Precision geoid determination by Fast Fourier Transform solutions of the Kernel functions of the gridded gravity anomalies and distances in the Oman Gulf
Abstract
The geoid is the fundamental surface that defines the figure of the Earth. It is approximated by mean sea level and undulates due to spatial variations in the Earth's gravity field.
The solution, that considers a global geopotential model (GM), gravity anomalies (Δg), and topographic effects, is used to determine the gravimetric geoid undulation. The EGM96 global geopotential model to degree 360 was used in order to determine the long wavelength effect of the geoid surface. By applying the remove-restore technique the geoid undulations were determined by combining a geopotential model, mean free-air gravity anomalies and height in a Digital Elevation Model (DEM). The long wavelength effects from a geopotential model and short wavelength effects from the topography are mathematically removed from the observed gravity anomalies in this technique. The Stoke’s formulation of the residual parts of the gravity anomalies yields the medium wavelength of the geoid height. The geoidal height of a point is determined by restoring the long and short wavelength components. If the area for determining local geoid is chosen small and is considered as planar, it can be divided into M by N grids while distances Δx and Δy are the grid intervals. The geoid undulations can be calculated from Fast Fourier Transform (FFT) solutions of the Kernel functions of the gridded gravity anomalies and distances.
This paper deals with the precision geoid determination by a gravimetric solution in around the Oman Gulf. The size of the study area is about 600 km by 660 km. A number of data files were compiled for this work, containing now more than 88000 point gravity data on ocean areas. The EGM96 global geopotential model to degree 360 was used in order to determine the long wavelength effect of the geoid surface. By applying the remove-restore technique the geoid undulations were determined by combining a geopotential model, mean free-air gravity anomalies.
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Introduction
The geoid can be described as the equipotential surface of the Earth’s gravity field which corresponds most closely with mean sea-level in the open oceans and ignores the effects of semi-dynamic sea surface topography. It defines the figure of the Earth and is used as the vertical datum surface in most countries. The determination of the geoid has attracted much attention within the discipline of geodesy, where both theoretical and practical problems are studied in order to improve the definition and accuracy of the geoid. This has been possible since the publication of the famous (to geodesists) integral formula by George Gabriel Stokes in 1849.At every point, the geoid surface is perpendicular to the local plumb line. It is then a natural datum or reference surface for orthometric heights measured along the curved plumb lines and, at the same time, the geoid is the best graphical representation of one equipotential surface of the Earth gravity field
Geoid determination is the process of calculation of the length of the ellipsoidal normal (geoid undulation) between the geoid surface and the reference ellipsoid. Various methods are used in determination of the geoid undulations.In Iran, Ardalan evaluated some geopotential models to determine the optimal reference field for the geoid solution. A comparison of the solutions with surface gravity data, GPS data and each models in Iran showed that the EGM96 and PGM2000A models to degree 360 gives the best fit ( Ardalan et al 2006).
Conclusion
In this study a gravimetric geoid solution was determined in Oman Gulf using all available gravity. This involves EGM96 to degree and order 360 as a reference model, and the computations are conducted by two dimensional spherical and plannar FFT. The comparison two methods yields the standard deviation of 5.78 m and 5.87 m for two methods respectively. The resulting geoid shows that the difference from the south-East to the North-West is about 28.63 meters across the Oman Gulf.
As a result of this study, the minimum and maximum absolute values of the differences between geoid undulations obtained from two approaches at a point -1.32 m and 1.37 m respectively. Obtained geoid undulations from combined solution showed that variation between maximum and minimum values and standard deviation are smaller on spherical approach with respect to planar approach.