Point-source Hyperbolas and Pattern of Energy

Point source hyperbolas (A) are generated from buried objects of a limited size. In this case the hyperbola on the right was generated from a metal pipe and the lower amplitude hyperbola on the left from a plastic pipe. The series of high amplitude reflections that are stacked vertically at location B were generated by a large piece of metal near the ground surface.

 

The conical projection of radar energy into the ground will allow radar energy to travel in an oblique direction to a buried point source (1) as seen in (A). The two-way time (t) is recorded and plotted in depth directly below the antenna where it was recorded (2). When many such reflections are recorded as the surface antennas move toward and then away from a buried object, the result is a reflection hyperbola (3), when all traces are viewed in profile, as seen in (B).

 

As the surface antenna moves closer to a buried point source, the receiving antenna will continue to record reflections from the point source prior to arriving directly on top of it, and continue to "see" it after it has passed. A reflection hyperbola is then generated because the time it takes for the energy to move from the antenna to the object along many oblique paths is greater the farther the antenna is away from the source of the reflection. As the antenna moves closer to the buried object the reflection from it is recorded closer in time until the antenna is directly on top of it. The same phenomena is repeated in reverse as the antenna passes away from the source, resulting in a hyperbola where only its apex denotes the actual location of the buried source, with the arms of the hyperbola creating a record of reflections that traveled the oblique wave paths.