Fourier Transform > Velocity correction: applied to a georadar (GPR) section

A) To determine the velocity of the formation, the delay distribution to apply is a linear function in terms of the emitter - receiver distance. The choice of velocity cursor is made by visualizing the stack (figure on the right). The right velocity corresponds to a maximum value for the amplitude of the stack.
B) Once the formation velocity is known, the lateral offset of the diffracting point is determined by looking for the hyperbolic delay distribution which corrects the curvature of the diffraction. After the curvature correction, the sum of the traces making up the radar section has to show a maximum of amplitude at the apex times of the hyperbola, if the value at the lateral offset of the diffracting point is correctly chosen.

The example on the left shows:

  • The initial radar section,
  • The corrected radar section with a linear delay distribution defined by the formation velocity. It is possible for you to find the formation velocity by choosing the velocity which brings the incident wave to a constant time whatever the receiver position,
  • The corrected radar section with a hyperbolic delay distribution defined by the lateral offset of the diffracting point, the velocity of the formation being known. It is possible for you to find the lateral offset of the diffracting point by choosing the distance which maximizes the amplitude of trace sum at the apex of diffraction hyperbola.

The example on the right shows: The summed trace obtained either

  • After velocity correction,
  • After correction of the curvature of the hyperbola.

The velocity of the formation associated with the propagation of the electromagnetic wave is in this example 124.13 m/µs. The lateral offset of the diffracting point is 51.5 m for an apex time of 956 ns.