Sensitivity analysis of gravity anomalies and vertical gravity gradient data for bathymetry inversion

Bathymetry is the measurement of the water depth similar to underwater topography. Gravity anomaly and vertical gravity gradient are important data used to inverse bathymetry. In this study, we investigate the sensitivities of the gravity anomalies and vertical gravity gradient data to bathymetry inversion. Firstly, the formulas of the gravity anomaly and vertical gravity gradient signals produced by the seabed terrain are derived, and then a series of numerical studies are designed to investigate the sensitivities. The results show that gravity anomalies and vertical gravity gradients have different sensitive bands to bathymetry inversion. Therefore, accuracy requirements for the gravity anomaly and vertical gravity gradient data are different for bathymetry inversion with different spatial resolutions and accuracies. With decreasing resolution, the accuracy requirement of the gravity anomaly gradually decreases, whereas the accuracy requirement of the vertical gravity gradient first decreases and then increases, indicating that the vertical gravity gradient is more sensitive to the short-wavelength signal than the gravity anomaly, especially in the 0-20km wavelength ranges. In addition, we perform a theoretical analysis that shows that the vertical gravity gradient has a band that is most sensitive to the seafloor topography. This study is capable to provide a reference for the design of future satellites to retrieve the bathymetry.