Anomalies produced by objects or features of small size (relative to the antenna frequency and other factors), like rocks, pipes, or a narrow wall, produce hyperbolas in GPR data. The shape of a hyperbola, in particular its relative width or roundness, is determined by the velocity of the radar energy in the medium under consideration, so measurement of its form can yield an estimate of velocity, and from this depth data can be obtained. It is possible to perform the measurements manually, shown here, but modern software allows automation of this task through direct computer measurement of hyperbolic form. The most accurate procedure for determining soil velocity, however, is to identify GPR reflections to objects of known depths using, for example, a pipe test.

This figure shows a GPR profile containing many hyperbolas obtained with a GSSI 400 MHz antenna. The horizontal axis represents meters with 10 cm tick marks indicated, obtained with a survey wheel using 50 scans/m. The range setting is 40 nS (10^-9 seconds) two-way travel time (TWTT). The ground surface reflection is approximately at 3 nS, the peak of the hyperbolic reflection is at approximately 9 nS, and a good choice for the "bottom" of the hyperbola is at about 25 nS TWTT, where its left side is lost. The width or distance (2D) of the hyperbola at 25 nS is approximately 1.6 m.

Here are the relevant data:

2D = 1.6 m; D = 0.8 m
t₁ = (25 - 3) / 2 = 11 nS   {divide by 2 to get one-way travel time}
t₂ = (9 - 3) / 2 = 3 nS

Soil Velocity:  V = D / (t₁² - t₂²)

(after Bevan 1998:50) and

V = 0.8 m / (11 nS² - 3 nS²) = 0.0756 m/nS

This figure represents the average radar velocity to the peak of the hyperbola.

Estimating Depth

With the peak of the hyperbola at approximately t₂ = (9 - 3) / 2 = 3 nS below the surface, the depth to the anomaly may be estimated at about 3 nS x 0.0756 m/nS = 0.23 m.

Relative Dielectric Permittivity (RDP)

With an estimate of soil velocity the relative dielectric permittivity (K) may be computed:

K = C / V

where C = speed of light in a vacuum (0.2998 m/nS) and V = velocity of radar energy as it passes through a material (in m/nS), so:

K = 0.2998 m/nS / 0.0756 m/nS = 3.966,

and

K = 15.73

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