scholarly journals Application of the nonlinear optimisation in regional gravity field modelling using spherical radial base functions

2021 ◽  
Author(s):  
Hany Mahbuby ◽  
Yazdan Amerian ◽  
Amirhossein Nikoofard ◽  
Mehdi Eshagh
Keyword(s):  
Gravity Anomaly ◽  
Gravity Field ◽  
Fundamental Equation ◽  
Physical Geodesy ◽  
Gravity Anomalies ◽  
Global Navigation Satellite Systems ◽  
Disturbing Potential ◽  
Gravity Field Model ◽  
Regional Gravity ◽  
Mean Square Errors

AbstractThe gravity field is a signature of the mass distribution and interior structure of the Earth, in addition to all its geodetic applications especially geoid determination and vertical datum unification. Determination of a regional gravity field model is an important subject and needs to be investigated and developed. Here, the spherical radial basis functions (SBFs) are applied in two scenarios for this purpose: interpolating the gravity anomalies and solving the fundamental equation of physical geodesy for geoid or disturbing potential determination, which has the possibility of being verified by the Global Navigation Satellite Systems (GNSS)/levelling data. Proper selections of the number of SBFs and optimal location of the applied SBFs are important factors to increase the accuracy of estimation. In this study, the gravity anomaly interpolation based on the SBFs is performed by Gauss-Newton optimisation with truncated singular value decomposition, and a Quasi-Newton method based on line search to solve the minimisation problems with a small number of iterations is developed. In order to solve the fundamental equation of physical geodesy by the SBFs, the truncated Newton optimisation is applied as the Hessian matrix of the objective function is not always positive definite. These two scenarios are applied on the terrestrial free-air gravity anomalies over the topographically rough area of Auvergne. The obtained accuracy for the interpolated gravity anomaly model is 1.7 mGal with the number of point-masses about 30% of the number of observations, and 1.5 mGal in the second scenario where the number of used kernels is also 30%. These accuracies are root mean square errors (RMSE) of the differences between predicted and observed gravity anomalies at check points. Moreover, utilising the optimal constructed model from the second scenario, the RMSE of 9 cm is achieved for the differences between the gravimetric height anomalies derived from the model and the geometric height anomalies from GNSS/levelling points.

Towards an updated, enhanced regional gravity field solution for Antarctica

2021 ◽  
Author(s):  
Mirko Scheinert ◽  
Philipp Zingerle ◽  
Theresa Schaller ◽  
Roland Pail ◽  
Martin Willberg
Keyword(s):  
Gravity Anomaly ◽  
Gravity Field ◽  
Gravity Data ◽  
Gravity Anomalies ◽  
Data Set ◽  
Gravity Field Model ◽  
Terrestrial Gravity ◽  
Field Solution ◽  
Gravity Disturbances ◽  
Regional Gravity

<p>In the frame of the IAG Subcommission 2.4f “Gravity and Geoid in Antarctica” (AntGG) a first Antarctic-wide grid of ground-based gravity anomalies was released in 2016 (Scheinert et al. 2016). That data set was provided with a grid space of 10 km and covered about 73% of the Antarctic continent. Since then a considerably amount of new data has been made available, mainly collected by means of airborne gravimetry. Regions which were formerly void of any terrestrial gravity observations and have now been surveyed include especially the polar data gap originating from GOCE satellite gravimetry. Thus, it is timely to come up with an updated and enhanced regional gravity field solution for Antarctica. For this, we aim to improve further aspects in comparison to the AntGG 2016 solution: The grid spacing will be enhanced to 5 km. Instead of providing gravity anomalies only for parts of Antarctica, now the entire continent should be covered. In addition to the gravity anomaly also a regional geoid solution should be provided along with further desirable functionals (e.g. gravity anomaly vs. disturbance, different height levels).</p><p>We will discuss the expanded AntGG data base which now includes terrestrial gravity data from Antarctic surveys conducted over the past 40 years. The methodology applied in the analysis is based on the remove-compute-restore technique. Here we utilize the newly developed combined spherical-harmonic gravity field model SATOP1 (Zingerle et al. 2019) which is based on the global satellite-only model GOCO05s and the high-resolution topographic model EARTH2014. We will demonstrate the feasibility to adequately reduce the original gravity data and, thus, to also cross-validate and evaluate the accuracy of the data especially where different data set overlap. For the compute step the recently developed partition-enhanced least-squares collocation (PE-LSC) has been used (Zingerle et al. 2021, in review; cf. the contribution of Zingerle et al. in the same session). This method allows to treat all data available in Antarctica in one single computation step in an efficient and fast way. Thus, it becomes feasible to iterate the computations within short time once any input data or parameters are changed, and to easily predict the desirable functionals also in regions void of terrestrial measurements as well as at any height level (e.g. gravity anomalies at the surface or gravity disturbances at constant height).</p><p>We will discuss the results and give an outlook on the data products which shall be finally provided to present the new regional gravity field solution for Antarctica. Furthermore, implications for further applications will be discussed e.g. with respect to geophysical modelling of the Earth’s interior (cf. the contribution of Schaller et al. in session G4.3).</p>

scholarly journals DETERMINATION AND MAPPING OF THE TERRESTRIAL GRAVITY ANOMALIES IN THE MOUNTAINOUS AREAS OF IRAQ

2021 ◽  
Vol 6 (24) ◽  
pp. 213-225
Author(s):  
Shazad Jamal Jalal ◽  
Tajul Ariffin Musa ◽  
Ami Hassan Md Din ◽  
Wan Anom Wan Aris
Keyword(s):  
Gravity Data ◽  
Physical Geodesy ◽  
Gravity Anomalies ◽  
Gravity Survey ◽  
Mountainous Areas ◽  
Entire Study ◽  
Terrestrial Gravity ◽  
The Past ◽  
Regional Gravity ◽  
Entire Study Area

Gravity data and computing gravity anomalies are regarded as vital for both geophysics and physical geodesy fields. The mountainous areas of Iraq are characterized by the lack of regional gravity data because gravity surveys are rarely performed in the past four decades due to the Iraq-Iran war and the internal unstable political situation of this particular region. In addition, the formal map of the available terrestrial gravity which was published by the French Database of Bureau Gravimetrique International (International Gravimetric Bureau-in English) (BGI), introduces Iraq and the study area as a remote area and in white color because of the unavailability of gravity data. However, a dense and local (not regional) gravity data is available which was conducted by geophysics researchers 13 years ago. Therefore, the regional gravity survey of 160 gravity points was performed by the authors at an average 11 km apart, which was covers the whole area of Sulaymaniyah Governorate (part of the mountainous areas of Iraq). In spite of Although the risk of mine fields within the study area, suitable safe routes as well as a helicopter was used for the gravity survey of several points on the top of mountains. The survey was conducted via Lacoste and Romberg geodetic gravimeter and GPS handheld. The objective of the study is to determine and map the gravity anomalies for the entire study area, the data of which would assist different geosciences applications.

scholarly journals Recovering Marine Gravity Over the Gulf of Guinea From Multi-Satellite Sea Surface Heights

2021 ◽  
Vol 9 ◽  
Author(s):  
Richard Fiifi Annan ◽  
Xiaoyun Wan
Keyword(s):  
Gravity Field ◽  
Gravity Anomalies ◽  
Sea Surface ◽  
Shallow Waters ◽  
Gulf Of Guinea ◽  
Gravity Field Model ◽  
The North ◽  
Marine Gravity ◽  
Sea Surface Heights ◽  
East Component

A regional gravity field product, comprising vertical deflections and gravity anomalies, of the Gulf of Guinea (15°W to 5°E, 4°S to 4°N) has been developed from sea surface heights (SSH) of five altimetry missions. Though the remove-restore technique was adopted, the deflections of the vertical were computed directly from the SSH without the influence of a global geopotential model. The north-component of vertical deflections was more accurate than the east-component by almost three times. Analysis of results showed each satellite can contribute almost equally in resolving the north-component. This is attributable to the nearly northern inclinations of the various satellites. However, Cryosat-2, Jason-1/GM, and SARAL/AltiKa contributed the most in resolving the east-component. We attribute this to the superior spatial resolution of Cryosat-2, the lower inclination of Jason-1/GM, and the high range accuracy of the Ka-band of SARAL/AltiKa. Weights of 0.687 and 0.313 were, respectively, assigned to the north and east components in order to minimize their non-uniform accuracy effect on the resultant gravity anomaly model. Histogram of computed gravity anomalies compared well with those from renowned models: DTU13, SIOv28, and EGM2008. It averagely deviates from the reference models by −0.33 mGal. Further assessment was done by comparing it with a quadratically adjusted shipborne free-air gravity anomalies. After some data cleaning, observations in shallow waters, as well as some ship tracks were still unreliable. By excluding the observations in shallow waters, the derived gravity field model compares well in ocean depths deeper than 2,000 m.

Harmonic Correction for Residual Terrain Modelling (RTM) Technique in Physical Geodesy Applications

2021 ◽  
Author(s):  
Meng Yang ◽  
Xiao-Le Deng ◽  
Min Zhong
Keyword(s):  
Gravity Anomaly ◽  
Gravity Field ◽  
Physical Geodesy ◽  
Geoid Height ◽  
Gravity Field Modelling ◽  
Field Modelling ◽  
Condensation Method ◽  
Residual Terrain Modelling ◽  
Harmonic Correction ◽  
Terrain Modelling

<p>       In physical geodesy, the harmonic correction (HC), as one of the main problems when using residual terrain modelling (RTM), has become a research focus of high-frequency gravity field modelling. Over past decades, though various methods have been proposed to handle the HC issues for RTM technique, most of them focused on the HC for RTM gravity anomaly rather than other gravity functionals, such as RTM geoid height and gravity gradient. In practice, the HC for RTM geoid height was generally assumed to be negligible, but a quantification is yet studied. In this study, besides the highlighted HC for gravity anomaly in previous studies, the expressions of HC terms for RTM geoid height are provided in the framework of the classical condensation method under infinite Bouguer plate approximation. The errors involved by various assumption of the classical condensation method, e.g., mass inconsistency between infinite masses in the HC and limited masses in the RTM, and planar assumption of the Earth’s surface, are further studied. Based on the derived formulas, the quantification of HC for RTM geoid height when reference surface is expanded to degree and order of 2,159 is given. Our results showed the significance of HC for RTM geoid height, with values up to ~10 cm, in cm-level and mm-level geoid determination. With integration masses extending up to a sufficient distance, such as 1° from calculation point for the determination of RTM geoid height, the errors due to an infinite Bouguer plate approximation are neglectable small. The validation through comparison with terrestrial measurements proved that the HC terms provided in this study can improve the accuracy of RTM derived geoid height and are expected to be useful for applications of RTM technique in regional and global gravity field modelling.</p>

scholarly journals Long Periodic Variation of Orbital Elements of A Satellite Perturbed by Discrete Gravity Anomalies

1978 ◽  
Vol 41 ◽  
pp. 240-240
Author(s):  
M.P. Ananda
Keyword(s):  
Gravity Field ◽  
Gravity Anomalies ◽  
Large Data ◽  
Periodic Variation ◽  
Static Case ◽  
Orbital Elements ◽  
Disturbing Potential ◽  
Data Set ◽  
Simple Matrix ◽  
Derivatives Of

AbstractA method for generating long periodic variations in satellite orbital elements when perturbed by discrete gravity anomalies is presented. The method consists of developing a disturbing potential as a function of orbital and gravity anomaly parameters, and generating partial derivatives of the potential with respect to the orbital elements. The partials are averaged over the period of the satellite to eliminate the short periodic variations. The averaged partials are substituted into the variation of parameter equations to give the mean orbital rates. Classically orbital elements are used in generating gravity field and thus the method is dynamic in nature. The problem is extremely cumbersome and complex when multi-state parameters have to be estimated from a considerably large data set. However, when mean orbital rates are used, the problem reduces to a simple linear static case, where only the gravity parameters have to be estimated, and it is a simple matrix inversion problem. Thus the method developed here was utilized in reducing Appolo 15 and 16 subsatellite radio tracking data to produce a lunar gravity field represented by point masses.

Empirical Determination of the Gravity Anomaly Covariance Function in Mountainous Areas

1980 ◽  
Vol 34 (3) ◽  
pp. 251-264 ◽  
Author(s):  
Gerard Lachapelle ◽  
K. P. Schwarz
Keyword(s):  
Gravity Anomaly ◽  
Covariance Function ◽  
Physical Geodesy ◽  
Gravity Anomalies ◽  
Mountainous Areas ◽  
The North ◽  
Regression Parameters ◽  
Free Air ◽  
Vening Meinesz ◽  
Free Air Gravity

An evaluation of the empirical gravity anomaly covariance function using over 95 000 surface gravity anomalies in the North American Western Cordillera was carried out. A regression analysis of the data exhibits a strong and quasi-linear correlation of free air gravity anomalies with heights. This height correlation is removed from the free air anomalies prior to the numerical evaluation of the gravity anomaly covariance function. This covariance function agrees well with that evaluated previously by the authors for the remainder of Canada. A possible use for such a covariance function of ‘height independent’ gravity anomalies in mountainous areas is described. First, the height independent gravity anomaly at a point of known height is evaluated by least squares prediction using neighboring measured height independent gravity anomalies. Secondly, the part caused by the height correlation is calculated using linear regression parameters estimated previously and added to the predicted height independent gravity anomaly to obtain a predicted standard free air anomaly. This technique can be used to densify the coverage of free air anomalies for subsequent use in integral formulas of physical geodesy, e.g., those of Stokes and Vening Meinesz. This method requires that point topographic heights be given on a grid.

scholarly journals GRAVITY ANOMALY ASSESSMENT USING GGMS AND AIRBORNE GRAVITY DATA TOWARDS BATHYMETRY ESTIMATION

2016 ◽  
Vol XLII-4/W1 ◽  
pp. 287-297
Author(s):  
A. Tugi ◽  
A. H. M. Din ◽  
K. M. Omar ◽  
A. S. Mardi ◽  
Z. A. M. Som ◽  
...  
Keyword(s):  
Gravity Anomaly ◽  
Gravity Field ◽  
Ocean Circulation ◽  
Gravity Data ◽  
Gravity Anomalies ◽  
Airborne Gravity ◽  
Satellite Gravity ◽  
Earth’S Gravity Field ◽  
Explorer Mission ◽  
Satellite Gravity Missions

The Earth’s potential information is important for exploration of the Earth’s gravity field. The techniques of measuring the Earth’s gravity using the terrestrial and ship borne technique are time consuming and have limitation on the vast area. With the space-based measuring technique, these limitations can be overcome. The satellite gravity missions such as Challenging Mini-satellite Payload (CHAMP), Gravity Recovery and Climate Experiment (GRACE), and Gravity-Field and Steady-State Ocean Circulation Explorer Mission (GOCE) has introduced a better way in providing the information on the Earth’s gravity field. From these satellite gravity missions, the Global Geopotential Models (GGMs) has been produced from the spherical harmonics coefficient data type. The information of the gravity anomaly can be used to predict the bathymetry because the gravity anomaly and bathymetry have relationships between each other. There are many GGMs that have been published and each of the models gives a different value of the Earth’s gravity field information. Therefore, this study is conducted to assess the most reliable GGM for the Malaysian Seas. This study covered the area of the marine area on the South China Sea at Sabah extent. Seven GGMs have been selected from the three satellite gravity missions. The gravity anomalies derived from the GGMs are compared with the airborne gravity anomaly, in order to figure out the correlation (R<sup>2</sup>) and the root mean square error (RMSE) of the data. From these assessments, the most suitable GGMs for the study area is GOCE model, GO_CONS_GCF_2_TIMR4 with the R<sup>2</sup> and RMSE value of 0.7899 and 9.886 mGal, respectively. This selected model will be used in the estimating the bathymetry for Malaysian Seas in future.

scholarly journals Regional Recovery of Gravity Anomaly from the Inversion of Diagonal Components of GOCE Gravitational Tensor: A Case Study in Ethiopia

2018 ◽  
Vol 53 (2) ◽  
pp. 55-74 ◽  
Author(s):  
Mehdi Eshagh ◽  
Andenet A. Gedamu ◽  
Tulu B. Bedada
Keyword(s):  
Gravity Anomaly ◽  
Gravity Field ◽  
Ocean Circulation ◽  
Opposite Sign ◽  
Joint Inversion ◽  
Gravity Anomalies ◽  
The Earth ◽  
Tikhonov Regularisation ◽  
The Difference

Abstract The tensor of gravitation is traceless as the gravitational field of the Earth is harmonic outside the Earth’s surface. Therefore, summation of the 2nd-order horizontal derivatives on its diagonal components should be equal to the radial one but with the opposite sign. The gravity field can be recovered locally from either of them, or even their combination. Here, we use the in-orbit diagonal components of the gravitational tensor measured by the gravity field and steady state ocean circulation explorer (GOCE) mission for recovering gravity anomaly with a resolution of 1°×1° at sea level in Ethiopia. In order to solve the system of equations, derived after discretisation of integral equations, the Tikhonov regularisation is applied and the bias of this regularisation is estimated and removed from the estimated gravity anomalies. The errors of the anomalies are estimated and their significance of recovery from these diagonal components is investigated. Statistically, the difference between the recovered anomalies from each scenario is not significant comparing to their errors. However, their joint inversion of the diagonal components improved the solution by about 1 mGal. Furthermore, the inversion processes are better stabilised when using errors of the input data compared with its exclusion, but at the penalty of degradation in accuracy of the estimates.

Constraining dynamic models in North America using the static gravity field

2020 ◽  
Author(s):  
Jesse Reusen ◽  
Bart Root ◽  
Javier Fullea ◽  
Zdenek Martinec ◽  
Wouter van der Wal
Keyword(s):  
Gravity Anomaly ◽  
Gravity Field ◽  
Upper Mantle ◽  
Lower Mantle ◽  
Mantle Convection ◽  
Dynamic Models ◽  
Gravity Anomalies ◽  
Mantle Flow ◽  
Seismic Velocities ◽  
Crust And Upper Mantle

&lt;p&gt;The negative anomaly present in the static gravity field near Hudson Bay bears striking resemblance to the area depressed by the Laurentide ice sheet during the Last Glacial Maximum, suggesting that it is at least partly due to Glacial Isostatic Adjustment (GIA), but mantle convection and density anomalies in the crust and the upper mantle are also expected to contribute. At the moment, the contribution of GIA to this anomaly is still disputed. Estimates, which strongly depend on the viscosity of the mantle, range from 25 percent to more than 80 percent. Our objective is to find the contributions from GIA and mantle convection, after correcting for density anomalies in the topography, crust and upper mantle. The static gravity field has the potential to constrain the viscosity profile which is the most uncertain parameter in GIA and mantle convection models. A spectral method is used to transform 3D spherical density models of the crust into gravity anomalies. Density anomalies in the lithosphere are estimated so that isostatic compensation is reached at a depth of 300 km. The dynamic processes of mantle flow are corrected for before isostasy is assumed. Upper and lower mantle viscosities are varied so that the gravity anomaly predicted from the dynamic models matches the residual gravity anomaly. We consider uncertainties due to the crustal model, the lithosphere-asthenosphere boundary (LAB), the conversion from seismic velocities to density and the ice history used in the GIA model. The best fit is found for lower mantle viscosities &gt;10&lt;sup&gt;22&lt;/sup&gt; Pa s.&lt;/p&gt;

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