@article{WatheletGuillierRouxetal.2018,
  author    = {Wathelet, Marc and Guillier, B. and Roux, P. and Cornou, C. and Ohrnberger, Matthias},
  title     = {Rayleigh wave three-component beamforming},
  series = {Geophysical journal international},
  volume    = {215},
  journal   = {Geophysical journal international},
  number    = {1},
  publisher = {Oxford Univ. Press},
  address   = {Oxford},
  issn      = {0956-540X},
  doi       = {10.1093/gji/ggy286},
  pages     = {507 -- 523},
  year      = {2018},
  abstract  = {The variation of Rayleigh ellipticity versus frequency is gaining popularity in site characterization. It becomes a necessary observable to complement dispersion curves when inverting shear wave velocity profiles. Various methods have been proposed so far to extract polarization from ambient vibrations recorded on a single three-component station or with an array of three-component sensors. If only absolute values were recovered 10 yr ago, new array-based techniques were recently proposed with enhanced efficiencies providing also the ellipticity sign. With array processing, higher-order modes are often detected even in the ellipticity domain. We suggest to explore the properties of a high-resolution beamforming where radial and vertical components are explicitly included. If N is the number of three-component sensors, 2N x 2N cross-spectral density matrices are calculated for all presumed directions of propagation. They are built with N radial and N vertical channels. As a first approach, steering vectors are designed to fit with Rayleigh wave properties: the phase shift between radial and vertical components is either -Pi/2 or Pi/2. We show that neglecting the ellipticity tilt due to attenuation has only minor effects on the results. Additionally, we prove analytically that it is possible to retrieve the ellipticity value from the usual maximization of the high-resolution beam power. The method is tested on synthetic data sets and on experimental data. Both are reference sites already analysed by several authors. A detailed comparison with previous results on these cases is provided.},
  language  = {en}
}
@article{DiGiulioSavvaidisOhrnbergeretal.2012,
  author    = {Di Giulio, Giuseppe and Savvaidis, Alexandros and Ohrnberger, Matthias and Wathelet, Marc and Cornou, Cecile and Knapmeyer-Endrun, Brigitte and Renalier, Florence and Theodoulidis, Nikos and Bard, Pierre-Yves},
  title     = {Exploring the model space and ranking a best class of models in surface-wave dispersion inversion application at European strong-motion sites},
  series = {Geophysics},
  volume    = {77},
  journal   = {Geophysics},
  number    = {3},
  publisher = {Society of Exploration Geophysicists},
  address   = {Tulsa},
  issn      = {0016-8033},
  doi       = {10.1190/GEO2011-0116.1},
  pages     = {B147 -- B166},
  year      = {2012},
  abstract  = {The inversion of surface-wave dispersion curve to derive shear-wave velocity profile is a very delicate process dealing with a nonunique problem, which is strongly dependent on the model space parameterization. When independent and reliable information is not available, the selection of most representative models within the ensemble produced. by the inversion is often difficult. We implemented a strategy in the inversion of dispersion curves able to investigate the influence of the parameterization of the model space and to select a "best" class of models. We analyzed surface-wave dispersion curves measured at 14 European strong..-motion sites within the NERIES EC-Project. We focused on the inversion task exploring the model space by means of four distinct pararneterization classes composed of layers progressively added over a half-space. The classes differ in the definition of the shear-wave velocity profile; we considered models with uniform velocity as well as models with increasing velocity with depth. At each site and for each model parameterization, we performed an extensive surface-wave inversion (200,100 models for five seeds) using the conditional neighborhood algorithm. We addressed the model evaluation following the corrected Akaike's information criterion (AlCc) that combines the concept of misfit to the number of degrees of freedom of the system. The misfit was computed as least-squares estimation between theoretical and observed dispersion curve. The model complexity was accounted in a penalty term by AlCc. By applying such inversion strategy on 14 strong-motion sites, we found that the best parameterization of the model space is mostly three to four layers over a half-space: where the shear-wave velocity of the uppermost layers can follow uniform or power-law dependence with depth. The shear-wave velocity profiles derived by inversion agree with shear-wave velocity profiles provided by borehole surveys at approximately 80\% of the sites.},
  language  = {en}
}