Abstract: At present, the main principle of the seafloor topography inversion method is to fit the most appropriate linear relationship between topography and gravity or gravity gradient. However, different topography will have different linear relationships. In order to overcome the constraint of uncertainty, this paper firstly derives the expression of vertical gravity gradient generated by cubic prism. Then, by gridding the research sea area, a functional relationship between vertical gravity gradient (VGG) and sea depth is established, i.e. the observation equations of sea depth. On the basis of which, it is that the observation equations have strong anti-error interference properties through simulation calculation. Because the observation equations are affected by the seamounts outside the study area (divided into boundary effects and far area effects), it is necessary to propose corresponding mathematical methods to deal with these effects. This paper proposes to expand the research sea area to obtain an expanded area, and then study the observation equations on the expanded sea. At this time, in order to avoid the singularity of the observation equations, a regularization method is introduced to solve the expanded observation equations and cut out the sea depth in the study area. Simulation experiments show that after using the regularization method, the root-mean-square error of the inverted sea depth is only 0.48 m. Finally, this paper inverts an actual seafloor topography of the South China Sea, and the results are compared with the 289 ship sounding data. The root-mean-square error of the inversion results can reach 109 m.

Key words: seafloor topography, vertical gravity gradient, boundary effect, far area effects, regularization