The Hotine-Helmert method for determining the regional quasi-geoid considering the complete Bouguer effect of water bodies

The conventional Hotine-Helmert method for determining the regional quasi-geoid fails to adequately consider the complete Bouguer effect of seawater, rivers, and lakes. This paper systematically evaluates the three effects the experimental area: Helmert condensation on disturbed gravity, seawater residual terrain effects, and complete Bouguer effect on river/lake water, revealing them to be of comparable magnitude. Height anomalies demonstrate maximum absolute values of decimeter-scale for Helmert condensation impacts, while millimeter-scale maxima emerge for both seawater residual terrain and river/lake complete Bouguer effects. Implementing generalized Hotine integral to determine the gravitational quasi-geoid, this papar innovatively incorporates combined terrain effects including the topographic Helmert condensation effect, seawater residual terrain effects, and complete Bouguer effect on river/lake water. The results indicate that maximum absolute influences of 0.310 m for seawater residual terrain and 0.095 m for river/lake Bouguer effects on grid-point quasi-geoid values. The standard deviation of differences between height anomalies of GNSS/leveling points and the gravitational quasi-geoid reaches ±0.036 m with seawater and river/lake effects contributing 3 mm and 2 mm (standard deviation), respectively. These represent a 12.2% improvement over traditional Hotine-Helmert method results. Post-integration, the quasi-geoid achieves internal and external root-mean-square accuracies of ±0.009 m and ±0.019 m respectively, validating the enhanced accuracy achieved by accounting for complete water body Bouguer effects in the Hotine-Helmert quasi-geoid determination.