Depth for Underwater Acoustic Detection in Deep-Sea (>5000 m) Complex Marine Environments Based on the Bellhop Model

Quantifying the detection efficiency of buoy-based sonar and optimizing deployment strategies in complex marine environments remain significant challenges. This study proposes a transceiver depth optimization method based on the Bellhop ray model to enhance underwater remote sensing data quality. For the first time, we validated the applicability of acoustic reciprocity in deep-sea environments exceeding 5000 m, characterized by non-uniform sound speed profiles, horizontal inhomogeneity, and steep seamount terrain, with a maximum relative error of <1.2%. This extends the applicable boundaries of the acoustic reciprocity theorem from idealized simple waveguides to complex, realistic deep-sea environments. Building on this validation, we developed a novel, equivalent, superposition modeling framework for bidirectional transmission loss (TL), which converts the computationally intractable TL from target to receiver into the calculable TL from receiver to target, thus significantly reducing computational complexity. Systematic simulations uncovered a depth-layered dependency mechanism: shallow sources (23.14~69.42 m) and deep sources (≥347.10 m) show robustness to large depth differences exceeding 500 m, whereas mid-layer sources (161.98~231.40 m) exhibit a distinct critical threshold effect. Static simulations identify a performance degradation cliff with an onset at an approximate depth difference of 185 m, leading to a 50% reduction in detection range and fragmented near-field detection coverage. To accommodate environmental temporal variability (e.g., internal waves), a conservative safety margin was incorporated, establishing a robust engineering threshold of 150 m. Accordingly, we define 160~350 m as the optimal detection depth window and propose a layered deployment protocol that fills a critical industry gap in quantitative deployment design for deep-sea acoustic detection. Specifically, transceiver depth differences should be strictly constrained to <150 m for mid-layer operations, while more-flexible depth configurations are permissible for shallow and deep sources. These findings furnish quantitative engineering criteria for the design of reliable underwater remote sensing networks, while balancing long-range detection stability and near-field coverage integrity.