The nonlinear effects in bathymetric prediction from altimetric gravity data

Most present-day bathymetric prediction solely addresses the linear mapping relationship between gravity signals and bathymetric data, disregarding nonlinearity’s effects, despite a probable nonlinear mapping between gravity signals and the seafloor topography. This paper investigates the consequences of excluding nonlinear terms in predicting bathymetry and reaches focused conclusions for different types of seafloor topography. The nonlinear effects were assessed by modelling the gravity signals generated by seafloor topographies with different topographic relief, topographic sizes, and basal depths. The results demonstrate that the nonlinear effect is more pronounced in shallow seas compared to deep seas for the same topographic relief. Furthermore, the consequences of ignoring nonlinear terms become more significant as topographic relief increases and topographic sizes decrease. The experiment on topographic sensitivity demonstrates that nonlinear gravity signals are able to detect small-scale topography more acutely, with higher orders corresponding to smaller sensitive topographic sizes. Using the Emperor seamount chain as an illustrative example, the nonlinear mapping is created by employing the eXtreme Gradient Boosting. The prediction accuracy of bathymetry using gravity anomalies has increased by 13%, whereas the predictive precision through vertical gravity gradient anomalies has risen by 7%. These results confirm the conclusions drawn from the simulation experiment. In addition, the results of the global nonlinear effects indicate that the regions most impacted are situated in the trenches along the plate boundaries, the eastern Pacific, and the Atlantic Ridge. The prediction of bathymetry will benefit from the consideration of nonlinear relationships, particularly for shallow sea and small-scale topography.