Removal of Crossed Artifacts from Multimodal Dispersion Curves with Modified Frequency–Bessel Method

Abstract

\n Frequency–Bessel (F-J) transform method can obtain higher-mode Rayleigh dispersion curves by multistation ambient noise data superposition (Wang et\xa0al., 2019). Because the dispersion curves of the overtones can provide more information compared with the single fundamental mode, the nonuniqueness of surface-wave inversion can be reduced. Because of the limited number of receivers, the integral in the process of transformation cannot be calculated precisely and there exists a kind of crossed artifacts which cuts off the real dispersion curves and contaminates the spectrum. Forbriger (2003) proposed to use the Hankel function instead of the Bessel function to conduct the transformation to remove the crossed artifacts. However, this method can reduce the resolution of the spectrum from ambient noise data. In this article, we give a complete workflow to deal with ambient noises which can eliminate the crossed artifacts without reducing the resolution. The Kramers–Kronig relations are used to obtain complete cross-correlation functions and a modified F-J transform is conducted to finally acquire the spectrum without crossed artifacts.