic gravity anomaly will be reduced for several disturbing signals.

  • 44.
    Sjöberg, Lars E.
    et al.
    KTH, School of Architecture and the Built Environment (ABE), Urban Planning and Environment, Geodesy and Geoinformatics.
    Bagherbandi, Mohammad
    KTH, School of Architecture and the Built Environment (ABE), Urban Planning and Environment, Geodesy and Geoinformatics.
    A numerical study of the analytical downward continuation error in geoid computation by EGM082011In: Journal of Geodetic Science, ISSN 2081-9919, E-ISSN 2081-9943, Vol. 1, no 1, p. 2-8Article in journal (Refereed)
    Abstract [en]

    Today the geoid can be conveniently determined by a set of high-degree spherical harmonics, such as EGM08 with a resolution of about 5'. However, such a series will be biased when applied to the continental geoid inside the topographic masses. This error we call the analytical downward continuation (DWC) error, which is closely related with the so-called topographic potential bias. However, while the former error is the result of both analytical continuation of the potential inside the topographic masses and truncation of a series, the latter is only the effect of analytical continuation.

    This study compares the two errors for EGM08, complete to degree 2160. The result shows that the topographic bias ranges from 0 at sea level to 5.15 m in the Himalayas region, while the DWC error ranges from -0.08 m in the Pacific to 5.30 m in the Himalayas. The zero-degree effects of the two are the same (5.3 cm), while the rms of the first degree errors are both 0.3 cm. For higher degrees the power of the topographic bias is slightly larger than that for the DWC error, and the corresponding global rms values reaches 25.6 and 25.3 cm, respectively, at nmax=2160. The largest difference (20.5 cm) was found in the Himalayas. In most cases the DWC error agrees fairly well with the topographic bias, but there is a significant difference in high mountains. The global rms difference of the two errors clearly indicates that the two series diverge, a problem most likely related with the DWC error.

  • 45.
    Sjöberg, Lars E.
    et al.
    KTH, School of Architecture and the Built Environment (ABE), Urban Planning and Environment, Geodesy and Geoinformatics.
    Bagherbandi, Mohammad
    KTH, School of Architecture and the Built Environment (ABE), Urban Planning and Environment, Geodesy and Geoinformatics.
    A study on the Fennoscandian post-glacial rebound as observed by present-day uplift rates and gravity field model GOCO02S2013In: Acta Geodaetica et Geophysica, ISSN 2213-5812, Vol. 48, no 3, p. 317-331Article in journal (Refereed)
    Abstract [en]

    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.

  • 46.
    Sjöberg, Lars E.
    et al.
    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. Faculty of Engineering and Sustainable Development University of Gävle.
    Encyclopedia of Geodesy: Isostasy – Geodesy2015In: Encyclopedia of Geodesy, Springer, 2015, p. 1-9Chapter in book (Other academic)
    Abstract [en]

    Isostasy (Greek isos “equal,” stasis “stand still”) is a term in geology, geophysics, and geodesy to describe the state of mass balance (equilibrium) between the Earth’s crust and upper mantle. It describes a condition to which the mantle tends to balance the mass of the crust in the absence of external forces.

  • 47.
    Sjöberg, Lars E.
    et al.
    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.
    Gravity inversion and integration: Theory and applications in geodesy and geophysics2017Book (Refereed)
    Abstract [en]

    This book contains theory and applications of gravity both for physical geodesy and geophysics. It identifies classical and modern topics for studying the Earth. Worked-out examples illustrate basic but important concepts of the Earth's gravity field. In addition, coverage details the Geodetic Reference System 1980, a versatile tool in most applications of gravity data. The authors first introduce the necessary mathematics. They then review classic physical geodesy, including its integral formulas, height systems and their determinations. The next chapter presents modern physical geodesy starting with the original concepts of M.S. Molodensky. A major part of this chapter is a variety of modifying Stokes' formula for geoid computation by combining terrestrial gravity data and an Earth Gravitational Model. Coverage continues with a discussion that compares today's methods for modifying Stokes' formulas for geoid and quasigeoid determination, a description of several modern tools in physical geodesy, and a review of methods for gravity inversion as well as analyses for temporal changes of the gravity field. This book aims to broaden the view of scientists and students in geodesy and geophysics. With a focus on theory, it provides basic and some in-depth knowledge about the field from a geodesist's perspective.

  • 48.
    Sjöberg, Lars E.
    et al.
    KTH, School of Architecture and the Built Environment (ABE), Urban Planning and Environment, Geodesy and Geoinformatics.
    Bagherbandi, Mohammad
    KTH, School of Architecture and the Built Environment (ABE), Urban Planning and Environment, Geodesy and Geoinformatics.
    Tenzer, Robert
    On gravity inversion by no-topography and new isostatic gravity anomalies2013Conference paper (Refereed)
  • 49.
    Sjöberg, Lars E.
    et al.
    KTH, School of Architecture and the Built Environment (ABE), Urban Planning and Environment, Geodesy and Geoinformatics.
    Bagherbandi, Mohammad
    KTH, School of Architecture and the Built Environment (ABE), Urban Planning and Environment, Geodesy and Geoinformatics. University of Gävle, Sweden.
    Tenzer, Robert
    On Gravity Inversion by No-Topography and Rigorous Isostatic Gravity Anomalies2015In: Pure and Applied Geophysics, ISSN 0033-4553, E-ISSN 1420-9136Article in journal (Refereed)
    Abstract [en]

    We discuss some theoretical aspects and practical consequences of using traditional versus “new”/rigorous formulations of the Bouguer and isostatic gravity anomalies/disturbances. In principle, the differences between these two concepts are in the definition of the so-called secondary indirect topographic effect (SITE) on the gravity data. Although we follow the tradition to call this effect SITE, we show that it is formally a direct topographic effect (DITE), needed to remove all topographic signal, but in practice not regarded as such. Consequently, there is a need for a no-topography gravity anomaly, which removes all topographic effects, leaving the below-crust Earth transparent for gravity inversion. Similarly, a rigorous isostatic gravity anomaly includes also a compensation effect for the SITE. By using a simple topographic model, we confirm a theoretically found ratio of 2/(n + 1) between the magnitudes of the SITE and DITE by wavelength (spherical harmonic degree n), both for the Bouguer and isostatic gravity anomalies. Finally, global gravity inversions are applied by utilizing the Vening Meinesz-Moritz isostatic model to determine the Moho geometry using the Bouguer gravity disturbances/anomalies and the no-topography gravity anomalies, and the results are compared. The numerical results confirm our theoretical findings that the Bouguer gravity disturbances and the no-topography gravity anomalies provide very similar results. A comparison of these gravimetrically computed Moho depths with the CRUST1.0 seismic model shows rms agreements of 4.3 and 4.5 km, respectively. This is a significant improvement when compared to the Moho result obtained by using the Bouguer gravity anomalies, yielding the rms difference of 7.3 km for the CRUST1.0 model. These results confirm a theoretical deficiency of the classical definition of the Bouguer and isostatic gravity anomalies, which do not take into consideration the SITE effects on the topography and its compensation.

  • 50. Tenzer, R.
    et al.
    Bagherbandi, Mohammad
    KTH, School of Architecture and the Built Environment (ABE), Urban Planning and Environment, Geodesy and Geoinformatics.
    Reference crust-mantle density contrast beneath Antarctica based on the Vening Meinesz-Moritz isostatic inverse problem and CRUST2.0 seismic model2013In: Earth Sciences Research Journal, ISSN 1794-6190, E-ISSN 2339-3459, Vol. 17, no 1, p. 7-12Article in journal (Refereed)
    Abstract [en]

    The crust-mantle (Moho) density contrast beneath Antarctica was estimated based on solving the Vening Meinesz-Moritz isostatic problem and using constraining information from a seismic global crustal model (CRUST2.0). The solution was found by applying a least-squares adjustment by elements method. Global geopotential model (GOCO02S), global topographic/bathymetric model (DTM2006.0), ice-thickness data for Antarctica (assembled by the BEDMAP project) and global crustal model (CRUST2.0) were used for computing isostatic gravity anomalies. Since CRUST2.0 data for crustal structures under Antarctica are not accurate (due to a lack of seismic data in this part of the world), Moho density contrast was determined relative to a reference homogenous crustal model having 2,670 kg/m3 constant density. Estimated values of Moho density contrast were between 160 and 682 kg/m3. The spatial distribution of Moho density contrast resembled major features of the Antarctic's continental and surrounding oceanic tectonic plate configuration; maxima exceeding 500 kg/m3 were found throughout the central part of East Antarctica, with an extension beneath the Transantarctic mountain range. Moho density contrast in West Antarctica decreased to 400-500 kg/m3, except for local maxima up to ~ 550 kg/m3 in the central Antarctic Peninsula.

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