The calculation of deflexions of the vertical from gravity anomalies

1950 ◽  
Vol 204 (1078) ◽  
pp. 374-395 ◽  
Keyword(s):  
Gravity Data ◽  
Gravity Anomalies ◽  
Sources Of Error ◽  
Free Air ◽  
Gravity Measurements ◽  
Standard Deviations ◽  
The Difference ◽  
Different Sources

The theory of the application of gravity measurements to geodetic calculations is discussed, and the errors involved in calculating deflexions of the vertical are estimated. If the gravity data are given as free air anomalies from Jeffreys’s (1948) formula, so thdt the second and third harmonics of gravity are assumed known, the orders of magnitude of the standard deviations of the different sources of error are the following: Single deflexion: neglect of gravity outside 20° 1" Difference of deflexions: neglect of gravity outside 5° 0"·5 Calculation of effects of gravity from 0º·05 to 5° 0"·1 Calculation of effects of gravity within 0º·05 between 0"·1 and 0"·5 Estimates of the deflexions are made for Greenwich, Herstmonceux, Southampton and Bayeux, and the difference between Greenwich and Southampton is compared with the astronomical and geodetic amplitudes.

Gravity data collection with a CG5 gravitymeter for densification of the gravity data around the AUT1 IHRF station

2021 ◽  
Author(s):  
Dimitrios A. Natsiopoulos ◽  
Elisavet G. Mamagiannou ◽  
Eleftherios A. Pitenis ◽  
Georgios S. Vergos ◽  
Ilias N. Tziavos ◽  
...  
Keyword(s):  
Gravity Data ◽  
Gravity Anomalies ◽  
Absolute Gravity ◽  
Dual Frequency ◽  
Height Determination ◽  
Free Air ◽  
Gravity Measurements ◽  
Gravity Database ◽  
Free Air Gravity ◽  
Geological Complexity

<p>Within the GeoGravGOCE project, funded by the Hellenic Foundation for Research Innovation, a main goal has been the densification of the available land gravity database around the eastern part of the city of Thessaloniki, Greece, where the core International Height Reference Frame (IHRF) station AUT1 is located in order to improve regional geoid and potential determination. Hence it was deemed necessary to densify the available gravity data within radiuses of 10 km, 20 km, 50 km and 100 km from the AUT1 core IHRF site. In that frame, and given the geological complexity of the region surrounding Thessaloniki and the significant variations of the terrain, gravity campaigns were appropriately designed and gravity measurements were carried out in order to densify the database and cover as much as possible traverses of varying altitude. The measurements have been carried out with the CG5 gravity meter of the GravLab group and dual-frequency GNSS receivers in RTK mode for orthometric height determination. In this  study we provide details of the gravity campaigns, the measurement principle and the finally derived gravity and free-air gravity anomalies. The mean measurement accuracy achieved was at the ~20 μGal level for the gravity measurements and ~3 cm for the orthometric heights. In all cases the final derived gravity value was based on the absolute point established by the GravLab team at the AUTH seismological station premises with the A10 (#027) absolute gravity meter.</p>

Airborne gravity measurements over mountainous areas by using a LaCoste & Romberg air‐sea gravity meter

Geophysics ◽  
2002 ◽  
Vol 67 (3) ◽  
pp. 807-816 ◽  
Author(s):  
Jérôme Verdun ◽  
Roger Bayer ◽  
Emile E. Klingelé ◽  
Marc Cocard ◽  
Alain Geiger ◽  
...  
Keyword(s):  
Data Reduction ◽  
Classical Method ◽  
Gravity Data ◽  
Airborne Gravity ◽  
Mountainous Area ◽  
Vertical Acceleration ◽  
Mountainous Areas ◽  
Free Air ◽  
Gravity Measurements ◽  
Free Air Anomaly

This paper introduces a new approach to airborne gravity data reduction well‐suited for surveys flown at high altitude with respect to gravity sources (mountainous areas). Classical technique is reviewed and illustrated in taking advantage of airborne gravity measurements performed over the western French Alps by using a LaCoste & Romberg air‐sea gravity meter. The part of nongravitational vertical accelerations correlated with gravity meter measurements are investigated with the help of coherence spectra. Beam velocity has proved to be strikingly correlated with vertical acceleration of the aircraft. This finding is theoretically argued by solving the equation of the gravimetric system (gravity meter and stabilized platform). The transfer function of the system is derived, and a new formulation of airborne gravity data reduction, which takes care of the sensitive response of spring tension to observable gravity field wavelengths, is given. The resulting gravity signal exhibits a residual noise caused by electronic devices and short‐wavelength Eötvös effects. The use of dedicated exponential filters gives us a way to eliminate these high‐frequency effects. Examples of the resulting free‐air anomaly at 5100‐m altitude along one particular profile are given and compared with free‐air anomaly deduced from the classical method for processing airborne gravity data, and with upward‐continued ground gravity data. The well‐known trade‐off between accuracy and resolution is discussed in the context of a mountainous area.

The gravity field over the Ungava Bay region from satellite altimetry and new land-based data: implications for the geology of the area

1999 ◽  
Vol 36 (1) ◽  
pp. 75-89 ◽  
Author(s):  
Hamid Telmat ◽  
Jean-Claude Mareschal ◽  
Clément Gariépy
Keyword(s):  
Satellite Altimetry ◽  
Gravity Data ◽  
Gravity Anomalies ◽  
Gravity Models ◽  
Crustal Thickening ◽  
Seismic Line ◽  
Crustal Thinning ◽  
Gravity Measurements ◽  
George River ◽  
Superior Craton

Gravity data were obtained along two transects on the southern coast of Ungava Bay, which provide continuous gravity coverage between Leaf Bay and George River. The transects and the derived gravity profiles extend from the Superior craton to the Rae Province across the New Quebec Orogen (NQO). Interpretation of the transect along the southwestern coast of Ungava Bay suggests crustal thickening beneath the NQO and crustal thinning beneath the Kuujjuaq Terrane, east of the NQO. Two alternative interpretations are proposed for the transect along the southeastern coast of the bay. The first model shows crustal thickening beneath the George River Shear Zone (GRSZ) and two shallow bodies correlated with the northern extensions of the GRSZ and the De Pas batholith. The second model shows constant crustal thickness and bodies more deeply rooted than in the first model. The gravity models are consistent with the easterly dipping reflections imaged along a Lithoprobe seismic line crossing Ungava Bay and suggest westward thrusting of the Rae Province over the NQO. Because no gravity data have been collected in Ungava Bay, satellite altimetry data have been used as a means to fill the gap in data collected at sea. The satellite-derived gravity data and standard Bouguer gravity data were combined in a composite map for the Ungava Bay region. The new land-based gravity measurements were used to verify and calibrate the satellite data and to ensure that offshore gravity anomalies merge with those determined by the land surveys in a reasonable fashion. Three parallel east-west gravity profiles were extracted: across Ungava Bay (59.9°N), on the southern shore of the bay (58.5°N), and onshore ~200 km south of Ungava Bay (57.1°N). The gravity signature of some major structures, such as the GRSZ, can be identified on each profile.

Sea floor topography modeling by cumulating different types of gravity information

2020 ◽  
Author(s):  
Lucia Seoane ◽  
Benjamin Beirens ◽  
Guillaume Ramillien
Keyword(s):  
New England ◽  
Gravity Data ◽  
Gravity Anomalies ◽  
Geoid Height ◽  
Extended Kalman Filtering ◽  
Sea Floor ◽  
Single Beam ◽  
Free Air ◽  
Free Air Gravity ◽  
Great Meteor Seamount

<p>We propose to cumulate complementary gravity data, i.e. geoid height and (radial) free-air gravity anomalies, to evaluate the 3-D shape of the sea floor more precisely. For this purpose, an Extended Kalman Filtering (EKF) scheme has been developed to construct the topographic solution by injecting gravity information progressively. The main advantage of this sequential cumulation of data is the reduction of the dimensions of the inverse problem. Non linear Newtonian operators have been re-evaluated from their original forms and elastic compensation of the topography is also taken into account. The efficiency of the method is proved by inversion of simulated gravity observations to converge to a stable topographic solution with an accuracy of only a few meters. Real geoid and gravity data are also inverted to estimate bathymetry around the New England and Great Meteor seamount chains. Error analysis consists of comparing our topographic solutions to accurate single beam ship tracks for validation.</p>

Effects of terrain on borehole gravity data

Geophysics ◽  
1980 ◽  
Vol 45 (2) ◽  
pp. 234-243 ◽  
Author(s):  
J. R Hearst ◽  
J. W. Schmoker ◽  
R. C. Carlson
Keyword(s):  
Gravity Data ◽  
Radial Distance ◽  
Ground Surface ◽  
Absolute Maximum ◽  
Near Surface ◽  
Free Air ◽  
Gravity Measurements ◽  
Terrain Elevation ◽  
Lower Magnitude ◽  
Terrain Features

The effect of terrain on gravity measurements in a borehole and on formation density derived from borehole gravity data is studied as a function of depth in the well, terrain elevation, terrain inclination, and radial distance to the terrain feature. The vertical attraction of gravity [Formula: see text] in a borehole resulting from a terrain element is small at the surface and reaches an absolute maximum at a depth of about one and one‐half times the radial distance to the terrain element, then decreases at greater depths. The effect of terrain on calculated formation density is proportional to the vertical derivative of [Formula: see text] and is maximum at the surface, passes through zero where |[Formula: see text]| is greatest, and reaches a second extremum of opposite sign to the first and of much lower magnitude. Accuracy criteria for borehole‐gravity terrain corrections show that elevation accuracy requirements are most stringent for a combination of nearby terrain features and near‐surface gravity stations. Sensitivity to terrain inclination is also greatest for this combination. The measurement of the free‐air gradient of gravity, commonly made’slightly above the ground surface, is extremely sensitive to topographic irregularities within about 300m of the measurement point. The effect of terrain features 21.9 to 166.7 km from the well [Hammer’s (1939) zone M through Hayford‐Bowie’s (1912) zone O] on calculated formation density is nearly constant with depth. At these distances, the terrain correction will be equivalent to a dc shift of about [Formula: see text] of average elevation above or below the correction datum. The effect of topography beyond 166.7 km is not likely to exceed [Formula: see text].

The Origin of Lunar Mascon Basins

Science ◽  
2013 ◽  
Vol 340 (6140) ◽  
pp. 1552-1555 ◽  
Author(s):  
H. J. Melosh ◽  
Andrew M. Freed ◽  
Brandon C. Johnson ◽  
David M. Blair ◽  
Jeffrey C. Andrews-Hanna ◽  
...  
Keyword(s):  
Gravity Data ◽  
Gravity Anomalies ◽  
Element Model ◽  
Isostatic Adjustment ◽  
Melt Pool ◽  
Free Air ◽  
Free Air Gravity ◽  
Bull's Eye ◽  
Gravity Recovery ◽  
The Impact

High-resolution gravity data from the Gravity Recovery and Interior Laboratory spacecraft have clarified the origin of lunar mass concentrations (mascons). Free-air gravity anomalies over lunar impact basins display bull’s-eye patterns consisting of a central positive (mascon) anomaly, a surrounding negative collar, and a positive outer annulus. We show that this pattern results from impact basin excavation and collapse followed by isostatic adjustment and cooling and contraction of a voluminous melt pool. We used a hydrocode to simulate the impact and a self-consistent finite-element model to simulate the subsequent viscoelastic relaxation and cooling. The primary parameters controlling the modeled gravity signatures of mascon basins are the impactor energy, the lunar thermal gradient at the time of impact, the crustal thickness, and the extent of volcanic fill.

scholarly journals The Regime of the Western Part of the Ross Ice Shelf Drainage System

1966 ◽  
Vol 6 (43) ◽  
pp. 55-68 ◽  
Author(s):  
M. Giovinetto ◽  
Edwin S. Robinson ◽  
C. W. M. Swithinbank
Keyword(s):  
Cross Sections ◽  
Drainage System ◽  
Gravity Anomalies ◽  
Ice Shelf ◽  
Glacier Surface ◽  
Ross Ice Shelf ◽  
Movement Data ◽  
Free Air ◽  
The Difference ◽  
Free Air Gravity

AbstractThe net mass budget is estimated for the western part of the Ross Ice Shelf drainage system. The area of the system is (1.75±0.26) × 106 km.2, and the drainage periphery extends along the eastern flank of the Trans-Antarctic Mountains between lat. 77° 58′ S., long. 164° 37′ E. and lat. 85° 27′ S., long. 147°50′ discharge is estimated from vertical cross-sections and corresponding ice-movement data for eight outlet glaciers. Free-air gravity anomalies, corrected for the effect of terrain above the glacier surface, are used to determine cross-sections of valleys by comparison with theoretical gravity profiles for several two-dimensional valley models. These data provide a basis for estimating the rate of ice discharge from the plateau, which is compared with the estimated rate of net accumulation at the surface, to determine the net budget of the ice sheet in the region. Representative mean rates of ice discharge measured in different types of glaciers are approximately 0.25 × 1015 g. km.−1 yr.−1 in outlet glaciers with large basins, and 0.05 × 1015 g. km.−1 yr.−1 in outlet glaciers with small basins. Taking into account the snowshcd area and the rate of accumulation, the rate of ice discharge in cirque and piedmont glaciers is estimated at about 0.02 × 1015 g. km.−1 yr.−1 The difference ((48±29) × 1015 g. yr.−1) between mass input ((96±25) × 1015 g. yr.−1) and mass output ((48±15) × 1015 g. yr.−1) is large enough relative to the estimated standard error to indicate a probable positive net budget.

The Mid-Atlantic Ridge Near 45 °N. XX. The Gravity Field

1972 ◽  
Vol 9 (8) ◽  
pp. 942-959 ◽  
Author(s):  
J. M. Woodside
Keyword(s):  
Gravity Data ◽  
Bouguer Anomaly ◽  
Gravity Anomalies ◽  
Spreading Rate ◽  
Survey Area ◽  
Free Air ◽  
Mid Atlantic Ridge ◽  
Sea Floor Spreading ◽  
Relationship Of ◽  
East West

Detailed maps of free-air, Bouguer, and residual gravity anomalies for a survey area 250 km wide across the Mid-Atlantic Ridge between 45° and 46 °N have been compiled. The Bouguer anomaly was terrain-corrected to a radius of 40 km. The residual anomaly was computed from the terrain-corrected Bouguer anomaly using an empirical linear relationship between the Bouguer anomaly and the bathymetry to predict a 'regional' Bouguer anomaly from the depth data. North–south and east–west trends in the gravity data are enhanced in the residual anomaly; and it is suggested that at least one short east–west transform fault may offset the ridge in a right-lateral sense. The offset is presumably a response to a change in sea-floor spreading direction from west–northwest/east–southeast to west/east about 10 m.y. ago. A change in spreading rate may have occurred at the same time. A difference in accretion rate on either side of the ridge axis is indicated by asymmetry in the gravity data and by differences in the topographic compensation across the axis. Variations in the relationship of terrain-corrected Bouguer anomaly to bathymetry within the survey area suggest that a density deficiency or buoyant forces in the upper mantle are responsible for the overall elevation of the crestal mountain region but that the topography of the high-fractured plateau may be partially compensated by undulations of the crust–mantle interface.

scholarly journals Usporedba različitih pristupa Bouguer-ove redukcije na temelju satelitskih gravimetrijskih podataka

Geofizika ◽  
2020 ◽  
Vol 37 (2) ◽  
pp. 237-261
Author(s):  
Fan Luo ◽  
Xin Tao ◽  
Guangming Fu ◽  
Chong Zhang ◽  
Kun Zhang ◽  
...  
Keyword(s):  
Gravity Anomaly ◽  
Gravity Data ◽  
Gravity Anomalies ◽  
Gravitational Effect ◽  
Seismic Profile ◽  
Bouguer Gravity ◽  
Seismic Profiles ◽  
Satellite Gravity ◽  
Free Air ◽  
Free Air Gravity

Satellite gravity data are widely used in the field of geophysics to study deep structures at the regional and global scales. These data comprise free-air gravity anomaly data, which usually need to be corrected to a Bouguer gravity anomaly for practical application. Bouguer reduction approaches can be divided into two methods based on the coordinate system: the spherical coordinates method (SBG) and the Cartesian coordinates method; the latter is further divided into the CEBG and CBG methods, which do and do not include the Earth’s curvature correction. In this paper, free-air gravity anomaly data from the eastern Tibetan Plateau and its adjacent areas were used as the basic data to compare the CBG, CEBG, and SBG Bouguer gravity correction methods. The comparison of these three Bouguer gravity correction methods shows that the effect of the Earth’s curvature on the gravitational effect increases with increasing elevation in the study area. We want to understand the inversion accuracy for the data obtained by different Bouguer gravity reduction approaches. The depth distributions of the Moho were obtained by the interface inversion of the Bouguer gravity anomalies obtained by the CBG, CEBG, and SBG, and active seismic profiles were used as references for comparison and evaluation. The results show that the depths of the Moho obtained by the SBG inversion are more consistent with the measured seismic profile depths. Therefore, the SBG method is recommended as the most realistic approach in the process of global or regional research employing gravity data.

scholarly journals Modelling Local Gravity Anomalies from Processed Observed Gravity Measurements for Geodetic Applications

2019 ◽  
pp. 144-162
Author(s):  
Eteje S. O. ◽  
Oduyebo O. F. ◽  
Oluyori P. D.
Keyword(s):  
Applied Sciences ◽  
Gravity Anomalies ◽  
Absolute Gravity ◽  
Bouguer Gravity ◽  
Benin City ◽  
Bouguer Gravity Anomalies ◽  
Free Air ◽  
Local Gravity ◽  
Gravity Measurements ◽  
Mean Square Errors

As the application of gravity data in applied sciences such as geodesy, geodynamics, astronomy, physics and geophysics for earth shape determination, geoid model determination, computation of terrestrial mass displacement, orbit computation of natural and artificial celestial bodies, realization of force standards and derived quantities and density distribution in the different layers in the upper crust and having considered the cost of direct gravity survey, the study presents modelling local gravity anomalies from processed observed gravity measurements for geodetic application in Benin City. A total of 22 points were used. The points were respectively observed with CHC900 dual frequency GNSS receivers and SCINTREX CG-5 Autograv to obtain their coordinates and absolute gravity values. The theoretical gravity values of the points were computed on the Clarke 1880 ellipsoid to obtain their local gravity anomalies. The free air and the Bouguer corrections were applied to the computed gravity anomalies to obtain the free air and the Bouguer gravity anomalies of the points. Least squares adjustment technique was applied to obtain the model variables coefficient/parameters, as well as to fit the fifth-degree polynomial interpolation surface to the computed free air and the Bouguer gravity anomalies. Kriging method was applied using Surfer 12 software to plot the computed and the models' free air and Bouguer gravity anomalies. Microsoft Excel programs were developed for the application of the models in the study area. The Root Mean Square Errors (RMSEs) and the standard errors of the two models were computed to obtain the dependability, as well as reliability of the models. It is recommended that whenever either free air or Bouguer gravity anomalies of points within Benin City are to be obtained for application in applied sciences, the determined models should be applied.

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