Untitled Document

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. It is possible to perform the measurements manually, but modern software allows automation of this task through direct computer measurement of hyperbolic form. The most accurate procedure for determining soil velocity is to identify GPR reflections to objects of known depths through a pipe test, for example.

This figure shows a GPR profile obtained with a GSSI 400 MHz antenna. The tick marks at top represent meter marks obtained with a survey wheel, using 50 scans/m. The range setting was 40 nS (10^-9 seconds) two-way travel time (TWTT). The ground surface reflection is approximately at 3 nS while the peak of the hyperbola is at approximately 13 nS. This anomaly was created by inserting a steel pipe (a one-inch soil corer) horizontally into a vertical exposure, illustrated elsewhere as a pipe test.

Modern GPR software allows the fitting of a mathematically generated hyperbola to the anomaly. The soil velocity determines its width or roundness. If soil velocity is very high, as might occur in a dry sand with a low relative dielectric permittivity (RDP), the hyperbola tends to be very wide. If the velocity is low, as in a clay with high RDP, the hyperbola is very narrow. Here, the hyperbola (in red) fitted with GSSI's RADAN software, indicates a soil velocity of approximately 0.1 m/nS. This figure agrees exactly with the results of the pipe test.

To see an animation of how hyperbola form varies with soil velocity click here.

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 / 0.1 m/nS = 2.998,

and

K = 8.99

Back to Main Topic Page