Analytical coverage modeling and adaptive opening-angle survey line planning for repeated multibeam bathymetric surveys

Repeated multibeam bathymetric surveys over complex seabed terrain require survey-line plans that balance survey efficiency, missed coverage, and excessive overlap. This study develops a computable geometric coverage model and an adaptive opening-angle planning method using prior coarse bathymetric data. The survey area is partitioned into approximately planar triangular subregions, for which analytical relationships are established among survey-line position, swath width, total survey-line length, overlap, and missed coverage. A sequence defined by an initial opening angle, a fixed angular increment, and a terminal opening angle is optimized under coverage and efficiency constraints. The effects of roll, pitch, yaw, translation, and heave are incorporated through effective-swath-width correction and sensitivity analysis. In the case study, the proposed scheme reduces total survey-line length by 45.43% relative to a fixed-opening-angle scheme, while the subregion-aggregated missed-coverage rate increases from 2.446% to a conservative estimate of 3.336%. Considering complementary coverage between adjacent subregions, the full-area missed-coverage rate is analytically bounded between 0.727% and 3.336%, rather than obtained from a direct full-area swath union. The framework identifies predicted coverage gaps and excessive-overlap segments, but the case study provides an internal analytical evaluation rather than independent validation against non-planar reference bathymetry or measured MBES footprints.