Active-source Rayleigh wave dispersion by the Aki spectral formulation

Abstract

Rayleigh wave imaging is efficient in estimating the shear- (S) wave velocity in near-surface exploration. The key is to accurately extract the dispersion of Rayleigh wave. We propose a method to calculate the dispersion of the active-source Rayleigh wavefield by using the Aki formulation. The spectrum after the cross correlation of two-channel records in the frequency domain is expressed by the Bessel function. Using the corresponding relation between the zero point of the spectrum real part and the Bessel function root, the phase velocity at the discrete frequency point is obtained and the dispersion curve is extracted. First, the theoretical basis and calculation method used in the active-source Rayleigh wave data are introduced. Then, three sets of theoretical models are calculated by this method and the results are consistent with the theoretical dispersion. Finally, we process a group of real Rayleigh wave data and obtain the phase velocity profiles and compared them with the results obtained by the multichannel surface wave analysis method. The effectiveness and applicability of the Aki method in active-source data processing are verified. Compared with multichannel wave processing, the advantage of the Aki method lies in the use of two-channel data in a single-shot record. When the number of acquisition channels in a shot gathers is insufficient or there is a bad channel, the quality of the extracted dispersion is guaranteed.