A buried point target makes a diffraction hyperbola. Match your fit curve to it to recover wave velocity and target depth.
The radargram below has one buried object (its true velocity is hidden). Adjust your fit until the amber curve overlies the hyperbola.
0.10
fit velocity (m/ns)
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implied εᵣ
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target depth (m)
Two-way time along the hyperbola: $t(x)=\dfrac{2\sqrt{d^2+(x-x_0)^2}}{v}$. Relative permittivity from velocity: $\varepsilon_r=\left(\dfrac{c}{v}\right)^2$ with $c=0.30$ m/ns. This fit assumes constant velocity, a point-like target, zero time offset, and negligible antenna separation.