A simplified frequency-domain beamforming approach for active and passive surface wave surveys

ABSTRACT Frequency-domain beamforming (FDBF) and cylindrical frequency-domain beamforming (CFDBF) techniques are among the most robust methods for extracting experimental phase velocity dispersion data from wavefields recorded during either active- or passive-source surface wave testing. FDBF and CFDBF transformations rely on calculating the spatiospectral correlation matrix to compute the steered power response spectrum, which is essential for extracting surface wave dispersion data. The dimensions of the spatiospectral correlation matrix are directly influenced by the frequency sampling and the number of sensors used in the survey setup. When the number of sensors is large, and/or the frequency range is broad, and/or the frequency sampling is dense, the spatiospectral correlation matrix size leads to a greater number of required computations to calculate the steered power response spectrum for the FDBF and CFDBF techniques. Therefore, we develop a simplified and computationally efficient FDBF algorithm for active and passive surface wave surveys. This method avoids the calculation of the spatiospectral correlation matrix and its multiplication with the Hermitian transpose of the steering vector, thereby reducing the computational complexity by an order of magnitude. Furthermore, by leveraging vectorization techniques, the developed algorithm uses matrix multiplications instead of loops, significantly heightening computational efficiency. We rigorously test the algorithm using surface wave data sets collected across diverse subsurface conditions with varying sensor arrays and acquisition parameters (e.g., sampling frequencies and window lengths) to evaluate its efficacy. The results demonstrate that our developed algorithm outperforms the conventional FDBF method in processing time, highlighting its practical effectiveness. This method shows promise for integration into surface wave data processing software, offering substantial improvements in computational efficiency without compromising accuracy.