A frequency-Hankel transform method to extract multimodal Rayleigh wave dispersion spectra from active and passive source surface wave data

Rayleigh wave dispersion energy spectra have been widely used to extract dispersion curves and invert underground S-wave velocity structures for engineering geophysics and seismology. We develop a frequency-Hankel (F-H) transform method to extract high-quality multimodal Rayleigh wave dispersion energy spectra from active and passive source Rayleigh wave data. The F-H transform method is inspired by the frequency-Bessel (F-J) transform method and considers the physical meaning of Green’s functions for Rayleigh wave dispersion analysis. The F-H transform method can naturally avoid crossed artifacts caused by converging waves on F-J spectrograms and obtain more multimodal dispersion spectra of the same quality with fewer Rayleigh wave data than the F-J transform method. Synthetic and field Rayleigh wave data from active and passive sources for near-surface exploration and ambient noise tomography are used to demonstrate the validity, accuracy, and applicability of the F-H transform method. The F-H transform method unifies the formulas of the F-J transform method and its modifications for active and passive sources of Rayleigh wave data. The F-H transform method is a robust and efficient multimodal Rayleigh wave dispersion analysis method for active and passive source Rayleigh wave data.