Time and Frequency Domain Wave Propagators

Abstract

Is this paper, a new time-domain wave propagator (TDWP) that was recently introduced, is compared against a frequency-domain one that has been in use for more than a decade. The new time-domain wave propagator is built by a two-dimensional (2D) finite-difference time-domain (FDTD) algorithm. The frequency-domain wave propagator is the Split-step Parabolic Equation (SSPE), which is the solution of (one-wave) wave equation in parabolic form. These two techniques can be both used for different kinds of 2D propagation problems. In this paper, ground wave problems, which are difficult to solve, have been taken into consideration in order to compare the methods and show their power. Assuming an azimuthal symmetry, ground wave propagation and surface and/or elevated ducts may be represented via transverse and/or longitudinal refractivity and boundary perturbations in 2D space. The 2D propagation space extends from x=0 (bottom) to x->infinity (top), vertically and from z-> negative infinity (left) to z-> inifity (right) horizontally. Pulse propagation is simulated in TDWP and while a moving window escorts the transmitted waveform from one end to the other end within the FDTD computation space, time histories are accumulated at choses observation points. Any vertical and/or horizontal field profile at a desired frequency is extracted by applying off-line discrete Fourier transformation (DFT). On the other hand, a given field profile is longitudinally ppropagated by moving back and forth between the transverse spatial and wavenumber domains in SSPE. The results of TDWP and SSPE are compared on different ducting and anti-ducting refractivity profiles and their agreement is presented.