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For site characterization, the elliptic particle motion of Rayleigh waves and its frequency dependence is a well-known property that aroused less interest than the frequency dependence of the phase velocity. More than 50 yr ago, ellipticity was already recognized as providing information independent from phase velocity, despite the difficulties inherent to its accurate and precise measurement. Several techniques were developed during the last two decades to extract the ellipticity curve from ambient vibration recordings, with a single three-component (3C) station, with pairs of 3C stations and more recently with 3C arrays. The latter has the advantage over the other approaches that the sign of the ellipticity can be retrieved. Moreover, higher order mode separation is possible under certain conditions. Nevertheless, Rayleigh Three-component BeamForming (RTBF) proposed by Wathelet et al. encounters difficulties in the presence of significant levels of incoherent noise when the true ellipticity is vanishing or when it has a high absolute value. In this work, the analytical expressions of the beam power for a single source wavefield are revised under more realistic assumptions for the incoherent noise azimuthal distribution. The proposed model also includes an asymmetric distribution of the incoherent noise between vertical and horizontal components, which was not the case in the original publication. Switching from ellipticity to angular ellipticity drastically simplifies the formalism. Moreover, it naturally leads to a new steering matrix (all-component ellipticity steering) which solves the limitation around zero and infinity observed for RTBF. Interestingly, the accuracy of the ellipticity is no longer influenced by the absolute level of incoherent noise but by the difference between the incoherent noise ratio on vertical and horizontal components. A method based on the second derivative of the beam power versus the radial wavenumber is finally proposed to experimentally measure the noise ratio difference, which allows experimental values to be corrected. The methodology is compared with classical vertical beamforming and RTBF for a synthetic case and three experimental data sets. [ABSTRACT FROM AUTHOR]

We propose a new surface wave tomography approach that benefits from densely sampled active-source arrays and brings together elements from active-source seismic-wave interferometry, full waveform inversion and dense-array processing. In analogy with optical interferometry, seismic Michelson interferometer (SMI) uses seismic interference patterns given by the data-based diffraction kernels in an iterative inversion scheme to image a medium. SMI requires no traveltime measurements and no spatial regularization, and it accounts for bent rays. Furthermore, the method does not need computation of complex synthetic models, as it works as a data-driven inversion technique that makes it computationally very fast. In an automatic way, it provides high-resolution phase-velocity maps and their error estimation. SMI can complete traditional surface wave tomography studies, as its use can be easily extended from land active seismic data to the virtual source gathers of ambient-noise-based studies with dense arrays. [ABSTRACT FROM AUTHOR]

We investigated the construction of diffraction kernels (DKs) for surface waves using two-point convolution and/or correlation from land active seismic data recorded in the context of exploration geophysics. The high density of controlled sources and receivers, combined with the application of the reciprocity principle, allows us to retrieve 2-D phase-oscillation DKs of surface waves between any two source or receiver points in the medium at each frequency (up to 15 Hz, at least). These DKs are purely data based as no model calculations and no synthetic data are needed. They naturally emerge from the interference patterns of the recorded wavefields projected on the dense array of sources and/or receivers. The DKs are used to obtain multimode dispersion relations of Rayleigh waves, from which near-surface shear velocity can be extracted. Using convolution versus correlation with a grid of active sources is an important step in understanding the physics of the retrieval of surface wave Green's functions. This provides the foundation for future studies based on noise sources or active sources with a sparse spatial distribution. [ABSTRACT FROM AUTHOR]