Regional Gravity Field Modeling with Adjusted Spherical Cap Harmonics in an Integrated Approach

Abstract

The main objective of this thesis is to develop an integrated approach for the computation of Height Reference Surfaces (HRS) in the context of GNSS positioning. For this purpose, the method of Digital Finite Element Height Reference Surface software (DFHRS) is extended, allowing the use of physical observations in addition to geometrical observation types. Particular emphasis is put on (i) using Adjusted Spherical Cap Harmonics to locally model the potential, (ii) developing a parameterization of coefficients for a least squares estimation, and (iii) optimizing the combination of data needed to calculate the coefficients. In particular, the selection of the terrestrial gravity measurements, height fitting points with known ellipsoidal and normal heights, and the use of the available global gravity models as additional observations are investigated. One of the main motivations is the need to compute a high precise local potential model with the ability to derive all components related to the potential W. These observation components are gravity , quasigeoid height , the geoid height , deflections of the vertical in the east and north direction ( ), the fitting points and the apriori information in terms of coefficients of a local potential model derived from the developed methods of a mapping of a global one.

This thesis provides a method for local and global gravity and geoid modelling. The Spherical Cap Harmonics (SCH) for modeling the Earth potential are introduced in detail, including their relationship to the normal Spherical Harmonics (SH). The different types of Spherical Cap Harmonics, such as Adjusted Spherical Cap Harmonics (ASCH), Translated-Origin Spherical Cap Harmonics (TOSCH) and the Revised Spherical Cap Harmonics (RSCH) are discussed. The ASCH method was chosen in further for modeling the local gravitational potential due to its simple principle, that the integer degree and order Legendre functions are preserved and lead to faster implementation algorithms. The ASCH are used in this thesis to transform the global gravity models like EGM2008 or EIGEN05c to local gravity models, guaranteeing a much smaller number of coefficients and making the calculations faster and easier.

Tests are applied to validate the use of ASCH for local gravity and potential modelling, with ASCH coefficients calculated in test areas. These coefficients were used to calculate the values of potential or the gravity for new points and then compared with the real measured values and reference values from global models. The tests include the transformation of global gravity models like EGM2008 and EIGEN05c to ASCH models and the integrated solution of heterogeneous groups of data including terrestrial gravity data, height fitting points and the locally mapped global gravity models.

The region of the federal state of Baden-Württemberg in Germany was used as a test area for this thesis to prove the concept. Nearly 15000 terrestrially measured gravity observations were used to implement an ASCH model in degree and order of 300 in order to achieve a resolution of 0.01 mGal that corresponds to the measurement accuracy.