Ray-Path Modeling in Layered Water Columns and Its Impact on Echo-Sounding Depth Accuracy

Abstract

The paper investigates the impact of the acoustic ray path in a stratified seawater environment on the accuracy of echo sounding measurements for marine mapping. Based on the theory of acoustic refraction (continuous form of Snell’s Law) and the Sound Speed Profile (SSP) model, the study develops a ray-tracing – based computation and correction procedure, validated using sound velocity data from the Khanh Hoa – Binh Thuan region. Two approaches for calculating the acoustic travel path are directly compared with the theoretical distance of 500 m: ( i) the layer-averaged travel time approach yields 512.717 m (an error of ±12.717 m); and (ii) the mean velocity for the entire water column combined with the actual measured travel time yields 499.974 m (an error of ±0.026 m). Comparison with national standards shows that approach (i ) exceeds the allowable limits of TCVN 10336:2015 – Class 3 (±11.543 m at 500 m) and TCVN 10337:2015 – Class B (±11.0 m), while approach (ii) meets and surpasses both standards. The results confirm that assuming a uniform sound velocity or applying layer-averaged timing without ray-tracing may lead to systematic errors of several meters at a 500 m depth. The paper recommends acquiring in-situ SSP data (via CTD/XBT) at sufficiently high temporal and spatial frequency, and integrating ray-tracing methods throughout the multibeam echo-sounding processing chain to ensure compliance with TCVN standards when producing marine maps for national defense, socioeconomic development, and climate change adaptation purposes.