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Antenna and ground
Radar waves travel at v = c / sqrt(eps_r). Echoes come from changes in permittivity; the two-way time of a target gives its depth and the antenna frequency sets the resolution.
Model checks
The science
What is modelled
Horizontal soil layers with a relative permittivity and a conductivity each, and point-like targets. For every antenna position the model traces a ray to each target by Snell's law, adds Fresnel reflections at layer boundaries, loss from conductivity, and a Ricker wavelet.
Equations
- Wave speed
v = c / sqrt(eps_r), two-way timet = 2 d / v. - Reflection
R = (n1 - n2) / (n1 + n2)withn = sqrt(eps_r). - Diffraction hyperbola
t(x) = 2 sqrt(d2 + x2) / vfor uniform ground. - Low-loss attenuation
alpha = sigma x 188.4 / sqrt(eps_r)nepers per metre.
Checks run in the page
- Speed in eps_r = 9 ground.
- Depth to time in a single layer.
- The layered ray tracer against the analytic hyperbola.
- First-interface reflection coefficient and the echo position in the trace.
Honest simplifications
A fast ray-and-wavelet model, not a full-wave simulation: no antenna pattern, no dispersion, simple target amplitudes and flat layers. It teaches interpretation, not survey processing.
What to try
- Press Buried foundations and read the two hyperbola apex times.
- Press Mixed soil, wet: the wet clay damps the deep echoes.
- Press Low frequency, deep to trade resolution for depth.