f Application of the wavelet transform to time-frequency filtering, multiples removal and lower crust frequency studies

The frequency content of recorded data carries information about the medium in which the waves travelled. The classical windowed Fourier transform analysis allows a very precise frequency content estimation. But the time information is lost. The analysing window must be large enough to avoid aliasing effects. The wavelet transform has been chosen to give a more precise time-frequency representation of the data. The frequency determination is less precise than the Fourier analysis but the time location of each event is much more precise. The wavelet transform works by attempting to fit a given wavelet (the analysing wavelet) on the signal at each time with the possibility to expand the waveform on time and to adapt the amplitude. This is obtained by taking the scalar product of the record with the family of analysing wavelets (corresponding to the initial wavelet expanded on time with a set of scaling parameters). The analysis yields two time-frequency maps (modulus and phase) in which elementary frequency components are separated. From these two panels, it is easy to synthesize the associated signal by a simple integration of the frequency components at each time.