Numerical models that account for realistic transmitter and receiver antenna behavior are necessary to develop waveform-based inversion methods for crosshole ground-penetrating radar (GPR) data. A challenge in developing such models is simulating the antennae in a computationally efficient manner so that inversions can be performed in a reasonable amount of time. We present an approach to efficiently simulate crosshole GPR transmission and reception in heterogeneous media. The core of our approach is a finite-difference time-domain (FDTD) solution of Maxwell's equations in 2D cylindrical coordinates. First, we determine the behavior of the current on a realistic GPR antenna in a borehole through detailed FDTD modeling of the antenna and its immediate surroundings. To model transmission and reception, we then replicate this antenna current behavior on a much-coarser grid using a superposition of point-electric-dipole source and receiver responses. Results obtained with our technique agree with analytical results, with numerical modeling results where the transmitter antenna and borehole are explicitly accounted for using a fine discretization, and with crosshole GPR field data.
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Irving et al. (2006) studied this question.
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