Extended Beam Approximation for High-Frequency Wave Propagation

The author presents an extension of the Airy beam, referred to as the Gaussian Airy beam, to simulate high-frequency wave propagation in inhomogeneous media. Theoretically, the Airy beam and the Gaussian beam satisfy the same fundamental paraxial wave equation. Here, the author combines the Airy beam and Gaussian beam concepts and derive the acoustic Gaussian Airy beam formulas. Starting from the acoustic paraxial wave equation in the ray-centered coordinate system, the author derives expressions for the Airy beam and quasi-ray tracing. The expression for the Airy beam is the same as that obtained from the Schrodinger equation, while the expressions for quasi-ray tracing can be used to obtain the parameters of the Gaussian beam. Relevant formulas for the Gaussian Airy beam in a homogeneous medium are derived. The author gives numerical solutions of the Gaussian Airy beam formulation and compare them with the Gaussian beam solutions. Furthermore, the author examines the effectiveness of the method for high-frequency wavefields by performing numerical simulations for models exhibiting pronounced heterogeneity.