Efficient Modeling of Underwater Target Radiation and Propagation Sound Field in Ocean Acoustic Environments Based on Modal Equivalent Sources

The equivalent source method (ESM) is a core algorithm in integrated radiation-propagation acoustic field modeling. However, in challenging marine environments, including deep-sea and polar regions, where sound speed profiles exhibit strong vertical gradients, the ESM must increase waveguide stratification to maintain accuracy. This causes computational costs to scale exponentially with the number of layers, compromising efficiency and limiting applicability. To address this, this paper proposes a modal equivalent source (MES) model employing normal modes as basis functions instead of free-field Green’s functions. This model constructs a set of normal mode bases using full-depth hydroacoustic parameters, incorporating water column characteristics into the basis functions to eliminate waveguide stratification. This significantly reduces the computational matrix size of the ESM and computes acoustic fields in range-dependent waveguides using a single set of normal modes, resolving the dual limitations of inadequate precision and low efficiency in such environments. Concurrently, for the construction of basis functions, this paper also proposes a fast computation method for eigenvalues and eigenmodes in waveguide contexts based on phase functions and difference equations. Furthermore, coupling the MES method with the Finite Element Method (FEM) enables integrated computation of underwater target radiation and propagation fields. Multiple simulations demonstrate close agreement between the proposed model and reference results (errors < 4 dB). Under equivalent accuracy requirements, the proposed model reduces computation time to less than 1/25 of traditional ESM, achieving significant efficiency gains. Additionally, sea trial verification confirms model effectiveness, with mean correlation coefficients exceeding 0.9 and mean errors below 5 dB against experimental data.