Measurement of Phase Velocity and Ellipticity of Multi‐Mode Surface Waves by Beamforming Multi‐Component Ambient Seismic Noise

Abstract Conventional beamforming of multi‐component ambient seismic noise typically utilizes only the vertical‐vertical (ZZ) component to extract Rayleigh wave dispersion curves or the transverse‐transverse (TT) component for Love waves. In this study, we extend weighted and modified beamforming to cross‐correlation functions between different components. We demonstrate that the beamforming output for all components from an array with finite stations can be represented theoretically by a cosine‐modulated sinc function multiplied by an amplitude factor. This representation explains the energy distribution features across mode branches in multi‐mode dispersion spectrum obtained through array‐based techniques. The method is validated using both synthetic test and field data from arrays at different scales. We successfully extract multi‐mode dispersion curves for both Rayleigh and Love waves, as well as Rayleigh wave ellipticity with polarity information. By comparing with the results outputted by the analytical formulation, the features of the multi‐mode dispersion spectrum are investigated by considering the excitation intensity of each mode. We observe both prograde and retrograde particle motion in the fundamental mode Rayleigh wave from field data at a local basin scale. We also observe that the phase velocity estimated from ZZ and RZ (radial‐vertical) component has a systematic difference from those estimated from RR and ZR component for some mode branches, implying that this can be used to characterize the polarization anisotropy of the earth. The proposed method shows potential for extracting multi‐mode surface wave dispersion curves and Rayleigh wave ellipticity from ambient seismic noise, including leaking modes.