Beamforming (BF) and Frequency-Bessel transform (F-J) have been demonstrated to extract multimode surface wave dispersion curves from ambient seismic noise. F-J method implicitly assumes the structure under the array is laterally isotropic. As for the conventional BF method, although the azimuth-dependence phase velocity can be measured, the fictitious azimuth anisotropy created by array geometry would be projected into the result. In this paper, the weighted and modified cross-correlation beamforming (WCBF and MCBF) schemes are proposed to extract the multimode surface wave dispersion curves with sufficient resolution using quite short noise recordings. Compared with the conventional BF, only the plane waves with the azimuth consistent with the interstation orientations are considered in MCBF and the search over the incident plane waves from different azimuth is omitted. The azimuth-dependence velocity can therefore be extracted by MCBF, independent of the array geometry. As far as the measurement of azimuth-averaged velocity is concerned, we show that BF is equivalent with F-J. The explicit relationship between BF and F-J methods is derived. For the finite sampling in practical applications, the theoretical representations of the dispersion image generated by BF technique under different imaging conditions are given. These representations can be used to investigate analytically the features of the dispersion images in frequency-velocity domain and how the aliasing is eliminated by improved imaging condition. The proposed methods are validated for the synthetic data as well as the real data from the dense array at different scales.

The 3D S-wave velocity of shallow structure, especially the Quaternary sediments at 0-1 km near the surface, is an important issue of concern in urban planning and construction for the requirements of seismic hazard assessment and disaster mitigation. Due to the facility and less dependence on the site environment, noise-based technique is an ideal way to acquire the fine structure of urban sedimentary basin. Based on the dense array composed of more than 900 stations deployed in Tongzhou at a local scale of 20 × 40 km2, we proved the lateral variation of the phase velocity of multi-mode surface waves can be estimated directly with adequate accuracy by beamforming seismic noise with moving subarray, without tomography. Rayleigh wave phase velocity maps, at frequencies between 0.3 and 2.5 Hz for the fundamental mode as well as 0.8 and 3.0 Hz for the first overtone, are obtained. The 3D S-wave velocity model at 0-1 km depth with lateral resolution of 1 km is then established by inverting phase velocity maps of two modes. The thickness of the sediments is delineated by the impedance interface given by microtremor H/V (horizontal-to-vertical) spectral ratio. The model is in good agreement with tectonic unit. The sedimentary thickness of Daxing high and two sags located around Gantang and Xiadian are respectively 100-400 m and 400-600 m, which correlates well with the isosurface of S-wave velocity at 1 km/s. The model also presents some evidence on the extension of Daxing fault along NE direction.