Accurate Depth Inversion Method for Coastal Bathymetry: Introduction of Water Wave High-Order Dispersion Relation

Abstract

This paper proposes a wave model for the depth inversion of sea bathymetry based on a new high-order dispersion relation which is more suitable for intermediate water depth. The core of this model, a high-order dispersion relation is derived in this paper. First of all, new formulations of wave over generally varying seabed topography are derived using Fredholm’s alternative theorem (FAT). In the new formulations, the governing equation is coupled with wave number and varying seabed effects. A new high-order dispersion relation can be obtained from the coupling equation. It is worth mentioning that both the slope square and curvature terms ( ( ∇ h ) 2 , ∇ 2 h , ( ∇ k ) 2 , ∇ 2 k , ∇ h ⋅ ∇ k ) of water wavenumber and seabed bottom are explicitly expressed in high-order dispersion relation. Therefore, the proposed method of coastal bathymetry reversion using the higher-order dispersion relation model is more accurate, efficient, and economic.