Simulation Code for Calculating Underwater Acoustic Far-Field Propagation Loss Using Parabolic Equation Method

The calculation of underwater sound far-field propagation loss represents a fundamental aspect of underwater acoustics research. The parabolic equation method serves as an efficient numerical approach for simulating sound propagation in far-field conditions. This method enables computation of both sound pressure and particle velocity fields at distances significantly greater than the acoustic wavelength, based on the reasonable assumption of plane wave propagation in ocean environments. To implement parabolic equation calculations, specialized simulation code is essential. The code must perform comprehensive computations that account for ocean medium characteristics such as sound speed profiles, density variations, and absorption coefficients. A typical implementation involves solving the wave equation through numerical discretization schemes, where the code handles boundary conditions, range-dependent environments, and modal decomposition. The MATLAB-based simulation code for parabolic equation method demonstrates these capabilities through its structured algorithm that includes: 1. Initial field initialization using Hankel functions or normal mode solutions 2. Range marching implementation using finite difference or split-step Fourier methods 3. Sound speed profile integration through environmental input parameters 4. Boundary condition handling at sea surface and bottom interfaces 5. Transmission loss calculation via pressure field normalization The code architecture typically features modular functions for environmental input parsing, propagation kernel computation, and result visualization. Key algorithms implement impedance boundary conditions using complex reflection coefficients and handle sediment interactions through bottom loss models. The range stepping algorithm employs stability criteria to ensure numerical accuracy throughout the propagation path. In practical implementation, the code calculates complex pressure fields through successive range steps, applying phase corrections for refractive effects and attenuation calculations for absorption losses. The final output provides transmission loss values in dB scale, which can be visualized as two-dimensional range-depth plots or one-dimensional transmission loss curves. This MATLAB implementation offers researchers an accessible platform for underwater acoustic modeling, featuring configurable parameters for frequency sources, environmental conditions, and computational resolution. The code's modular design allows for extensions to three-dimensional propagation scenarios and incorporation of advanced oceanographic models, making it suitable for both educational purposes and professional research applications in underwater acoustics.