A finite difference time domain (FDTD) simulation of electromagnetic wave propagation and scattering in a partially conducting layered Earth

Abstract

A finite difference time domain (FDTD) simulation of electromagnetic propagation in partially conducting layers was performed. The simulation was constructed to model the case of a source antenna in close proximity to the Earth's surface with receiving antennas both in the ground and on the Earth's surface. The objective of the modeling and simulation was the prediction of the back scattered temporal and spatial waveforms from various objects buried in the partially conducting subsurface layers of the Earth. In the author's investigation three primary modifications were performed to the simulation code. First, the code was ported from a mainframe computer to a Sun work station. This involved splitting the simulation into a data calculation phase and an interactive data display phase. During the calculation phase, all the simulation results are computed to create time histories of the total electromagnetic field in a region of space which included both the source antenna and all the receive antenna locations. The receive antennas were located both on the surface of the Earth as well as buried within the subsurface layers of the Earth. The calculation phase creates a large matrix of time histories of the transmitted, scattered and total electromagnetic fields at all the sampled receive locations. An interactive display module was developed using MATLAB on the Sun workstation to view the results of the simulation. The second extension of the simulation code was the incorporation of coherent transmit and receive waveforms into the simulation. An analytic formulation of the transmit pulse into real and imaginary parts allows coherent signal generation and analysis. This permits the calculation of both amplitude and phase information for the incident, scattered and total electromagnetic fields during the calculation phase of the simulation. The third modification to the simulation code was the inclusion of the capability to place multiple scattering objects within the subsurface layers. The objects were allowed to be partially conducting and to have random statistical distributions of both size and spatial location. This represents a first attempt at providing simulation results for a simple two media model of an inhomogeneous layer. The simulation results to be shown include a variety of antenna and scattering object locations for various combinations of layered Earth models. The results are shown as color plots of the two dimensional maps of the electromagnetic fields as well as a pseudo animation of the two dimensional spatial maps. These pseudo animation results were obtained by sampling the hard copy color outputs of the simulation and display and combining them into a temporal record which approximates the time history animation results obtainable using the interactive display module. The matrix of simulation results of the complex values of the vector E and H fields may be processed with signal processing algorithms to create detection maps and image reconstructions. The model produces time histories of the complex field values at all points in the simulation volume. Since the field values are coherent, the data created by the simulation may be processed with temporal and spatial signal processing algorithms to develop simulated results of particular Earth models and scattering object geometries. This allows the creation of performance predictions of candidate signal sensing and processing approaches for the detection of man made objects buried in the Earth. A proposed sensing and processing system is described which allows the detection and imaging of man made buried objects.