An investigation into the effects of different parameters on high-resolution geoid modeling accuracy in the context of height system modernization

Abstract

In contemporary times, many countries have focused on obtaining orthometric heights through satellite-based positioning techniques, utilizing ellipsoidal heights and geoid heights derived from geoid models, as part of height system modernization efforts. This shift is primarily driven by several factors: the inherent limitations of traditional leveling, which is a costly, labor-intensive, and time-consuming process; the economic advantages of employing geoid models in conjunction with satellite-based positioning systems; the ability to obtain real-time physical height information; and the diminished susceptibility to the deformative effects of the Earth's crust. Given the ability to obtain highly accurate ellipsoidal heights using GNSS, the accuracy of regional geoid models directly impacts the determination of orthometric heights. In many methods used for the computation of gravimetric geoids, similar to the least squares modification of Stokes formula with additive corrections (LSMSA) technique utilized in this thesis, gridded free-air anomaly data are employed as input. Observed gravity data from the Earth's surface is heavily influenced by the gravitational field of the Earth due to topographic masses and cannot be directly utilized in the gridding process. Consequently, observed gravity data are first transformed into anomalies and then reduced to the geoid using Bouguer reduction, where the topography is represented by a Bouguer plate (or shell). The resulting Bouguer anomalies obtained in this manner are suitable for the gridding process and create a smooth surface. The selection of the Bouguer anomaly type (simple or complete) is performed considering the topography of the study area. Simple Bouguer anomalies can be used in studies conducted in plain areas with minimal topographic variations. However, complete Bouguer anomalies, which also incorporate the terrain correction (TC) effect, are essential for applications carried out in rough topography despite their higher computational burden. The determination of the most suitable Bouguer anomaly to be used in the gridding process in the study area of Auvergne, France, is conducted through numerical tests in the first part of this thesis. The investigations reveal differences exceeding 55.6 mGal between the two anomaly grids and 27 cm between the geoids generated from these grids. Therefore, in areas with complex topography such as Auvergne, the use of complete Bouguer anomalies incorporating terrain correction effects is crucial for obtaining precise gravimetric geoids. In the second numerical application of the study, a series of tests are conducted to determine the optimal parameters to be used in LSMSA, selected as the computation method for gravimetric geoids. The parameters identified here are adopted as the fundamental parameters for the geoids computed throughout the entire study. The third numerical application, constituting the main focus of this thesis, investigates the impact of interpolation methods on gravimetric geoid computation. Both the areal difference maps and absolute validation results obtained in this section demonstrate that the conventional methods such as Inverse Distance to a Power (IDP), Nearest Neighbor, and Kriging, which have been widely used for gridding gravity data in geodesy and geophysics for a long time, provide similar and reliable results. On the other hand, the Artificial Neural Network (ANN), a complex, optimization-based soft computing method with proven effectiveness in many fields, does not yield superior results compared to these three methods. As a conclusion, it is inferred that the interpolation algorithms have an impact on the gravity gridding outcomes and, consequently, the determination of the geoid model. GPS/Leveling points are typically measured in plain terrain rather than rugged areas due to the inherent challenges of their establishment in such environments. Absolute validation processes are conducted in both plain and rugged terrain during the 4th numerical test, revealing differences of up to two-times of magnitude between the validation results obtained in these two different terrains. This disparity stems from the denser and more homogenous distribution of points in plain areas, which more accurately captures the topography. As the final numerical application, the applicability of the ANN algorithm for gravity gridding is investigated. The conducted experiments demonstrated that the complete Bouguer anomalies gridded using the ANN approach yield distinct results each time, regardless of the employed parameters (neurons - epochs). Consequently, it is concluded that the ANN technique has not produced satisfactory results in the gravity gridding process, which is an important part of gravimetric geoid computation, in this thesis study. In summary of the conducted studies, the findings highlight the crucial role of the interpolation algorithm employed in high-precision geoid undulation calculations. Additionally, it has been concluded that the ANN method does not perform as well in the gridding process compared to traditional interpolation methods such as Kriging, IDP, and Nearest Neighbor. Furthermore, the type of Bouguer anomaly used in gridding is crucial, especially for rugged study areas. Lastly, it is noted that the distribution of GPS/leveling points used in absolute validation affects the validation results.