A simple objective method for minimizing crossover errors in marine gravity data

Geophysics ◽  
1984 ◽  
Vol 49 (7) ◽  
pp. 1070-1083 ◽  
Author(s):  
Roger A. Prince ◽  
Donald W. Forsyth
Keyword(s):  
Least Squares ◽  
Gravity Data ◽  
Original Data ◽  
Free Air ◽  
Percent Confidence Level ◽  
Individual Segment ◽  
Marine Gravity ◽  
Anomaly Map ◽  
Free Air Anomaly ◽  
The Right

A method is presented which does not require a model for the source of crossover errors in marine gravity data in order to minimize them. The cruises are divided up into straight line segments and the assumption is made that whatever the sources of error, their net effect will be constant over the length of the track segment. A least‐squares approach is used where the crossover differences in the original data are the observations which it is desired to match. The desired set of constant corrections, one for each segment, is that which will minimize the sum of the squares of the residual crossover errors. This method has the advantage of reducing the crossover errors while simultaneously preserving the relative gravity anomalies along individual ship’s profiles. A data set consisting of gravity measurements made on nine cruises in the region of the Vema fracture zone in the equatorial Atlantic is used as a case study. The resulting least squares solution reduces the root mean square (rms) of 298 crossover errors from 10.3 mGals in the original data to 2.9 mGals after the calculated segment corrections are made. An F‐test shows that the reduced rms deviation from the mean is statistically significant at the 99 percent confidence level. A least‐squares fit was also done to find the best single cruise corrections for each of the 9 cruises for the 204 crossings between cruises. The original rms error is reduced from 11.4 to 7.8 mGals and the improvement is again significant at the 99 percent confidence level. An analysis of the variances shows that 37.5 percent of the total variance can he explained by constant corrections to each of the 9 cruises, while an additional 49.5 percent of the total variance can be explained by individual segment corrections. A linear regression analysis of the segment corrections as a function of elapsed time in the cruise suggests that for two of the cruises, drift of the gravity meter was not properly corrected for in the original data. Analysis of the segment corrections as a function of ship’s heading suggests that for two other cruises, cross‐coupling effects were not properly corrected. Eötvös corrections caused by navigational errors are the most likely explanation for many of the remaining individual segment corrections. After the calculated corrections were made, a free‐air anomaly map of the region was drawn. A comparison with an earlier published, free‐air anomaly map of the right half of this region shows that the contours are similar, but that the new map is shifted by a few mGals relative to the older map. This discrepancy between the old and new maps is a consequence of matching the data between the left and right sides of the new map and does not arise if the right side is considered alone with the least‐squares technique.

scholarly journals Evaluation of the BGM-3 sea gravity meter system onboard R/V Conrad

Geophysics ◽  
1986 ◽  
Vol 51 (7) ◽  
pp. 1480-1493 ◽  
Author(s):  
Robin E. Bell ◽  
A. B. Watts
Keyword(s):  
Gravity Anomaly ◽  
Gravity Data ◽  
Gravity Anomalies ◽  
Test Range ◽  
Free Air ◽  
Marine Gravity ◽  
Abrupt Changes ◽  
Spring Type ◽  
Free Air Gravity ◽  
Free Air Anomaly

The first Bell Aerospace BGM-3 Marine Gravity Meter System available for academic use was installed on R/V Robert D. Conrad in February, 1984. The BGM-3 system consists of a forced feedback accelerometer mounted on a gyrostabilized platform. Its sensor (requiring no cross‐coupling correction) is a significant improvement over existing beam and spring‐type sea gravimeters such as the GSS-2. A gravity survey over the Wallops Island test range together with the results of subsequent cruises allow evaluation of the precision, accuracy, and capabilities of the new system. Over the test range, the BGM-3 data were compared directly to data obtained by a GSS-2 meter onboard R/V Conrad. The rms discrepancy between free‐air gravity anomaly values at intersecting ship tracks of R/V Conrad was ±0.38 mGal for BGM-3 compared to ±1.60 mGal for the GSS-2. Moreover, BGM-3’s platform recovered from abrupt changes in ship’s heading more rapidly than did the platform of GSS-2. The principal factor limiting the accuracy of sea gravity data is navigation. Over the test range, where navigation was by Loran C and transit satellite, a two‐step filtering of the ship’s velocity and position was required to obtain an optimal Eötvös correction. A spectral analysis of 1 minute values of the Eötvös correction and the reduced free‐air gravity anomaly determined the filter characteristics. To minimize the coherence between the Eötvös and free‐air anomaly, it was necessary to prefilter the ship’s position and velocity. Using this procedure, reduced free‐air gravity anomalies with wavelengths as small as a few kilometers can be resolved.

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.

Free Air Anomaly Map of Canada from Piece-Wise Surface Fittings Over Half-Degree Blocks

1973 ◽  
Vol 27 (4) ◽  
pp. 293-300 ◽  
Author(s):  
Dezsö Nagy
Keyword(s):  
Gravity Anomaly ◽  
Extreme Values ◽  
Free Air ◽  
Equivalent Length ◽  
Order Polynomial ◽  
Standard Deviations ◽  
Anomaly Map ◽  
Half Degree ◽  
Free Air Anomaly ◽  
Polynomial Surface

The region of Canada, which has been covered by gravity surveys (including 1970 data), has been subdivided into 2,923 surface elements of sides of a half-degree along the meridian and approximately equivalent length along the parallels. The gravity anomaly at the center of each element was estimated by fitting a low-order polynomial surface to the free air anomalies within each element. The extreme values are —160 and 96 milligals, with over 85 per cent of the anomalies being in the range of —40 and 20 milligals. About two thirds of all computed anomalies are estimated to have standard deviations less than ±10 milligals.

Processing steps for the compiling AAGRG gravity maps

2020 ◽  
Author(s):  
Pavol Zahorec ◽  
Juraj Papčo ◽  
Roman Pašteka ◽  
Keyword(s):  
Gravity Data ◽  
Atmospheric Correction ◽  
Bouguer Anomaly ◽  
Taylor Series Expansion ◽  
Methodological Innovation ◽  
Atmospheric Effect ◽  
Free Air ◽  
Point Data ◽  
Anomaly Map ◽  
Bouguer Anomaly Map

<p>First unified complete Bouguer anomaly map of AlpArray area compiled from terrestrial gravity data is in preparation. The following steps to calculate the first version of the map were performed: 1. unification of different spatial, height and gravity systems, 2. getting available detailed (mainly LiDAR-based) elevation models and their transformation from physical to ellipsoidal heights, 3. calculation of mass corrections (gravity effect of the topography between the surface and ellipsoid level) with density 2 670 kg/m<sup>3</sup>, 4. calculation of bathymetric corrections for water masses below the ellipsoid (correction density -1 640 kg/m<sup>3</sup>), 5. calculation of lake correction for great alpine lakes (correction density -1 670 kg/m<sup>3</sup>), 6. calculation of the final complete Bouguer anomalies based on normal field (Somigliana formula with GRS80 parameters, free-air correction using Taylor series expansion to the 2<sup>nd</sup> order) and particular corrections including also the atmospheric correction.</p><p>The quality control of input data was performed based on the height differences between the point data and particular elevation models. Several thousand points with height residuals higher than chosen threshold (±50 m) were excluded. The available detailed local elevation models (resolution 10 – 20 m) were compared with global model MERIT (resolution 25 m).</p><p>The most significant methodological innovation is the ellipsoidal heights concept using straightforward calculation of mass/bathymetric corrections in respect to the ellipsoid instead of using the geophysical indirect effect computation. Our specially developed program Toposk was used for mass/bathymetric correction calculation (the standard distance of 166.7 km was used for the first version of the map) as well as for the calculation of lake corrections. Mass corrections amount to hundreds of mGal, while the lake corrections reach more than 5 mGal locally. Atmospheric effect taking into account topography was also calculated and compared with standard atmospheric correction.</p><p> </p>

scholarly journals THE EVALUATION OF THE NEW ZEALAND'S GEOID MODEL USING THE KTH METHOD / NAUJOSIOS ZELANDIJOS GEOIDO MODELIO VERTINIMAS KTH METODU / ОЦЕНКА МОДЕЛИ ГЕОИДА НОВОЙ ЗЕЛАНДИИ С ПРИМЕНЕНИЕМ МЕТОДА КТН

2011 ◽  
Vol 37 (1) ◽  
pp. 5-14 ◽  
Author(s):  
Ahmed Abdalla ◽  
Robert Tenzer
Keyword(s):  
New Zealand ◽  
Least Squares ◽  
Gravity Data ◽  
Spherical Approximation ◽  
Geopotential Model ◽  
Gravimetric Geoid ◽  
Geoid Model ◽  
Marine Gravity ◽  
Gravity Database ◽  
Stokes Integral

We compile a new geoid model at the computation area of New Zealand and its continental shelf using the method developed at the Royal Institute of Technology (KTH) in Stockholm. This method utilizes the least-squares modification of the Stokes integral for the biased, unbiased, and optimum stochastic solutions. The modified Bruns-Stokes integral combines the regional terrestrial gravity data with a global geopotential model (GGM). Four additive corrections are calculated and applied to the approximate geoid heights in order to obtain the gravimetric geoid. These four additive corrections account for the combined direct and indirect effects of topography and atmosphere, the contribution of the downward continuation reduction, and the formulation of the Stokes problem in the spherical approximation. The gravimetric geoid model is computed using two heterogonous gravity data sets: the altimetry-derived gravity anomalies from the DNSC08 marine gravity database (offshore) and the ground gravity measurements from the GNS Science gravity database (onshore). The GGM coefficients are taken from EIGEN-GRACE02S complete to degree 65 of spherical harmonics. The topographic heights are generated from the 1×1 arc-sec detailed digital terrain model (DTM) of New Zealand and from the 30×30 arc-sec global elevation data of SRTM30_PLUS V5.0. The least-squares analysis is applied to combine the gravity and GPS-levelling data using a 7-parameter model. The fit of the KTH geoid model with GPS-levelling data in New Zealand is 7 cm in terms of the standard deviation (STD) of differences. This STD fit is the same as the STD fit of the NZGeoid2009, which is the currently adopted official quasigeoid model for New Zealand. Santrauka Stokholmo Karališkajame technologijos institute (KTH) sukurtu metodu apskaičiuotas naujas Naujosios Zelandijos ir kontinentinio šelfo geoido modelis. Taikoma Stokso integralo mažiausiųjų kvadratų modifikacija, įvertinant paklaidas ir jų nevertinant bei ieškant optimalių stochastinių sprendinių. Modifikuotas Bruno ir Stokso integralas sieja regioninius žemyninius gravimetrinius duomenis su globaliuoju geopotencialo modeliu (GGM). Gravimetriniam geoidui gauti skaičiuojamos keturios papildomos pataisos: topografinės situacijos ir atmosferos tiesioginės ir netiesioginės įtakos, redukcijos įtakos ir Stokso integralo taikymo sferiniam paviršiui. Gravimetrinis geoido modelis apskaičiuotas pagal du duomenų rinkinius: DNSC08 jūrinių gravimetrinių duomenų bazėje (šelfas) esančias altimetriniu metodu nustatytas sunkio pagreičio anomalijas ir žemyninės dalies gravimetrinių matavimų duomenis iš GNS gravimetrinės duomenų bazės (pakrantė). GGM koeficientai imti iš EIGEN-GRACE02S modelio sferinių iki 65 laipsnio harmonikų. Topografiniai aukščiai sugeneruoti iš Naujosios Zelandijos 1×1 sekundės detaliojo skaitmeninio reljefo modelio ir iš 30×30 sekundžių globaliojo aukščių modelio SRTM30_PLUS V5.0. Gravimetriniams ir GPS niveliacijos duomenims sujungti taikytas mažiausiųjų kvadratų 7 parametrų metodas. KTH metodu sudaryto geoido modelio vidutinė kvadratinė paklaida 7 cm. Tai sutampa su NZGeoid 2009 geoido modelio, taikomo Naujoje Zelandijoje, tikslumu. Резюме Модель геоида континентального шельфа Новой Зеландии построена с применением метода, созданного в Королевском технологическом институте Стокгольма. Данный метод основан на модификации решения интеграла Стокса методом наименьших квадратов с оценкой или без оценки погрешностей и поиском оптимальных статистических решений. Модифицированный интеграл БрунаСтокса объединяет региональные надземные гравиметрические данные с глобальной геопотенциальной моделью (GGM). Для определения гравиметрического геоида вычисляются дополнительные поправки прямого и косвенного влияния топографии и атмосферы, редукции и применения проблемы Стокса для сферической поверхности. Гравиметрическая модель геоида вычисляется на основе двух баз данных: альтиметрическим методом определенных аномалий силы тяжести в базе морских гравиметрических данных DNSC08 (шельф) и надземной части гравиметрических измерений из базы данных GNS. Коэффициенты GGM взяты из сферических гармоник до 65 степени модели EIGENGRACEO2S. Топографические высоты сгенерированы из детальной цифровой модели рельефа Новой Зеландии с сеткой 1×1 секунду и из глобальной модели высот SRTM30_PLUSv5.0 с сеткой 30×30 секунд. Для объединения гравиметрических и GPSнивелирных данных применялся метод наименьших квадратов с 7 параметрами. Среднеквадратическая погрешность модели геоида, созданной по методу КТН, равна 7 см. Точность аналогична точности применяемой в Новой Зеландии модели геоида NZGeoid2009.

scholarly journals GRAVIMETRIC GEOID MODELLING OVER PENINSULAR MALAYSIA USING TWO DIFFERENT GRIDDING APPROACHES FOR COMBINING FREE AIR ANOMALY

2019 ◽  
Vol XLII-4/W16 ◽  
pp. 515-522
Author(s):  
M. F. Pa’suya ◽  
A. H. M. Din ◽  
J. C. McCubbine ◽  
A. H. Omar ◽  
Z. M. Amin ◽  
...  
Keyword(s):  
Gravity Data ◽  
Reference Signal ◽  
Digital Terrain Model ◽  
Peninsular Malaysia ◽  
Airborne Gravity ◽  
Geopotential Model ◽  
Gravimetric Geoid ◽  
Geoid Model ◽  
Free Air ◽  
Free Air Anomaly

Abstract. We investigate the use of the KTH Method to compute gravimetric geoid models of Malaysian Peninsular and the effect of two differing strategies to combine and interpolate terrestrial, marine DTU17 free air gravity anomaly data at regular grid nodes. Gravimetric geoid models were produced for both free air anomaly grids using the GOCE-only geopotential model GGM GO_CONS_GCF_2_SPW_R4 as the long wavelength reference signal and high-resolution TanDEM-X global digital terrain model. The geoid models were analyzed to assess how the different gridding strategies impact the gravimetric geoid over Malaysian Peninsular by comparing themto 172 GNSS-levelling derived geoid undulations. The RMSE of the two sets of gravimetric geoid model / GNSS-levelling residuals differed by approx. 26.2 mm. When a 4-parameter fit is used, the difference between the RMSE of the residuals reduced to 8 mm. The geoid models shown here do not include the latest airborne gravity data used in the computation of the official gravimetric geoid for the Malaysian Peninsular, for this reason they are not as precise.

scholarly journals Regional Seafloor Topography by Extended Kalman Filtering of Marine Gravity Data without Ship-Track Information

2021 ◽  
Vol 14 (1) ◽  
pp. 169
Author(s):  
Lucía Seoane ◽  
Guillaume Ramillien ◽  
Benjamin Beirens ◽  
José Darrozes ◽  
Didier Rouxel ◽  
...  
Keyword(s):  
Gravity Data ◽  
Geoid Height ◽  
Extended Kalman Filtering ◽  
Seafloor Topography ◽  
Single Beam ◽  
Beam Depth ◽  
Marine Gravity ◽  
Gravity Measurements ◽  
Polynomial Series ◽  
Free Air Anomaly

An iterative Extended Kalman Filter (EKF) approach is proposed to recover a regional set of topographic heights composing an undersea volcanic mount by the successive combination of large numbers of gravity measurements at sea surface using altimetry satellite-derived grids and taking the error uncertainties into account. The integration of the non-linear Newtonian operators versus the radial and angular distances (and its first derivatives) enables the estimation process to accelerate and requires only few iterations, instead of summing Legendre polynomial series or using noise-degraded 2D-FFT decomposition. To show the effectiveness of the EKF approach, we apply it to the real case of the bathymetry around the Great Meteor seamount in the Atlantic Ocean by combining only geoid height/free-air anomaly datasets and using ship-track soundings as reference for validation. Topography of the Great Meteor seamounts structures are well-reconstructed, especially when regional compensation is considered. Best solution gives a RMS equal to 400 m with respect to the single beam depth observations and it is comparable to RMS obtained for ETOPO1 of about 365 m. Larger discrepancies are located in the seamount flanks due to missing high-resolution information for gradients. This approach can improve the knowledge of seafloor topography in regions where few echo-sounder measurements are available.

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