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\begin{document}

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



\author[1]{Tongwei Qin}%
\author[2]{Laiyu Lu}%
\affil[1]{Institute of Geophysics}%
\affil[2]{Institute of Geophysics, China Earthquake Administration}%


\vspace{-1em}



  
  \date{May 18, 2024}


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\begin{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
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.%
\end{abstract}%



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