<title>Effects of small-scale stochastic heterogeneity on the tomographic inversion of cross-hole georadar data</title>

Abstract

Analyses of traveltimes and amplitudes of crosshole georadar data provide estimates of the electromagnetic velocity and attenuation of the probed media. In contrast to inversions of traveltimes, which are well established and robust, ray-based inversions of amplitudes depend critically on a priori assumptions about the directive properties of the antennas. In particular, the influence of electric material property fluctuations on antenna performance may lead to serious distortions of the radiation pattern. Such distortions cannot be accounted for by currently employed ray-based amplitude inversion algorithms. To explore the problem of antenna coupling to local heterogeneities, we generate synthetic crosshole georadar data for a suite of stochastic models using a finite-difference time-domain (FDTD) solution of Maxwell's equations in cylindrical coordinates. Analyses of the radiation patterns extracted from the synthetic data indicate that distortions of the radiation patterns are primarily due to propagation effects and not to dipolecoupling effects. We do, however, find that the quality of the amplitude tomograms diminishes rapidly with increasing heterogeneity, probably because of inherent inadequacies in ray-based inversion methods. In contrast, the quality of ray-based traveltime tomograms is surprisingly high, even in the presence of strong heterogeneity.