A Modified Cross-correlation Beamforming (MCBF) for Extracting Multimode Surface Wave Dispersion Curves from Ambient Seismic Noise

Abstract

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 crosscorrelation 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.