In the section dealing with the Fourier transform, we have introduced the convolution operation between two functions. Here, we tackle the correlation operation which is similar but which has a very different objective. It consists of putting in place a comparison measure between two signals by adopting a criteria such that the correlated signals do not differ except by one delay or amplitude term. Auto-correlation serves to measure the repetitive character of a signal and to gain an appreciation of its duration (or brevity). Intercorrelation allows measurement of the delay between two different signals and to localize instants where a seismic trace resembles the source signal. Correlation equally allows the signal to noise ratio to be evaluated for seismic data. We will present various applications of the correlation function.

In particular, we will show:

Autocorrelation of a signal composed of 2 delayed Dirac.
Intercorrelation, measurement of the delay between two borehole seismic traces (VSP).
Autocorrelation of a function representing a frequency sweep and its application to vibro-seismics.
Vibro-seismic soundings.