Sammendrag
Stokes's formula published by George Gabriel Stokes in 1849 is still the most important formula in physical geodesy. It enables us to compute the geoidal height N from the gravity anomaly data. But, the major drawback of the Stokes's formula is that it needs the coverage of the gravity over the whole Earth. To diminish this problem, we limit the integration area to a spherical cap with radius $\psi_{0}$ around the computation point and to reduce the truncation error committed, a modification of Stokes's integral is implemented. In the modified Stokes's formula, the long-to-medium-wavelength components of the geoid are determined from a global Earth Gravity Model (here, EGM96), whereas the short-wavelength contributions are obtained from terrestrial gravity information. A geoid model built up in this way has high relative accuracy and resolution, but its absolute accuracy is poor due to the long-wavelength errors in the geopotential model as the adopted reference. The geoid serves as the most important reference surface for vertical datums. Conventional levelling heights, orthometric heights, are referred to the geoid surface. Hence, having an accurate geoid results in precise orthometric heights, which is very important to most of the geodetic and engineering projects. With the advent of satellite positioning, especially Global Positioning System (GPS), the geoid has become directly observable on land through a combination of GPS ellipsoidal height, h, and precise orthometric height H through levelling. The geoid derived with this method has high absolute and relative accuracy, but it is not enough dense to produce a national levelling reference surface. This thesis is based on 11 papers, which are given in Part II. Part I begins with a brief introduction (Chapter 1). Chapter 2 deals with the concept of geoidal height computations using the modified Stokes's formula and the GPS-levelling derived geoid. Chapter 3, which is a major contribution of this study, treats the problems encountered in compiling an accurate geoid model. To have a more accurate estimate of the geoid, we have reformulated the terrain corrections. Downward continuation of mean gravity anomalies is investigated. Kernel modification of Poisson's kernel, low frequency contribution, and truncation error are implemented in downward continuation. Atmospheric direct and indirect effects on geoid are reformulated and investigated precisely in the classical and truncated, as well as modified Stokes's formula. Chapter 4 is devoted to the numerical integration of terrestrial gravity anomalies with the modified Stokes's integral. Numerical investigations, including all corrections and geoid determination over Sweden are discussed in Chapter 4.
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