Presets
Playback
Soil, probe and instrument
Wet soil has a high permittivity, which slows the pulse: the rod round trip is 2 L sqrt(eps) / c. Each change of impedance, at the rod entrance, at a horizon interface and at the open tip, sends part of the pulse back.
Model checks
The science
What is modelled
A one-dimensional transmission line: a 50 ohm cable feeding two parallel rods inserted into one or two soil horizons. The rod line impedance falls as the soil permittivity rises; each impedance step reflects a fraction of the pulse, and the recursive wave-splitting model also keeps multiple internal reflections. The permittivity of each horizon comes from the Topp et al. (1980) empirical cubic.
Equations
ε = 3.03 + 9.3 θ + 146 θ² - 76.7 θ³.v = c / √ε, round tript = 2 L √ε / c.Γ = (Z2 - Z1) / (Z2 + Z1), withZ = 235 Ω / √εfor the rods.
Checks run in the page
- The Topp curve value at 0.20 and its inversion.
- Open-tip echo time against 2 L sqrt(eps) / c plus the cable delay.
- The entrance reflection coefficient against (Z - 50)/(Z + 50).
- Water content recovered from the apparent permittivity for uniform soil.
Honest simplifications
No dispersion, no temperature correction, an ideal open tip and an empirical loss proxy for salinity. The estimate is a bulk apparent value, not a depth-resolved inversion, and the Topp curve is calibrated for mineral soil only.
What to try
- Press Dry over wet layer: the trace shows an interface step before the tip echo.
- Press Saturated, salty: the pulse is attenuated and the tip echo shrinks.
- Press Slow instrument: a long rise time smears the interface and tip steps together.