The case of one single and instantaneous point source is considered here. The sensors and the source points are usually distributed along a line. Contrary to ambient vibrations, there is a total control over the source parameters (location, type of source, frequency content, time of occurrence, ...). On the recorded signals, the body waves (P and/or S) and the surface waves are generally visible. The last ones appear at the end of the signal with high amplitudes and a triangular dispersion pattern. During the last 20 years, surface wave properties have been intensively exploited by various authors. The first applications consist of inverting the measured dispersion curve as the fundamental Rayleigh mode including eventual on or more clearly identified higher modes (Stokoe et al. (1989); Gabriels et al. (1987); Socco and Strobbia (2004); Malagnini et al. (1995); McMechan and Yedlin (1981); Herrmann (1994); Foti (2000)). Inversions of the measured curve taking into account the mode contributions or inversions of the full waveforms were recently proposed (Yoshizawa and Kennett (2002); Forbriger (2003b)).
Here, we are only considering the inversion of the theoretical dispersion curve to adopt an approach consistent with the ambient vibration method for which no other type of inversion is currently feasible. The body and the surface wave are hence analysed separately.