A Method for Full-Depth Sound Speed Profile Reconstruction Based on Average Sound Speed Extrapolation

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The speed of sound in seawater plays a crucial role in determining the accuracy of multibeam bathymetric measurements. In deep-sea multibeam measurements, the challenge of inadequate longitudinal coverage of sound speed profiles arises from variations in seafloor topography, meteorological conditions, measurement equipment, and operational efficiency, resulting in diminished measurement precision. Building upon the EOF (Empirical Orthogonal Function), a method employed to analyze spatiotemporal data such as sound speeds, this paper addresses the limitations of the EOF method caused by the shallowest sampling depth of the sound speed profile samples. It proposes two methods for EOF reconstruction of measured sound speed profiles extended to full water depth by splicing measured sound speed profiles at non-full water depths with historical average sound speed profiles of the surveyed sea area. Specially, Method 2 introduces the latest metaheuristic optimization algorithm, CPO (Crested Porcupine Optimizer), which exhibited superior performance on multiple standard test functions in 2024. The study reconstructs randomly sampled measured sound speed profiles using the two proposed methods and commonly employed substitution and splicing methods, followed by a comparative analysis of the experimental outcomes. At a sampling depth of 200 m, Method 2 demonstrates performance superior to other methods, with RMSE, MAE, MAPE, and R2 values of 0.9511 m/s, 0.8492 m/s, 0.0566%, and 0.9963, respectively. Method 1 yields corresponding values of 0.9594 m/s, 0.8492 m/s, 0.0568%, and 0.9962, respectively. Despite its slightly inferior performance compared with Method 2, it offers substantial advantages over the substitution and splicing methods. Varying the sampling depth of measured sound speed profiles reveals that Methods 1 and 2 exhibit inferior reconstruction performance in shallow water compared with the substitution and splicing methods. Nevertheless, when the sampling depth surpasses the depth range of initial spatial modes with abrupt variations, both methods achieve notably higher reconstruction accuracy compared with the substitution and splicing methods, reaching a stabilized state. Sound ray tracing reveals that the reconstructed sound speed profiles from both methods meet the stringent accuracy standards for bathymetric measurements, achieving an effective beam ratio of 100%. The proposed methods not only provide rapid reconstruction of sound speed profiles, thereby improving the efficiency of multibeam bathymetric surveys, but also provide references for the reasonable determination of sampling depths of sound speed profiles to ensure reconstruction accuracy, demonstrating practical application value.