Accurate Determination of Underground GPR Wavefront and B-Scan Shape From Above-Ground Point Sources

While the determination of the wavefront shape radiated by ground-penetrating radar (GPR) in contact with the ground is trivial, the refraction of rays at the ground surface from a point source in the air makes accurate determination of the transmitted wavefront challenging. Impulse GPRs usually have their emitters in air, transmitting waves through a quasi-planar interface into the soil. The waves radiated initially in air can be approximated as circular, but once they enter the soil half-space, they propagate with a wavefront shape that resembles a hyperbola. The exact shape is derived and shown to be well approximated by a hyperbola with specific parameters depending on the relative dielectric constant of the half-space epsiv´ ( = n²), the height of the source h, and the propagation time from source to wavefront multiplied by the wave velocity in the half-space p. A correction formula is provided to reduce the error between the approximate hyperbola and the exact shape. In addition, an equation for the shape of the B-scan contour of a point scatterer is derived.