Seismic research uses Discrete Fourier Transform (DFT) and the Fast FT(FFT). If you look at the history of the FFT you will find that one of the original uses for the FFT was to distinguish between natural seismic events and nuclear test explosions because they generate different frequency spectra.

The (fast) Fourier transform is used to convert the signal into the frequency domain, where convolution between two signals is obtained simply multiplying them together. Once again the Fourier Transform is used as a tool in Digital Signal Processing to perform other operations, rather than producing an end result itself.