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An algorithm and a program for transformation of gravity anomalies for large territories are presented. They use a spherical shape of the Earth and the geodetic coordinates of measuring points. The calculations employ the "quasi-ellipsoidal" model of V.V. Kavraisky, which allows the transition from the geodetic to the spherical coordinate system with increased accuracy. The algorithm is based on a sourcewise approximation of the field values located at the nodes of a regular grid with the latitude-dependent depths of the equivalent sources. To determine the source masses, the system of linear algebraic equations is solved by the steepest descent gradient method with an accelerated calculation of the step. The results of transformation of the gravitational field in the Bouguer reduction for the Kuril Island arc, the adjacent water and land areas located within 40°–54° N, 142°–162° E and having a total area of about 2.4 mln km2, are presented. A slight difference between the results of recalculating the gravity anomalies into the upper half-space using the "spherical" and "quasi-ellipsoidal" models of the Earth is experimentally established. [ABSTRACT FROM AUTHOR]

Are the National Geodetic Survey's surface gravity data sufficient for supporting the computation of a 1 cm-accurate geoid? This paper attempts to answer this question by deriving a few measures of accuracy for this data and estimating their effects on the US geoid. We use a data set which comprises $${\sim }1.4$$ million gravity observations collected in 1,489 surveys. Comparisons to GRACE-derived gravity and geoid are made to estimate the long-wavelength errors. Crossover analysis and $$K$$-nearest neighbor predictions are used for estimating local gravity biases and high-frequency gravity errors, and the corresponding geoid biases and high-frequency geoid errors are evaluated. Results indicate that 244 of all 1,489 surface gravity surveys have significant biases $${>}2$$ mGal, with geoid implications that reach 20 cm. Some of the biased surveys are large enough in horizontal extent to be reliably corrected by satellite-derived gravity models, but many others are not. In addition, the results suggest that the data are contaminated by high-frequency errors with an RMS of $${\sim }2.2$$ mGal. This causes high-frequency geoid errors of a few centimeters in and to the west of the Rocky Mountains and in the Appalachians and a few millimeters or less everywhere else. Finally, long-wavelength ( $${>}3^{\circ }$$) surface gravity errors on the sub-mGal level but with large horizontal extent are found. All of the south and southeast of the USA is biased by +0.3 to +0.8 mGal and the Rocky Mountains by $$-0.1$$ to $$-0.3$$ mGal. These small but extensive gravity errors lead to long-wavelength geoid errors that reach 60 cm in the interior of the USA. [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]

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]

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]

The Global Geopotential Models (GGMs) are very significant because of their usefulness in determination of the parameters like geoidal undulations, height anomalies, gravity anomalies, and so on. In this paper, first, we review the calculation of such parameters and then present the GGMCalc software, which is prepared in Fortran 95 under GNU/Linux Operating System. This software is capable of using the files presented by the International Center for Global Earth Models (ICGEM) directly without need to apply any changes on them. The software is completely structural and user friendly and could be used conveniently for academic purposes. [ABSTRACT FROM AUTHOR]

The vertical gradients of gravity anomaly and gravity disturbance can be related to horizontal first derivatives of deflection of the vertical or second derivatives of geoidal undulations. These are simplified relations of which different variations have found application in satellite altimetry with the implicit assumption that the neglected terms-using remove-restore-are sufficiently small. In this paper, the different simplified relations are rigorously connected and the neglected terms are made explicit. The main neglected terms are a curvilinear term that accounts for the difference between second derivatives in a Cartesian system and on a spherical surface, and a small circle term that stems from the difference between second derivatives on a great and small circle. The neglected terms were compared with the dynamic ocean topography (DOT) and the requirements on the GOCE gravity gradients. In addition, the signal root-mean-square (RMS) of the neglected terms and vertical gravity gradient were compared, and the effect of a remove-restore procedure was studied. These analyses show that both neglected terms have the same order of magnitude as the DOT gradient signal and may be above the GOCE requirements, and should be accounted for when combining altimetry derived and GOCE measured gradients. The signal RMS of both neglected terms is in general small when compared with the signal RMS of the vertical gravity gradient, but they may introduce gradient errors above the spherical approximation error. Remove-restore with gravity field models reduces the errors in the vertical gravity gradient, but it appears that errors above the spherical approximation error cannot be avoided at individual locations. When computing the vertical gradient of gravity anomaly from satellite altimeter data using deflections of the vertical, the small circle term is readily available and can be included. The direct computation of the vertical gradient of gravity disturbance from satellite altimeter data is more difficult than the computation of the vertical gradient of gravity anomaly because in the former case the curvilinear term is needed, which is not readily available. [ABSTRACT FROM AUTHOR]

A new gravimetric geoid model, USGG2009 (see Abbreviations), has been developed for the United States and its territories including the Conterminous US (CONUS), Alaska, Hawaii, Guam, the Commonwealth of the Northern Mariana Islands, American Samoa, Puerto Rico and the US Virgin Islands. USGG2009 is based on a 1′ × 1′ gravity grid derived from the NGS surface gravity data and the DNSC08 altimetry-derived anomalies, the SRTM-DTED1 3′′ DEM for its topographic reductions, and the global geopotential model EGM08 as a reference model. USGG2009 geoid heights are compared with control values determined at 18,398 Bench Marks over CONUS, where both the ellipsoidal height above NAD 83 and the Helmert orthometric height above NAVD 88 are known. Correcting for the ellipsoidal datum difference, this permits a comparison of the geoid heights to independent data. The standard deviation of the differences is 6.3 cm in contrast to 8.4 cm for its immediate predecessor- USGG2003. To minimize the effect of long-wavelength errors that are known to exist in NAVD88, these comparisons were made on a state-by-state basis. The standard deviations of the differences range from 3-5 cm in eastern states to about 6-9 cm in the more mountainous western states. If the GPS/Bench Marks-derived geoid heights are corrected by removing a GRACE-derived estimate of the long-wavelength NAVD88 errors before the comparison, the standard deviation of their differences from USGG2009 drops to 4.3 cm nationally and 2-4 cm in eastern states and 4-8 in states with a maximum error of 26.4 cm in California and minimum of −32.1 cm in Washington. USGG2009 is also compared with geoid heights derived from 40 tide-gauges and a physical dynamic ocean topography model in the Gulf of Mexico; the mean of the differences is 3.3 cm and their standard deviation is 5.0 cm. When USGG2009-derived deflections of the vertical are compared with 3,415 observed surface astro-geodetic deflections, the standard deviation of the differences in the N-S and E-W components are 0.87′′ and 0.94′′, respectively. [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]

Gravity anomaly reference fields, required e.g. in remove-compute-restore (RCR) geoid computation, are obtained from global geopotential models (GGM) through harmonic synthesis. Usually, the gravity anomalies are computed as point values or area mean values in spherical approximation, or point values in ellipsoidal approximation. The present study proposes a method for computation of area mean gravity anomalies in ellipsoidal approximation ('ellipsoidal area means') by applying a simple ellipsoidal correction to area means in spherical approximation. Ellipsoidal area means offer better consistency with GGM quasigeoid heights. The method is numerically validated with ellipsoidal area mean gravity derived from very fine grids of gravity point values in ellipsoidal approximation. Signal strengths of (i) the ellipsoidal effect (i.e., difference ellipsoidal vs. spherical approximation), (ii) the area mean effect (i.e., difference area mean vs. point gravity) and (iii) the ellipsoidal area mean effect (i.e., differences between ellipsoidal area means and point gravity in spherical approximation) are investigated in test areas in New Zealand and the Himalaya mountains. The impact of both the area mean and the ellipsoidal effect on quasigeoid heights is in the order of several centimetres. The proposed new gravity data type not only allows more accurate RCR-based geoid computation, but may also be of some value for the GGM validation using terrestrial gravity anomalies that are available as area mean values. [ABSTRACT FROM AUTHOR]

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]

USGeoid09 is the new Australia-wide gravimetric quasigeoid model that has been a posteriori fitted to the Australian Height Datum (AHD) so as to provide a product that is practically useful for the more direct determination of AHD heights from Global Navigation Satellite Systems (GNSS). This approach is necessary because the AHD is predominantly a third-order vertical datum that contains a ~1 m north-south tilt and ~0.5 m regional distortions with respect to the quasigeoid, meaning that GNSS-gravimetric-quasigeoid and AHD heights are inconsistent. Because the AHD remains the official vertical datum in Australia, it is necessary to provide GNSS users with effective means of recovering AHD heights. The gravimetric component of the quasigeoid model was computed using a hybrid of the remove-compute-restore technique with a degree-40 deterministically modified kernel over a one-degree spherical cap, which is superior to the remove-compute-restore technique alone in Australia (with or without a cap). This is because the modified kernel and cap combine to filter long-wavelength errors from the terrestrial gravity anomalies. The zero-tide EGM2008 global gravitational model to degree 2,190 was used as the reference field. Other input data are ~1.4 million land gravity anomalies from Geoscience Australia, 1′ × 1′ DNSC2008GRA altimeter-derived gravity anomalies offshore, the 9′′ × 9′′ GEODATA-DEM9S Australian digital elevation model, and a readjustment of Australian National Levelling Network (ANLN) constrained to the CARS2006 mean dynamic ocean topography model. To determine the numerical integration parameters for the modified kernel, the gravimetric component of AUSGeoid09 was compared with 911 GNSS-observed ellipsoidal heights at benchmarks. The standard deviation of fit to the GNSS-AHD heights is ±222 mm, which dropped to ±134 mm for the readjusted GNSS-ANLN heights showing that careful consideration now needs to be given to the quality of the levelling data used to assess gravimetric quasigeoid models. The publicly released version of AUSGeoid09 also includes a geometric component that models the difference between the gravimetric quasigeoid and the zero surface of the AHD at 6,794 benchmarks. This a posteriori fitting used least-squares collocation (LSC) in cross-validation mode to determine a correlation length of 75 km for the analytical covariance function, whereas the noise was taken from the estimated standard deviation of the GNSS ellipsoidal heights. After this LSC surface fitting, the standard deviation of fit reduced to ±30 mm, one-third of which is attributable to the uncertainty in the GNSS ellipsoidal heights. [ABSTRACT FROM AUTHOR]

In this paper we focused on understanding the isostatic compensation of the Ninetyeast Ridge in the overall context of the Bay of Bengal oceanic lithosphere and the interaction of the ridge system with the north Andaman subduction zone from north of 7-18°N. This region is characterized by the initial interaction of the Kerguelen hotspot with the Bay of Bengal oceanic lithosphere. We used satellite altimeter-derived marine geoid, as it should comprehensively reflect the compensations caused by large spatial wavelength dominated deeper anomaly sources in a hotspot affected lithospheric load like the Ninetyeast Ridge. Our analyses of the geoid-to-topography ratio (GTR), residual geoid, gravity-to-topographic kernel and upward continuation of anomalies show the existence of two different types of source compensation bodies beneath the northern (12-18°N) and southern (7-12°N) Ninetyeast Ridge. In the northern region, the geoid to topography ratio varies from 0.63 ± 0.05 to 0.44 ± 0.03, while in the southern region it ranges from 1.34 ± 0.09 to 1.31 ± 0.07 which resulted in a north to south increase in the apparent compensation depth from ~9 to 28 km. The presence of a shallow Moho, low GTR, broader gravity to topography kernel and the absence of a ridge anomaly from the mantle density dominated upward continued anomaly at z = 300 km indicates that at the northern segment the underplated low density crustal melt is the dominant isostatic compensating body. However, at the southern ridge segment the high GTR, strong gravity-to-topography kernel and the subsistence of the anomaly at long wavelengths, even at z = 300 km represents the existence of large volumes of hotspot related underplated dense material as the source of compensation. The proximity of the dense source compensating body of the southern Ninetyeast Ridge to the Andaman subduction zone affected the regional mantle driven density gradient flow, as observed from the z = 300 km continued gravity anomaly. The existence of a southern Ninetyeast Ridge in such a transpressional regime has caused the formation of a forearc sliver at its eastern flank, which is a major crustal deformational structure developed as a result of ridge-trench collision. [ABSTRACT FROM AUTHOR]

Vening Meinesz’ inverse problem in isostasy deals with solving for the Moho depth from known Bouguer gravity anomalies and “normal” Moho depth ( , known, e.g. from seismic reflection data) using a flat Earth approximation. Moritz generalized the problem to the global case by assuming a spherical approximation of the Earth's surface, and this problem is also treated here. We show that has an exact physical meaning. The problem can be formulated mathematically as that of solving a non-linear Fredholm integral equation of the first kind, and we present an iterative procedure for its solution. Moreover, we prove the uniqueness of the solution. Second, the integral equation is modified to a more suitable form, and an iterative solution is presented also for this. Also, a second-order approximate formula is derived, which determines the Moho depth to first/linear order by an earth gravitational model (EGM), and the remaining short-wavelength/non-linear part, of the order of 2 km, can be determined by iteration. A direct, second-order formula, in principle accurate to the order of 25 m, combines the first-order solution from an EGM with a second-order term, which may include terrestrial Bouguer gravity anomalies around the computation point. [ABSTRACT FROM AUTHOR]

Gravity data in Estonia have been collected by different institutions over many decades. This study assesses the suitability of available gravity data for ensuring a 1 cm geoid modelling accuracy over Estonia and in the Baltic Sea region in general. The main focus of this study is on the determination and elimination of discrepancies between three nationwide datasets. It was detected that one tested historic gravity dataset contained inadmissible systematic biases with respect to other tested datasets. Possible ways of gravity data improvement are discussed. More specifically, new field observation campaigns and aspects of using their outcomes in subsequent regional geoid modelling are suggested. [ABSTRACT FROM AUTHOR]

Abstract: A statistical comparison has been made between gravity field parameters derived from different global geopotential models (GGMs) and observed gravity anomalies, gravimetric geoid and GPS-Leveling data. The motivation behind this study is the selection of best possible global geopotential model that best matches statistically with the local observed data in Pakistan. This will facilitate in decreasing the load on observed data for the development of regional gravimetric geoid in remove-compute-restore technique when used in the Stokes’s integral for computation of the residual part. It is observed that combined geopotential models such as EGM96 and PGM200A, EIGEN-GL04C and EIGEN-CG03C reflect the better match in the total spectral range of gravity and GPS-Leveling data. Results of the precise local geoid model also indicate similar characteristics. A very-high-degree model “EGM2008” (degree/order 2160) exhibits relatively superior statistical fit with observed ground data in Pakistan region. For satellite-only models an increasing trend in the standard deviation can be seen with maximum of about ∼4m in difference between GPS-Leveling and corresponding GGM’s geoid with increase in the order from 50 to 120 and then it decreases afterwards. However, for the EIGEN-CHAMP03SP, standard deviation saturates to a value of 3.4m. This is an indication of contamination in the long to medium wavelength part, i.e. 50–100° for the satellite-only models. Moreover, the models DEOS-CHAMP-01C, GGM02C and then ITG-GRACE03 appear to have better fit for medium to long wavelength and can possibly be recommended for use as long wavelength part with the local observed data. While a hybrid geopotential model selection can be achieved through the selection from either of DEOS-CHAMP-01C, GGM02C, GGM02S, EIGEN-GRACE02S or ITG-GRACE03 in the long wavelength (to degree and order 40) and EGM96, PGM200A, EIGEN-GL04C, EIGEN-CG03C or even EGM2008 in medium to short wavelength, i.e. from degree 41 to maximum degree and order. [Copyright &y& Elsevier]

Abstract  This paper deals with the analysis of gravity anomaly and precise levelling in conjunction with GPS-Levelling data for the computation of a gravimetric geoid and an estimate of the height system bias parameter No for the vertical datum in Pakistan by means of least squares collocation technique. The long term objective is to obtain a regional geoid (or quasi-geoid) modeling using a combination of local data with a high degree and order Earth gravity model (EGM) and to determine a bias (if there is one) with respect to a global mean sea surface. An application of collocation with the optimal covariance parameters has facilitated to achieve gravimetric height anomalies in a global geocentric datum. Residual terrain modeling (RTM) technique has been used in combination with the EGM96 for the reduction and smoothing of the gravity data. A value for the bias parameter No has been estimated with reference to the local GPS-Levelling datum that appears to be 0.705 m with 0.07 m mean square error. The gravimetric height anomalies were compared with height anomalies obtained from GPS-Levelling stations using least square collocation with and without bias adjustment. The bias adjustment minimizes the difference between the gravimetric height anomalies with respect to residual GPS-Levelling data and the standard deviation of the differences drops from 35 cm to 2.6 cm. The results of this study suggest that No adjustment may be a good alternative for the fitting of the final gravimetric geoid as is generally done when using FFT methods. [ABSTRACT FROM AUTHOR]

Abstract  Airborne gravity data is usually attached with satellite positioning of data points, which allow for the direct determination of the gravity disturbance at flight level. Assuming a suitable gridding of such data, Hotine’s modified integral formula can be combined with an Earth Gravity Model for the computation of the disturbing potential (T) at flight level. Based on T and the gravity disturbance data, we directly downward continue T to the geoid, and we present the final solution for the geoid height, including topographic corrections. It can be proved that the Taylor expansion of T converges if the flight level is at least twice the height of the topography, and the terrain potential will not contribute to the topographic correction. Hence, the simple topographic bias of the Bouguer shell yields the only topographic correction. Some numerical results demonstrate the technique used for downward continuation and topographic correction. [ABSTRACT FROM AUTHOR]

The available geoid undulations on the WGS84 ellipsoid at over two hundred GPS stations are interpolated using a least-squares surface fitting technique to determine the geoid of the central highlands in Sri Lanka. However, it is not possible to interpolate these points directly to prepare a detailed map of the geoid surface as the geoid separation varies intense due to the rugged local topography making the interpolation inaccurate. The gravity potential and subsequently the undulation of the local geoid due to the topography have been calculated separately using a topographic model and removed from the available geoid undulations. This model was created using information obtained from 1:50 000 digital topographic maps provided by the Survey department of Sri Lanka. The resulting geoid separations were interpolated and three surface polynomials were employed to determine the geoid using the least-squares surface fitting technique. To avoid possible artefacts in regions without observations, an area including central highlands was selected to determine the geoid. Finally, the geoid undulations due to the topography were added back to the Bouguer co-geoid represented by three mathematical surfaces to create a detailed map of the geoid of Sri Lanka. A local positive geoid surface superimposing a large negative regional surface has been obtained and the local maximum value of the geoid undulation is about --92.05 m in the vicinity of Piduruthalagala peak. [ABSTRACT FROM AUTHOR]

Abstract: Instantaneous flow numerical calculations in a three-dimensional spherical shell are employed to investigate the effects of lateral viscosity variations (LVVs) in the lithosphere and mantle on the long-wavelength geoid anomaly. The density anomaly model employed is a combination of seismic tomography and subducting slab models based on seismicity. The global strain-rate model is used to represent weak (low-viscosity) plate margins in the lithosphere. LVVs in the mantle are represented on the basis of the relation between seismic velocity and temperature (i.e., temperature-dependent rheology). When highly viscous slabs in the upper mantle are considered, the observed positive geoid anomaly over subduction zones can be accounted for only when the viscosity contrast between the reference upper mantle and the lower mantle is approximately or lower, and weak plate margins are imposed on the lithosphere. LVVs in the lower mantle exert a large influence on the geoid pattern. The calculated geoid anomalies over subduction zones exhibit generally positive patterns with quite high amplitudes compared with observations, even when the low activation enthalpy of perovskite in the lower mantle is employed. Inferred weak slabs in the lower mantle may be explained in terms of recent mineral physics results, highlighting the possibility of grain-size reduction due to the postspinel phase transition. [Copyright &y& Elsevier]

Abstract: Gravimetric methods commonly used to constrain crustal parameters such as the mean crustal thickness and density are ambiguous with a noted trade-off between these parameters. However, combining two different methods, the geoid–topography ratio and Bouguer inversion, in regions that are homogeneous with respect to lateral density variations and compensation state can help to constrain a maximum density of the crust. For the Martian Noachian southern highlands a combination of these methods gives us a maximum crustal density of 3020±70 kg m−3, assuming a single-layer crustal structure. We also test various two-layer crustal structures to check how they influence the results. We find a possibility to fit the observed data with a crust having a dense uniformly thick lower crust, but in these models the upper crustal density was also limited to ~3000 kg m−3. The obtained results together with the findings on crustal densities (and composition) of other regions on Mars are consistent with various scenarios of crustal evolution: a temporal increase in the crustal density or a large scale density variation that has been already manifested in the early evolution during the formation of the crustal dichotomy. [Copyright &y& Elsevier]

Abstract: The Earth’s asthenosphere and lower continental crust can regionally have viscosities that are one to several orders of magnitude smaller than typical mantle viscosities. As a consequence, such shallow low-viscosity layers could induce high-harmonic (spherical harmonics 50–200) gravity and geoid anomalies due to remaining isostasy deviations following Late-Pleistocene glacial isostatic adjustment (GIA). Such high-harmonic geoid and gravity signatures would depend also on the detailed ice and meltwater loading distribution and history. ESA’s Gravity field and steady-state Ocean Circulation Explorer (GOCE) satellite mission, planned for launch in Summer 2008, is designed to map the quasi-static geoid with centimeter accuracy and gravity anomalies with milligal accuracy at a resolution of 100km or better. This might offer the possibility of detecting gravity and geoid effects of low-viscosity shallow earth layers and differences of the effects of various Pleistocene ice decay scenarios. For example, our predictions show that for a typical low-viscosity crustal zone GOCE should be able to discern differences between ice-load histories down to length scales of about 150km. One of the major challenges in interpreting such high-harmonic, regional-scale, geoid signatures in GOCE solutions will be to discriminate GIA-signatures from various other solid-earth contributions. It might be of help here that the high-harmonic geoid and gravity signatures form quite characteristic 2D patterns, depending on both ice load and low-viscosity zone model parameters. [Copyright &y& Elsevier]

The salar de Uyuni in the Bolivian Andes is the largest salt flat on Earth, exhibiting less than 1 m of vertical relief over an area of 9000 km2. We report on a kinematic Global Positioning System (GPS) survey of a 45-by-54 km area in the eastern salar, conducted in September 2002 to provide ground truth for the Ice Cloud and land Elevation Satellite (ICESat) mission. GPS post-processing included corrections for long-period GPS noise that significantly improved survey accuracy. We fit corrected GPS trajectories with 2-D Fourier basis functions, from which we created a digital elevation model (DEM) of the surface whose absolute accuracy we estimate to be at least 2.2 cm RMSE. With over two magnitudes better vertical resolution than the Shuttle Radar Topography Mission data, this DEM reveals decimetre-level topography that is completely absent in other topographic data sets. Longer wavelengths in the DEM correlate well with mapped gravity, suggesting a connection between broad-scale salar topography and the geoid similar to that seen over the oceans. [ABSTRACT FROM AUTHOR]

Abstract: The compensation of the Azores Plateau is re-examined by means of a 3D admittance study involving computations of the admittance between the bathymetry and (1) the geoid, (2) the free air gravity and (3) the mantle Bouguer anomalies. The geoid to bathymetry relationship, rather than being analysed in the space domain, is studied in the spectral domain. In this way, the information related to the flexural response of the lithosphere is retained in the geoid to bathymetry signal and can be compared to that of the gravity to bathymetry. We find that the anomalously shallow depths of the Azores Plateau are not due to dynamic forces sustained by mantle upwelling. The Plateau is supported by a thickened crust, which mainly results from large volumes of accreted extrusives and consequent deflection of the underlying elastic plate. Both the free air gravity and the mantle Bouguer admittance point to a flexural isostatic model with a Moho depth of 12 km and an elastic thickness in the range of 3–6 km. However, the analysis of the coherency between bathymetry and the mantle Bouguer anomaly indicates that buoyant material at the base of the crust partially accounts for the uplift of the Plateau. In our best-fitting model, the average elastic thickness is 4 km and the amplitude of the buoyant load at the Moho is 1/3 of that of the surface volcanic load. Buoyancy forces at the Moho may arise from underplated material resulting from subcrustal plutonism. [Copyright &y& Elsevier]

Abstract: In general, sedimentary basins are characterized by negative free-air and Bouguer gravity anomalies. However, the extensional basins of the Ross Sea are paradoxical in that positive gravity anomalies overlay the Victoria Land Basin, Northern Basin, Central Trough and Northern Central Trough while basement highs are associated with negative gravity anomalies. Measured basement densities from DSDP basement cores give values between 2600–2800 kg/m3 while bulk sediment densities range from 1210–2200 kg/m3, indicating a normal density relationship between basement and sediment infill. In contrast, the relatively young and narrow Terror Rift is associated with negative free-air and Bouguer gravity anomalies, but has a different geological history as compared to the larger Ross Sea basins. Process-oriented gravity modeling indicates that magmatic underplating and crustal intrusions are inconsistent with the observed gravity and basement geometry of the Ross Sea basins. The magma volume necessary to account for the distribution and amplitude of the positive gravity anomaly of the Central Basin and be isostatically balanced would need to be comparable to the tholeiitic flood basalt volume of the Columbia River province—it is thus unlikely that the volume of Neogene volcanics of the Ross Sea region is sufficient to explain the observed gravity relationship by modifying the bulk density of the crust. We demonstrate that positive free-air and Bouguer gravity anomalies over extensional basins are the consequence of a relatively low flexural strength of the lithosphere during rifting being contrasted by higher flexural strengths later during sedimentation. As the difference between the rigidity of the lithosphere during sedimentation increases relative to the rigidity of the rifted lithosphere, the gravity over the basin becomes progressively more positive but only for a limited range of wavelengths. The narrow width of the Terror Rift precludes it from having a positive gravity anomaly while the opposite is true for the large Ross Sea basins. For the Ross Sea region, such a loading scenario requires a significant delay between extension and the timing of sediment infilling of the basins, consistent with the late Cretaceous extension of the Ross Sea region and the sedimentary succession being dominated by large-scale late Eocene–Neogene glaciogenic progradational sequences. Sediment source was presumably from the denudation of the Transantarctic Mountains, which commenced in the late Paleogene. The time delay between the late Cretaceous formation of the Transantarctic Mountains, late Paleogene exhumation, and the generation of significant Paleogene paleobathymetry requires either the Ross Sea region to be sub-aerial and sediment starved for most of the Paleogene and/or the Paleogene climate was ineffective in producing clastics until the onset of glaciation in the late Eocene–early Oligocene. [Copyright &y& Elsevier]

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

The geoid gradient over the Darling Fault in Western Australia is extremely high, rising by as much as 38 cm over only 2 km. This poses problems for gravimetric-only geoid models of the area, whose frequency content is limited by the spatial distribution of the gravity data. The gravimetric-only version of AUSGeoid98, for instance, is only able to resolve 46% of the gradient across the fault. Hence, the ability of GPS surveys to obtain accurate orthometric heights is reduced. It is described how further gravity data were collected over the Darling Fault, augmenting the existing gravity observations at key locations so as to obtain a more representative geoid gradient. As many of the gravity observations were collected at stations with a well-known GRS80 ellipsoidal height, the opportunity arose to compute a geoid model via both the Stokes and the Hotine approaches. A scheme was devised to convert free-air anomaly data to gravity disturbances using existing geoid models, followed by a Hotine integration to geoid heights. Interestingly, these results depended very weakly upon the choice of input geoid model. The extra gravity data did indeed improve the fit of the computed geoid to local GPS/Australian Height Datum (AHD) observations by 58% over the gravimetric-only AUSGeoid98. While the conventional Stokesian approach to geoid determination proved to be slightly better than the Hotine method, the latter still improved upon the gravimetric-only AUSGeoid98 solution, supporting the viability of conducting gravity surveys with GPS control for the purposes of geoid determination. [ABSTRACT FROM AUTHOR]

In a modern application of Stokes? formula for geoid determination, regional terrestrial gravity is combined with long-wavelength gravity information supplied by an Earth gravity model. Usually, several corrections must be added to gravity to be consistent with Stokes? formula. In contrast, here all such corrections are applied directly to the approximate geoid height determined from the surface gravity anomalies. In this way, a more efficient workload is obtained. As an example, in applications of the direct and first and second indirect topographic effects significant long-wavelength contributions must be considered, all of which are time consuming to compute. By adding all three effects to produce a combined geoid effect, these long-wavelength features largely cancel. The computational scheme, including two least squares modifications of Stokes? formula, is outlined, and the specific advantages of this technique, compared to traditional gravity reduction prior to Stokes? integration, are summarised in the conclusions and final remarks. [ABSTRACT FROM AUTHOR]

A regular 1.5 'X 3 'grid of free-air gravity anomalies over Estonia is computed. The study comprises the improved gravity data coverage in the Baltic Sea region during the past few years. The estimated precision of the predicted anomalies is 2.4 mGal in Estonia. The gravity anomaly grid and the geopotential model EGM96 are utilized in the computation of the Estonian gravimetric geoid model EST-01 by the least squares modification of Stokes' formula. The model is fitted to a set of 26 high-precision GPS-levelling points, yielding an accuracy of 3.0 cm for the post-fitting residuals, which indicates the suitability of EST-01 for many practical applications. [ABSTRACT FROM AUTHOR]

Investigates the reduction of aliasing in gravity anomalies and geoid heights using digital terrain data in Australia. Effect of irregular sampling geometry on gravimetry; Reduction the amount of aliasing; Determination of gravimetric geoid.

In this paper, methods for the generation of residual and prospecting geoids and free-air gravity anomaly using satellite altimeter data are developed. Maps of residual geoid, gravity anomaly, and their spectral components generated over Indian offshore using ERS-1 altimeter data are presented and interpreted. A number of known megastructures over the study area, for example, Bombay High, Saurastra platform, 90 east ridge, etc., are interpreted successfully from these maps. Some of the anomalous zones (the basins near Mangalore and off Bombay High in the western offshore and Palar basin off Madras coast in the eastern offshore) have been identified as potential sites for occurrences of hydrocarbon-bearing structures, for which detailed ship-borne geophysical surveys have been commissioned by the Oil & Natural Gas Corporation (ONGC), Dehradun, India. [ABSTRACT FROM AUTHOR]