Computation of Surface Wave's Dominating Mode For Stratified Media

Surface waves propagating through stratified media exhibit multiple theoretical modes. The traditional forward modeling methods, such as the propagator matrix method, stiffness matrix method, and thin-layer method, provide all the possible theoretical modes within the given frequency range. However, not all of these modes are excitable or detectable on the free surface of the layered media. Consequently, the theoretically calculated modes from these methods do not fully represent the dispersive trends observed in the surface wavefield experiment, where multiple modes often dominate in the specific frequency band. This study presents a higher-order thin-layer method-based forward modeling approach to determine the theoretical dominating mode of Rayleigh wave propagating through horizontally layered media. The proposed approach incorporates relative modal energy into all the theoretical dispersion curves, providing a more realistic and intuitive representation of the dispersion characteristics. The dominating mode dispersion curve is determined by considering the maximum spectral amplitude among all the propagating modes. As a result, the predominant frequency band of different modes becomes distinctly evident, especially for irregularly dispersive profiles. The behavior of the dominating mode is analyzed for a wide range of mediums, starting from thin composite plate to crustal-scale geological model and from normally dispersive to high-velocity layer and low-velocity layer soil profiles. The dominant dispersion trends obtained from all the profiles exhibit excellent agreement with the results from the 2D numerical simulation. Overall, the enhanced forward modeling method offers a more realistic theoretical dispersion curve representation and generates a single predominant mode, which can be utilized to develop a more advanced inversion scheme.