Corrélation de transformées en ondelettes et ondes sismiques

(eng) In this work, we present the mathematical derivation of the formulas to be used in the cross-correlation analysis, using the wavelet transform as a basis. Although we are using sismic waves as an example, we can also apply this formalism to other global geophysical quantities. First, we use the wavelet power spectrum and the wavelet cross-correlation between the various components in a station to detect the arrival time of body waves. secondaly, we use wavelet cross-correlation between stations to discriminate real sismic events from noise, comparing it with the method of coincidences between stations. We use the Morlet wavelet with correction term, in order to respect the admissibility condition. The analysis made on the data corresponding to the earthquakes of 12th and 23rd August 2008 and the recording of 2 hours of 3rd March 2009 shows that we detect much better the S-waves than P-waves, because of the direction of the latter. As we use also the wavelet modulus maxima which gives us the skeleton, we focus on the length of the ridges. We must take a long ridge length, because the energy and velocity spectra of the data analysed of Brabant Wallon are broad.