Effects of stochastic heterogeneity on ray-based tomographic inversion of crosshole georadar amplitude data

Abstract

Analyses of traveltimes and amplitudes of crosshole georadar data provide estimates of the electromagnetic velocity and attenuation structures of the probed media. Ray-based tomographic inversion of georadar traveltimes is identical to the well-established crosshole seismic approach and considered to be rather robust. In contrast, ray-based inversions of crosshole georadar amplitudes depend critically on the assumption that the radiative properties of the transmitter and receiver antennas correspond to those prevailing in a homogeneous full-space. The validity of this a priori assumption as well as the potential implications of its violation are unknown. In particular, it is not known to what extent the radiation patterns are affected by coupling of dipole-type georadar antennas to local variations of the electric material properties. To explore this problem, 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 radiation patterns extracted from the synthetic data indicate that radiation pattern distortions are primarily due to scattering and attenuation effects along the wave propagation path and not to changes in antenna coupling to local variations in the electrical material properties. In principle, such “path effects” are the target of tomographic amplitude inversions. This interpretation is supported by the fact that increasing heterogeneity enhances the amplitudes of “artefacts” in ray-based tomographic reconstructions of the crosshole georadar amplitude data, but does not systematically degrade the quality of the tomograms. Ray-based amplitude tomography is strictly valid only for homogeneous media and cannot account for scattering effects. As a consequence, artefacts related to scattering effects show a rather vague spatial relation to the corresponding structural features and their magnitude scales with increasing standard deviation of the heterogeneity. This suggests that ray-based amplitude tomography is quite useful for detecting prominent conductivity anomalies, whereas the structural and petrophysical details of such tomographic reconstructions should be regarded as rather qualitative in nature.