FRESNEL VOLUME ATTENUATION DIFFERENCE INVERSION OF BOREHOLE GEORADAR DATA USING ANALYTICALLY COMPUTED SENSITIVITIES

Hydrogeologic models of complex heterogeneous aquifers are often limited by data sparseness and resolution. Several researchers have demonstrated the value of utilizing geophysical data as a source of supplementary information to increase the efficacy of and confidence in hydrogeologic models and parameter estimates. Borehole georadar tomography is a particularly useful tool for imaging the distribution of electrical properties between boreholes that have strong correlations to properties of interest to hydrogeologists, such as porosity or some chemical concentration. Dielectric constant and electrical conductivity are known to be functions of the porosity, fluid content, and chemistry of porous media. The most common method of cross-borehole tomography is based on ray theory, which allows inversion of large data sets but is physically correct only for infinite frequency wave propagation. Ray theory inversions using finite frequency data commonly cause smearing in the tomograms or artifacts, and a loss of resolution. Also, ray theory sensitivity matrices often require a significant amount of regularization, often in the form of an arbitrary smoothing function, which further reduces resolution. We here propose an efficient method of using analytically computed attenuation sensitivities with respect to bulk conductivity to construct bulk conductivity difference tomograms using Fresnel zone inversions. The Fresnel zone sensitivity matrix includes sensitivities due to finite frequency propagation that are absent in ray theory, and can help rectify many of the shortcomings (such as smearing) inherent to approaches using ray theory. We show that using Fresnel zone attenuation difference tomography to interpret borehole georadar data has the potential to improve the interpretability and accuracy of attenuation difference tomograms, and increase the utility of georadar in hydrogeological modeling other applications.