Fresnel Volume Georadar Attenuation-Difference Tomography

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Georadar attenuation-difference tomography is a useful tool for imaging temporal and spatial changes in bulk electrical conductivity due to fluid flow and other subsurface processes. The most common method of attenuation-difference tomography employs the ray approximation where waves are assumed to propagate at infinite frequency. Ray approximation causes significant model error that generates artefacts and loss of resolution in tomographic images. In this paper we propose an efficient method of computing Fresnel volume sensitivities using scattering theory. These sensitivities account for finite frequency propagation and represent the physics of electromagnetic propagation more accurately than ray theory. As expected, Fresnel volume sensitivities provide better data prediction than ray-based sensitivities. We use singular value decomposition analysis to show how and why this physical improvement allows Fresnel volume inversions to recover localized targets and resolve bulk conductivity changes better than ray-based inversions. The model basis functions and singular values corresponding to the scattering theory sensitivity kernel are similar to the exact full-waveform basis functions and singular values. The similarity of the basis functions and singular values suggests that the scattering theory inverse estimates are close to the full-waveform estimates, but they are obtained with a significant decrease in computational effort.