GPR velocity and target depth

Ground penetrating radar times an electromagnetic pulse from the antenna to a reflector and back. The pulse travels at v = c/√εr, where c is 299.79 mm/ns and εr is the relative permittivity of the medium, so depth is d = v·t/2 for a two-way travel time t. Reflections occur wherever permittivity changes — at a reinforcing bar, a void, a delamination, the back face of a slab, or a change in moisture — and the strength of the reflection depends on how big that contrast is.

Permittivity is the whole ballgame, and it is dominated by water. Dry concrete sits around 6, moist structural concrete around 8–10, and saturated concrete can exceed 15; free water itself is 81. Because depth scales as 1/√εr, assuming 6 when the true value is 9 overstates every depth by 22%. Never report depths from a nominal permittivity on work that matters: calibrate on site, either by fitting the hyperbola from a point reflector or, more simply, by timing a target whose depth is known from a core, a drilled hole or an exposed bar, and solving εr = (c·t/2d)².

Resolution and penetration pull against each other through frequency. The wavelength in the material is λ = v/f, and two reflectors need to be separated by roughly a quarter of a wavelength to be resolved as two — about 16 mm for a 1.6 GHz antenna in moist concrete. Higher frequencies resolve finer detail but attenuate faster; lower frequencies penetrate deeper and see less. Attenuation, not the arithmetic here, sets the real depth limit, and it rises steeply with moisture, chloride content and conductive fills, which is why a wet, salted deck can be all but opaque at 1.6 GHz.

Two geometric cautions. The velocity above is for the vertical two-way path, so the timing must be taken at the apex of a hyperbola directly over the target, not on its flanks. And a bar's apparent depth is to the top of the reflector, with the pulse spreading in a cone, so closely spaced bars in the top mat can mask everything beneath them.

v = c / √εr,   c = 299.79 mm/ns
d = v · t / 2
εr = (c · t / (2 · d_known))²
λ = v / f;   vertical resolution ≈ λ / 4