Applying petrophysical models to radar travel time and electrical resistivity tomograms: Resolution-dependent limitations

[1] Geophysical imaging has traditionally provided qualitative information about geologic structure; however, there is increasing interest in using petrophysical models to convert tomograms to quantitative estimates of hydrogeologic, mechanical, or geochemical parameters of interest ( e. g., permeability, porosity, water content, and salinity). Unfortunately, petrophysical estimation based on tomograms is complicated by limited and variable image resolution, which depends on ( 1) measurement physics ( e. g., electrical conduction or electromagnetic wave propagation), ( 2) parameterization and regularization, ( 3) measurement error, and ( 4) spatial variability. We present a framework to predict how core-scale relations between geophysical properties and hydrologic parameters are altered by the inversion, which produces smoothly varying pixel-scale estimates. We refer to this loss of information as "correlation loss.'' Our approach upscales the core-scale relation to the pixel scale using the model resolution matrix from the inversion, random field averaging, and spatial statistics of the geophysical property. Synthetic examples evaluate the utility of radar travel time tomography (RTT) and electrical-resistivity tomography (ERT) for estimating water content. This work provides ( 1) a framework to assess tomograms for geologic parameter estimation and ( 2) insights into the different patterns of correlation loss for ERT and RTT. Whereas ERT generally performs better near boreholes, RTT performs better in the interwell region. Application of petrophysical models to the tomograms in our examples would yield misleading estimates of water content. Although the examples presented illustrate the problem of correlation loss in the context of near-surface geophysical imaging, our results have clear implications for quantitative analysis of tomograms for diverse geoscience applications.