Accuracy analysis of topography estimation from geoid heights and vertical gravity and vertical gravity gradient

This study investigates the accuracy requirements for predicting seafloor topography using anomalies in geoid height (GH), vertical gravity (VG), and vertical gravity gradient (VGG), based on their analytic formulas for rectangular prisms. Simulations conducted under a specified observation accuracy demonstrate that VGG anomalies are more effective for high-resolution topography estimation in shallow seas, whereas lower resolution is preferable in deep-sea regions. Furthermore, we formulate observation equations linking GH, VG and VGG anomalies to topography and verify through simulation that these equations are well-posed and solvable. The robustness of these observation equations against errors is also evaluated. When random and systematic errors in the GH, VG and VGG anomalies are set to 3 cm, 1 mGal, and 1 E (Eötvös, 1 E = 10⁻⁹ s⁻²), respectively, the root mean square (RMS) errors of the predicted topography remain below 70 m. Additionally, the simulations indicate that the observation equations exhibit greater resistance to systematic errors than to random errors. The impacts of density and reference depth errors on the observation equations are also examined. The results reveal a strong correlation between these errors and the prediction accuracy. With a 20% relative error in the density constant, the RMS errors for topography derived from GH, VG and VGG data are all under 130 m. Moreover, the RMS error increases approximately linearly with the reference depth error. Finally, to reduce the influence of boundary and far-field effects, the sea area outside the study region is divided into a boundary zone and a far zone, with “regularization” and “remove-compute-restore” techniques applied accordingly.