| Résumé : |
(auteur) Due to the increasing availability of global high-resolution digital terrain models (DTMs), it has nowadays become possible to obtain a detailed image of the Earth’s topography. This enables to precisely determine the gravitational effect of the topographic masses on the Earth’s gravity field. The central technique for this aim is gravity forward modeling (GFM), which is based on Newton’s law of universal gravitation, and allows to convert topographic heights along with suitable density assumptions into corresponding values of the gravitational potential and its derivatives. This topographic gravity forward modeling attracts a growing interest in various areas of geodetic gravity field determination and geophysical studies of the Earth’s composition and structure (e.g., solid-earth sciences). However, previous GFM methods have proven unsuitable for the increasing accuracy requirements stemming from an improved precision of geodetic measurements. This is due to commonly used simplifications and approximations, such as (i) the use of condensed heights for water and ice masses (rock-equivalent heights), (ii) mass discretizations or arrangements based on planar and spherical approximations, and (iii) assumptions regarding the spectral consistency between band-limited topographic heights and induced gravity, as in residual terrain modeling (RTM) techniques. This thesis contributes to state-of-the-art GFM in the space domain by providing effective techniques and refinements that overcome these limitations. More concretely, the theory of the Rock-Water-Ice (RWI) approach is developed that encompasses a more realistic modeling of the Earth’s topographic and isostatic masses, i.e., the masses of the continents, oceans, lakes, ice sheets and shelves, as well as their deeper lying (isostatic) compensation masses in the Earth’s interior. The RWI method is characterized by a three-layer decomposition of the Earth’s topography that accounts for a rigorous separate modeling of the rock, water, and ice masses with variable density values. Furthermore, a modified Airy-Heiskanen isostatic concept is applied that is enhanced by additional geophysical information in terms of a seismologically derived depth model of the Mohorovicic discontinuity, i.e., the boundary surface between the Earth’s crust and mantle. To counteract the increased computational demand of the more complex modeling, an efficient numerical algorithm is needed for the forward modeling. For space domain GFM, it has become more and more customary to use a mass discretization based on tesseroids, which are mass bodies bounded by geocentric spherical coordinate lines, and hence are directly linked to the curvature of the Earth. Several studies have demonstrated their superiority over classical prism methods with respect to precision and computation time. However, for global applications based on high-resolution DTMs, any computational speed-up with respect to a single mass body leads to a massive improvement in the overall computation time. This thesis presents a considerable optimization of previously used tesseroid formulas, where the gravitational field of a tesseroid and its derivatives up to second-order are represented in a compact and computationally attractive form. This allows an efficient numerical evaluation that reduces the overall runtime by about 20 to 55%, depending on the evaluated gravity field functional. Additionally, to correctly locate topographic masses in space, tesseroids are arranged on an ellipsoidal reference surface. Within this thesis, the novel tesseroid-based RWI approach is applied to different topographic input data and is used for various gravity field functionals in two main applications. Both are connected to ESA’s satellite mission GOCE (Gravity field and steady-state Ocean Circulation Explorer) that measured the second-order derivatives of the gravitational potential, commonly known as gravity gradients. In the first application, RWI-based topographic-isostatic effects are calculated along the orbit of the GOCE satellite and are subtracted from the gravity gradient observations. In this way, the measurement signal is smoothed so that interpolation and prediction tasks, such as harmonic downward continuation of the gradients from satellite altitude to the Earth’s surface, can be executed with an improved numerical stability. While in previous studies such a concept was applied to simulated gravity gradients, this thesis presents the application to real GOCE measurements. As the smoothing effect strongly depends on the variability of the topography crossed by the satellite, this procedure is particularly suitable for regional applications. For a time series when the satellite passed the Himalayan region, a comparison of the observed gradients to the reduced ones reveals significant smoothing effects that are quantified by analyses in the space and frequency domain. The second application contributes to the task of height system unification, which aims to connect the different locally defined reference levels, conventionally used for national height systems. This is achieved by a satellite-based method which employs global geopotential models derived from data of the GOCE mission, whose limited spectral resolution is extended by high-frequency topographic effects of the RWI approach. To extract these high-frequency signals, a novel (residual) gravity forward modeling method is proposed that allows to perform the required high pass filtering directly in the gravity domain, thus, avoiding the above-mentioned assumption (iii) of the RTM method. By using three representative study areas in Germany, Austria, and Brazil, the benefit and importance of high-frequency topography-implied gravity signals for an accurate estimation of height datum offsets is demonstrated. As a highlight of this thesis, the RWI approach is utilized to generate a series of topographic-isostatic gravity field models. These RWI models provide a high-resolution representation of the Earth’s topographic-isostatic gravitational potential in terms of spherical harmonics expanded up to degree and order 1800 (Release 2012), and 2190 (Release 2015). The spherical harmonic coefficients of these models are obtained from a spherical harmonic analysis of global gridded potential values, which have been calculated by massive parallel computing on high-performance computer systems. By using spherical harmonic synthesis, the RWI model can be used to efficiently calculate various functionals of the topographic-isostatic potential in different heights. For this purpose, the RWI models are publicly available via the database of the International Centre for Global Earth Models (ICGEM) and have already been used in a wide range of studies by other research groups. |
Gravity forward modeling with a tesseroid-based rock-water-ice approach (2017)
