Near Surface Geophysics, 2004, 211-221 © 2004 European Association of Geoscientists & Engineers 211 Surface-wave inversion using a direct search algorithm and its application to ambient vibration measurements M. Wathelet 1, 2* , D. Jongmans 1 and M. Ohrnberger 3 1 LIRIGM, Université Joseph Fourier, BP 53, 38041 Grenoble cedex 9, France 2 GEOMAC, Université de Liège, 1 Chemin des Chevreuils, Bât. B52, 4000 Liège, Belgium 3 Institut für Geowissenschaften der Universität Potsdam, POB 601553, D-14415 Potsdam, Germany Received January 2004, revision accepted August 2004 ABSTRACT Passive recordings of seismic noise are increasingly used in earthquake engineering to measure in situ the shear-wave velocity profile at a given site. Ambient vibrations, which are assumed to be mainly composed of surface waves, can be used to determine the Rayleigh-wave dispersion curve, with the advantage of not requiring artificial sources. Due to the data uncertainties and the non-lin- earity of the problem itself, the solution of the dispersion-curve inversion is generally non-unique. Stochastic search methods such as the neighbourhood algorithm allow searches for minima of the misfit function by investigating the whole parameter space. Due to the limited number of parame- ters in surface-wave inversion, they constitute an attractive alternative to linearized methods. An efficient tool using the neighbourhood algorithm was developed to invert the one-dimensional V s profile from passive or active source experiments. As the number of generated models is usually high in stochastic techniques, special attention was paid to the optimization of the forward compu- tations. Also, the possibility of inserting a priori information into the parametrization was intro- duced in the code. This new numerical tool was successfully tested on synthetic data, with and without a priori infor- mation. We also present an application to real-array data measured at a site in Brussels (Belgium), the geology of which consists of about 115 m of sand and clay layers overlying a Palaeozoic base- ment. On this site, active and passive source data proved to be complementary and the method allowed the retrieval of a V s profile consistent with borehole data available at the same location. is of major importance in earthquake engineering, and ambient vibrations measured by an array of vertical sensors are increas- ingly applied for determining V s profiles (e.g. Horike 1985; Tokimatsu 1995; Ishida et al. 1998; Miyakoshi et al. 1998; Yamamoto 1998; Satoh et al. 2001; Scherbaum et al. 2003). In a first step, the Rayleigh phase-velocity dispersion curve is derived from the processing of simultaneous ground-motion recordings at various stations. The recording time is usually greater than or equal to half an hour and the number of stations is generally between 6 and 10, depending upon the available equipment (sensors, synchronized or multichannel stations) and time (the set-up may take quite a long time for a large number of sensors). The geometry of the station layout is not strictly imposed by the processing method itself, but a circular shape ensures an equal response of the array for waves coming from all azimuths. The common approaches used to derive the dispersion curve from the raw signals can be classified into two main fam- ilies: frequency–wavenumber (Lacoss et al. 1969; Capon 1969; Kvaerna and Ringdahl 1986; Ohrnberger 2001) and spatial auto- INTRODUCTION For the majority of seismic prospecting methods, natural or cul- tural ambient vibrations constitute an undesired part of the signal, which has to be eliminated as much as possible. However, the noise field is influenced by the subsurface structure and the use of array records of seismic noise has been recognized as a method for deriving the S-wave velocity profile at a given site (e.g. Aki 1957; Asten 1978; Tokimatsu 1995). The hypothesis behind the method is that ambient vibrations mainly consist of surface waves, whose dispersion characteristics depend primarily on the body-wave velocities (V p for compressional-wave velocities and V s for shear-wave velocities), the density and the thickness of the different layers (Murphy and Shah 1988; Aki and Richards 2002). Noise energy depends upon the source locations and upon the impedance contrast between the rocky basement and the overly- ing soft sediments (Chouet et al. 1998; Milana et al. 1996). A knowledge of the shear-wave velocity (V s ) profile at a given site * marc.wathelet@ujf-grenoble.fr