The multi-beam measurement system plays a crucial role in ocean mapping and underwater terrain detection. By simultaneously transmitting multiple beams, the system can accurately receive sound waves reflected from the seabed, providing more precise and comprehensive water depth information while effectively revealing the complexity and characteristics of underwater terrain. Building upon the background and application provided by Question B of the 2023 National Mathematical Contest in Modeling for College Students, this paper investigates the relationship between ocean floor width measurement and factors such as beam position, angle, and slope. Utilizing geometric relations, trigonometric similarity, and sine theorem, a mathematical model is established to determine adjacent strip coverage width and overlap ratio. Furthermore, an optimal strategy is determined using a greedy algorithm, while binary search backtracking is employed to derive the interval of the next adjacent survey line with the required overlap ratio in order to obtain an optimal terrain detection strategy.

翻译：多波束测量系统在海洋测绘和水下地形探测中发挥着关键作用。该系统通过同时发射多个波束，能够精确接收海底反射的声波，在提供更精确、更全面的水深信息的同时，有效揭示水下地形的复杂性和特征。本文基于2023年全国大学生数学建模竞赛B题所给出的背景与应用，研究了海底宽度测量与波束位置、角度及坡度等因素之间的关系。利用几何关系、三角相似性及正弦定理，建立了数学模型以确定相邻条带覆盖宽度与重叠率。进一步地，采用贪心算法确定了最优策略，同时运用二分搜索回溯法推导出满足所需重叠率的下一相邻测线区间，从而获得最优地形探测策略。