This abstract was published in the Proceedings of Symposium Institute of Electrical and Electronics Engineers, Baltimore, Maryland, Jul. 22-26, Copyright 1996 by IEEE.

Transient excitation of thin-wire antennas above two half spaces

Jean-Paul Van Gestel, Evert C. Slob, Department of Mining and Petroleum Engineering, Delft University of Technology, Delft, The Netherlands.

The transient excitation of a straight thin-wire segment, by either a voltage gap or an incident electric field, has been analyzed by many people. In these cases, a wire segment is located in free space and the analysis leads to a one-dimensional integral equation for the current along the wire. Several versions of Pocklington's and Hallén's original formulations exist. We have derived a general form of the integral equation using the field reciprocity theorem. This theorem interrelates two non-identical states that occur in the same background, one is the actual state to be computed while the other is an auxiliary state, to be chosen freely. We show that both Pocklington's and Hallén's integral equation formulations follow from different choices of this auxiliary state.

For applications in Ground Penetrating Radar, GPR, we have derived an integral equation for the transient excitation of the wire segment placed at the air/earth interface, where the earth is modeled as a lossy homogeneous half-space. Most commonly used GPR antennas are tuned to a center frequency of the excitation signal. GPR field data obtained with antennas with different center frequencies at fixed positions on the ground, provide information about the same subsurface, but with different frequency contents. It is not clear if the use of these different center frequencies effectively provides additional information about the subsurface compared to data obtained with a single antenna combination. We investigate the radiation characteristics of an antenna as a function of the frequency content of the excitation signal. The importance of the analysis is to see if data obtained with one antenna can be understood as a scaled version of data obtained with an antenna using a different center frequency. If this is the case, then the effective source signature that is radiated into the ground can be computed from multi center frequency data. If this is not the case, then there is additional information in the data that can be used to obtain a better image of the subsurface. Finally, we will show radiation characteristics of the antenna as a function of frequency and of the electric permittivity and conductivity of the half-space. This shows the need for antenna shielding and is of great importance to understand the antenna coupling to the ground, which is one of the key problems in the successful processing of GPR data.

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