An Analytical Method to Estimate Seabed Topography Only from Vertical Gravitational Gradient

Abstract

In the present methods to estimate seafloor topography from gravimetric data, some parameters need be computed in advance from the known bathymetric data, which leads some uncertainties in applying the methods. To overcome such uncertainties, an analytical method to estimate the seafloor topography from the vertical gravity gradient (VGG) is introduced in the paper. Based on the expression of VGG generated by a cubic prism, the observation equations for the seabed depth are established firstly. Then, the simulation results show that the observation equations established are solvable. Especially, the piecewise bilinear interpolation is introduced to separate the influence of the far-field anomalous bodies on VGG. In addition, some imitation arithmetic examples are given in order to examine the solvability of the observation equations and estimate the accuracies of their solutions. Finally, an actual seafloor topography located in South China Sea (117.6-118.25°E, 17-17.65°N), is estimated by the method proposed in the paper, and compared with ship depth sounding, the root mean square (RMS) error of bathymetry prediction is 77 m.

Keywords:

• Boundary effect
• gravity-geological method
• piecewise bilinear interpolation
• seabed topography
• vertical gravitational gradient

Acknowledgments

The authors thank to GFZ and NGDC for supplying actual data.

Author contributions

Derivations for main formulas, designs of computations and writing original draft, Yu Jinhai; Software, computations for arithmetic examples and analysis for computational results, Xu Huan; Analysis for actual topography and review paper, Wan Xiaoyun. All authors have read and agreed to the published version of the manuscript.

Additional information

Funding

This work is funded jointly by the Major Research Plan of China (No. 2016YFB0501702), the National Nature Science Funds of China (No. 41774089, 41674026) and Fundamental Research Funds for the Central Universities (No. 2652018027).