Theoretical Analysis of Electromagnetic Modes in Stratified Media

Abstract

Electromagnetic wave propagation in stratified conducting media is a fundamental problem in underwater wireless communication and geophysical exploration. However, the accurate modeling of such environments is computationally challenging due to the highly oscillatory nature of the Bessel functions within the Sommerfeld integrals. This thesis develops a numerical method for analyzing electromagnetic modes in a three- layer model consisting of air, seawater, and seabed. The Global Matrix Method (GMM) is employed to formulate the boundary value problem, allowing for the rigorous treatment of multiple reflections at the interfaces. To resolve the numerical instability associated with the Sommerfeld integrals, a cus- tom integration solver was developed utilizing Romberg integration accelerated by the Shanks transformation (Wynn’s ε-algorithm)[1]. This hybrid approach ensures sta- ble convergence for the oscillatory integrands, overcoming the limitations of standard quadrature methods. Using this solver, the electromagnetic field components generated by a submerged Horizontal Magnetic Dipole (HMD) were explicitly calculated. The results confirm the transition from direct wave dominance in the near-field to lateral wave propaga- tion in the far-field, demonstrating the efficacy of the proposed method for modeling propagation in lossy stratified environments.