This paper establishes a mathematical model for the layout problem of the multibeam detection system in seabed exploration and analyzes the seabed detection problem from both two-dimensional and three-dimensional perspectives. Initially, utilizing trigonometric functions and the sine theorem, we calculate the water depth, coverage width, and coverage rate of the survey lines, formed by the tangent angles between the line spacing and the seabed depth. Subsequently, using a Cartesian coordinate system, we construct equations based on the relationships between vectors to compute the multibeam coverage width of survey lines at different distances from the center of the sea area. Under certain assumptions, we aim to cover the entire sea area with a minimal set of survey lines. Simplifying the seabed topography to two slopes of different gradients, we select contour lines formed by connecting two higher contour points to design the direction lines for the survey, thereby computing parameters such as the total length of the survey lines. This model is practical and effectively addresses the proposed issues, holding significance as a reference in the field of marine exploration.

Zhuofan Zheng, Qirong Luo, Liga Wuri. Routing Optimization Model of Submarine Multi-beam Detection System Based on Trigonometric Function and Coordinate System. Academic Journal of Engineering and Technology Science (2023) Vol. 6, Issue 12: 56-64. https://doi.org/10.25236/AJETS.2023.061209.

[1] Lurton, X. (2010). An introduction to underwater acoustics: principles and applications. Springer Science & Business Media.https://doi.org/10.1007/978-3-642-13835-5

[2] Lamarche, G., & Lurton, X. (2015). Quantitative characterisation of seafloor substrate and bedforms using advanced processing of multibeam backscatter—Application to Cook Strait, New Zealand. Continental Shelf Research, 105, 6-24.https://doi.org/10.1016/j.csr.2010.06.001

[3] Hughes Clarke, J. E. (2016). First wide-angle view of channelized turbidity currents links migrating cyclic steps to flow characteristics. Nature Communications, 7, 11896.https://doi.org/ 10.1038/ ncomms11896

[4] Menna, F., Nocerino, E., Troisi, S., & Remondino, F. (2013, May). A photogrammetric approach to survey floating and semi-submerged objects. In Videometrics, Range Imaging, and Applications XII; and Automated Visual Inspection (Vol. 8791, pp. 117-131). SPIE.https://doi.org/10.1117/12.2020464

[5] Brown, C. J., Smith, S. J., Lawton, P., & Anderson, J. T. (2011). Benthic habitat mapping: A review of progress towards improved understanding of the spatial ecology of the seafloor using acoustic techniques. Estuarine, Coastal and Shelf Science, 92(3), 502-520.https://doi.org/ 10.1016/j. ecss. 2011.02.007

[6] Mayer, L. A. (2006). Frontiers in seafloor mapping and visualization. Marine Geophysical Research, 27(1), 7-17.https://doi.org/10.1007/s11001-005-0267-x

[7] Pirenne, B., Mayer, L. A., & Hughes Clarke, J. E. (2015). Multibeam sonar backscatter data processing. In Seafloor Mapping Along Continental Shelves (pp. 153-175). Springer, Cham.https://doi. org/ 10. 1007/s11001-018-9341-z

[8] Hamden, M. H., & Md Din, A. H. (2018, July). A review of advancement of hydrographic surveying towards ellipsoidal referenced surveying technique. In IOP Conference Series: Earth and Environmental Science (Vol. 169, p. 012019). IOP Publishing.

[9] Mitchell, G. A., Orange, D. L., Gharib, J. J., & Kennedy, P. (2018). Improved detection and mapping of deepwater hydrocarbon seeps: Optimizing multibeam echosounder seafloor backscatter acquisition and processing techniques. Marine Geophysical Research, 39, 323-347.https://doi. org/10. 1007/s11001-018-9345-8

[10] Wynn, R. B., Huvenne, V. A., Le Bas, T. P., Murton, B. J., Connelly, D. P., Bett, B. J., ... & Morris, K. J. (2014). Autonomous Underwater Vehicles (AUVs): Their past, present and future contributions to the advancement of marine geoscience. Marine Geology, 352, 451-468.https://doi. org/10. 1016/j. margeo. 2014.03.012