Geoid modeling by the least squares modified hotine formula using voronoi cell structures

Increasing use of satellite based positioning techniques in combination with geoid based vertical datum definition for height determination motivates studies on precise geoid modeling. This is supported by the developments in spatial data acquisition techniques and progress in computational methodologies that facilitate computations of accurate and high resolution geoid models. Even though several recent dedicated gravimetric satellite missions (such as GRACE and GOCE) have enhanced accuracy and spatial resolution global geopotential models (GGMs), however, the spatial resolution of GGMs remains still insufficient for many applications. The benefits of these improvements at the long and middle wavelengths of the gravity field signal to the regional geoid mapping become more accurate. This study provides the methodological characteristics of the gravity field modeling and shows a mathematical comparison among the frequently applied methodologies. In spherical approximation, geoid undulation can be determined by using a modified Stokes formula, which combines local terrestrial gravity anomalies and the GGM-derived long wavelength component in a truncated Stokes's integral (LSMSA). As an alternative, this study proposes the Least Squares Modified Hotine Formula with Additive Corrections (LSMHA) for geoid modeling. Once the approximate geoid with the Least Squares Modified Hotine Function is computed, the additive corrections should be implemented to the model. The present study tests the method by conducting an experimental geoid modeling in Auvergne area of France (43N and 49N latitudes, -1E and 7E longitudes). The GOCO05C geopotential model, digital terrain model data (grid form with 0.005 degrees spacing), homogeneously distributed dense point gravity data and GNSS/leveling data are employed in the computations. The Hotine function requires the use of gravity disturbances instead of anomalies. Gravity disturbance is a function of GNSS-derived ellipsoidal heights. Therefore the Hotine approach can be considered as a more practical approach in comparison with Stokes. Usually, uniform grid of gravity quantities is needed as an input for Stokesian/Hotine's integration. However, since unsuitable gridding methods may produce false or spurious data that might lead to an inaccurate geoid, this study attempts to avoid conventionally gridded gravity data as an input to geoid modeling. Instead, the gravity data of the target area is partitioned into convex and adjacent polygons; each holds the original values of the gravity disturbances. Within the integration area, the polygonal figures in Voronoi cell structures are used since the algorithm enables to preserve the actual characteristics of the observed gravity signal content. The resulting geoid models are assessed by the GNSS/leveling data and also compared to traditional geoid modeling approaches. Numerical results are provided in the conclusions of the study.