A simple procedure to evaluate Sommefeld integrals in layered media problems

In this work, we develop a numerical method to evaluate the Sommerfeld Integrals appearing in layered media problems using Chebyshev polynomials of the first kind. Chebyshev polynomials are important in approximation theory because the roots of the Chebyshev polynomials of the first kind can be used for polynomial interpolation to a high degree of accuracy. The resulting algorithm is much simpler than the conventional discrete complex image method. A few representative numerical examples are presented to illustrate the applicability of the new method.