Stokes-Helmert Method For Geoid Determination

This dissertation mainly focuses on the theories and realizations of geoid determination based on the Stokes-Helmert method in the spherical coordination. The main works and contributions are summarized as follows:1. The Stokes-Helmert BVP and linearization of its boundary condition are elaborated. The transformation of observed values of gravity, both of terrestrial and spatial origin, into the Helmert space is provided by a series of corrects.The topography above the geoid, which is treated as a spherical surface, is subdivided a spherical shell part and a roughness part. Based on the second Helmert condensation and the mean condensed topographical density assumption, the formulas of the effects of the topography on potential are derived for the points on the surface of the earth and the geoid. The practical formulas for the potential of the roughness part in the near and far zone are presented. The formula of the elliopsoid correction for gravity anomaly is derived and analyzed for the test area.2. The formulas of the direct effects and the secondary indirect effects of the topography on the gravity,and the indirect effects of the topography on the potential for the poits on the surface and the geoid are derived and analyzed in the spherical approximation.The direct effect of the topography on the gravity being of short wave is mainly caused by the rough terrain,as a result, the finer the terrain is the better the direct of the topography on the gravity is calculated.The indirect effect of the topography on the geoid is mainly decided by the height of point.it is pointed out that a deviation can occur in geoid when the terrain density is replaced by the mean density of the crust.The formula of the secondary indirect effect of the topography on gravity is derived and its effect on the geoid is small.3. Two methods of the downward continuation of the Helmert gravity anomaly are used in the paper. The possoin downward continuation needs to consider many influencing factors, and it also can easily enlarge the high-frequency noise.By contrast, the analytical downward continuation is easy and fast.The result shows that the analytical downword continuation method with an 0.5° integral radius is better.4. The interpolation methods of Helmert gravity anomaly for the grids are studied. The traditional method is so-called indirect method characterized by means of the isostatic gravity anomaly or bougher gravity anomaly. Instead the direct interpolation method is used in this paper from the Helmert gravity anomalies in the form of point values. It is showed by the comparsion of the two methods that direct method is simpler and less effect by the model parameters.5. Research and analysis to improve access to the high precision and high resolution earth gravity field of the long wave ability. There are realations between the degree of the gravity field model, the wave-length of the gravity field and its spatial resolution. The long-wave of the gravity field is calculated by the gravity field model. During the formation of the high resolution of gridding, the high-frequency noise or frequency aliasing phenomena may be introduced. The spline smoothing or the low-pass filter is proposed to resolve the phenomenon. The experiment result shows that the spline smoothing as well as the low-pass filter can improve the precision of long-wave counonents.6. Stokes-Helmert method for geoid determination is presented in detail. Different ways to improve the geoid accuracy. Various modified Stokes kernel functions are used to caluculate the residual geoid, the VK-Stokes is proved to be the best one. Eight GPS/leveling points are used to test the accuracy of the geoid, the result shows that the accuracy of the geoid is about 10cm. By this token, the Stokes-Helmert method can determine the geoid with the high precision and resolution. So it can provide the technical support for future work to establish 1-cm geoid.