Introduction

During the last twenty years, several major earthquakes (Mexico 1985, Loma Prieta 1989, Kobe 1995, Izmit 1999, El Salvador 2001, Bam 2003, ...) were directly responsible of tens of thousands of persons killed and injured. The damage to human infrastructures and the disturbances of the local life represent an inestimable cost for national and local authorities, usually requiring international cooperation. Most of the cities and high populated areas are located on soft sediments (valleys, estuaries, recent deposits, ...) the soil structure of which are prone to amplify seismic waves (Bard (1994); Murphy and Shah (1988)). This phenomenon is usually called site effect or site amplification since the amplitude of the motion highly depends upon the local properties of the soil. Consequently, the risk mitigation requires fine investigations of each geological setting. The investments necessary with conventional techniques, i.e. boreholes, are prohibitive for developing countries and for regions with a moderate seismic activity (e.g. Western Europe). In this context, the European project SESAME (Site EffectS assessment using AMbient Excitation, Project EVG1-CT-2000-00026) was initiated in 2001 to study the reliability of low cost methods based on the measurement of ambient vibrations¹. The focus was put on two methods: the so-called H/V (Horizontal to vertical ratio) which became widely used after the work of Nakamura (1989), and the more complex array measurements based on the simultaneous recordings of the ambient vibrations at various locations. This thesis, which has been partly financed by the SESAME project, focuses on the array methods, which aim at inferring the one-dimensional shear-wave velocity profile at a given site.

Seismic wave propagation in a geological structure depends on its characteristics: the geometry of the layers, the shear and compressional-wave velocities, the density, and the attenuation factor inside each of them. For one-dimensional geological environments (property variations limited to the vertical axis), it can be theoretically shown that the shear-wave velocity ($V_s$ ) has the greatest influence. Conventional methods to access this parameter usually require the drilling of invasive and expensive boreholes which might be very disturbant for the inhabitants of dense cities. The determination of $V_s$ in the layers close to the surface (down to few tens of metres) is now possible without destructive methods thanks to the development of the surface wave methods during the last fifteen years, i.e spectral analysis of surface waves (SASW, Tokimatsu (1997); Stokoe et al. (1989); Socco and Strobbia (2004); Foti et al. (2003)). Surface waves travel along the ground surface (at the soil-air interface). In vertically heterogeneous media, surface waves are dispersive: their velocity varies as a function of frequency, which in turn controls their penetration depth (Aki and Richards (2002)). This dispersion property can be used to derive $V_s$ versus depth through an inversion process (Wathelet et al. (2004); Herrmann (1994)).

Though attractive on many aspects, the surface wave methods using artificial sources generally offer a restricted investigation depth (a few tens of metres usually) due to the limited frequency range of the signals (Tokimatsu (1997); Jongmans and Demanet (1993)). Moreover, in various geological environment with thick soft sediments (e.g. 500 m for Grenoble in France), the site effects depend also upon the properties of the deep structure. The improvement of the penetration is possible through the use of higher energy sources rich of low frequency. In an urban context, the use of explosive loads or mechanical generators is limited to avoid disturbance to the neighbouring houses and buildings. For regions with high seismicity and a dense observation network, the experience of past events is intensively used for inferring the site dynamic response. However, for regions with a moderate seismicity, the observation networks are less dense and there are fewer significant events. Consequently, it is necessary to develop other techniques to calculate the site transfer function, for which $V_s$ is a key parameter.

On the other hand, the frequency content of microtremor record is distributed over a wider range and the measurement of ambient vibrations through an array of sensors has appeared as a promising option to complement active sources (Tokimatsu (1997); Wathelet et al. (2004); Bettig et al. (2001); Asten and Henstridge (1984); Satoh et al. (2001); Nguyen et al. (2004)). Noise energy depends upon the source locations and upon the impedance contrast between the rocky basement and the overlying soft sediments (Chouet et al. (1998); Milana et al. (1996)). The main hypothesis for using ambient vibrations is that they are dominantly composed of surface waves, which allows the dispersion property to be used (Tokimatsu (1997); Chouet et al. (1998)).

The properties of the sources that generate the measured ground excitation are generally unknown. Consequently, the interpretation is generally a two-step process. First, the velocity of the travelling waves at a given frequency is derived from the processing of simultaneous ground-motion recordings at various stations. The common approaches used to derive the dispersion curve from the raw signals can be classified into two main families: frequency-wavenumber methods (Lacoss et al. (1969); Capon (1969); Kvaerna and Ringdahl (1986); Ohrnberger (2001)) and spatial auto-correlation methods (Aki (1957); Roberts and Asten (2004)). At the second stage, the dispersion curve is inverted to obtain the $V_s$ (and eventually the $V_p$ ) vertical profile, as in the classical active-source methods (Stokoe et al. (1989), Malagnini et al. (1995)). Like all surface wave methods, the obtained geometry is purely one-dimensional and is averaged across the array, implying that the technique is not suitable when strong lateral variations are present.