Ambient vibrations

The main objective when processing ambient vibration recordings is to measure the velocity of surface waves which varies with frequency. The first assumption is hence that the wavefield mainly consists of surface waves. For a horizontally stratified soil structure, the measured velocities might be the body wave velocities ($V_p$ and $V_s$ ) or the dispersion curve of surface waves including the fundamental and the higher modes (Aki and Richards (2002)). If the direction of propagation is known and if one single wave dominates, the velocity can be calculated by picking the arrival time at two sensors separated by a fixed distance. However, the ambient wavefield is made of the superposition of many waves travelling in any direction. Picking is no longer possible because the individual propagating waves cannot be identified, and more sensors are necessary to scan all potential azimuths. Signal processing techniques are essential to retrieve the apparent velocities. We restrict our work to the vertical component of the wavefield which does not contain Love contributions.

Theoretically, better velocity measurements are achieved when numerous sensors are available to sample the wavefield at the ground surface. Ideally, the number of stations should be greater than the number of waves present at one time (Asten and Henstridge (1984)). Practically, the ambient wavefield is recorded by a limited number of sensors for cost and logistical reasons (ten to a few tens of elements per array, Scherbaum et al. (2003); Chouet et al. (1997); Saccorotti et al. (2003)). The three components are generally recorded simultaneously at each station. The optimum of the array geometry is still a matter of debates. However, the array output must be identical for all incident azimuths because there is generally no prior knowledge about the characteristics of the ambient wavefield (Asten and Henstridge (1984)). Hence, a roughly circular shape is probably the best option. All sensors must not necessarily lay on the same circle, but there must be a certain kind of rotational symmetry in the sensor positions. In section 1.1.1 on page , a quantitative method is proposed to analyse the efficiency of arrays.

Once the signals are recorded for a sufficient duration (at least half an hour, or longer for deep soil structures that require low frequency information), they are processed with the three techniques described hereafter, which extract the same velocity information from the raw signals in three different ways. Agreement between the three methods is usually expected for good quality results. Tests of the three processing methods on a synthetic and a real case are given in chapter 6. Other methods, like multiple signal classification (MUSIC, Cornou et al. (2003); Schmidt (1981)) are not considered here.