Three-dimensional transient electromagnetic modeling for investigating the spatial sensitivity of time domain reflectometry measurements

Abstract

[1] A three-dimensional (3-D) transient electromagnetic modeling based on a full-wave formulation (Maxwell's equations) has been undertaken in order to study the impact of heterogeneities located near a time domain reflectometry (TDR) probe. We focused on 3-D heterogeneities located at the ends of rods: (1) interface perpendicular to the probe plane located below the end of rods and (2) 3-D (cubic and parallelepipedic) heterogeneities whose characteristic lengths are similar to that of the probe. Whatever the rod separation and whatever the dielectric constant contrasts, an interface located just beneath the end of the rod does not affect significantly a simulated TDR signal when the interface is farther than one rod diameter. However, all the simulations carried out with cubic and parallelepipedic heterogeneities located along TDR rods have shown that a significant longitudinal sensitivity exists. The lower the constant dielectric value of heterogeneity, the higher the longitudinal sensitivity. In particular, parallelepipedic heterogeneities parallel to the rods induce significant changes in the travel times, compared to cubic heterogeneities, whose characteristic length is equal to the rod diameter. Moreover, 3-D numerical calculations have shown that TDR signals are not only sensitive to the heterogeneity volume itself but also to their orientation. Static 2-D analysis is shown to provide correct qualitative representation of spatial sensitivity analysis, though accurate quantitative estimation of the apparent permittivity requires a complete 4-D (x, y, z, and time) calculation. Copyright 2005 by the American Geophysical Union.