Measurement and modeling of the TDR signal propagation through layered dielectric media

Layered dielectric materials are often encountered in the natural environment due to differences in water content caused either by a wetting or drying front. This is especially true for coarse-grained materials such as sandy soils, sediments, and some rocks that have very distinctive layers of water content. This paper examines the issue of how the permittivity along a time domain reflectometry (TDR) probe is averaged as a function of layer thickness and probe orientation. Measurements of apparent permittivity using TDR are presented for two-, three-, and multi-layer materials. Time domain reflectometry waveforms are modeled for multiple layers of varying thickness and show a change in the averaging of the apparent permittivity from refractive index to arithmetic when more thin layers are present. Analysis of the modeled results shows that the averaging regime is frequency-dependent. However, broadband techniques applied to materials with a few layers will generally produce refractive averaging. A transition to arithmetic averaging is found for systems having many (>4 layers). Narrow-band methods may be very sensitive to layering and may perform in a highly non-refractive way when layering with a strong permittivity contrast is present.