## 1 Introduction
However, it needs more extensive validation in various geological environments, which may limit its broader application [14]. Figure 1: This figure illustrates the principles of operation and the effects of an MBES system. (**a**) It depicts the fundamental operation of the MBES system. Sound waves propagate in straight lines at a consistent velocity in a homogeneous medium, undergoing reflection at different interfaces. By leveraging this fundamental principle, the system utilizes a transducer to simultaneously emit multiple beams within a plane that is perpendicular to the survey line. The transducer then receives the sound waves that bounce back from the seabed, recording the time from wave emission to signal reception. The depth of the water is calculated based on the speed and travel time of the sound waves through the water. (**b**) It shows that within a flat seabed area, the MBES system can measure a complete coverage depth strip aligned with and extending across the survey vessel’s track, having a certain width. Similarly, the marine habitat mapping study conducted by [PERSON], [PERSON] and his team using a multibeam echosounder and underwater video observations in Tioman Marine Park offered new methods. However, it was limited to a single case study, potentially failing to capture variations across different marine habitats [15]. The study by [PERSON], [PERSON] and [PERSON], examining the effectiveness of a vertical error budget model for a portable multibeam echosounder in a shallow water bathymetric survey, demonstrated significant improvements in measurement precision, yet its performance in deeper or more turbulent waters remains untested [16]. Additionally, the polar ocean multibeam survey line layout system designed and implemented by [PERSON] and [PERSON], though adapted to extreme conditions, did not consider its adaptability in non-extreme environments or different seabed compositions [17]. [PERSON]'s discussion on applying MBES systems in marine channel measurement highlighted its importance and utility in channel mapping. However, the study did not explore the economic impacts of widespread implementation [18]. Finally, the comprehensive analysis of the current status and precision of seabed terrain detection and model development by [PERSON], [PERSON], and [PERSON], although providing an evaluation of the accuracy and efficiency of existing technology, also called for further innovation to enhance current techniques [19]. This study has developed a new set of multibeam echosounder algorithms and models, tailored to meet the seabed terrain measurement needs of various maritime areas. By deeply analyzing the mechanisms of sound wave propagation in seawater and their interactions with seabed topography, a depth measurement model based on spatial geometric relationships has been established to address the challenges of complex and variable seabed terrain. This research aims to enhance measurement efficiency and accuracy, providing crucial data support and technical assurance for seabed scientific research and resource exploration. The main contributions of this study include the following:  
1. A new multibeam echosounder model was developed utilizing geometric optimization techniques, significantly enhancing measurement accuracy and data integrity, particularly in complex seabed terrains. 2. An optimized multibeam measurement algorithm was designed capable of dynamically adjusting survey line configurations in regions requiring frequent measurements, thus improving efficiency and reducing data overlap and resource wastage. 3. The performance of multibeam echosounding technology in practical applications was enhanced, providing critical support for marine science research and seabed resource exploration.