Classic surface wave imaging relies mainly on the dispersion of Rayleigh waves or Love waves. In addition to these types of waves, waveforms that arrive prior to the S wave also exhibit dispersion. These early dispersed waves are controlled mainly by the leaking modes and are rarely used for imaging. We applied the frequency-Bessel transform method to waveforms that arrive before the S wave and successfully extracted multiple leaking mode dispersion curves. The extracted “0th” mode shows continuous sensitivity to S-wave velocity (Vs) and mass density structure whereas the “higher” modes behave more like surface waves that are sensitive to P-wave velocity (Vp) structure in the crust. Thus, the “higher” modes can be used to invert the Vp structure, which can compensate for the fact that conventional surface wave imaging methods are mainly sensitive to Vs structure.

Some features in late coda correlations have now been commonly treated as “the inter- station body waves”. In general, however, large earthquakes releasing coda waves mostly situate at the continental boundaries. It remains unclear as to how such a discrete and non- uniform distribution of earthquakes influences these features. To understand the impacts, here we introduce geometric ray theory to explore the body wave cross-correlation. In the stationary phase integral, we show that the distribution geometry of earthquakes and the dimension of the stationary phase zone significantly influence the correlation phases. The dimension of the stationary phase zone is inversely proportional to the k-κ coefficient which, as a newly-proposed terminology, is composed of the seismic wave-number and the coda propagation distance. In late coda correlations, most of the large earthquakes situate in the stationary phase zone for constructing the inter-station wave due to the small k- κ coefficient. However, because earthquakes are not always at the stationary points, the correlation signals may appear a little earlier than their counterparts in Green’s function. We have verified the theoretical analyses with the synthetic and realistic coda correlations.This theory is also applicable in other physics fields allowing for geometric ray theory. It demonstrates that the event-receiver geometry can result in the travel time variation up to 1/6 of the body wave correlation period. Thus, researchers should carefully investigate the impacts when utilizing the correlation signals as inter-station body waves for the future work of illuminating the Earth’s discontinuities.

Thousands of deep seismic sounding profiles have been obtained worldwide to detect crustal and lithospheric structures; unfortunately, fine near-surface/shallow sedimentary structures are difficult to determine through large-scale seismic surveys. To improve the near-surface/shallow sedimentary structure resolution, we extract multimodal dispersion curves with the frequency-Bessel transform (F-J) method from deep seismic sounding profiles in the Atlantic coastal plain and explore the joint inversion of multimodal dispersion curves and refraction. Three-layer sedimentary structures of the Atlantic coastal plain, which are highly consistent with drillhole data, are obtained by joint inversion with the Monte Carlo method. In the preferred sedimentary structure, the second layer of the models is identified mainly by the P-wave refraction, while the velocity discontinuity and shallower velocity are sensitive mostly to the multimodal dispersion curves. Although the dispersion curves are not sensitive to the second layer of the models, the pattern of the F-J spectrogram can be greatly influenced by the second layer. The preferred sedimentary models exhibit an extremely low sedimentary Vp/Vs ratio, which has a profound influence on the dispersion curves. The inversion of dispersion curves would lead to incorrect results without the Vp/Vs ratio constrained by P- and S-wave refractions. These results demonstrate that the F-J method is an effective approach to extract multimodal dispersion curves from deep seismic sounding data and that an accurate fine sedimentary structure can be obtained by the joint inversion of multimodal dispersion curves and refraction.

Although higher-mode surface wave dispersion curves can provide additional constraints on the subsurface velocity structure, their extraction from ambient noise data remains more intractable than the extraction of fundamental-mode dispersion curves. Recently, the frequency-Bessel transform (F-J) method was developed to extract multimodal dispersion curves from ambient noise. Here, we propose an alternative compressed sensing (CS) method for extracting multimodes from ambient noise. We solve the CS inverse problem by using two methods: an l1-based optimization algorithm and a Bayesian method. Synthetic and field data examples are conducted to validate our method. The dispersion curves extracted by our method are consistent with those extracted by the F-J method, but our method is more efficient and can extract higher-resolution dispersion energy images than the F-J method. Our method can quickly and reliably extract multimodes from ambient noise, thereby facilitating studies of ambient noise tomography.