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Direct Inversion of Spatial Autocorrelation Curves with the Neighborhood Algorithm

¹ LIRIGM, Université Joseph Fourier
BP 53
38041 Grenoble cedex 9, France
marc.wathelet{at}ujf-grenoble.fr
 (M.W., D.J.)

² GEOMAC, Université de Liège
1 Chemin des Chevreuils, Bât. B52
4000 Liège, Belgium
 (M.W.)

³ Institut für Geowissenschaften der Universität Potsdam
POB 601553
D-14415 Potsdam, Germany
 (M.O.)

Ambient vibration techniques are promising methods for assessing the subsurface structure, in particular the shear-wave velocity profile (V_s). They are based on the dispersion property of surface waves in layered media. Therefore, the penetration depth is intrinsically linked to the energy content of the sources. For ambient vibrations, the spectral content extends in general to lower frequency when compared to classical artificial sources. Among available methods for processing recorded signals, we focus here on the spatial autocorrelation method. For stationary wavefields, the spatial autocorrelation is mathematically related to the frequency-dependent wave velocity c(). This allows the determination of the dispersion curve of traveling surface waves, which, in turn, is linked to the V_s profile. Here, we propose a direct inversion scheme for the observed autocorrelation curves to retrieve, in a single step, the V_s profile. The powerful neighborhood algorithm is used to efficiently search for all solutions in an n-dimensional parameter space. This approach has the advantage of taking into account the existing uncertainty over the measured curves, thus generating all V_s profiles that fit the data within their experimental errors. A preprocessing tool is also developed to estimate the validity of the autocorrelation curves and to reject parts of them if necessary before starting the inversion itself.

We present two synthetic cases to test the potential of the method: one with ideal autocorrelation curves and another with autocorrelation curves computed from simulated ambient vibrations. The latter case is more realistic and makes it possible to figure out the problems that may be encountered in real experiments. The V_s profiles are correctly retrieved up to the depth of the first major velocity contrast unless low-velocity zones are accepted. We demonstrate that accepting low-velocity zones in the parameterization has a dramatic influence on the result of the inversion, with a considerable increase in the nonuniqueness of the problem. Finally, a real data set is processed with the same method.

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