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  • 1.
    Abrehdary, Majid
    et al.
    Högskolan Väst, Institutionen för ingenjörsvetenskap, Avdelningen för Matematik, Data- och Lantmäteriteknik.
    Sjöberg, Lars
    Högskolan Väst, Institutionen för ingenjörsvetenskap, Avdelningen för Matematik, Data- och Lantmäteriteknik. Royal Institute of Technology, Stockholm (SWE).
    A New Moho Depth Model for Fennoscandia with Special Correction for the Glacial Isostatic Effect2021Inngår i: Pure and Applied Geophysics, ISSN 0033-4553, E-ISSN 1420-9136, Vol. 178, nr 3, s. 877-888Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    In this study, we present a new Moho depth model in Fennoscandia and its surroundings. The model is tailored from data sets of XGM2019e gravitationl field, Earth2014 topography and seismic crustal model CRUST1.0 using the Vening Meinesz-Moritz model based on isostatic theory to a resolution of 1° × 1°. To that end, the refined Bouguer gravity disturbance is determined by reducing the observed field for gravity effect of topography, density heterogeneities related to bathymetry, ice, sediments, and other crustal components. Moreover, stripping of non-isostatic effects of gravity signals from mass anomalies below the crust due to crustal thickening/thinning, thermal expansion of the mantle, Delayed Glacial Isostatic Adjustment (DGIA), i.e., the effect of future GIA, and plate flexure has also been performed. As Fennoscandia is a key area for GIA research, we particularly investigate the DGIA effect on the gravity disturbance and gravimetric Moho depth determination in this area. One may ask whether the DGIA effect is sufficiently well removed in the application of the general non-isostatic effects in such an area, and to answer this question, the Moho depth is determined both with and without specific removal of the DGIA effect prior to non-isostatic effect and Moho depth determinations. The numerical results yield that the RMS difference of the Moho depth from our model HVMD19 vs. the seismic CRUST19 and GRAD09 models are 3.8/4.2 km and 3.7/4.0 km when the above strategy for removing the DGIA effect is/is not applied, respectively, and the mean value differences are 1.2/1.4 km and 0.98/1.4 km, respectively. Hence, our study shows that the specific correction for the DGIA effect on gravity disturbance is slightly significant, resulting in individual changes in the gravimetric Moho depth up to − 1.3 km towards the seismic results. On the other hand, our study shows large discrepancies between gravimetric and seismic Moho models along the Norwegian coastline, which might be due to uncompensated non-isostatic effects caused by tectonic motions.

    Fulltekst (pdf)
    fulltext
  • 2.
    Abrehdary, Majid
    et al.
    Högskolan Väst, Institutionen för ingenjörsvetenskap, Avdelningen för Matematik, Data- och Lantmäteriteknik.
    Sjöberg, Lars
    Högskolan Väst, Institutionen för ingenjörsvetenskap, Avdelningen för Matematik, Data- och Lantmäteriteknik. Division of Geodesy and Satellite Positioning, Royal Institute of Technology (KTH), SE-10044 Stockholm, (SWE).
    Moho density contrast in Antarctica determined by satellite gravity and seismic models2021Inngår i: Geophysical Journal International, ISSN 0956-540X, E-ISSN 1365-246X, Vol. 225, nr 3, s. 1952-1962Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    As recovering the crust-mantle/Moho density contrast (MDC) significantly depends on the properties of the Earth’s crust and upper mantle, varying from place to place, it is an oversimplification to define a constant standard value for it. It is especially challenging in Antarctica, where almost all the bedrock is covered with a thick layer of ice, and seismic data cannot provide a sufficient spatial resolution for geological and geophysical applications. As an alternative, we determine the MDC in Antarctica and its surrounding seas with a resolution of 1°x 1° by the Vening Meinesz-Moritz gravimetric-isostatic technique using the XGM2019e Earth Gravitational Model and Earth2014 topographic/bathymetric information along with CRUST1.0 and CRUST19 seismic crustal models. The numerical results show that our model, named HVMDC20, varies from 81 kg m-3 in the Pacific Antarctic mid-oceanic ridge to 579 kg m-3 in the Gamburtsev Mountain Range in the central continent with a general average of 403 kg m-3. To assess our computations, we compare our estimates with those of some other gravimetric as well as seismic models (KTH11, GEMMA12C, KTH15C and CRUST1.0), illustrating that our estimates agree fairly well with KTH15C and CRUST1.0 but rather poor with the other models. In addition, we compare the geological signatures with HVMDC20, showing how the main geological structures contribute to the MDC. Finally, we study the remaining glacial isostatic adjustment effect on gravity to figure out how much it affects the MDC recovery, yielding a correlation of the optimum spectral window (7< n <12) between XGM2019e and W12a GIA models of the order of ~0.6 contributing within a negligible \pm 14 kg m-3 to the MDC. 

    Fulltekst (pdf)
    Geophysical Journal International
  • 3.
    Abrehdary, Majid
    et al.
    Högskolan Väst, Institutionen för ingenjörsvetenskap, Avdelningen för Matematik, Data- och Lantmäteriteknik.
    Sjöberg, Lars
    Högskolan Väst, Institutionen för ingenjörsvetenskap, Avdelningen för Matematik, Data- och Lantmäteriteknik. Royal Institute of Technology (KTH), Division of Geodesy and Satellite Positioning, Stockholm, SE-10044, Sweden.
    Recovering Moho constituents from satellite altimetry and gravimetric data for Europe and surroundings2019Inngår i: Journal of Applied Geodesy, ISSN 1862-9016, E-ISSN 1862-9024, Vol. 13, nr 4, s. 291-303Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    In this research, we present a local Moho model, named MOHV19, including Moho depth and Moho density contrast (or shortly Moho constituents) with corresponding uncertainties, which are mapped from altimetric and gravimetric data (DSNSC08) in addition to seismic tomographic (CRUST1.0) and Earth topographic data (Earth2014) to a resolution of 1° × 1° based on a solution of Vening Meinesz-Moritz' theory of isostasy. The MOHV19 model covers the area of entire European plate along with the surrounding oceans, bounded by latitudes (30 °N–82 °N) and longitudes (40 °W–70 °E). The article aims to interpret the Moho model resulted via altimetric and gravimetric information from the geological and geophysical perspectives along with investigating the relation between the Moho depth and Moho density contrast. Our numerical results show that estimated Moho depths range from 7.5 to 57.9 km with continental and oceanic averages of 41.3 ± 4.9 km and 21.6 ± 9.2 km, respectively, and an overall average of 30.9 ± 12.3 km. The estimated Moho density contrast ranges from 60.2 to 565.8 kg/m3, with averages of 421.8 ± 57.9 and 284.4 ± 62.9 kg/m3 for continental and oceanic regions, respectively, with a total average of 350.3 ± 91.5 kg/m3. In most areas, estimated uncertainties in the Moho constituents are less than 3 km and 40 kg/m3, respectively, but they reach to much more significant values under Iceland, parts of Gulf of Bothnia and along the Kvitoya Island. Comparing the Moho depths estimated by MOHV19 and those derived by CRUST1.0, MDN07, GRAD09 and MD19 models shows that MOHV19 agree fairly well with CRUST1.0 but rather poor with other models. The RMS difference between the Moho density contrasts estimated by MOHV19 and CRUST1.0 models is 49.45 kg/m3.

  • 4.
    Abrehdary, Majid
    et al.
    Högskolan Väst, Institutionen för ingenjörsvetenskap, Avdelningen för Matematik, Data- och Lantmäteriteknik.
    Sjöberg, Lars E.
    Högskolan Väst, Institutionen för ingenjörsvetenskap, Avdelningen för Matematik, Data- och Lantmäteriteknik. Royal Institute of Technology (KTH), Division of Geodesy and Satellite Positioning, Stockholm, SE-100 44, Sweden.
    Sampietro, Daniele
    GReD S.r.l., Via Cavour 2, Lomazzo (CO), 22074, Italy.
    Contribution of satellite altimetry in modelling Moho density contrast in oceanic areas2019Inngår i: Journal of Applied Geodesy, ISSN 1862-9016, E-ISSN 1862-9024, Vol. 3, nr 1, s. 33-40Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The determination of the oceanic Moho (or crust-mantle) density contrast derived from seismic acquisitions suffers from severe lack of data in large parts of the oceans, where have not yet been sufficiently covered by such data. In order to overcome this limitation, gravitational field models obtained by means of satellite altimetry missions can be proficiently exploited, as they provide global uniform information with a sufficient accuracy and resolution for such a task. In this article, we estimate a new Moho density contrast model named MDC2018, using the marine gravity field from satellite altimetry in combination with a seismic-based crustal model and Earth's topographic/bathymetric data. The solution is based on the theory leading to Vening Meinesz-Moritz's isostatic model. The study results in a high-accuracy Moho density contrast model with a resolution of 1° × 1° in oceanic areas. The numerical investigations show that the estimated density contrast ranges from 14.2 to 599.7 kg/m3 with a global average of 293 kg/m3. In order to evaluate the accuracy of the MDC2018 model, the result was compared with some published global models, revealing that our altimetric model is able to image rather reliable information in most of the oceanic areas. However, the differences between this model and the published results are most notable along the coastal and polar zones, which are most likely due to that the quality and coverage of the satellite altimetry data are worsened in these regions.

  • 5.
    Abrehdary, Majid
    et al.
    Högskolan Väst, Institutionen för ingenjörsvetenskap, Avdelningen för Matematik, Data- och Lantmäteriteknik.
    Sjöberg, Lars Erik
    Hogskolan i Gavle, Gavle, Sweden .
    Estimating a combined Moho model for marine areas via satellite altimetric: gravity and seismic crustal models2020Inngår i: Studia Geophysica et Geodaetica, ISSN 0039-3169, E-ISSN 1573-1626, Vol. 64, s. 1-25Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Isostasy is a key concept in geoscience in interpreting the state of mass balance between the Earth's lithosphere and viscous asthenosphere. A more satisfactory test of isostasy is to determine the depth to and density contrast between crust and mantle at the Moho discontinuity (Moho). Generally, the Moho can be mapped by seismic information, but the limited coverage of such data over large portions of the world (in particular at seas) and economic considerations make a combined gravimetric-seismic method a more realistic approach. The determination of a high-resolution of the Moho constituents for marine areas requires the combination of gravimetric and seismic data to diminish substantially the seismic data gaps. In this study, we estimate the Moho constituents globally for ocean regions to a resolution of 1° × 1° by applying the Vening Meinesz-Moritz method from gravimetric data and combine it with estimates derived from seismic data in a new model named COMHV19. The data files of GMG14 satellite altimetry-derived marine gravity field, the Earth2014 Earth topographic/bathymetric model, CRUST1.0 and CRUST19 crustal seismic models are used in a least-squares procedure. The numerical computations show that the Moho depths range from 7.3 km (in Kolbeinsey Ridge) to 52.6 km (in the Gulf of Bothnia) with a global average of 16.4 km and standard deviation of the order of 7.5 km. Estimated Moho density contrasts vary between 20 kg m-3 (north of Iceland) to 570 kg m-3 (in Baltic Sea), with a global average of 313.7 kg m-3 and standard deviation of the order of 77.4 kg m-3. When comparing the computed Moho depths with current knowledge of crustal structure, they are generally found to be in good agreement with other crustal models. However, in certain regions, such as oceanic spreading ridges and hot spots, we generally obtain thinner crust than proposed by other models, which is likely the result of improvements in the new model. We also see evidence for thickening of oceanic crust with increasing age. Hence, the new combined Moho model is able to image rather reliable information in most of the oceanic areas, in particular in ocean ridges, which are important features in ocean basins.

    Fulltekst (pdf)
    fulltext
  • 6.
    Bagherbandi, Mohammad
    et al.
    Royal Institute of Technology (KTH),Division of Geodesy and Geoinformatics .
    Eshagh, Mehdi
    Royal Institute of Technology (KTH),Division of Geodesy and Geoinformatics, .
    Crustal thickness recovery using an isostatic model and GOCE data2012Inngår i: Earth Planets and Space, ISSN 1343-8832, E-ISSN 1880-5981, Vol. 64, nr 11, s. 1053-1057Artikkel i tidsskrift (Fagfellevurdert)
    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 gradiometric 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.

  • 7.
    Bagherbandi, Mohammad
    et al.
    Royal Institute of Technology (KTH), Division of Geodesy and Geoinformatics.
    Eshagh, Mehdi
    Department of Surveying, Islamic Azad University, Shahr-e-Rey Branch, Tehran, Iran.
    Recovery of Moho's undulations based on the Vening Meinesz-Moritz theory from satellite gravity gradiometry data: A simulation study2012Inngår i: Advances in Space Research, ISSN 0273-1177, E-ISSN 1879-1948, Vol. 49, nr 6, s. 1097-1111Artikkel i tidsskrift (Fagfellevurdert)
    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.

  • 8.
    Drottz, Linda
    et al.
    Högskolan Väst, Institutionen för ingenjörsvetenskap, Avdelningen för Matematik, Data- och Lantmäteriteknik.
    Rizk, Sally
    Högskolan Väst, Institutionen för ingenjörsvetenskap, Avdelningen för Matematik, Data- och Lantmäteriteknik.
    Sea level rise and land uplift over Fennoscandia and the Baltic Sea: A statistical test2021Independent thesis Basic level (professional degree), 10 poäng / 15 hpOppgave
    Abstract [en]

    Abstract

    We have studied the land uplift and the relative sea level in Fennoscandia and the Baltic sea in northern Europe. This area is interesting to study because it has the largest number of land uplift related observations. To observe the past changes in sea level and land uplift, we have used time series from tide gauges and the gravity field and climate experiment, GRACE satellite mission, from various observation points. We have also used data from NKG2016 land up lift model for comparison.

    To statistacally compare land uplift data with sea level change, a regression line was calculated over the various observation points. A t-test was used to see if the differences were significant. The computed rates of uplift from geodetic observations show that change in the region is significant and happens faster inrelation to changes in sea level. In conclusion, there is a rising trend in both land uplift and sea level rates within Fennoscandia and the Baltic Sea.

    This study also shows that GRACE data does not differ from NKG2016 data. From a sustainable economic perspective, this can mean reduced costs, which contributes to more accurate forecasts of rising sea levels in coastal communities.

  • 9.
    Eshagh, Mehdi
    Royal Institute of Technology (KTH),Division of Geodesy and Geoinformatics, .
    A strategy towards an EGM08-based Fennoscandian geoid model2012Inngår i: Journal of Applied Geophysics, ISSN 0926-9851, E-ISSN 1879-1859, Vol. 87, s. 53-59Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Today, the recent global Earth's gravity model, EGM08, is successfully utilised for different purposes in geosciences. Here, EGM08 is used to compute a geoid model for Fennoscandia and since it is restricted to degree and order 2160, the higher frequencies of the geoid, or the truncation bias, is recovered directly from terrestrial gravity anomalies using a simple formula. The total topographic and atmospheric effects are computed and added to the derived geoid as well. A very simple EGM08-based non-integral geoid estimator is developed and applied for computing the geoid of Fennoscandia. The outcome of the estimator is compared with the Global Positioning System (GPS)/levelling data of Sweden, Denmark, Finland and Norway. Numerical results show the successful performance of the presented estimator as the geoid become closer to GPS/levelling data than the one computed solely with EGM08. This study will show that considering the truncation bias of EGM08 will reduce the root mean square error (RMSE) of the differences between the geoid and GPS/levelling data by about 1.3 cm and the additive topographic and atmospheric corrections by 1 cm further. It is shown that the correlations among the data have no significant influence on the estimated geoid.

  • 10.
    Eshagh, Mehdi
    Högskolan Väst, Institutionen för ingenjörsvetenskap, Avdelningen för data-, elektro- och lantmäteriteknik.
    A theoretical discussion on Vening Meinesz-Moritz inverse problem of isostasy2016Inngår i: Geophysical Journal International, ISSN 0956-540X, E-ISSN 1365-246X, Vol. 207, nr 3, s. 1420-1431Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The Moho surface can be determined according to isostatic theories and the recent Vening Meinesz-Moritz (VMM) theory of isostasy has been successful for this purpose. In this paper, we will study this method from a theoretical prospective and try to find its connection to the Airy-Heiskanen (AH) and Vening Meinesz original theories. We develop Jeffrey’s inverse solution to isostasy according to the recent developments of the VMM method and compare both methods in similar situations. We will show that they are generalisations of the AH model in a global and continuous domain. In the VMM spherical harmonic solution for Moho depth, the mean Moho depth contributes only to the zero-degree term of the series, whilst in Jeffrey’s solution it contributes to all frequencies. We improve the VMM spherical harmonic series further so that the mean Moho can contribute to all frequencies of the solution. This modification makes the VMM global solution superior to the Jeffrey one, but in a global scale, the difference between both solutions is less than 3 km. Both solutions are asymptotically-convergent and we present two methods to obtain smooth solutions for Moho from them. 

  • 11.
    Eshagh, Mehdi
    Högskolan Väst, Institutionen för ingenjörsvetenskap.
    A theoretical study on terrestrial gravimetric data refinement by earth gravity models2014Inngår i: Geophysical Prospecting, ISSN 0016-8025, E-ISSN 1365-2478, Vol. 62, nr 1, s. 158-171Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The idea of this paper is to present estimators for combining terrestrial gravity data with Earth gravity models (EGMs) and produce a high-quality source of the Earth's gravity field data through all wavelengths. To do so, integral and point-wise estimators are mathematically developed, based on the spectral combination theory, in such a way that they combine terrestrial data with one and/or two Earth gravity models. The integral estimators are developed so that they become biased or unbiased to a priori information. For testing the quality of the estimators, their global mean square errors (MSEs) are generated using an Earth gravity model08 model and one of the recent products of the gravity field and steady-state ocean circulation explorer (GOCE) mission. Numerical results show that the integral estimators have smaller global root mean square errors (RMSEs) than the point-wise ones but they are not efficient practically. The integral estimator of the biased type is the most suited due to its smallest global root mean square error comparing to the rest of the estimators. Due largely to the omission errors of Earth gravity models the point-wise estimators are not sensitive to the Earth gravity model commission error; therefore, the use of high-degree Earth gravity models is very influential for reduction of their root mean square errors. Also it is shown that the use of the ocean circulation explorer Earth gravity model does not significantly reduce the root mean square errors of the presented estimators in the presence of Earth gravity model08. All estimators are applied in the region of Fennoscandia and a cap size of 2° for numerical integration and a maximum degree of 2500 for generation of band-limited kernels are found suitable for the integral estimators.

  • 12.
    Eshagh, Mehdi
    Högskolan Väst, Institutionen för ingenjörsvetenskap, Avd för elektro, lantmäteri och naturvetenskap.
    An integral approach to regional gravity field refinement using Earth gravity models2013Inngår i: Journal of Geodynamics, ISSN 0264-3707, E-ISSN 1879-1670, Vol. 68, s. 18-28Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

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

  • 13.
    Eshagh, Mehdi
    Högskolan Väst, Institutionen för ingenjörsvetenskap, Avdelningen för Matematik, Data- och Lantmäteriteknik.
    An optimal design of GNSS interference localisation wireless security network based on time-difference of arrivals for the Arlanda international airport2022Inngår i: Journal of Geodetic Science, ISSN 2081-9919, E-ISSN 2081-9943, Vol. 12, nr 1, s. 154-164Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Today, most of the aircrafts are navigated by global navigation satellite systems (GNSSs). Landing is a dangerous phase of a flight especially when an airport runway is not clearly seen from the aircrafts. In such cases, GNSSs are useful for a safe landing under the circumstances that healthy signals, free of any interference, reach to GNSSs receiver antennas mounted on the aircrafts. This shows the importance of establishing GNSS interference localisation security networks around airports. Designing a good configuration for the points with GNSS antennas at for receiving interference signals is important for a successful localisation of the interference device. Here, the time-difference of the arrivals of an interference signal to such points or anchor nodes (ANs), are used as observables, and a security network with four ANs is optimally designed along the runways of the Arlanda airport to reduce the dilution of precision (DOP) of the network. Our study showed that by such an optimisation, the maximum DOP value can reduce by 50% meaning a significant increase in the probability of a successful interference device localisation.

    Fulltekst (pdf)
    fulltext
  • 14.
    Eshagh, Mehdi
    Högskolan Väst, Institutionen för ingenjörsvetenskap, Avdelningen för Matematik, Data- och Lantmäteriteknik.
    Analysis of the gravity field, direct and inverse problems2022Inngår i: Journal of Geodetic Science, ISSN 2081-9919, E-ISSN 2081-9943, Vol. 12, nr 1, s. 244-245Artikkel, omtale (Fagfellevurdert)
    Abstract [en]

    This new book deals with, as its titles says, the analysis and process of gravity field of the Earth. The book is mathematically oriented, and the authors have explained how Mathematics is used for local analysis of the gravity field. The basic and required background knowledge, needed for understanding the book, are given in early chapters as well as appendices. They are used for explaining gravity field analysis from measurement surveys, corrections, and processes to direct and inverse problems in exploration Geophysics with interesting exercises, numerical and real examples.

    Fulltekst (pdf)
    fulltext
  • 15.
    Eshagh, Mehdi
    Högskolan Väst, Institutionen för ingenjörsvetenskap, Avd för elektro, lantmäteri och naturvetenskap.
    Determination of Moho Discontinuity from Satellite Gradiometry Data: Linear Approach2014Inngår i: Geodynamics Reseach International Bulletin, E-ISSN 2345-4997, Vol. 1, nr 2, s. 1-13Artikkel i tidsskrift (Annet vitenskapelig)
    Abstract [en]

    The satellite gradiometry data (SGD) can be used for studying the crustal structure in addition to the Earth’s gravity field. This paper will show how this type of data is related to the Moho discontinuity or the boundary between the Earth’s crust and mantle. Here, the Vening Meinesz-Moritz (VMM) theory of isostasy is used and its mathematical formulae are modified to use the SGD instead of the Earth gravity models. A linear integral equation with a well-behaving kernel is presented by approximating the Moho depth formula derived based on the VMM theory. The error of this approximation is less than 300 m in Iran as the study area. Furthermore, this paper shows that the contribution of the higher degree harmonics than 215 is less than 1% with respect to the total signal of Moho undulations. This means that the use of SGD is meaningful as they sense the harmonics of the Earth’s gravity field to this degree. Two methods of one-step and two-step are proposed for Moho determination and applied in Iran.  It is shown that to reduce the effect of spatial truncation error of the integral formulae of both methods the central area should be smaller by 6 than the inversion area. Numerical studies show that the two-step approach is superior to the other one and the root mean squared error of differences between the Moho model recovered by an Earth gravity model and SGD is about 1.5 km in Iran.

  • 16.
    Eshagh, Mehdi
    Högskolan Väst, Institutionen för ingenjörsvetenskap, Avdelningen för Matematik, Data- och Lantmäteriteknik.
    Elastic thickness determination based on Vening Meinesz-Moritz and flexural theories of isostasy2018Inngår i: Geophysical Journal International, ISSN 0956-540X, E-ISSN 1365-246X, Vol. 213, nr 3, s. 1682-1692Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Elastic thickness (Te) is one of mechanical properties of the Earth's lithosphere. The lithosphere is assumed to be a thin elastic shell, which is bended under the topographic, bathymetric and sediment loads on. The flexure of this elastic shell depends on its thickness or Te. Those shells having larger Te flex less. In this paper, a forward computational method is presented based on the Vening Meinesz–Moritz (VMM) and flexural theories of isostasy. Two Moho flexure models are determined using these theories, considering effects of surface and subsurface loads. Different values are selected for Te in the flexural method to see by which one, the closest Moho flexure to that of the VMM is achieved. The effects of topographic/bathymetric, sediments and crustal crystalline masses, and laterally variable upper mantle density, Young's modulus and Poisson's ratio are considered in whole computational process. Our mathematical derivations are based on spherical harmonics, which can be used to estimate Te at any single point, meaning that there is no edge effect in the method. However, the Te map needs to be filtered to remove noise at some points. A median filter with a window size of 5° × 5° and overlap of 4° works well for this purpose. The method is applied to estimate Te over South America using the data of CRUST1.0 and a global gravity model.

  • 17.
    Eshagh, Mehdi
    Högskolan Väst, Institutionen för ingenjörsvetenskap, Avd för elektro, lantmäteri och naturvetenskap.
    From satellite gradiometry data to the sub-crustal stress due to the mantle convection2014Inngår i: Pure and Applied Geophysics, ISSN 0033-4553, E-ISSN 1420-9136, Vol. 171, nr 9, s. 2391-2406Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Subcrustal stress induced by mantle convection can be determined by the Earth's gravitational potential. In this study, the spherical harmonic expansion of the simplified Navier–Stokes equation is developed further so satellite gradiometry data (SGD) can be used to determine the subcrustal stress. To do so, we present two methods for producing the stress components or an equivalent function thereof, the so-called S function, from which the stress components can be computed numerically. First, some integral estimators are presented to integrate the SGD and deliver the stress components and/or the S function. Second, integral equations are constructed for inversion of the SGD to the aforementioned quantities. The kernel functions of the integrals of both approaches are plotted and interpreted. The behaviour of the integral kernels is dependent on the signal and noise spectra in the first approach whilst it does not depend on extra information in the second method. It is shown that recovering the stress from the vertical–vertical gradients, using the integral estimators presented, is suitable, but when using the integral equations the vertical–vertical gradients are recommended for recovering the S function and the vertical–horizontal gradients for the stress components. This study is theoretical and numerical results using synthetic or real data are not given.

  • 18.
    Eshagh, Mehdi
    Högskolan Väst, Institutionen för ingenjörsvetenskap, Avd för elektro, lantmäteri och naturvetenskap.
    From tensor to vector of gravitation2014Inngår i: Artificial Satellites, ISSN 2083-6104, Vol. 49, nr 2, s. 63-80Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Different gravitational force models are used for determining the satellites’ orbits. The satellite gravity gradiometry (SGG) data contain this gravitational information and the satellite accelerations can be determined from them. In this study, we present that amongst the elements of the gravitational tensor in the local north-oriented frame, all of the elements are suitable for this purpose except Txy. Three integral formulae with the same kernel function are presented for recovering the accelerations from the SGG data. The kernel of these integrals is well-behaving which means that the contribution of the far-zone data is not very significant to their integration results; but this contribution is also dependent on the type of the data being integrated. Our numerical studies show that the standard deviations of the differences between the accelerations recovered from Tzz, Txz and Tyz  and those computed by an existing Earth´s gravity model reduce by increasing the cap size of integration. However, their root mean squared errors increase for recovering Tyfrom Tyz.  Larger cap sizes than 5   is recommended for recovering Tx and Tz  but smaller ones for Ty.

  • 19.
    Eshagh, Mehdi
    Högskolan Väst, Institutionen för ingenjörsvetenskap, Avd för elektro, lantmäteri och naturvetenskap.
    Integral Approaches to Determine Sub-Crustal Stress from Terrestrial Gravimetric Data2016Inngår i: Pure and Applied Geophysics, ISSN 0033-4553, E-ISSN 1420-9136, Vol. 173, nr 3, s. 805-825Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The spherical harmonic expressions of the horizontal sub-crustal stress components induced by the mantle convection are convergent only to low degrees. In this paper, we use the method of stress (S) function with numerical differentiation and present a formula for determining the degree of convergence from the mean Moho depth. We found that for the global mean Moho depth, 23 km, this convergence degree is 622 and for Iran, 35 km, it is 372. Also, three methods are developed and applied for computing the sub-crustal stress, (1) direct integration with a spectral kernel limited up to the degree of convergence, (2) integral inversion with a kernel having closed-form formula without any frequency limit, and (3) solving an integral equation with limited spectral kernel to the convergence degree. The second method has no divergence problem and its kernel function is well behaving so that the system of equations from which the S function is determined is stable, and no regularisation is needed to solve it. It should be noted that for using this method the resolution of the recovery should be higher than 0.5° × 0.5°, otherwise the recovered S function and correspondingly the stress components will have smaller magnitude than those derived from the other two methods. Our numerical studies for stress recovery in Iran and its surrounding areas show that the methods, which use the limited spectral kernels to the convergence degree, deliver consistent results to that of the spherical harmonic expansion.

  • 20.
    Eshagh, Mehdi
    Högskolan Väst, Institutionen för ingenjörsvetenskap, Avd för elektro, lantmäteri och naturvetenskap.
    Integral developments of Vening Meinesz-Moritz formula for local determination of Moho discontinuity and their applications in Iran2014Inngår i: Geodynamics Research International Bulletin, E-ISSN 2345-4997, Vol. 2, nr 3, s. I-IXArtikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Global models of the Earth gravity field and topographic/bathymetric data can be used for the gravimetric determination of the Moho discontinuity based on the Vening Meinesz-Moritz theory. In this paper, we mathematically develop this method in such a way that the local data can be used for Moho modelling. Two integral formulae are presented, one for integrating the data and one for their inversion. The kernels of both integrals are well-behaving meaning that the contribution of far-zone quantities being integrated are not very significant in the results. Both of these methods are applied for computing the Moho model of Iran and their results are compared to the Moho model determined based on the global models. Consistency of the computed Moho models from the simulated data and the global models verifies the correctness of both approaches. The presented methods are consistent even for the case of using real data. Numerical results show that the minimum value of the Moho models derived by the simulated data and global models are about 31 km, whilst those derived from the real data are about 3 km smaller. Similarly, the mean value of Moho depths derived from real data is about 1 km smaller than that from the global models.

  • 21.
    Eshagh, Mehdi
    Högskolan Väst, Institutionen för ingenjörsvetenskap, Avdelningen för data-, elektro- och lantmäteriteknik.
    Local recovery of lithospheric stress tensor from GOCE gravitational tensor2017Inngår i: Geophysical Journal International, ISSN 0956-540X, E-ISSN 1365-246X, Vol. 209, nr 1, s. 317-333Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The sub-lithospheric stress due to mantle convection can be computed from gravity data and propagated through the lithosphere by solving the boundary-value problem of elasticity for the Earth's lithosphere. In this case, a full tensor of stress can be computed at any point inside this elastic layer. Here, we present mathematical foundations for recovering such a tensor from gravitational tensor measured at satellite altitudes. The mathematical relations will be much simpler in this way than the case of using gravity data as no derivative of spherical harmonics or Legendre polynomials is involved in the expressions. Here, new relations between the spherical harmonic coefficients of the stress and gravitational tensor elements are presented. Thereafter integral equations are established from them to recover the elements of stress tensor from those of the gravitational tensor. The integrals have no closed-form kernels, but they are easy to invert and their spatial truncation errors are reducible. The integral equations are used to invert the real data of the gravity field and steady-state ocean circulation explorer (GOCE) mission, in November 2009, over the South American plate and its surroundings to recover the stress tensor at a depth of 35 km. The recovered stress fields are in good agreement with the tectonic and geological features of the area.

  • 22.
    Eshagh, Mehdi
    Högskolan Väst, Institutionen för ingenjörsvetenskap, Avdelningen för data-, elektro- och lantmäteriteknik.
    Non-singular expressions for vector and gradient tensor of gravitation in a geocentric spherical frame2008Inngår i: Computers & Geosciences, ISSN 0098-3004, E-ISSN 1873-7803, Vol. 34, nr 12, s. 1762-1768Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The traditional expressions of the gravitational vector (GV) and the gravitational gradient tensor (GGT) have complicated forms depending on the first- and the second-order derivatives of associated Legendre functions (ALF), and also singular terms when approaching the poles. This article presents alternative expressions for the GV and GGT, which are independent of the derivatives, and are also non-singular. By using such expressions, it suffices to compute the ALF to two additional degrees and orders, instead of computing the first and the second derivatives of all the ALF. Therefore, the formulas are suitable for computer programming. Matlab software as well as an output of a numerical computation around the North Pole is also presented based on the derived formulas.

  • 23.
    Eshagh, Mehdi
    Högskolan Väst, Institutionen för ingenjörsvetenskap, Avd för elektro, lantmäteri och naturvetenskap. Högskolan Väst, Institutionen för ingenjörsvetenskap, Avdelningen för Matematik, Data- och Lantmäteriteknik.
    Numerical aspects of EGM08-based geoid computations in Fennoscandia regarding the applied reference surface and error propagation2013Inngår i: Journal of Applied Geophysics, ISSN 0926-9851, E-ISSN 1879-1859, Vol. 96, s. 28-32Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    So far the recent Earth's gravity model, EGM08, has been successfully applied for different geophysical and geodetic purposes. In this paper, we show that the computation of geoid and gravity anomaly on the reference ellipsoid is of essential importance but error propagation of EGM08 on this surface is not successful due to downward continuation of the errors. Also we illustrate that some artefacts appear in the computed geoid and gravity anomaly to lower degree and order than 2190. This means that the role of higher degree harmonics than 2160 is to remove these artefacts from the results. Consequently, EGM08 must be always used to degree and order 2190 to avoid the numerical problems. © 2013 Elsevier B.V.

  • 24.
    Eshagh, Mehdi
    Högskolan Väst, Institutionen för ingenjörsvetenskap, Avdelningen för Matematik, Data- och Lantmäteriteknik.
    On the approximations in formulation of the Vening Meinesz-Moritz theory of isostasy2017Inngår i: Geophysical Journal International, ISSN 0956-540X, E-ISSN 1365-246X, Vol. 210, nr 1, s. 500-508Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Different approximations are used in Moho modelling based on isostatic theories. The well-known approximation is considering a plate shell model for isostatic equilibrium, which is an oversimplified assumption for the Earth’s crust. Considering a spherical shellmodel, as used in the Vening Meinesz-Moritz (VMM) theory, is a more realistic assumption, but it suffers from different types of mathematical approximations. In this paper, the idea is to investigate such approximations and present their magnitudes and locations all over the globe. Furthermore, we show that the mathematical model of Moho depth according to the VMM principle can be simplified to that of the plate shell model after four approximations. Linearisation of the binomial term involving the topographic/bathymetric heights is sufficient as long as their spherical harmonic expansion is limited to degree and order 180. The impact of the higher order terms is less than 2 km. The Taylor expansion of the binomial term involving the Moho depth (T) up to second order with the assumption of T-2 = TT0, T-0 is the mean compensation depth, improves this approximation further by up to 4 km over continents. This approximation has a significant role in Moho modelling over continents; otherwise, loss of frequency occurs in the Moho solution. On the other hand, the linear approximation performs better over oceans and considering higher order terms creates unrealistic frequencies reaching to a magnitude of 5 km in the Moho solution. Involving gravity data according to the VMM principle influences the Moho depth significantly up to 15 km in some areas.

  • 25.
    Eshagh, Mehdi
    Högskolan Väst, Institutionen för ingenjörsvetenskap, Avd för elektro, lantmäteri och naturvetenskap.
    On the relation between Moho and sub-crustal stress induced by mantle convection2015Inngår i: Journal of Geophysics and Engineering, ISSN 1742-2132, E-ISSN 1742-2140, Vol. 12, nr 1, s. 1-11Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The sub-crustal stress components due to mantle convection have a direct relation with the spherical harmonic coefficients of the Earth's disturbing potential like those of the Moho model, developed by the Vening–Meinesz–Moritz theory. In this paper, the relation between the stress components and the global and local models of Moho is mathematically developed in three different ways. Here, we present the S function (S) with a numerical differentiation approach to generate the stress components and we show that its spherical harmonic series is convergent to a degree of about 600 based on a mean global Moho depth of 23 km. An integral approach is developed for integration of a local Moho model for the stress recovery, but the kernels of this integral are not likely to be convergent and should be generated by their spectral forms to a limited degree. Another method is developed based on integral inversion, which is free of any mathematical problem and suitable for recovering S from an existing model of Moho. Our numerical presentation shows that the stress has a good agreement with the tectonic boundaries and the places at which the curvature of the Moho surface changes.

  • 26.
    Eshagh, Mehdi
    Högskolan Väst, Institutionen för ingenjörsvetenskap, Avd för elektro, lantmäteri och naturvetenskap.
    On the reliability and error calibration of some recent Earth's gravity models of GOCE with respect to EGM082013Inngår i: Acta Geodaetica et Geophysica Hungarica, ISSN 1217-8977, E-ISSN 1587-1037, Vol. 48, nr 2, s. 199-208Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The Gravity field and steady-state Ocean Circulation Explorer (GOCE) mission is dedicated to recover spherical harmonic coefficients of the Earth's gravity field to degree and order of about 250 using its satellite gradiometric data. Since these data are contaminated with coloured noise, therefore, their inversion will not be straightforward. Unsuccessful modelling of this noise will lead to biases in the harmonic coefficients presented in the Earth's gravity models (EGMs). In this study, five of the recent EGMs of GOCE such as two direct, two time-wise and one space-wise solution are used to degree and order 240 and their reliability is investigated with respect to EGM08 which is assumed as a reliable EGM. The detected unreliable coefficients and their errors are replaced by the corresponding ones from EGM08 as a combination strategy. A condition adjustment model is organised for each two corresponding coefficients of GOCE EGMs and EGM08; and errors of the GOCE EGMs are calibrated based on a scaling factor, obtained from a posteriori variance factor. When the factor is less than 2.5 it will be multiplied to the error otherwise the error of EGM08 coefficient will be considered as the calibrated one. At the end, a simple geoid estimator is presented which considers the EGMs and their errors and its outcomes are compared with the corresponding geoid heights derived from the Global Positioning System (GPS) and the levelling data (GPS/levelling data), over Fennoscandia. This comparison shows that some of the combined-calibrated GOCE EGMs are closer to the GPS/levelling data than the original ones.

  • 27.
    Eshagh, Mehdi
    Högskolan Väst, Institutionen för ingenjörsvetenskap, Avdelningen för data-, elektro- och lantmäteriteknik.
    On Vening Meinesz-Moritz and flexural theories of isostasy and their comparison over Tibet Plateau2016Inngår i: Journal of Geodetic Science, ISSN 2081-9919, E-ISSN 2081-9943, Vol. 6, s. 139-151Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Gravity and topographic/bathymetric data are used for gravimetric modelling of Moho discontinuity by hydrostatic or flexural theories of the isostasy. Here, two hydrostatic models, based on the Vening Meinesz-Moritz (VMM) principle, and two based on the loading theories and flexural isostasy are compared over Tibet Plateau. It is shown that the Moho models generated based on the VMM theory and flexural isostasy have very good agreements if the mean compensation depth and the mean elastic thickness are selected properly. However, the model computed based on the flexural isostasy is smoother. A more rigorous flexural model, which considers the membrane stress and curvature of the lithosphere, is used to model the Moho surface over the study area. It is shown that the difference between the Moho models, derived by considering and ignoring these parameters, is not significant. By combination of the flexural and VMM hydrostatic models new mathematical formulae for crustal gravity anomalies are provided and it is shown that the crustal gravity anomalies produced by them are also equivalent.

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  • 28.
    Eshagh, Mehdi
    Högskolan Väst, Institutionen för ingenjörsvetenskap, Avdelningen för Matematik, Data- och Lantmäteriteknik.
    Optimization of Basepoint Configuration in Localization of Signal Interference Device2023Inngår i: Journal of Surveying Engineering, ISSN 0733-9453, E-ISSN 1943-5428, Vol. 149, nr 1, artikkel-id 1150Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Precise navigation, as a method for guiding vehicles from one point to another, is an important subject these days especially in navigation of aircraft. Global navigation satellite systems (GNSSs) are capable tools for such a purpose. Any intentional or unintentional interference in satellite signals may cause risks of deadly accidents. Therefore, it is tremendously important to control airports or harbors and locate any existing radio frequency interference device. This localization can be done based on measuring time of arrival (TOA), angle of arrival (AOA), or time difference of arrival (TDOA) of signals from the device to sensors or receivers at some basepoints. In this article, a method is proposed based on these arrivals for optimizing the configuration created by these basepoints from a large grid of points covering a control area. Furthermore, a simulation test was performed to verify the theory, and after that a control network was designed and optimized for the international Landvetter Airport of Sweden. Our simulation studies show that when the AOA is used, our optimization is more robust with respect to the control grid resolution. In addition, optimization based on the TDOA improves the coverage over the control area with a significant reduction of error of control points, but because of the special geometric shape of the Landvetter Airport, such an optimization was not successful. 

    Fulltekst (pdf)
    fulltext
  • 29.
    Eshagh, Mehdi
    Högskolan Väst, Institutionen för ingenjörsvetenskap, Avd för elektro, lantmäteri och naturvetenskap. Department of Geodesy, K.N.Toosi University of Technology, Tehran.
    Spectral combination of spherical gradiometric boundary-value problems: a theoretical study2012Inngår i: Pure and Applied Geophysics, ISSN 0033-4553, E-ISSN 1420-9136, Vol. 169, s. 2201-2215Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The Earth’s gravity potential can be determined from its second-order partial derivatives using the spherical gradiometric boundary-value problems which have three integral solutions. The problem of merging these solutions by spectral combination is the main subject of this paper. Integral estimators of biased- and unbiased-types are presented for recovering the disturbing gravity potential from gravity gradients. It is shown that only kernels of the biased-type integral estimators are suitable for simultaneous downward continuation and combination of gravity gradients. Numerical results show insignificant practical difference between the biased and unbiased estimators at sea level and the contribution of far-zone gravity gradients remains significant for integration. These contributions depend on the noise level of the gravity gradients at higher levels than sea. In the cases of combining the gravity gradients, contaminated with Gaussian noise, at sea and 250 km levels the errors of the estimated geoid heights are about 10 and 3 times smaller than those obtained by each integral

  • 30.
    Eshagh, Mehdi
    * Islamic Azad University, Shahre-Rey Branch, Tehran, Iran .
    Step-variable numerical orbit determination of a low earth Orbiting Satellite2005Inngår i: Jounal of the Earth and Space Physics, Vol. 31, nr 1, s. 1-12Artikkel i tidsskrift (Fagfellevurdert)
  • 31.
    Eshagh, Mehdi
    Högskolan Väst, Institutionen för ingenjörsvetenskap, Avdelningen för Matematik, Data- och Lantmäteriteknik.
    The Earth’s Gravity Field Role in Geodesy and Large-Scale Geophysics2021Inngår i: Geodetic Sciences: Theory, Applications and Recent Developments / [ed] Erol, Bihter & Erol, Serdar, IntechOpen , 2021Kapittel i bok, del av antologi (Fagfellevurdert)
    Abstract [en]

    The Earth gravity field is a signature of the Earth’s mass heterogeneities and structures and applied in Geodesy and Geophysics for different purposes. One of the main goals of Geodesy is to determine the physical shape of the Earth, geoid, as a reference for heights, but Geophysics aims to understand the Earth’s interior. In this chapter, the general principles of geoid determination using the well-known methods of Remove-Compute-Restore, Stokes-Helmert and least-squares modification of Stokes’ formula with additive corrections are shortly discussed. Later, some Geophysical applications like modelling the Mohorovičić discontinuity and density contrast between crust and uppermantle, elastic thickness, ocean depth, sediment and ice thicknesses, sub-lithospheric and lithospheric stress, Earthquakes and epicentres, post-glacial rebound, groundwater storage are discussed. The goal of this chapter is to briefly present the roll of gravity in these subjects.

  • 32.
    Eshagh, Mehdi
    Royal Institute of Technology (KTH), Division of Geodesy and Geoinformatics.
    The effect of spatial truncation error on integral inversion of satellite gravity gradiometry data2011Inngår i: Advances in Space Research, ISSN 0273-1177, E-ISSN 1879-1948, ISSN 0273-1177, Vol. 47, nr 7, s. 1238-1247Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

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

  • 33.
    Eshagh, Mehdi
    et al.
    Högskolan Väst, Institutionen för ingenjörsvetenskap, Avdelningen för Matematik, Data- och Lantmäteriteknik.
    Ashargie, Andenet
    Bedada, Tulu B.
    Regional recovery of gravity anomaly from the inversion of diagonal components of GOCE gravitational tensor: A Case Study in Ethiopia, Artificial Satellites2018Inngår i: Artificial Satellites : he Journal of Space Research Centre of Polish Academy of Sciences, E-ISSN 2083-6104, Vol. 53, nr 2, s. 55-74Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The tensor of gravitation is traceless as the gravitational field of the Earth is harmonic outside the Earth's surface. Therefore, summation of the 2nd-order horizontal derivatives on its diagonal components should be equal to the radial one but with the opposite sign. The gravity field can be recovered locally from either of them, or even their combination. Here, we use the in-orbit diagonal components of the gravitational tensor measured by the gravity field and steady stateocean circulation explorer (GOCE) mission for recovering gravity anomaly with a resolution of 1°×1° at sea level in Ethiopia. In order to solve the system of equations, derived after discretisation of integral equations, the Tikhonov regularisation is applied and the bias of thi sregularisation is estimated and removed from the estimated gravity anomalies. The errors of the anomalies are estimated and their significance of recovery from these diagonal components is investigated. Statistically, the difference between the recovered anomalies from each scenario isnot significant comparing to their errors. However, their joint inversion of the diagonal components improved the solution by about 1 mGal. Furthermore, the inversion processes arebetter stabilised when using errors of the input data compared with its exclusion, but at the penalty of degradation in accuracy of the estimates.

  • 34.
    Eshagh, Mehdi
    et al.
    Högskolan Väst, Institutionen för ingenjörsvetenskap, Avd för naturvetenskap, lantmäteri- och maskinteknik.
    Bagherbandi, Mohammad
    University of Gävle, Department of Industrial Development.
    Combined Moho Estimators2014Inngår i: Geodynamics Research International Bulletin, E-ISSN 2345-4997, Vol. 1, nr 3, s. 1-11Artikkel i tidsskrift (Annet vitenskapelig)
    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 Moho surface.

  • 35.
    Eshagh, Mehdi
    et al.
    Högskolan Väst, Institutionen för ingenjörsvetenskap, Avd för elektro, lantmäteri och naturvetenskap. K N Toosi University of Technology, Department of Geodesy, Tehran, Iran.
    Bagherbandi, Mohammad
    University of Gävle, Department of Industrial Development, IT and Land Management .
    Quality description for gravimetric and seismic Moho models of Fennoscandia through a combined adjustment2012Inngår i: Acta Geodaetica et Geophysica Hungarica, ISSN 1217-8977, E-ISSN 1587-1037, Vol. 47, nr 4, s. 388-401Artikkel i tidsskrift (Fagfellevurdert)
    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.

  • 36.
    Eshagh, Mehdi
    et al.
    Islamic Azad University, Shahr-e-Rey branch, Tehran.
    Bagherbandi, Mohammad
    Royal Institute of Technology (KTH), Stockholm.
    Smoothing impact of isostatic crustal thickness models on local integral inversion of satellite gravity gradiometry data,2011Inngår i: Acta Geophysica, ISSN 1895-7455, Vol. 59, nr 5, s. 891-906Artikkel i tidsskrift (Fagfellevurdert)
    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. Herewe 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 onVening 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.

  • 37.
    Eshagh, Mehdi
    et al.
    Högskolan Väst, Institutionen för ingenjörsvetenskap, Avdelningen för Matematik, Data- och Lantmäteriteknik.
    Berntsson, Jenny
    Högskolan Väst, Institutionen för ingenjörsvetenskap, Avdelningen för Matematik, Data- och Lantmäteriteknik.
    On quality of NKG2015 geoid model over the Nordic countries2019Inngår i: Journal of Geodetic Science, ISSN 2081-9919, E-ISSN 2081-9943, Vol. 9, nr 1, s. 97-110Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The NKG2015 geoid model covers the Nordic and Baltic countries and has been computed based on the least-squares modification of Stokes’ formula with additive corrections method. New and precise terrestrial, airborne and shipborne gravimetric measurements, the recent global gravity model of the gravity field and steady-state ocean circulation explorer (GOCE) and detailed digital terrain models over each territory have been used for computing this new geoid model. Some estimates for the error of this model have been roughly presented by comparing it with the global navigation satellite system(GNSS) data over each country. In this paper, our goal is to have a closer look at the relative error of this model by performing some statistical tests and finding the proper corrective surface for absorbing the systematic errors over each country. Our main assumption is realisticity of the errors of GNSS/levelling data and we will investigate its consequences in estimating the error of the geoid model. Our results show that the 4-parameter corrective surface is suitable for modelling the systematic trends of the differences between the gravimetric and GNSS geoid heights in Sweden, Denmark and Finland, but a filtered discrepancies by a confidence interval of 95% should be used for Sweden. A 7-aparameter model is suitable for the filtered discrepancies with the confidence interval of 95% in Norway. Based on the selected corrective surface and our newly developed regional iterative variance estimator, the confidence interval for the error of NKG2015 geoid model in Sweden, Denmark and Norway yielded 0-6.5 mm, 1.8-5.2 mm, 14.8-17.7 mm, respectively with a confidence level of 95%. We could not estimate the geoid error in Finland because the given error of the GNSS/levelling heights is significantly larger than the size of residuals. Based on the selected corrective surfaces and our presented local variance estimator, the average error of geoid becomes 3.6, 2.4, 8.8 and 5.8 mm with a confidence interval of 68%, respectively, over Sweden, Denmark, Norway and Finland.

  • 38.
    Eshagh, Mehdi
    et al.
    Högskolan Väst, Institutionen för ingenjörsvetenskap, Avd för elektro, lantmäteri och naturvetenskap. Högskolan Väst, Institutionen för ingenjörsvetenskap, Avdelningen för Matematik, Data- och Lantmäteriteknik.
    Ebadi, Sahar
    K.N.Toosi University of Technology, Tehran, Iran.
    A strategy to calibrate errors of Earth gravity models2014Inngår i: Journal of Applied Geophysics, ISSN 0926-9851, E-ISSN 1879-1859, Vol. 103, nr April, s. 215-220Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    In this paper, three independent Earth gravity models (EGMs) ofGO_CONS_GCF_2_TIM_R4, AIUB-GRACE03S and ULux_CHAMP2013s are combined to degree and order 120. The geoid models of these EGMs are computed and compared with the Global Positioning System (GPS) and levelling data over Fennoscandia. We found that the simple mean of these geoid models is closer to the GPS/levelling data than their weighted mean. This means that errors of the EGMs are not properly estimated as they are used in the weighted mean solution. We develop a method based on solving a nonlinear condition adjustment model to calibrate the errors so that the result of weighted mean becomes the same as that of the simple mean. Numerical results show slight changes in the errors of GRACE03S but large ones in those of GO_CONS_GCF_2_TIM_R4 and ULux_CHAMP2013s. Furthermore, the weighted mean solution considering the calibrated errors and some additional constraints is better than GOCO03S to degree and order 120 over Fennoscandia.

  • 39.
    Eshagh, Mehdi
    et al.
    Högskolan Väst, Institutionen för ingenjörsvetenskap, Avd för elektro, lantmäteri och naturvetenskap.
    Ebadi, Sahar
    Department of Geodesy, K.N.Toosi University of Technology.
    Geoid modelling based on EGM08 and the recent Earth gravity models of GOCE2013Inngår i: Earth Science Informatics, ISSN 1865-0473, Vol. 6, nr 3, s. 113-125Artikkel i tidsskrift (Fagfellevurdert)
  • 40.
    Eshagh, Mehdi
    et al.
    Högskolan Väst, Institutionen för ingenjörsvetenskap, Avdelningen för data-, elektro- och lantmäteriteknik.
    Ebadi, Sahar
    University of Tehran, Department of Surveying Engineering, Iran.
    Tenzer, Robert
    University of West Bohemia, New Technologies for the Information Society (NTIS), Czech Republic.
    Isostatic GOCE Moho model for Iran2017Inngår i: Journal of Asian Earth Sciences, ISSN 1367-9120, E-ISSN 1878-5786, Vol. 138, s. 12-24Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    One of the major issues associated with a regional Moho recovery from the gravity or gravity-gradient data is the optimal choice of the mean compensation depth (i.e., the mean Moho depth) for a certain area of study, typically for orogens characterised by large Moho depth variations. In case of selecting a small value of the mean compensation depth, the pattern of deep Moho structure might not be reproduced realistically. Moreover, the definition of the mean compensation depth in existing isostatic models affects only low-degrees of the Moho spectrum. To overcome this problem, in this study we reformulate the Sjöberg and Jeffrey’s methods of solving the Vening-Meinesz isostatic problem so that the mean compensation depth contributes to the whole Moho spectrum. Both solutions are then defined for the vertical gravity gradient, allowing estimating the Moho depth from the GOCE satellite gravity-gradiometry data. Moreover, gravimetric solutions provide realistic results only when a priori information on the crust and upper mantle structure is known (usually from seismic surveys) with a relatively good accuracy. To investigate this aspect, we formulate our gravimetric solutions for a variable Moho density contrast to account for variable density of the uppermost mantle below the Moho interface, while taking into consideration also density variations within the sediments and consolidated crust down to the Moho interface. The developed theoretical models are applied to estimate the Moho depth from GOCE data at the regional study area of the Iranian tectonic block, including also parts of surrounding tectonic features. Our results indicate that the regional Moho depth differences between Sjöberg and Jeffrey’s solutions, reaching up to about 3 km, are caused by a smoothing effect of Sjöberg’s method. The validation of our results further shows a relatively good agreement with regional seismic studies over most of the continental crust, but large discrepancies are detected under the Oman Sea and the Makran subduction zone. We explain these discrepancies by a low quality of seismic data offshore.

  • 41.
    Eshagh, Mehdi
    et al.
    Högskolan Väst, Institutionen för ingenjörsvetenskap, Avdelningen för Matematik, Data- och Lantmäteriteknik. K. N. Toosi University of Technology, Faculty of Geodesy and Geomatics Engineering, Tehran, Iran (IRN).
    Fatolazadeh, Farzam
    Université de Sherbrooke, Departement de Geomatique Appliquée, Sherbrooke, Québec, Canada (CAN).
    Tenzer, Robert
    Hong Kong Polytechnic University, Department of Land Surveying and Geo-Informatics, Hong Kong (HKG).
    Lithospheric stress, strain and displacement changes from GRACE-FO time-variable gravity: case study for Sar-e-Pol Zahab Earthquake 20182020Inngår i: Geophysical Journal International, ISSN 0956-540X, E-ISSN 1365-246X, Vol. 223, nr 1, s. 379-397Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Temporal variations in the Earth’s gravity field can be used for monitoring of lithospheric deformations. The network of continuously operating gravity stations is required for this purpose but a global coverage by such network is currently extremely sparse. Temporal variations in long-wavelength part of the Earth’s gravity field have been, however, observed by two satellite missions, namely the Gravity Recovery And Climate Experiment (GRACE) and the GRACE Follow-On (GRACE-FO). These satellite gravity observations can be used to study long-wavelength deformations of the lithosphere. Consequently, considering the lithosphere as a spherical elastic shell and solving the partial differential equation of elasticity for it, the stress, strain and displacement inside the lithosphere can be estimated. The lower boundary of this shell is assumed to be stressed by mantle convection, which has a direct relation to the Earth’s gravity field according to Runcorn’s theory. Changes in gravity field lead to changes in the sublithospheric stress and the stress propagated throughout the lithosphere. In this study, we develop mathematical models in spherical coordinates for describing the stress propagation from the sublithosphere through the lithosphere. We then organize a system of observation equations for finding a special solution to the boundary-value problem of elasticity in the way that provides a stable solution. In contrast, models presented in previously published studies are ill-posed. Furthermore, we use constants of the solution determined from the boundary stresses to determine the strain and displacements leading to these stresses, while in previous studies only the stress has been considered according to rheological properties of the lithosphere. We demonstrate a practical applicability of this theoretical model to estimate the stress–strain redistribution caused by the Sar-e-Pol Zahab 2018 earthquake in Iran by using the GRACE-FO monthly solutions.

  • 42.
    Eshagh, Mehdi
    et al.
    Högskolan Väst, Institutionen för ingenjörsvetenskap, Avd för elektro, lantmäteri och naturvetenskap.
    Ghorbannia, Morteza
    K.N. Toosi University of Technology, Department of Geodesy, Tehran.
    The effect of spatial truncation error on the variance of gravity anomalies derived from inversion of satellite orbital and gradiometric data2014Inngår i: Advances in Space Research, ISSN 0273-1177, E-ISSN 1879-1948, Vol. 54, nr 2, s. 261-271Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

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

  • 43.
    Eshagh, Mehdi
    et al.
    Högskolan Väst, Institutionen för ingenjörsvetenskap, Avd för elektro, lantmäteri och naturvetenskap.
    Ghorbannia, Morteza
    Department of Geodesy, K.N.Toosi University of Technology.
    The use of Gaussian equations of motions of a satellite for local gravity anomaly recovery2013Inngår i: Advances in Space Research, ISSN 0273-1177, E-ISSN 1879-1948, Vol. 52, nr 1, s. 30-38Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

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

  • 44.
    Eshagh, Mehdi
    et al.
    Högskolan Väst, Institutionen för ingenjörsvetenskap, Avdelningen för data-, elektro- och lantmäteriteknik.
    Hussain, Matloob
    Högskolan Väst, Institutionen för ingenjörsvetenskap. Earth Sciences department, Quaid-i-Azam University, Islamabad, Pakistan.
    Relationship amongst gravity gradients, deflection of vertical, Moho deflection and the stresses derived by mantle convections: a case study over Indo-Pak and surroundings2015Inngår i: Geodynamics research international bulletin, E-ISSN 2345-4997, Vol. 3, nr 4, s. I-XIII, artikkel-id 12Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    All  quantities,  which are  measured  in  the  gravity  field  of  the  Earth are affected by  the  field,  therefore,  there should  be correlations  amongst  them.  Here,  we  focus  on  some  gravimetrically-determined  quantities  like  deflections  of  vertical, deflections of Moho, vertical-horizontal gravity gradients and the shear sub-lithospheric stress components due to mantle convection. We show that how these quantities are related to each other mathematically so that one of them can be written in term of another. This somehow proves the presence of the mentioned correlations theoretically. Also, we generate the maps of these quantities over the Indo-Pak and surrounding areas and show how similar they are. Thereafter, they are explained and  interpreted  geologically.  Our  investigations  show  that  the  maps  of  these  quantities  are  in  good  agreements  with topographic and geological features. The map of the vertical-horizontal gravity gradients shows more detailed information of the  gravity field due to  signal amplification at high  degrees,  that of Moho deflection shows sub-surface features due to reduction of the effect of topographic masses. The map of the shear sub-lithospheric stress components is much smoother than the gradients, as expected, and has good agreement with the collisional and subduction zones as well. 

    Relationship amongst gravity gradients, deflection of vertical, Moho deflection and the stresses derived by mantle convections-a case study over Indo-Pak and surroundings. Available from: https://www.researchgate.net/publication/292538682_Relationship_amongst_gravity_gradients_deflection_of_vertical_Moho_deflection_and_the_stresses_derived_by_mantle_convections-a_case_study_over_Indo-Pak_and_surroundings [accessed Feb 1, 2016].

    Fulltekst (pdf)
    fulltext
  • 45.
    Eshagh, Mehdi
    et al.
    Högskolan Väst, Institutionen för ingenjörsvetenskap, Avdelningen för data-, elektro- och lantmäteriteknik.
    Hussain, Matloob
    Högskolan Väst, Institutionen för ingenjörsvetenskap, Avdelningen för data-, elektro- och lantmäteriteknik. Quaid-i-Azam University, Department of Earth Sciences, Islamabad 45320, Pakistan.
    Tenzer, Robert
    Wuhan University, The Key Laboratory of Geospace Environment and Geodesy, Wuhan 430079, China.
    Romeshkani, Mohsen
    University of Tehran, School of Surveying and Geospatial Engineering, College of Engineering, Tehran 14395-515, Iran.
    Moho density contrast in central Eurasia from GOCE gravity gradients2016Inngår i: Remote Sensing, E-ISSN 2072-4292, Vol. 8, nr 5, s. 1-18, artikkel-id 418Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Seismic data are primarily used in studies of the Earth's inner structure. Since large partsof the world are not yet sufficiently covered by seismic surveys, products from the Earth's satellite observation systems have more often been used for this purpose in recent years. In this study we use the gravity-gradient data derived from the Gravity field and steady-state Ocean Circulation Explorer (GOCE), the elevation data from the Shuttle Radar Topography Mission (SRTM) and other global datasets to determine the Moho density contrast at the study area which comprises most of the Eurasian plate (including parts of surrounding continental and oceanic tectonic plates). A regional Moho recovery is realized by solving the Vening Meinesz-Moritz's (VMM) inverse problem of isostasy and a seismic crustal model is applied to constrain the gravimetric solution. Our results reveal that the Moho density contrast reaches minima along the mid-oceanic rift zones and maxima under the continental crust. This spatial pattern closely agrees with that seen in the CRUST1.0 seismic crustal model as well as in the KTH1.0 gravimetric-seismic Moho model. However, these results differ considerably from some previously published gravimetric studies. In particular, we demonstrate thatt here is no significant spatial correlation between the Moho density contrast and Moho deepening under major orogens of Himalaya and Tibet. In fact, the Moho density contrast under most of the continental crustal structure is typically much more uniform.

    Fulltekst (pdf)
    fulltext
  • 46.
    Eshagh, Mehdi
    et al.
    Högskolan Väst, Institutionen för ingenjörsvetenskap, Avdelningen för data-, elektro- och lantmäteriteknik.
    Hussain, Mutloob
    Department of Earth Sciences, Quad-i-Azam University, Islamabad 45320, Pakistan.
    An approach to Moho discontinuity recovery from on-orbit GOCE data with application over Indo-Pak region2016Inngår i: Tectonophysics, ISSN 0040-1951, E-ISSN 1879-3266, Vol. Part B, s. 253-262Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    In this research, a modified form of Vening Meinesz-Moritz (VMM) theory of isostasy for the second-order radial derivative of gravitational potential, measured from the Gravity field and steady-state Ocean Circulation Explorer (GOCE), is developed for local Moho depth recovery. An integral equation is organised for inverting the GOCE data to compute a Moho model in combination with topographic/bathymetric heights of SRTM30, sediment and consolidated crystalline basement and the laterally-varying density contrast model of CRUST1.0. A Moho model from EGM2008 to degree and order 180 is also computed based on the same principle for the purpose of comparison. In addition, we compare both of them with the 3 available seismic Moho models; two global and one regional over the Indo-Pak region. Numerical results show that our GOCE-based Moho model is closer to the all seismic models than that of EGM2008. The model is closest to the regional one with a standard deviation of 5.5 km and a root mean squares error of 7.8 km, which is 2.3 km smaller than the corresponding one based on EGM2008.

  • 47.
    Eshagh, Mehdi
    et al.
    Högskolan Väst, Institutionen för ingenjörsvetenskap, Avdelningen för data-, elektro- och lantmäteriteknik.
    Hussain, Mutloob
    Quaid-i-Azam University, Department of Earth Sciences, 45320 Islamabad, Pakistan.
    Tiampo, Kristy F.
    University of Colorado at Boulder, Department of Geological Sciences and CIRES, USA.
    Towards sub-lithospheric stress determination from seismic Moho, topographic heights and GOCE data2016Inngår i: Journal of Asian Earth Sciences, ISSN 1367-9120, E-ISSN 1878-5786, Vol. 129, s. 1-12Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Sub-lithospheric stresses can be estimated by analysis of gravity field measurements. Depending on the measured gravimetric quantity, different methods can be employed to estimate those sub-lithospheric stresses. Here, we further develop the Runcorn's theory for estimation of mantle stresses (1967) such that a Moho model and full topographic information are used to recover the function from which the stress can be computed by taking derivatives northwards and eastwards. We develop new integral equations for such a purpose and recover this function by solving those integral equations locally over the Indo-Pak (India-Pakistan) region from (1) a gravimetric Moho model computed from the SRTM (Shuttle Radar Topography Mission) and the Earth gravity model EGM2008, (2) SRTM and the seismic Moho model of CRUST1.0 and (3) data and measurements of the GOCE (Gravity field and steady-state Ocean Circulation Explorer) mission. Finally, we perform a joint inversion of seismic and GOCE data for the same purpose. The numerical results show that the use of a seismic Moho model recovers information about the stress field which is not seen in the results derived from a gravimetric Moho model. A combination of the seismic Moho model, SRTM and GOCE yields a better stress field than that of either the seismic and/or gravimetric data alone. The magnitudes of the sub-lithospheric stress are computed from the shear stress components over the area and good agreement is seen between the recovered combined stress field, the regional tectonic boundaries and the seismicity of the World Stress Map 2008 database.

  • 48.
    Eshagh, Mehdi
    et al.
    Royal Institute of Technology, Division of Geodesy, Stockholm, Sweden .
    Lars E., Sjöberg
    Royal Institute of Technology, Division of Geodesy, Stockholm, Sweden .
    Impact of topography and atmosphere over Iran on validation and inversion of GOCE gradiometric data2008Inngår i: Journal of the Earth and Space Physics, ISSN 1025-8647, Vol. 34, nr 3, s. 15-30Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The dedicated satellite mission GOCE will sense various small mass variations along its path around the Earth. Here we study the effect of the Earth's topography and atmosphere on GOCE data. The effects depend on the magnitude of topographic height, and they will therefore vary by region. As the effect of the atmosphere and topography must be removed from the total gravity anomaly prior to geoid determinations, these effects should also be removed to simplify the downward continuation of the GOCE data to the sea level. The main goal of this article is to investigate the direct topographic and atmospheric effects in a rough region like Iran. Maps of the direct effects and their statistics are presented and discussed. Numerical results show maximum direct topographic and atmospheric effects on the GOCE data can reach 2.64 E and 5.53 mE, respectively, when the satellite flies over Iran. The indirect effect of the atmospheric and topographic masses are also formulated and presented.

  • 49.
    Eshagh, Mehdi
    et al.
    Högskolan Väst, Institutionen för ingenjörsvetenskap, Avdelningen för data-, elektro- och lantmäteriteknik. Division of Geodesy, Royal Institute of Technology, Stockholm, Sweden.
    Lars E., Sjöberg
    Division of Geodesy, Royal Institute of Technology, Stockholm, Sweden.
    Ramin, Kiamehr
    Department of Geodesy and Geomatics, Zanjan University, Zanjan, Iran.
    Evaluation of robust techniques in suppressing the impact of outliers in a deformation monitoring network – A case study on the Tehran Milad tower network2007Inngår i: Acta Geodaetica et Geophysica Hungarica, ISSN 1217-8977, E-ISSN 1587-1037, Vol. 42, nr 4, s. 449-463Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The problem of handling outliers in a deformation monitoring network is of special importance, because the existence of outliers may lead to false deformation parameters. One of the approaches to detect the outliers is to use robust estimators. In this case the network points are computed by such a robust method, implying that the adjustment result is resisting systematic observation errors, and, in particular, it is insensitive to gross errors and even blunders. Since there are different approaches to robust estimation, the resulting estimated networks may differ. In this article, different robust estimation methods, such as the M-estimation of Huber, the “Danish”, and the L 1-norm estimation methods, are reviewed and compared with the standard least squares method to view their potentials to detect outliers in the Tehran Milad tower deformation network. The numerical studies show that the L 1-norm is able to detect and down-weight the outliers best, so it is selected as the favourable approach, but there is a lack of uniqueness. For comparison, Baarda’s method “data snooping” can achieve similar results when the outlier magnitude of an outlier is large enough to be detected; but robust methods are faster than the sequential data snooping process.

  • 50.
    Eshagh, Mehdi
    et al.
    Royal Institute of Technology (KTH),Division of Geodesy and Geoinformatics.
    Lemoine, Jean-Michel
    Department of Space Geodesy (GRGS), French Space Agency (CNES), Toulouse, France.
    Gegout, Pascal
    Department of Space Geodesy (GRGS), French Space Agency (CNES), Toulouse, France.
    Biancale, Richard
    Department of Space Geodesy (GRGS), French Space Agency (CNES), Toulouse, France.
    On regularized time varying gravity field models based on GRACE data and their comparisons with hydrological models2013Inngår i: Acta Geophysica, ISSN 1895-6572, Vol. 61, nr 1, s. 1-17Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Determination of spherical harmonic coefficients of the Earth's gravity field is often an ill-posed problem and leads to solving an ill-conditioned system of equations. Inversion of such a system is critical, as small errors of data will yield large variations in the result. Regularization is a method to solve such an unstable system of equations. In this study, direct methods of Tikhonov, truncated and damped singular value decomposition and iterative methods of ν, algebraic reconstruction technique, range restricted generalized minimum residual and conjugate gradient are used to solve the normal equations constructed based on range rate data of the gravity field and climate experiment (GRACE) for specific periods. Numerical studies show that the Tikhonov regularization and damped singular value decomposition methods for which the regularization parameter is estimated using quasioptimal criterion deliver the smoothest solutions. Each regularized solution is compared to the global land data assimilation system (GLDAS) hydrological model. The Tikhonov regularization with L-curve delivers a solution with high correlation with this model and a relatively small standard deviation over oceans. Among iterative methods, conjugate gradient is the most suited one for the same reasons and it has the shortest computation time

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