Research on the design of multibeam bathymetric survey line based on geometric derivation

Based on the working principle of multibeam bathymetric system, this paper establishes a multibeam line design optimization model and coverage width geometric model by establishing a spatial right-angled coordinate system, dichotomy method, moving surface method and other methods. A two-dimensional geometric model of the coverage width and the overlap rate of adjacent strips is established in the two-dimensional plane. Then, based on the geometric model, the relationship equations of seawater depth at the centre of different lines are obtained by triangulation, and then the sine equations of seawater depth at the centre of the line, coverage width and coverage rate are obtained by the sine theorem. Then the equations of the line plane, the multibeam plane and the seabed slope are solved in 3D space, and finally the geometric model of the line perpendicular to the gradient and the optimisation model of the line parallel to the gradient are established respectively. Finally, comparing the total lengths of the lines in the two directions, it is determined that the line direction is east-west, the total number of lines is 34, the total length of the lines is 125936m, and the interval between the lines decreases with the increase of gradient.