Here is an example of convolution and correlation.
Convolution is used to make a synthetic seismogram.
The input signal is long and changes frequency with time, this is similar to a vibroseis signal. We also need a stratigraphic section represented as a series of reflection coefficients. Now do the convolution. The first two reflections in the synthetic seismogram demonstrate that a change in the sign of the reflection coefficient changes the polarity of the resulting wavelet. Reflections three and four show superposition from reflection coefficients of opposite sign.