Mathematical model of echoes in laser-based aerial bathymetric surveying

A mathematical model is proposed in which the effects of light propagation are represented geometrically by a cone of propagation. The cone is described by the position of its axis as a function of depth, an effective angle of dispersion and an effective power distribution inside the cone. The analytical model is used to obtain ocean bottom echo-pulse shapes. These results are compared to existing experimental waveforms and existing simulation models which are more accurate but also more computationally intensive than the model presented. This model is shown to depict qualitatively well the effects exhibited by experimental data and by more accurate models. At shallow depths, when most of the photons are not scattered by water, the echo-pulse shape is dependent mainly on the geometry of transmission (nadir angle), and straightline propagation can be assumed. For larger depths, when multiple scattering becomes the dominant source of dispersion, traveling of the optical pulse in water is better modeled by including a dispersion angle that increases with depth and the bending effect of the geometric cone of propagation