Non-linear Inversion of Noise Cross-correlations Using Probability Density Functions of Surface Waves Dispersion

Abstract:

Cross-correlations of ambient seismic noise are widely used to retrieve the information of the medium between pairs of stations. For periods between 1 and 50 s, the diffuse wavefield is dominated by microseismic energy which travels mostly as surface waves. Therefore, such waves are mainly reconstructed in the cross-correlations, and information about the structure are obtained using dispersion analysis, i.e computing phase or group velocities. Classical group velocity determination relies on tracking the maximum energy in the dispersion diagrams in order to get a unique dispersion curve. This procedure may often present problems due to the presence of several maxima. Moreover, the estimation of associated measurement errors usually depends on ad hoc user's criteria. We handle the non-unicity of the problem by inverting the whole dispersion diagram using a non-linear inversion scheme. For each frequency, the seismic energy is mapped into a time-dependent probability density function. The resulting map is inverted for the S-wave velocity structure using a Markov-chain Monte Carlo algorithm. Each time a new model is randomly sampled, the misfit value is computed according to the position of the corresponding group velocity curve in the probability density functions map. This method is applied for the analysis of vertical component noise cross-correlations computed from seismic data recorded in western Europe by the temporary PYROPE and IBERARRAY networks. The inversion of the fundamental mode Rayleigh wave dispersion diagrams between 5 and 50 s period gives a set of 1D S-wave velocity models, which are regionalized to infer a 3D S-wave velocity model of western France.