The Frequency‐Bessel Spectrograms of Multicomponent Cross‐Correlation Functions From Seismic Ambient Noise

Abstract

The recently developed frequency‐Bessel transformation (F‐J) method is effective to extract multimode surface wave dispersion curves from ambient noise cross‐correlation functions (CCFs). However, this method is currently limited to the vertical‐vertical component CCFs, and only Rayleigh wave dispersion curves can be obtained. In this study, we first relate the F‐J spectrogram to the spatial autocorrelation coefficients; we then extend the F‐J method to the full multicomponent CCFs tensor, including the radial‐radial, transverse‐transverse, and the mixed‐component CCFs. Using the newly derived formulation, not only the signal of higher‐mode Rayleigh wave phase velocity dispersion can be enhanced, but also the multimode Love wave phase velocity dispersion curves and the higher‐mode Rayleigh wave ellipticity can be extracted. The formulation is tested in several numerical examples and is applied to field data in North America. Our derivation and formulation provide an extension to the current F‐J method and help to take usage of multicomponent CCFs. The resulting higher‐mode surface wave dispersions and Rayleigh wave ellipticity provide complementary constraint on the Earth structures.

Extraction of Multimodal Dispersion Curves From Ambient Noise With Compressed Sensing

“…To compare the dispersion curves extracted by the three methods quantitatively, we manually pick the dispersion curves by tracking the energy peaks of each spectrogram (Figure 4). The F-J spectrogram of Rayleigh waves (Figure 3a) is generally consistent with the results of Wang et al (2019) and Hu et al (2020). In the F-J spectrogram (Figure 3a), we can identify the Rayleigh wave fundamental mode in the frequency range of 2.5-25 Hz, the first overtone in the frequency ranges of 4.5-7.5 and 19.5-25 Hz, the second overtone in the small frequency range of 18.3-19.5 Hz, and an osculation between the first and second overtones at 19.5 Hz (Figure 4a).…”

“…The main features of the F‐J spectrogram are similar to the results of Hu et al. (2020), but there are some differences in the frequency range where the overtones can be identified (Figures 5a and 6a). This may be caused by the different approaches for synthesizing the ambient noise, including the different methods employed to calculate the synthetic seismograms and the different source distributions.…”

“…(2019) and Hu et al. (2020). In the F‐J spectrogram (Figure 3a), we can identify the Rayleigh wave fundamental mode in the frequency range of 2.5–25 Hz, the first overtone in the frequency ranges of 4.5–7.5 and 19.5–25 Hz, the second overtone in the small frequency range of 18.3–19.5 Hz, and an osculation between the first and second overtones at 19.5 Hz (Figure 4a).…”

“…The second synthetic test model (Model 2) contains two layers representing soil overlaying a half-space (Figure 1b and Table 1). The model is the same as that in Hu et al (2020). Again, we use the above method to synthesize the ambient noise of Model 2.…”

Joint Inversion of Rayleigh and Love Dispersion Curves Extracted from Ambient Seismic Noise Based on Secular Function

“…Compared with the traditional method, it has a clearer image of the higher-order mode [1]. In 2020, Hu used the multi-component cross-correlation coefficient to extract the Love wave dispersion curve from the ambient seismic noise data [3]. These two research results have greatly promoted the development of ambient seismic noise exploration, and the dispersion curves of Love waves and Rayleigh waves can be extracted from seismic records at the same time.…”