Multibeam bathymetry technology finds extensive applications in underwater depth exploration. This paper focuses on constructing a concrete mathematical model for the multibeam bathymetry problem, conducting research, and discussions. The developed model is applied to address the route planning issue for multibeam survey systems in seabed exploration. Initially, we employ mathematical methods from analytical geometry to establish a mathematical model concerning the coverage width and overlap rate between adjacent swathes in multibeam bathymetry. We compute the corresponding indicator values based on this model. Subsequently, utilizing the mathematical model in conjunction with an enumeration method, we design a set of survey lines that satisfy overlap rate requirements, minimize measurement lengths, and completely cover the entire target area. Finally, an optimization model is constructed for the survey layout of the bathymetric measurement vessel, meeting the specified criteria. The result is an optimized multibeam survey layout design. The proposed model aligns well with practical considerations, offering a rational solution to the posed problem. It demonstrates practical utility, algorithmic intuitiveness, and is pertinent in the field of marine exploration.

Jieyan Han, Xiaoyu Zheng. Optimization Problem of Multibeam Bathymetry Based on Analytical Geometry. Academic Journal of Mathematical Sciences (2024) Vol. 5, Issue 1: 13-19. https://doi.org/10.25236/AJMS.2024.050103.

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