ELECTROMAGNETIC PULSE PROPAGATION OVER NONUNIFORM EARTH SURFACE: NUMERICAL SIMULATION

Abstract

Parabolic equation method proposed by Leontowich and Fock [1,2] is an efficient simulation approach to VHF propagation over the earth surface. Deep physical analysis and advanced mathematical methods [3,4] turned Leontovich’s PE into a universal tool of diffraction theory. Its applications go far beyond the initial problem circle – e. g. [5-8]. The key role in this development played the decisive turn to straightforward numerical techniques pioneered by Malyuzhinets and Tappert [9,10]. In radio wave propagation, PE was used first to derive explicit analytical formulae for the EM field strength in model environments. A simplification has been reached by introducing the impedance boundary condition (BC) [11]. Taking into account tropospheric refraction ducts required the use of sophisticated asymptotic methods [12]. Further development (almost exclusively towards numerical implementation) was aimed at refined PE modifications [13-15], account for irregular terrain [16], introducing artificial transparent boundaries [17,18] and nonlocal BC to describe rough interfaces [19]. A non-stationary PE counterpart and a finite-difference (FD) scheme for its solution have been proposed by Claerbout and applied to seismic problems [13]. Afterwards, this “time-domain parabolic equation” (TDPE) was used to calculate acoustic propagation in ocean [20]. At the same time, little attempts of using TDPE to simulate EM pulse propagation in realistic environments are known. In this paper, we consider computational aspects of EM pulse propagation along the nonuniform earth surface. For ultrawide-band pulses without carrier, TDPE results directly from the exact wave equation written in a narrow vicinity of the wave front. To solve it by finite differences, we introduce a time-domain analog of the impedance BC and a nonlocal BC of transparency reducing the open computational domain to a strip of finite width. Numerical examples demonstrate the influence of soil conductivity on the received pulse waveform which can be used in remote sensing.