Approximating the surface impedance of a homogeneous lossy half-space: An example of "dialable" accuracy

We present an approximation by exponentials of the time-domain surface impedance of a lossy half space. Gauss-Chebyshev quadrature of order N-1 is employed to approximate an integral representation of the modified Bessel functions comprising the time-domain impedance kernel. An explicit error estimate is obtained in terms of the physical parameters, the computation time, and the number of quadrature points N. We show our approximation as accurate as other approaches, which do not come with such an error estimate. The conditions under which the error estimate derived herein, also applies to the approximation in [5] are investigated.