Abstract Acoustic ray tracing (RT) is of interest in several areas of engineering, physics, and medicine. The problem of RT modeling in a medium with smooth changes in acoustic impedance has been widely addressed by solving the ordinary differential equation (ODE) of the ray equation (RT). However, the issue of modeling a medium with interfaces (boundaries with sudden jumps in impedance) is not yet completely resolved. Linear and nonlinear continuous functions have been proposed to model interfaces, a requirement for solving the ray equation. For fast-changing functions, a fine resolution is needed to increase accuracy, though at a computational cost. In this work, a new approach using differential operator kernels as an alternative to solving the ODE ray equation is investigated. This proposed method (Sobel ray tracing (SRT)) is based on the Sobel differential operator, which, combined with Snell’s law, is used to determine the refraction angle after the interaction between the acoustic field and an interface. The two approaches, RT and SRT, are evaluated based on error estimation of refraction direction in a discretized medium with interfaces. It was shown theoretically and numerically that the refraction angle accuracy predicted by the RT method is independent of the function used to model the interface but dependent on the values of the refractive index on either side of the interface. This was found to be correct for incident angles away from the critical angle, but the error increases near the critical angle, violating the total reflection law. The results show that SRT can accurately predict the location of the interface; however, its orientation requires the interface to be quantized based on the average value between the impedances on either side of the interface. The results show that refraction direction predictions with SRT are comparable to RT, but with lower computational complexity.
Baltazar et al. (2026) studied this question.