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This paper examines how Holocaust poets use the image of earth to convey a shattered world. Earth features as world or planet, but also as ground and soil, and in both meanings is participant in and witness to genocide. Moreover, earth becomes a figure for understanding the natural world and its relation to human horror. Valuable observations are made about how, in the Holocaust setting, humans experienced their environment and how they represent it poetically. Though the ecocritical view often calls for moving away from the anthropocentric standpoint, the poets examined ultimately insist on the centrality of the human victim. [ABSTRACT FROM AUTHOR]

A Moon‐based sensor can observe the Earth as a single point and achieve disk‐integrated measurements of outgoing longwave radiation (OLR), which significantly differs from low orbital, geostationary, and Sun–Earth L1 point platforms. In this study, a scheme of determining the disk‐integrated Earth's OLR based on a Moon‐based platform is proposed. The observational solid angle was theoretically derived based on the Earth's ellipsoid model and the disk‐integrated observational anisotropic factor was estimated to eliminate the effects of the Earth's radiant anisotropy. The simulated disk‐integrated Earth's OLR obtained from a Moon‐based platform varies periodically, due to changes in the observation geometry and Earth's scene distribution within the observed Earth's disk. Clouds, meteorological parameters, and the land cover distribution notably affect the disk‐integrated Earth's OLR. By analyzing the disk‐integrated Earth's OLR from a Moon‐based platform, significant variabilities were investigated. Additionally, the Earth's shape and radiant anisotropy that affecting the disk‐integrated Earth's OLR were estimated. In conclusion, a more realistic Earth's shape, the latest version of the angular distribution model (ADM), and accurate land cover and meteorological datasets are needed when determining the disk‐integrated Earth's OLR. It is expected the unique variability captured by this platform and its ability to complement traditional satellite data make it a valuable tool for studying Earth's radiation budget and energy cycle, and contributing to diagnostic of the climate General Circulation Models (GCM) performance. Plain Language Summary: Observing large‐scale geoscience phenomena poses a significant challenge, necessitating observations that guarantee spatial continuity and temporal consistency. Equipping sensors on the lunar surface can observe the whole Earth's disk, which is a feasible way to complement the existing satellites. Determining the disk‐integrated Earth's OLR from a Moon‐based platform helps in exploring its potential for detecting geoscience phenomena at different scales. Our study finds that the Moon‐based disk‐integrated Earth's OLR would provide full coverage of the whole Earth's phase angle during one sidereal month. The day‐night and land‐ocean effects on the Moon‐based disk‐integrated OLR during one sidereal month would provide substantial variability to compare to similarly sampled GCM output comparison that is not available from conventional satellite data. Such these unique variabilities in the Moon‐based disk‐integrated Earth's OLR make the Moon a valuable Earth observation platform for studying Earth's radiation budget and energy cycle, and evaluating the performance of GCMs. Key Points: Disk‐integrated Earth's outgoing longwave radiation are estimated considering Earth's shape and radiant anisotropyOverall understanding of the variability on Moon‐based disk‐integrated Earth's outgoing longwave radiationDiscussing the characteristics of Moon‐based disk‐integrated Earth's outgoing longwave radiation [ABSTRACT FROM AUTHOR]

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In this case, we first observed that the Sun appears to move across the sky-as evidenced by the moving shadow-but why does the Sun appear to move across the sky? Your shadow is long when the Sun is low in the sky.) PART 2: OBSERVING DAILY MOVEMENT OF THE SUN Students can use the same idea as the pencil and flashlight to see how their shadow changes over the course of the day. However, Earth's revolution around the Sun is not why the Sun appears to move across the sky over the course of the day. [Extracted from the article]

Abstract: This paper describes a hybrid MPI/OpenMP approach to using diskless computing clusters to solve time-consuming problems related to ultra-high-degree and -order spherical harmonic analysis using the EGM2008 geopotential model with least-squares collocation to improve the accuracy of EGM2008-derived geoid heights. The proposed hybrid approach conducted 2190-degree and -order spherical harmonic analysis and least-squares collocation fitting using a cluster system of low-performance nodes and achieved a maximum parallel efficiency of 99%. Calculation of the associated Legendre functions and numerical stability were ensured for both 64 and 128bits in an EGM2008 spherical harmonic analysis for the Korean Peninsula using parallelization modeling. EGM2008 not only described the gravity field of the Korean Peninsula well, but its results were also very accurate compared to those of other global geopotential models. EGM2008-derived geoid heights were fitted with GPS/leveling data from least-squares collocation, which improved their accuracy. For this procedure, parallelization modeling was used to explore the optimum correlation length representing the highest accuracy. After the geoid heights were fitted, their accuracy was evaluated for several cases to determine the optimum distance of GPS/leveling points for least-squares fitting around the Korean Peninsula, and to determine the optimum correlation length by comparing the various results. A correlation length of 119.4km showed the best fitting results for the case using 102 GPS/leveling points with 40-km intervals. [Copyright &y& Elsevier]

Abstract: Precise determination of local geoid is of particular importance for establishing height control in geodetic GNSS applications, since the classical leveling technique is too laborious. A geoid model can be accurately obtained employing properly distributed benchmarks having GNSS and leveling observations using an appropriate computing algorithm. Besides the classical multivariable polynomial regression equations (MPRE), this study attempts an evaluation of learning based computing algorithms: artificial neural networks (ANNs), adaptive network-based fuzzy inference system (ANFIS) and especially the wavelet neural networks (WNNs) approach in geoid surface approximation. These algorithms were developed parallel to advances in computer technologies and recently have been used for solving complex nonlinear problems of many applications. However, they are rather new in dealing with precise modeling problem of the Earth gravity field. In the scope of the study, these methods were applied to Istanbul GPS Triangulation Network data. The performances of the methods were assessed considering the validation results of the geoid models at the observation points. In conclusion the ANFIS and WNN revealed higher prediction accuracies compared to ANN and MPRE methods. Beside the prediction capabilities, these methods were also compared and discussed from the practical point of view in conclusions. [Copyright &y& Elsevier]

Abstract: This paper focuses on studying long distance height datum transfer across seas by a method, using GPS/leveling and gravimetric geoid fitting with an additional parameter. The method combines earth gravitational model EGM2008 with ellipsoidal height derived from GPS, to determine the height datum difference between a mainland and an island. Fitting function is given as a polynomial surface. An iteration algorithm by using different regularization parameters is adopted to solve the ill-conditioned matrix in the normal equation. The precision of the additional parameter is estimated. The feasibility of the proposed method is validated by practical data of two bridge constructions. It can obtain the height datum parameter and quasi-geoid model successively. The objective of long distance height datum transfer is then achieved. Comparing the computed value with known value, the results show that the inconsistencies of the height datum difference are small. No matter how many the differences are, they can be computed precisely. Precision of the computed height datum can satisfy the engineering requirement of the height. Therefore it can be applied in practical engineering, or to validate the reliability of other methods for long distance leveling. This method is low cost, efficient and reliable, and can be generally used in geodesy. [Copyright &y& Elsevier]

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. [ABSTRACT FROM AUTHOR]

Abstract: Geoid data are more sensitive to density distributions deep within the Earth, thus the data are useful for studying the internal processes of the Earth leading to formation of geological structures. In this paper, we present much improved version of high resolution (1′×1′) geoid anomaly map of the northern Indian Ocean generated from the altimeter data obtained from Geodetic Missions of GEOSAT and ERS-1 along with ERS-2, TOPEX/POSIDEON and JASON satellites. The geoid map of the Indian Ocean is dominated by a significant low of −106m south of Sri Lanka, named as the Indian Ocean Geoid Low (IOGL), whose origin is not clearly known yet. The residual geoid data are retrieved from the geoid data by removing the long-wavelength core–mantle density effects using recent spherical harmonic coefficients of Earth Gravity Model 2008 (EGM2008) up to degree and order 50 from the observed geoid data. The coefficients are smoothly rolled off between degrees 30–70 in order to avoid artifacts related to the sharp truncation at degree 50. With this process we observed significant improvement in the residual geoid data when compared to the previous low-spatial resolution maps. The previous version was superposed by systematic broad regional highs and lows (like checker board) with amplitude up to ±12m, though the trends of geoid in general match in both versions. These methodical artifacts in the previous version may have arisen due to the use of old Rapp’s geo-potential model coefficients, as well as sharp truncation of reference model at degree and order 50. Geoid anomalies are converted to free-air gravity anomalies and validated with cross-over corrected ship-borne gravity data of the Arabian Sea and Bay of Bengal. The present satellite derived gravity data matches well with the ship-borne data with Root Mean Square Error (RMSE) of 5.1–7.8mGal, and this is found to be within the error limits when compared with other globally available satellite data. Spectral analysis of ship-borne and satellite data suggested that the satellite gravity data have a resolution down to 16–18km. Further, the geoid, residual geoid and gravity anomalies are integrated with seismic data along two profiles in the Bay of Bengal and Arabian Sea, and inferences have been made in terms of density distributions at different depths. The new residual geoid anomaly map shows excellent correlation with regional tectonic features such as Sunda subduction zone, volcanic traces (Chagos–Laccadive, Ninetyeast and 85°E ridges) and mid-ocean ridge systems (Central Indian and Carlsberg ridges). [Copyright &y& Elsevier]

Abstract: Current and new applications of 2D storm surge models such as the Dutch Continental Shelf Model (DCSM) require that the models provide proper estimates of the instantaneous water levels expressed relative to a particular geoid, rather than only the tide and surge components expressed relative to the ill-defined model''s zero height surface. For DCSM, this is realized by adding the depth-averaged horizontal baroclinic pressure gradients to the model equations, which are derived from 4D salinity and temperature fields provided by the Proudman Oceanographic Laboratory hydrodynamic model (POL''s hindcast). The vertical datum of the extended model is fixed to that of the European Gravimetric Geoid model 2008 (EGG08). This is done by an adjustment of the model parameters that depend on the choice of the reference surface (e.g., bathymetry) and by referring the water levels along the open boundaries to this reference surface. Using different numerical experiments we investigate the effects on the water levels of several approximations we have made during the implementation. The ability of the model to reproduce both the mean sea level (MSL) and instantaneous water levels is assessed by a comparison with the MSL derived from POL''s hindcast as well as with instantaneous water levels acquired by various radar altimeter satellites. From this comparison we conclude that our modeled MSL is in good agreement with the MSL derived from POL''s hindcast; the standard deviation of the differences is below 2cm. However, larger differences in MSL are observed when comparing the model output with the MSL derived from radar altimeter data. They are attributed to either geoid errors or errors in the used salinity and temperature fields. The root mean squared (rms) differences between observed and modeled instantaneous water levels over the entire model domain varies from 9cm for data acquired by the TOPEX satellite to 11cm for data acquired by the GFO-1 satellite. These numbers improve to 8–10cm on the North Sea, for data acquired by the TOPEX and ERS-2 satellites, respectively. These numbers are a factor two to three larger than the expected accuracy of water levels derived from radar altimeter data (which is ). About 25% of these differences can be explained by a bias between the modeled and observed water levels of a single satellite pass. These biases are attributed to errors in the applied correction for the net steric expansion/contraction of the global oceans as this is not captured by DCSM that makes use of the Boussinesq approximation, as well as other errors in model and data. [Copyright &y& Elsevier]

In the framework of the ESA High Processing Facility (HPF), eight gravity models have been computed from the GOCE data since the beginning of the mission in 2009. The accuracy of these models for oceanographic application is assessed and compared with other geoid models (i.e., ITG-GRACE 2010S, EGM2008, EIGEN6C). For that purpose, ocean Mean Dynamic Topography (MDT) estimates are computed by subtracting the different geoids from an altimetric Mean Sea Surface. The MDT assessments were carried out by analyzing their associated geostrophic surface currents at different maximum harmonic degrees and by comparing them with independent in situ oceanographic data. Compared with GRACE-only geoid models, GOCE-only geoid models are in better agreement with independent data at scales smaller than 150 km while they show similar performances at scales larger than 200 km. Regional comparisons show that at 125 km the HPF releases compare well to independent observations with significant improvement with the last releases that use more GOCE data. At 100 km the western boundary currents are well resolved by the last releases, but the satellite-only geoid models need to be further improved to resolve smaller scales and reach the targeted 100 km resolution with higher accuracy. [ABSTRACT FROM AUTHOR]

Recent accomplishments in advancement of accurate astrometric reference star catalogues, development of digital imaging technology, high accuracy tiltmeter technology, and geocentric coordinate availability provided by GNSS, have made possible accurate, fast and automated determination of vertical deflections using astrometric methods. Zenith cameras for this kind of measurements have been developed or are being developed by several research groups. The paper describes a research project by Institute of Geodesy and Geoinformation, intended to design a portable digital zenith camera for vertical deflection determination with 0.1" expected accuracy. Camera components are described, proposed data processing algorithm and preliminary results, obtained with prototype instrument, are presented. [ABSTRACT FROM AUTHOR]

SUMMARY The precession and obliquity frequencies of the Earth's rotational motion are functions of the dynamic ellipticity of the Earth's gravitational figure, and this connection has provided a novel bridge between studies of palaeoclimate and geodynamics. In particular, analyses of tuned climate proxy records have yielded bounds on the mean relative perturbation in dynamic ellipticity over both the last 3 Myr and 25 Myr that are less than ∼3 per cent of the non-hydrostatic component of the ellipticity. We demonstrate that this apparent consistency actually defines an important geophysical enigma. Over the last 3 Myr, changes in the Earth's figure are likely dominated by ice age forcings-in this case, a small perturbation to dynamic ellipticity implies significant isostatic compensation of the ice-ocean surface mass loads and, hence, a relatively low mantle viscosity. In contrast, over the last 25 Myr, changes in the Earth's long-wavelength gravitational form are likely dominated by mantle convective flow, and in this case, the small perturbation to dynamic ellipticity implies sluggish convection and a relatively high mantle viscosity. There are at least four possible routes to resolving this enigma: The viscosity in the Earth's mantle is transient (i.e. dependent on the timescale of the applied forcing), tidal dissipation changed in a manner between the last 3 Myr and 25 Myr that was sufficient to resolve the issue, the observationally inferred bounds are unrealistically restrictive, or earth models exist in which the ice age and convection effects approximately cancel leading to no net perturbation. In this paper, we compute a suite of numerical predictions of ice age and convection-induced perturbations to the dynamic ellipticity to illustrate the enigma described above. [ABSTRACT FROM AUTHOR]

Abstract: 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 1.3cm and the additive topographic and atmospheric corrections by 1cm further. It is shown that the correlations among the data have no significant influence on the estimated geoid. [Copyright &y& Elsevier]

To understand the dynamics of the Earth's fluid, iron-rich outer core, only indirect observations are available. The Earth's magnetic field, originating mainly within the core, and its temporal varia-tions can be used to infer the fluid motion at the top of the core, on a decadal and subdecadal time-scale. Gravity variations result-ing from changes in the mass distribution within the Earth may also occur on the same time-scales. Such variations include the signa-ture of the flow inside the core, though they are largely dominated by the water cycle contributions. Our study is based on 8 y of high-resolution, high-accuracy magnetic and gravity satellite data, pro-vided by the CHAMP and GRACE missions. From the newly derived geomagnetic models we have computed the core magnetic field, its temporal variations, and the core flow evolution. From the GRACE CNES/GRGS series of time variable geoid models, we have obtained interannual gravity models by using specifically designed postprocessing techniques. A correlation analysis between the magnetic and gravity series has demonstrated that the interannual changes in the second time derivative of the core magnetic field under a region from the Atlantic to Indian Ocean coincide in phase with changes in the gravity field. The order of magnitude of these changes and proposed correlation are plausible, compatible with a core origin; however, a complete theoretical model remains to be built. Our new results and their broad geophysical significance could be considered when planning new Earth observation space missions and devising more sophisticated Earth's interior models. [ABSTRACT FROM AUTHOR]

Abstract: In mountainous regions, a gravimetric geoid determination is a difficult task which needs special attention to obtain reliable results satisfying the demands, e.g. of the engineering infrastructure. The present study compares the KTH (Royal Institute of Technology) method with the remove–compute–restore (RCR) technique to attain a precise geoid model for the Konya Closed Basin (KCB) and thus aims to clarify the theoretical and numerical differences between these techniques. The KCB located in the central part of Turkey is a mountainous area with a very limited amount of the ground gravity data. Various data sources, such as the Turkish Digital Elevation Model with resolution (TRDEM3), a recently published satellite-only global geopotential model and terrestrial gravity observations are combined in the gravimetric geoid models of the KCB by applying the KTH and RCR techniques, separately. The both gravimetric geoid models (KG-KTH11 and KG-RCR11) are compared with GNSS/levelling data at the control points in the target area, resulting the RMS (Root Mean Square Error) differences of ±6.7cm and ±9.8cm in the absolute sense, respectively. These results show that the KTH method gives more reasonable accuracy than the RCR technique in a mountainous area with scarce terrestrial gravity data. [Copyright &y& Elsevier]

In mountainous regions with scarce gravity data, gravimetric geoid determination is a difficult task that needs special attention to obtain reliable results satisfying the demands, e.g., of engineering applications. The present study investigates a procedure for combining a suitable global geopotential model and available terrestrial data in order to obtain a precise regional geoid model for Konya Closed Basin (KCB). The KCB is located in the central part of Turkey, where a very limited amount of terrestrial gravity data is available. Various data sources, such as the Turkish digital elevation model with 3 ″ × 3″ resolution, a recently published satellite-only global geopotential model from the Gravity Recovery and Climate Experiment satellite (GRACE) and the ground gravity observations, are combined in the least-squares sense by the modified Stokes' formula. The new gravimetric geoid model is compared with Global Positioning System (GPS)/levelling at the control points, resulting in the Root Mean Square Error (RMS) differences of ±6.4 cm and 1.7 ppm in the absolute and relative senses, respectively. This regional geoid model appears to be more accurate than the Earth Gravitational Model 2008, which is the best global model over the target area, with the RMS differences of ±8.6 cm and 1.8 ppm in the absolute and relative senses, respectively. These results show that the accuracy of a regional gravimetric model can be augmented by the combination of a global geopotential model and local terrestrial data in mountainous areas even though the quality and resolution of the primary terrestrial data are not satisfactory to the geoid modelling procedure. [ABSTRACT FROM AUTHOR]

Recently it was proved that the classical formula for computing the geoid to quasigeoid separation (GQS) by the Bouguer gravity anomaly needs a topographic correction. Here we generalize the modelling of the GQS not only to Bouguer types of anomalies, but also to arbitrary reductions of topographic gravity. Of particular interest for practical applications should be isostatic and Helmert types of reductions, which provide smaller and smoother components, more suitable for interpolation and calculation, than the Bouguer reduction. [ABSTRACT FROM AUTHOR]

Abstract: We compare 14 glacial isostatic adjustment (GIA) models from different authors to assess how well the GIA effect could be removed from space geodetic data, such as those of the Gravity Recovery and Climate Experiment (GRACE) satellites, to study climate related and other mass changes within the Earth system. Direct comparisons of model outputs confirm unacceptably large discrepancies among models. Here we use two approximate relations within any GIA model without rotational feedback discovered by Wahr et al. (1995), i.e., an uplift–geoid relation and an uplift–gravity relation, to test the models for internal consistency. We find that all models without rotational feedback fit the relations reasonably well with only one exception, which still appears to fit the relations, but not as well. However, some models with rotational feedback fit the relations reasonably well, while some do not. As a result, the discrepancies arising from differences in formulations or computational methods, especially rotational feedback formulations, appear to dominate over those arising from differences in ice history and Earth rheology. We conclude that the accuracy and consistency of GIA models, especially agreement of results obtained using different formulations and computational methods, need to be substantially improved to full exploit contemporary space geodetic data, such as GRACE data, to enhance the constraints on ice-sheet mass balance and the mass component of global sea-level change. [Copyright &y& Elsevier]

SUMMARY The geoid is the true physical figure of the Earth, a particular equipotential surface of the Earth's gravity field that accounts for the effect of all subsurface density variations. Its shape approximates best (in the sense of least squares) the mean level of oceans, but the geoid is more difficult to determine over continents. Satellite missions carry out distance measurements and derive the gravity field to provide geoid maps over the entire globe. However, they require calibration and extensive computations including integration, which is a non-unique operation. Here we propose a direct method and a new tool that directly measures geopotential differences on continents using atomic clocks. General relativity theory predicts constant clock rate at sea level, and faster (slower) clock rate above (below) sea level. The technology of atomic clocks is on the doorstep of reaching an accuracy level in clock rate (frequency ratio inaccuracy of 10−18), which is equivalent to 1 cm in determining equipotential surface (including geoid) height. We discuss the value and future applicability of such measurements including direct geoid mapping on continents, and joint gravity-geopotential surveying to invert for subsurface density anomalies. Our synthetic calculations show that the geoid perturbation caused by a 1.5 km radius sphere with 20 per cent density anomaly buried at 2 km depth in the Earth's crust is already detectable by atomic clocks of achievable accuracy. Therefore atomic clock geopotential surveys, used together with relative gravity data to benefit from their different depth sensitivities, can become a useful tool in mapping density anomalies within the Earth. [ABSTRACT FROM AUTHOR]

The effect of the Earth's compression on the physical libration of the Moon is studied using a new vector method. The moment of gravitational forces exerted on the Moon by the oblate Earth is derived considering second order harmonics. The terms in the expression for this moment are arranged according to their order of magnitude. The contribution due to a spherically symmetric Earth proves to be greater by a factor of 1.34 × 10 than a typical term allowing for the oblateness. A linearized Euler system of equations to describe the Moon's rotation with allowance for external gravitational forces is given. A full solution of the differential equation describing the Moon's libration in longitude is derived. This solution includes both arbitrary and forced oscillation harmonics that we studied earlier (perturbations due to a spherically symmetric Earth and the Sun) and new harmonics due to the Earth's compression. We posed and solved the problem of spinorbital motion considering the orientation of the Earth's rotation axis with regard to the axes of inertia of the Moon when it is at a random point in its orbit. The rotation axes of the Earth and the Moon are shown to become coplanar with each other when the orbiting Moon has an ecliptic longitude of L = 90° or L = 270°. The famous Cassini's laws describing the motion of the Moon are supplemented by the rule for coplanarity when proper rotations in the Earth-Moon system are taken into account. When we consider the effect of the Earth's compression on the Moon's libration in longitude, a harmonic with an amplitude of 0.03″ and period of T = 9.300 Julian years appears. This amplitude exceeds the most noticeable harmonic due to the Sun by a factor of nearly 2.7. The effect of the Earth's compression on the variation in spin angular velocity of the Moon proves to be negligible. [ABSTRACT FROM AUTHOR]

Abstract: A collection of numerical simulations of 2D axi-symmetric thermal convection is presented here. The aim is to investigate the shape of geoid anomalies and dynamic topography above a plume. The simulation is based on the Boussinesq approximation and infinite Prandtl number and is carried out in the spherical shell with strongly temperature- and depth-dependent Arrhenius-type viscosity. According to the Arrhenius law, plume models with purely depth-dependent rheology are unphysical and should be taken with care. The strongly coupled temperature- and depth-dependent viscosity enables us to better understand the plume''s behavior inside the Earth. The topography and geoid anomalies produced from plumes are sensitive to rheology of the mantle and rheology of the plume; both have effects on shape and amplitude of the geoid anomalies. We determined different categories of the geoid which are related to various rheology. Depth-dependent viscosity models show a geoid with a negative sign above the plume, and temperature-dependent viscosity models depict a bell-shaped geoid. We identified different behaviors in the combined model with temperature- and pressure-dependent viscosity. [Copyright &y& Elsevier]

Abstract: Joint inversion of the observed geoid and seismic velocities has been commonly used to constrain mantle properties and convection flow. However, most of the employed tomography models have been obtained without considering the effect of the mantle transition zone (TZ). We use the new-generation tomography model of , in which seismic velocity perturbations are estimated together with variations of the main TZ boundaries. In the inversion of this model with the observed geoid the velocity-to-density scaling factor and density jump at these discontinuities are determined simultaneously. By this, the mantle flow across TZ is defined self-consistently: the undulations of the TZ boundaries suppress or accelerate mantle currents depending on the determined density contrast. For the 410-km discontinuity we obtain the scaling factor and density jump, which are close to mineral physics predictions. Therefore, we conclude that these effects are decoupled in the tomography model. In contrast, the calculated density jump at the 660 discontinuity is approximately 4 times less than the PREM value. We suggest that this is the effect of multiple phase transitions within a depth range of 640–720km. Under normal thermal conditions, the post-spinel phase transformation is relatively sharp (∼5km) and clearly visible in seismic models. On the other hand, the transition of majorite garnet to perovskite is much broader (up to ∼50km) and, therefore hardly detectable. Due to the different sign of the Clapeyron slope, the total gravity effect is drastically decreased. To fit the obtained results, the required value of the Clapeyron slope for the majorite garnet to perovskite transformation should be equal to about +1.7MPa/K. In the cold zones the same effect might be produced by the transition from ilmenite to perovskite at 610–640km depth, which is in agreement with multiple reflections revealed in regional seismic studies near the bottom of TZ (). The estimated amplitude of the mantle flow across TZ is about ±20mm/year, which corresponds to the whole-mantle convection scheme. The calculated geoid better fits to the observed one than the obtained without considering the TZ effect. [Copyright &y& Elsevier]

SUMMARY The aim of this work is to propose a first-order estimate of the crustal and lithospheric mantle geometry of the Arabia-Eurasia collision zone and to separate the measured Bouguer anomaly into its regional and local components. The crustal and lithospheric mantle structure is calculated from the geoid height and elevation data combined with thermal analysis. Our results show that Moho depth varies from ∼42 km at the Mesopotamian-Persian Gulf foreland basin to ∼60 km below the High Zagros. The lithosphere is thicker beneath the foreland basin (∼200 km) and thinner underneath the High Zagros and Central Iran (∼140 km). Most of this lithospheric mantle thinning is accommodated under the Zagros mountain belt coinciding with the suture between two different mantle domains on the Sanandaj-Sirjan Zone. The regional gravity field is obtained by calculating the gravimetric response of the 3-D crustal and lithospheric mantle structure obtained by combining elevation and geoid data. The calculated regional Bouguer anomaly differs noticeably from those obtained by filtering or just isostatic methods. The residual gravity anomaly, obtained by subtraction of the regional components to the measured field, is analyzed in terms of the dominating upper crustal structures. Deep basins and areas with salt deposits are characterized by negative values (∼−20 mGal), whereas the positive values are related to igneous and ophiolite complexes and shallow basement depths (∼20 mGal). [ABSTRACT FROM AUTHOR]

Abstract: This paper attempts to review the descriptions on the genetic series of neotectonic forms in Eurasia. Morphotectonically, the Eurasian continental block exhibits a radial-concentric pattern consisting of four kinds of tectonic units: platforms, rejuvenated and youthful mobile belts, and the continent-ocean transition zones. Vast areas of young and ancient platforms, such as Siberia, have experienced slow-rate Late-Cenozoic uplift and little interior deformation. The youthful orogenic belts are clustered into the giant Alpine-Himalayan megabelt. The rejuvenated mountain belts are characterized by a variety of structural-morphological types of orogens, such as domelike uplifts, block uplifts and intermountain basins. The continent-ocean transition zones in Eastern Asia, including marginal rifts and extensional basins, are resulted from interaction between the continental block and Pacific Ocean and Philippine Sea since the Late Cenozoic. One of the conspicuous features of Eurasia is that most areas lie in the largest geoid depression of the Earth, and the NS trending Uralian-Oman lineament expresses a break on the geoid slope, implying a relationship to deep structure, including density inhomogeneities, downward to the core-mantle interface. Besides, the Eurasian continent fully demonstrates morphotectonic and recent geodynamic features of the Northern Hemisphere of the Earth, just in contrast to that of the Southern Hemisphere. It is best to view the surface morphotectonics and deep structure of the Earth as a geodynamic ensemble which has spawned the large-scale geomorphic features on the surface. [Copyright &y& Elsevier]

Abstract: Nowadays cartographic products are usually obtained from data sources which provide large amount of data. LiDAR acquisition system is a good example of the great quantity of data obtained, such as points with spatial coordinates in a determined reference system. The height of these points is usually related to a global ellipsoid (e.g. WGS84), but the local vertical reference system, and so the corresponding orthometric heights, are usually measured from a local geoid which is adjusted for a country or region. Orthometric height determination can be performed for each point by knowing the undulation value which relates the ellipsoid to the geoid for each position. However, this operation may not be necessary for all points if we take into account the LiDAR specifications. Thus we can use a simplification which minimizes the processing time for this calculation. In this paper we present the results obtained by applying several simplifications to drastically shorten the number of point-to-point computations to obtain the orthometric height from the raw LiDAR point cloud data. [Copyright &y& Elsevier]

Precise information of geoid undulations is essential for obtaining the orthometric heights from Global Positioning System (GPS) measurements over any region; apart from providing the information of subsurface density distribution. This paper presents computation of geoid undulations over a part of southern Indian region from terrestrial gravity and elevation data using remove-restore technique that involves spherical Fast Fourier Transform (FFT) to compute 'Stokes' coefficients. Computed geoid undulations are compared with geoid obtained from global geopotential models such as EGM2008 and EIGEN-GRACE02S and measured GPS-levelling records at 67 locations. Statistical analysis of comparison suggests that the computed gravimetric geoid model has a good match with the geoid determined from GPS-levelling with rms of 0.1 m whereas EGM2008 has 0.46 m. The differences of GPS-levelling with EGM2008 at majority of stations fall in the range of ±0.5 m, which indicates that EGM2008 may be used for orthometric height determination with an accuracy of <0.5 m in the south Indian region and offers a reasonably good transformation platform from ellipsoid to local datum. However, local determination of geoid is necessary for better accuracy of orthometric height from GPS. The gravimetric geoid calculated from the available gravity data shows considerable improvement to the global model and can be used to achieve orthometric height with an accuracy of 0.1 m. [ABSTRACT FROM AUTHOR]

Abstract: In this work we have modeled the thermal structure of the lithosphere of the Spanish Central System and the Tajo Basin, and their implications for lithospheric strength. For this, we have used refined heat-producing elements (HPE) values to obtain new estimates of heat production rates in the Spanish Central System and Tajo Basin areas, which have been used joined to the relation between topography and thermal structure of the lithosphere to calculate the best-fit surface heat flows in the study area. Moreover, we have implemented a temperature-dependent thermal conductivity (appropriate for olivine) for the lithospheric mantle to improve the calculations of temperature profiles in the mantle. The geotherms so obtained, together with the implementation of a new rheological law for the upper lithospheric mantle, have been used to calculate refined estimations of the strength and effective elastic thickness of the lithosphere. We have obtained surface heat flow values of 84mWm−2 and ∼82mWm−2 for the Spanish Central System and the Tajo Basin, respectively. The thermal state of the lithosphere affects mantle temperatures, and hence may be playing an important role in the uplift and maintenance of the Spanish Central System. [Copyright &y& Elsevier]

As the number of Earth geopotential models (EGM) grows with the increasing number of data collected by dedicated satellite gravity missions, CHAMP, GRACE and GOCE, measuring the differences among the models and monitoring the improvements in gravity field recovery are required. This study assesses the performance of recent EGMs derived from CHAMP, GRACE, and other data in comparison to the earlier two models in Turkish territory. Also the improvement capacities of these EGMs using local terrestrial data are inspected with two different approaches. In the first approach, the spherical harmonic coefficients of EGMs are modified depending on the local gravity data. In the second part, the original EGMs with their maximum harmonic expansions are employed in Remove Compute Restore algorithm for high resolution local geoid modelling. The assessment results with the local terrestrial data exhibited large disagreements among the models in Turkey. The outputs from regional improvements of EGMs using the gravity observations clarified the important role of the ground truth data contribution in geopotential models. The validations of the computed high resolution geoids rely on the EGMs at the GNSS/levelling networks, having 451 and 309 benchmarks, provided an absolute accuracy by means of standard deviations of the geoid height differences around 20 cm. These results from the final stage of the case study provide a comparison among the EGMs by means of their fit to the local gravity field. [ABSTRACT FROM AUTHOR]

ABSTRACT From the late 1990s, many studies on local geoid construction have been made in South Korea. However, the precision of the previous geoid has remained about 15 cm due to distribution and quality problems of gravity and GPS/levelling data. Since 2007, new land gravity data and GPS/levelling data have been obtained through many projects such as the Korean Land Spatilaization, Unified Control Point and Gravity survey on the Benchmark. The newly obtained data are regularly distributed to a certain degree and show much better improvement in their quality. In addition, an airborne gravity survey was conducted in 2008 to cover the Korean peninsula (South Korea only). Therefore, it is expected that the precision of the geoid could be improved. In this study, the new South Korean gravimetric geoid and hybrid geoid are presented based on land, airborne, ship-borne, altimeter gravity data, geopotential model and topographic data. As for the methodology, the general remove-restore approach was applied with the best chosen parameters in order to produce a precise local geoid. The global geopotential model EGM08 was used to remove the low-frequency components using degree and order up to 360 and the short wavelength part of the gravity signal was dealt with by using the Shuttle Radar Topography Mission data. The parameters determined empirically in this study include for Stokes' integral 0.5° and for Wong-Gore kernel 110-120°, respectively and 10 km for both the Bjerhammar sphere depth and attenuation factor. The final gravimetric geoid in South Korea ranges from 20-31 m with a precision of 5.45 cm overall compared to 1096 GPS/levelling data. In addition, the South Korean hybrid geoid produces 3.46 cm and 3.92 cm for degrees of fitness and precision, respectively and a better statistic of 2.37 cm for plain and urban areas was achieved. The gravimetric and hybrid geoids are expected to improve further when the refined land gravity data are included in the near future. [ABSTRACT FROM AUTHOR]

While it is obvious that large-scale gravity studies should account for the sphericity of the Earth, each case should be examined. If a geometry model is very large for the 3D-gravity calculation, it cannot be correctly defined in Cartesian coordinates. Because of the Earth's curvature it is necessary to use spherical coordinates, the importance of which is shown in this paper. The calculation of the gravity for a cylinder reveals, 1 m above the center of the cylinder, a relative difference of 13% between the models with Cartesian and spherical coordinates. [ABSTRACT FROM AUTHOR]

Abstract: Free air anomaly map of Himalaya, Tibet and adjoining regions derived from global models including satellite observations reflect most of the tectonic elements of this region. Fold and thrust belts and suture zones are characterized by small wave length free air high anomalies representing shallow high density mafic/ultramafic rocks including ophiolitic mélange. On the other hand, medium to large wavelength negative gravity anomalies which are related to crustal thickening due to isostatic compensation are better visualized in the Bouguer anomaly map. This emphasizes the importance of both free air and Bouguer anomaly maps of complex orogenic belts. Spectral analysis of the Bouguer and the geoid anomaly maps and their low pass filtered maps and modeling along a N–S profile (90°E) constrained from various seismic studies suggest low density rocks (3250kg/m3) in the lithospheric mantle between depths of ∼130–320km under Tibet. The low pass filtered geoid anomaly shows a prominent geoid low in the same depth range oriented NE–SW, in the direction of motion of the Indian plate that is near perpendicular to the prominent tectonics features. It coincides with the NE–SW oriented seismic anisotropy in the central part of the Himalayan collision zone. Low density rocks in the lithospheric mantle suggest under thrusted Indian and Asian lithospheres in this section that constitutes the thick lithosphere under Tibet. The Moho in general lies at a depth of 50–75km under Tibet with deepest being under South Tibet. The Low density rocks in the upper mantle make this region buoyant that explains large scale uplifts. The prominent negative free air, Bouguer and geoid anomalies are observed over the Hindu Kush – Pamir Seismic Zone between the Kohistan arc towards the south and Pamir towards the north suggesting predominance of low density rocks approximately at a depth of ∼120km in the lithospheric mantle. Gravity anomalies and its modeling along a profile (73°E) constrained from the hypocenters of deep focus earthquakes in this region and results from receiver function analysis in adjoining regions suggest following characteristics of the subduction model in this section: (i) the subducting plates from two sides, viz. the Indian (Kohistan arc) and the Asian plates show relatively high angle subductions compared to the east of it. (ii) The subducting plates are affected by the strike slip Chamman – Panjshir faults towards the west and Karakoram strike slip fault towards the east. (iii) The subducting plates from the two sides interact with each other in the lithospheric mantle. (iv) The subducted rocks in this section are generally comprised of high density mafic/ultramafic rocks of the Kohistan arc and Tien Shan. Combination of these factors would induce fast subduction and slab break off that usually facilitate deep focus earthquakes, as observed in case of Mariana type subductions. Similar is the case along the Burmese arc that is the only other section characterized by deep focus earthquakes in the long Himalayan collision zone (∼5000km). Modeling of the Bouguer anomaly along 23.5°N in this case also shows relatively high angle subduction of the Indian plate which is affected by the Sagaing strike slip fault towards the east that would facilitate slab break off and generation of deep focus earthquakes as described above. Gravity modeling across Tibet, Hindu Kush and Burmese arc suggest the presence of high density rocks (∼3100kg/m3) in the lower crust and low density rocks (∼3250kg/m3) in the upper mantle that may be attributed to partial eclogitization and serpentinization of rocks, respectively in these sections that are typical of several orogenic belts. Such conditions are expected to facilitate delamination and detachment. [Copyright &y& Elsevier]

Important though indirect information about the internal structure of Venus is provided by its topography and geoid. In the last decades this information has been used to constrain the Venus mantle viscosity structure and its dynamic regime. Recently, the geodynamic inversion of the Venus' geoid and topography resulted in a group of best fitting viscosity profiles. We use these viscosity models here as an input to our mantle convection code. We carry out simulations of the Venus' mantle evolution in a 3D spherical shell with depth dependent viscosity and check whether the character of the dynamic topography and the geoid represented by their power spectra fits the observed quantities. We compare the results with several other models obtained for different viscosity stratifications (constant, constant with highly viscous lithosphere, linear increase of viscosity). Further, we estimate the effect of other factors such as internal heating and varying Rayleigh number. We use a 2D spherical axisymmetric convection code to study the effect of lateral viscosity variations. In these 2D models we monitor the topography and the geoid developing above the axisymmetric plume and compare them with the observed elevations of Venus' geoid and topography in several Regia. Though none of the models fits observed data perfectly, we can generally conclude, that the best fit between the observed and predicted quantities is reached for viscosity profiles with 200 km thick lithosphere followed by a gradual increase of viscosity with depth and with the upper mantle viscosity of 2 × 10 Pa s. For all viscosity profiles the predicted geoid and topography spectra match the observed ones only up to the degree 40, thus indicating other than dynamic origin of these quantities for higher degrees. [ABSTRACT FROM AUTHOR]

SUMMARY In the absence of seismological measurements, observations of the topography and gravity fields of solid planets are the primary constraints on their internal structure. To compute the synthetic geoid and topography induced by the dynamics of planetary interiors, we introduce a 3-D numerical tool describing mantle convection beneath an elastic lithosphere. Although the energy conservation is treated in the whole spherical domain, the deformation aspect is solved using a hybrid technique (finite volume method for the viscous flow, spectral method for elastic deformation). The mechanical coupling is achieved via the imposition of the traction at the surface of the viscous flow as a basal boundary condition for the elastic deformation. We present both response functions and full thermal convection cases computed with our new method for planetary bodies of varying dimensions: the filtering effect of the lithosphere on the dynamic topography and geoid is specific for each planetary body, justifying the importance of such a tool. Furthermore, since our approach specifically focuses on the mechanical coupling at the base of the lithosphere, it will permit future, more elaborate, rheological treatments. It also enables to discriminate between the radial and tangential components of the viscous traction. The latter is found to have a significant influence on the elastic deformation. The effect on geoid is prominent. More specifically, while a thin elastic lithosphere is usually considered to play little role on the dynamic topography and geoid of Venus, a ∼35 per cent reduction is obtained for geoid height in the numerical example we propose. On a planet with thicker elastic lithosphere such as Mars, the consequence of this filtering effect is to rule out the possibility of a dynamical support for the Tharsis Rise, even for the lowest admissible values of elastic thickness in this region. [ABSTRACT FROM AUTHOR]

Abstract: Long wavelength gravity anomalies derived from satellite data have limitations of spatial resolution and accuracy. To complement these weak points, combined datasets merged with shipborne/land gravity data and satellite data are generally compiled using global spherical harmonic, rectangular harmonic, or spherical cap harmonic analysis etc. However, each method also has a different resolution and accuracy. In this study, gravity anomalies and geoid undulations of South Korea and its vicinity are calculated using the spherical cap harmonic method, and the results are compared with those of GGM02C and EGM2008. Absolute and relative geoid height differences between GPS/leveling data and the results of various other methods show that the method used in this study has the lowest RMS error (0.271m vs 0.344–0.416m) and standard deviation (0.236m vs 0.309–0.362m). This implies that the spherical cap harmonic method has better resolution and accuracy than the other methods. The short wavelength gravity anomalies derived from the spherical cap harmonic coefficients are used to estimate the sediment thickness of the Ulleung Basin, which is poorly known. The sediment thickness of the Ulleung Basin is about 5km at the center of the basin, and about 12km at the southern margin. [Copyright &y& Elsevier]

Abstract: New studies on the influence of inter-satellite range on the accuracy of the Earth''s gravitational field recovery were carried out based on the Inter-satellite Range Interpolation Method (IRIM). Firstly, the IRIM observation equation by introducing the precise inter-satellite range into the Line-Of-Sight (LOS) component of the relative orbital position vector was established for the first time using the original satellite observations including the orbital position of the spaceborne Global Positioning System (GPS) receiver, the inter-satellite range of the K-Band Ranging (KBR) system and the non-conservative force of the accelerometer (ACC). Secondly, the nine-point IRIM formula is shown by a comparison of multipoint IRIM formulas to be preferable for effectively improving the accuracy of the Earth''s gravitational field recovery. Thirdly, the WHIGG-GEGM01S (GRACE Earth Gravity Model developed by Wuhan Institute of Geodesy and Geophysics) global gravity field model, complete up to degree and order 120, is produced using the GRACE Level-1B data products, acquired during 2008-01-01 to 2008-12-31 and released by the American Jet Propulsion Laboratory (JPL). Cumulative geoid height and gravity anomaly errors are 1.098×10−1 m and 1.741×10−6 m/s2 at degree 120, respectively. Finally, the availability of the WHIGG-GEGM01S model is validated by the GPS/Levelling observations in the U.S., Europe and Australia. [Copyright &y& Elsevier]

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Abstract: Gravimetric geoid computation is often based on modified Stokes''s integration, where Stokes''s integral is evaluated with some stochastic or deterministic kernel modification. Accurate numerical evaluation of Stokes''s integral requires the modified kernel to be integrated across the area of each discretised grid cell (mean kernel). Evaluating the modified kernel at the center of the cell (point kernel) is an approximation, which may result in larger numerical integration errors near the computation point, where the modified kernel exhibits a strongly nonlinear behavior. The present study deals with the computation of whole-of-the-cell mean values of modified kernels, exemplified here with the kernel modification [Featherstone, W.E., Evans, J.D., Olliver, J.G., 1998. A Meissl-modified Vaníček and Kleusberg kernel to reduce the truncation error in gravimetric geoid computations. Journal of Geodesy 72(3), 154–160]. We investigate two approaches (analytical and numerical integration), which are capable of providing accurate mean kernels. The analytical integration approach is based on kernel weighting factors which are used for the conversion of point to mean kernels. For the efficient numerical integration, Gauss–Legendre quadrature is applied. The comparison of mean kernels from both approaches shows a satisfactory mutual agreement at the level of 10−4 and better, which is considered to be sufficient for practical geoid computation requirements. Closed-loop tests based on the EGM2008 geopotential model demonstrate that using mean instead of point kernels reduces numerical integration errors by ∼65%. The use of mean kernels is recommended in remove–compute–restore geoid determination with the kernel or any other kernel modification under the condition that the kernel changes rapidly across the cells in the neighborhood of the computation point. [Copyright &y& Elsevier]

Abstract: The geoid low over French Polynesia has been previously interpreted as the signature of an upper mantle upwelling associated with a low-viscosity zone located immediately below the lithosphere. We propose here an alternative explanation using new high-quality satellite gravity data and fluid mechanics constraints. We thus discuss the origin of the high concentration of hotspots in the Central Pacific, which is still debated. Satellite gravity data from the GRACE mission analyzed with wavelets allow us to better characterize the geoid low on French Polynesia and the large-scale positive geoid anomaly 600km east of the Line Islands chain. We show that the geoid anomalies are consistent with thermochemical oscillating domes and we bring constraints on their density contrast and their upper limit depth under this hypothesis. The Central Pacific mantle would contain two thermochemical instabilities at different stages of their development: a rising dome (lighter) extending approximately from the CMB up to the transition zone beneath the South Pacific Superswell, toped by secondary plumes that generate short-lived hot spot chains, and a sinking dome (denser) in the lower mantle beneath the area located 600km east of the Line Islands chain. Plate reconstructions further show that the latter could also have generated the Southern Line Islands 35M.y. ago and Shatsky Rise 140M.y. ago when it was in its ascending phase, while the South Pacific dome probably created Darwin Rise 100M.y. ago in a same type of event. [Copyright &y& Elsevier]

Abstract: Sudan is characterized by vast area with flat terrains in most of the country’s regions and therefore the existence of a high-resolution geoid model is considered very important especially with the widespread of the GPS technology in the country. A few studies were previously conducted to compute a geoid model for Sudan, the current study is the second of its kind to compute the Sudanese geoid model by means of gravimetric method. In this study, a new gravimetric geoid model (KTH-SDG08) is computed for Sudan, we apply the method developed at the Royal Institute of Technology (KTH) Stockholm-Sweden. The method utilizes the least-squares modification (LSM) of Stokes formula providing three stochastic solutions (biased, unbiased and optimum). The three solutions are quite similar however in this study we select the optimum solution which provides the best agreement with GPS-levelling data. The modified Stokes formula combines the regional terrestrial gravity data together with the long-wavelength gravity information from a global gravitational model (GGM). We use two sets of regional gravity data: the first set is provided by the GETECH, the points of this set cover discretely some parts of Sudan while the rest of the country’s area are still not covered, the second set was provided by BGI contains a few points scattered over the neighbouring countries. Both datasets (GETECH and BGI) are unified together into one dataset and evaluated by Cross validation technique. Due to the lack of gravity observations we construct our final grid for geoid computation with spatial resolution of 5×5 arc-min. The long-wavelength contribution is donated by two geopotential models, EIGEN-GRACE02S satellite-only model is employed in the modified Stokes formula whereas the EIGEN-GL04C combined model is used to enrich the local gravity coverage over the areas with missing data. The Digital Elevation Model (DEM), SRTM generated byNASAand theNational Imagery and Mapping Agency (NIMA) is used to compute topography effects on the geoid. Four additive corrections are computed over the entire target area and applied to the approximate geoid heights obtaining the final geoid solution. The new Sudanese gravimetric geoid model KTH-SDG08 is computed on a 5×5 arc-min geographical grid over the computation area bounded by the parallels of 4 and 23arc-deg northern latitude, and the meridians of 22 and 38arc-deg of eastern longitude. The gravimetric geoid is validated using GPS-levelling information at 19 points distributed over the whole country. The results show that the standard deviation (STD) of differences between the gravimetric and geometric geoid heights at 19 GPS-levelling points is about 0.3m. [Copyright &y& Elsevier]

Abstract: Large earthquakes do not only heavily deform the crust in the vicinity of the fault, they also change the gravity field of the area affected by the earthquake due to mass redistribution in the upper layers of the Earth. Besides that, for sub-oceanic earthquakes deformation of the ocean floor causes relative sea level changes and mass redistribution of water that have again a significant effect on the gravity field. To model these deformations, sea level changes and gravity field perturbations self-consistently we use an adapted version of the sea level equation (SLE) that has been used for glacial isostatic adjustment studies. The sea level equation, next to our normal mode model for seismic solid earth modeling, allows us to compute a gravitationally self-consistent solution for the co-seismic relative sea level, surface deformation and geoid height changes. We apply our geographically detailed models to the case of the 2004 December 26 Sumatra–Andaman earthquake. Recent studies that have modeled the ocean mass effect on co-seismic gravity change for this specific earthquake show model results that indicate a broad negative change in geoid height around the fault due to ocean water redistribution (de Linage et al., 2009; Melini et al., 2010). Our model results for the ocean contribution to geoid height differ from these studies in the sense that we find a pattern similar to the elongated dipole pattern of the solid earth model outputs for gravity and vertical deformation, together with a relatively small broad negative geoid height change. We explain the relation between outcomes for geoid height, relative sea level and vertical deformation of the ocean floor and we confront our model results with a least squares estimation of the co-seismic discontinuity in GRACE-derived gravity field time series. We show that taking into account the contribution of ocean water redistribution to the co-seismic geoid height change next to a compressible solid earth model is essential to explain the predominant negative co-seismic geoid anomalies from the GRACE gravity field solutions. Besides, we introduce a detailed approach to modeling an earthquake in a normal mode model that better approximates realistic continuous slip on the fault plane than models that do not distribute slip with depth. To demonstrate the importance of the slip distribution we show the differences in outcomes for modeled geoid height and vertical deformation. [Copyright &y& Elsevier]