Optimal modeling of line paths based on multibeam bathymetric system

Abstract

Multibeam ocean bathymetry is one of the major issues in exploring the ocean. For problems such as multibeam line ocean bathymetry, this paper starts from the related theory, analyzes the inherent geometric features of the problem, comprehensively establishes a multibeam line model with generalized significance within a certain error range, and according to the method of least squares, gives a model of the line with a fixed opening angle of the multibeam transducer in a certain range of the sea area. Firstly, from the geometrical point of view, the interpreted diagram and the schematic diagram given in the title are combined and simplified into a problem of solving a triangle. The trigonometric equations are listed through the sine theorem and solved algebraically. A mathematical model is developed about the coverage width and adjacent strips. Then, from the question, we know that we need to solve the modeling differences caused by the different angles of the measuring lines in different directions, i.e., to elevate the two-dimensional problem of solving triangles to a three-dimensional problem of three-dimensional geometry. By finding the angle between the coverage width and the horizontal plane , we know the relationship between it and the angle between the direction of the survey line  and the slope angle  , so as to establish the model of the coverage width of multibeam bathymetry. Summarized by the verification of the previous conclusions, this paper obtains: when controlling the width of two adjacent survey lines exactly meets the overlap rate of 10% with the previous survey line, and the survey line direction is perpendicular to the seafloor slope in the projection, the measurement length is the shortest at this time. Using the above summary as a constraint, the shortest path is calculated to be 66 nautical miles using the trigonometric method.