@article{fdi:010074336,
  title = {{R}ayleigh wave three-component beamforming : signed ellipticity assessment from high-resolution frequency-wavenumber processing of ambient vibration arrays},
  author = {{W}athelet, {M}arc and {G}uillier, {B}ertrand and {R}oux, {P}. and {C}ornou, {C}{\'e}cile and {O}hrnberger, {M}.},
  editor = {},
  language = {{ENG}},
  abstract = {{T}he variation of {R}ayleigh ellipticity versus frequency is gaining popularity in site characterization. {I}t becomes a necessary observable to complement dispersion curves when inverting shear wave velocity profiles. {V}arious 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. {I}f only absolute values were recovered 10 yr ago, new array-based techniques were recently proposed with enhanced efficiencies providing also the ellipticity sign. {W}ith array processing, higher-order modes are often detected even in the ellipticity domain. {W}e suggest to explore the properties of a high-resolution beamforming where radial and vertical components are explicitly included. {I}f {N} is the number of three-component sensors, 2{N} x 2{N} cross-spectral density matrices are calculated for all presumed directions of propagation. {T}hey are built with {N} radial and {N} vertical channels. {A}s a first approach, steering vectors are designed to fit with {R}ayleigh wave properties: the phase shift between radial and vertical components is either -{P}i/2 or {P}i/2. {W}e show that neglecting the ellipticity tilt due to attenuation has only minor effects on the results. {A}dditionally, we prove analytically that it is possible to retrieve the ellipticity value from the usual maximization of the high-resolution beam power. {T}he method is tested on synthetic data sets and on experimental data. {B}oth are reference sites already analysed by several authors. {A} detailed comparison with previous results on these cases is provided.},
  keywords = {{F}ourier analysis ; {T}ime-series analysis ; {S}ite effects ; {S}urface waves and ; free oscillations ; {W}ave propagation},
  booktitle = {},
  journal = {{G}eophysical {J}ournal {I}nternational},
  volume = {215},
  numero = {1},
  pages = {507--523},
  ISSN = {0956-540{X}},
  year = {2018},
  DOI = {10.1093/gji/ggy286},
  URL = {https://www.documentation.ird.fr/hor/fdi:010074336},
}