Abstract: In near-surface surface wave exploration, especially in typical sedimentary basins, mode-kissing of the fundamental and first-order modes is often observed for the dispersion image in the frequency-phase velocity domain. In the mode theory of waves, surface wave mode in the frequency domain is associated with a series of poles determined by the dispersion equation. In the generalized ray theory, the multipath in the spatial-temporal domain gives rise to the multimode in the frequency domain. Combined with the generalized theory and the mode theory, the influence of the $\bar{P}$ pole and the $\bar{S}$ pole on dispersion curves is studied to explain the mode-kissing phenomenon. For a two-layer model, the characteristics of the dispersion curves, eigen displacement, and polarization of the particle, which varies with the moving of $\bar{P}$ pole in the complex ray parameter plane, are studied by changing the S wave velocity β⁽²⁾ of the bottom half space, both for the fundamental and the first overtone. It is found that mode-kissing appears when the $\bar{P}$ pole passes through the branch point 1/β⁽²⁾ in the complex ray parameter plane and just enter the area belongs to the normal mode. The particle motion of the first leaky mode corresponding to the $\bar{P}$ pole is a prograde ellipse, but the eigen displacement shows the characteristic of the classical surface wave, i.e., the displacement mainly concentrates near the surface and decays rapidly with depth.

Key words: Generalized ray, Eigenvalue, Dispersion curve, Cagniard-de Hoop method, Generalized reflection-transmission coefficient, Free surface wave, Trapped wave