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It is the purpose of this thesis to investigate different regional geoid determination methods with respect to their feasibility for use with a future GOCE satellite-only Earth Gravity Model (EGM). This includes investigations of various techniques, which involve different approximations, as well as the expected accuracy. Many, but not all, of these tasks are tested by means of Synthetic Earth Gravity Models (SEGMs). The study is limited to remove-compute-restore methods using Helmert condensation and to Sjöberg's combined approach (method with additive corrections). First, a number of modifications of Stokes' formula are tested with respect to their compatibility with a GOCE EGM having negligible commission error. It is concluded that the least squares modification method should be preferred. Next, two new point-mass SEGMs are constructed in such a way that the resulting models have degree variances representative for the full and topographically reduced gravity fields, respectively. These SEGMs are then used to test different methods for modified Stokes' integration and downward continuation. It is concluded that the combined method requires dense observations, obtained from the given surface anomalies by interpolation using a reduction for all known density anomalies, most notably the topography. Examples of other conclusions are that the downward continuation method of Sjöberg (2003a) performs well numerically. To be able to test topographic corrections, another SEGM is constructed starting from the reduced point-mass model, to which the topography, bathymetry and isostatic compensation are added. This model, which is called the Nordic SEGM, is then applied to test one strict and one more approximate approach to Helmert's condensation. One conclusion here is that Helmert's 1st method with the condensation layer 21 km below sea level should be preferred to Helmert's 2nd condensation strategy. The thesis ends with a number of investigations of Sjöberg's combined approach to geoid determination, which include tests using the Nordic SEGM. It is concluded that the method works well in practice for a region like Scandinavia. It is finally shown how the combined strategy may preferably be used to estimate height anomalies directly.

QC 20100713

<p>It is the purpose of this thesis to investigate different regional geoid determination methods with respect to their feasibility for use with a future GOCE satellite-only Earth Gravity Model (EGM). This includes investigations of various techniques, which involve different approximations, as well as the expected accuracy. Many, but not all, of these tasks are tested by means of Synthetic Earth Gravity Models (SEGMs). The study is limited to remove-compute-restore methods using Helmert condensation and to Sjöberg's combined approach (method with additive corrections).</p><p>First, a number of modifications of Stokes' formula are tested with respect to their compatibility with a GOCE EGM having negligible commission error. It is concluded that the least squares modification method should be preferred.</p><p>Next, two new point-mass SEGMs are constructed in such a way that the resulting models have degree variances representative for the full and topographically reduced gravity fields, respectively. These SEGMs are then used to test different methods for modified Stokes' integration and downward continuation. It is concluded that the combined method requires dense observations, obtained from the given surface anomalies by interpolation using a reduction for all known density anomalies, most notably the topography. Examples of other conclusions are that the downward continuation method of Sjöberg (2003a) performs well numerically.</p><p>To be able to test topographic corrections, another SEGM is constructed starting from the reduced point-mass model, to which the topography, bathymetry and isostatic compensation are added. This model, which is called the Nordic SEGM, is then applied to test one strict and one more approximate approach to Helmert's condensation. One conclusion here is that Helmert's 1st method with the condensation layer 21 km below sea level should be preferred to Helmert's 2nd condensation strategy.</p><p>The thesis ends with a number of investigations of Sjöberg's combined approach to geoid determination, which include tests using the Nordic SEGM. It is concluded that the method works well in practice for a region like Scandinavia. It is finally shown how the combined strategy may preferably be used to estimate height anomalies directly.</p>

The Mohorovičič discontinuity (Moho), which is the surface separating the Earth’s crust from the mantle, is of great interest among geoscientists. The Moho depth can be determined by seismic and gravimetric methods. The seismic methods are expensive, time-consuming and suffer from lack of global coverage of data, while the gravimetric methods use inexpensive and mostly already available global and regional data based on an isostatic model. The main reasons for studying an isostatic model are on one hand the gaps and uncertainties of the seismic models, and, on the other hand, the generous availability of gravity data from global models for the gravimetric-isostatic model. In this study, we present a new gravimetric-isostatic Moho model, called the Vening Meinesz-Moritz (VMM) model. Also, a combined Moho model based on seismic and gravimetric models is presented. Classical isostatic hypotheses assume that the topographic potential is fully compensated at all wavelengths, while is not the case in reality. We found that the maximum degree of compensation for the topographic potential based on the new Moho model is 60, corresponding to the resolution of about 330 km. Other (dynamic) isostatic effects (such as temporal compensation, plate tectonics, post-glacial rebound, etc) should be considered as well, which are disregarded in this thesis. Numerical results imply that the dynamic phenomena affect mostly the long-wavelengths. The VMM model is applied for different purposes. The Moho density contrast is an important parameter for estimating the Moho depth, and we present a technique to simultaneously estimate Moho depth and density contrast by the VMM and seismic models. Another application is the recovery of gravity anomaly from Satellite Gravity Gradiometry (SGG) data by a smoothing technique, and we show that the VMM model performs better than the Airy-Heiskanen isostatic model. We achieved an rms difference of 4 mGal for the gravity anomaly estimated from simulated GOCE data in comparison with EGM08, and this result is better than direct downward continuation of the data without smoothing. We also present a direct method to recover Moho depth from the SGG mission, and we show that the recovered Moho is more or less of the same quality as that obtained from terrestrial gravimetric data (with an rms error of 2 km). Moreover, a strategy is developed for creating substitutes for missing GOCE data in Antarctica, where there is a polar gap of such data. The VMM model is further used for constructing a Synthetic Earth Gravity Model (SEGM). The topographic-isostatic potential is simple to apply for the SEGM, and the latter can be an excellent tool to fill data gaps, extending the EGMs to higher degrees and validating a recovery technique of the gravity field from a satellite mission. Regional and global tests of the SEGM yield a relative error of less than 3 % vs. EGM08 to degree 2160. / QC 20110405