## 2 Research Content and Methodology
### Coverage and Measurement Accuracy Standards  
Traditional survey methods often use fixed grid patterns or simple parallel lines, which fail to adapt to the varying geometries of the seabed. This lack of adaptation often results in inefficiencies and potential data gaps. In contrast, our geometrically optimized approach dynamically adjusts survey lines to align closely with the seabed's natural contours. By integrating real-time topographical data and strategically planning the orientations and spacings of survey lines, our method significantly enhances the accuracy and efficiency of seabed mapping. Unlike traditional techniques, our approach effectively addresses inefficiencies, optimizes coverage, and minimizes data redundancy. Such adaptability is crucial for navigating complex marine environments and ensuring thorough and efficient seabed surveys.  
In practical marine exploration, the overlap rate is introduced as an evaluation metric to meet the requirements for cost-effective and efficient detection [20]. Figure 2 illustrates the geometric diagram of the overlap rate. The coverage width \(W\) of the multibeam echosounder swath varies with the transducer's beam angle \(\theta\) and the water depth \(D\). If the survey lines are parallel and the seabed is flat, the overlap rate between adjacent swaths is given by: \(\eta=1-\frac{d}{W}\) where \(d\) is the distance between adjacent survey lines, and \(W\) is the swath coverage width. If \(\eta<0\), it indicates gaps in coverage. To ensure convenience in measurement and data integrity, there should be an overlap of 10% to 20% between adjacent swaths [21].  
Due to the significant variations in actual seabed topography, as shown in Figure 3. Using the average depth of a sea area to design survey line spacing while ensuring an average overlap rate that meets requirements can lead to gaps in coverage in shallower areas, affecting the quality of measurements. Conversely, using the shallowest depth in the area to determine survey line spacing ensures sufficient overlap in the shallowest parts. However, it leads to excessive overlap in deeper areas, creating redundant data and reducing measurement efficiency. Therefore, developing an efficient multibeam survey line model has significant practical importance.  
Figure 3: This figure illustrates the effects of significant variations in actual seabed topography on the design of survey line spacing: (**a**) When the average depth of the sea area is used to design the survey line spacing, gaps in coverage can occur in shallower areas. (**b**) When the shallowest depth of the sea area is used to design the survey line spacing, excessive overlap occurs in deeper areas.  
Figure 2: This figure illustrates the relationship between the coverage width \(W\), survey line spacing \(d\), and overlap rate \(\eta\) of an MBES system. Each triangle in the diagram represents a coverage area of a multibeam transmission, where the coverage width \(W\) is the total width of a transmission area. The survey line spacing \(d\) is the distance between two adjacent survey lines. The overlap rate \(\eta\) is the proportion of the overlapping area between two adjacent coverage areas. By adjusting the survey line spacing \(d\) and coverage width \(W\), the overlap rate \(\eta\) can be controlled, thereby optimizing measurement precision and efficiency.