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On the pitfalls and limitations of applying petrophysical models to tomograms: examples in cross-borehole radar and electrical resistivity tomography

Frederick D. Day-Lewis, Kamini Singha, and Andrew Binley


Geophysical field data have traditionally provided qualitative information on aquifer structure for hydrogeologic characterization; however, there is increasing interest in the application of petrophysical models to convert geophysical tomograms of electrical resistivity or radar velocity, for example, to hydrologic parameters, such as permeability, porosity, water content, and (or) salinity. Unfortunately, application of theoretical or empirical petrophysical models may be inappropriate in many situations, given the limited and variable resolution of tomographic estimates. The resolution of tomograms is a function of (1) the measurement physics, for example, electrical conduction or electromagnetic wave propagation; (2) the parameterization and regularization used for inversion; (3) measurement error; and (4) the length scale of heterogeneity. We present a framework to predict how core-scale relations between geophysical properties and hydrologic parameters break down in the inversion, which produces smoothly-varying pixel-scale estimates. Our approach upscales the core-scale relationship to the pixel-scale based on the model resolution matrix from the inversion, random field averaging, and spatial statistics of the geophysical property. In synthetic examples, we use the approach to evaluate the utility of tomograms for quantitative hydrologic estimation, in light of their resolution-dependent limitations. Comparison of examples for cross-borehole electrical resistivity tomography and radar tomography demonstrates the role of the measurement physics on the spatially-variable pixel-scale relationships between geophysical estimates and hydrologic parameters of interest. The goals of this work are to (1) raise awareness of the limitations of geophysical data, (2) provide a framework to improve survey design and assess tomograms for hydrologic estimation, and (3) promote additional research to improve the links between geophysical and hydrogeologic characterization.

Final copy as submitted to EOS for publication as: Day-Lewis, F.D., Singha, Kamini, and Binley, A.M., 2004, On the pitfalls and limitations of applying petrophysical models to tomograms: examples in cross-borehole radar and electrical resistivity tomography: EOS Trans., AGU, v. 85, no. 17, Jt. Assem. Suppl., Abstract NS13A-03.

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