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.

A semi-analytical spectral element method (SASEM) is proposed to solve for the normal and leaky modes of elastic waves propagating in a planar waveguide with a half-space substrate. For the SH-wave modes, the transparent boundary condition is used to model the SH wavefields in the half-space substrate. To solve for the PSV-wave normal modes on the (+, +) Riemann sheet and leaky modes on the (+, −) Riemann sheet, the elastic wavefields in the finite-thickness layers are modeled using the displacements, whereas the wavefields in the half-space are modeled using the P- and S-wave potentials. In the substrate, the transparent boundary condition is used for the shear wavefields, whereas semi-infinite elements are introduced to treat the radiative boundary condition of the P wavefields. Then, a polynomial eigenvalue problem is derived, which can be transformed into a standard linear eigenvalue problem. Solving the eigenvalue problem, we can obtain the solutions of the normal and leaky modes. Several numerical tests were performed to verify the effectiveness of SASEM, as well as to demonstrate its high accuracy. Modal analyses of the oscillations of the solved modes demonstrate that the leaky modes differ from the normal modes because of the increasing wavefields in the half-space. Moreover, the guided-P modes are confirmed to be more dependent on the P-waves, whereas the normal and organ-pipe modes are primarily determined by the S-waves. Besides the crustal model composed of several homogeneous layers, SASEM is applied to a vertically inhomogeneous offshore model to demonstrate its applicability. The good agreement between the theoretical guided-P modes and the dispersion spectra not only shows the correctness of SASEM when analyzing waveguides composed of gradient layers but also indicates the potential for constraining the P-wave velocity using the guided-P modes.

In the past two decades, surface wave imaging based on seismic ambient noise cross-correlation (CC) has been one of the most important technologies in the field of seismology. With the development of this technology, high-mode surface waves have received increasing attention, especially after the proposition of the frequency-Bessel transform (F-J) method, which can effectively extract multimode dispersion curves from ambient noise data. In the past few years, our research group has made many attempts to improve this method. We summarized these experiences and the corresponding algorithm for fast CC, and packaged them into a Python package called CC-FJpy. It is commonly understood that CC takes a good deal of time. However, we found that a simple reorganization of the CC logic can achieve computational acceleration by a multiple of tens or even hundreds in comparison with classical CC open-source programs for N stations. For the F-J method, we use Nvidia’s graphics processing unit (GPU) to speed up computation, and this approach achieves a hundreds-fold computational acceleration. We have encapsulated our experiences and technologies into CC-FJpy and submitted it to various types of data tests to ensure its speed and ease of use. We hope that providing the open source of CC-FJpy can benefit the development of surface wave studies and make it easier to start with high-mode surface waves. We look forward to your use and valuable suggestions.