Phase Speed Inversion for Shallow Water Bathymetry Mapping

Abstract

This study explored the use of top-view movies of propagating gravity water waves to reconstruct the underwater bed profile of shallow water bodies. Water waves of 2.8 and 3.1 Hz were generated by a microcontroller-driven flat flap in a wave flume of dimensions 0.48 × 1.80 × 0.40 m $^{3}$ . Three different bed profiles, i.e., sloped, stepped, and split surfaces, were used to imitate typical seabeds near shorelines. Top-view movies of the propagating waves were recorded and converted to spatial phase-speed images via video analysis. The phase speed images can be used to reconstruct the underwater bed profile using the dispersion relation of linear water waves. We also proposed a demodulation method to correct the phase-speed alteration due to wave interference. The correction method helped improve the mean average percentage error for depth profile predictions from 15% to 10% for the sloped profile and from 45% to 15% for the stepped profile. However, the approach was inferior for the split profile due to wall effects and complex interference patterns. This study suggests the proposed approach can determine the depth level around shorelines using time-evolution or video data with an adequate accuracy of 10% with minimal interference.