Fourier Transform > Two dimensional Fourier transform

The time-distance diagram in top represents the simulated recording of a seismic wave (a seismic section). The vertical axis represents a receiver's distance in relation to the source, the horizontal axis represents the length of time recorded. Two types of visualization of the seismic section are proposed. The galvanometric representation is the classic representation of function in the form of a curve. The variable area representation consists of showing and darkening the positive arches of the function.
The slope of the wave is a function of the propagation velocity of sound in the medium concerned. It is represented here by the delay of a wave's arrival time between two receivers. After application of a double Fourier Transform over time and distance variables, the seismic recording is represented by its modulus in the frequency-wavenumber plane (F,K plane). The velocity is obtained from f/k relationship.

Settings:

  • The delay (expressed in number of samples) between two receivers can be changed and its effect seen in the F,K plane,
  • The velocity correction consists of delaying each trace of the recording by a time proportional to the distance between emitter and receiver.