Depth-dependent surface wave dispersion equation calculated by the impedence matrix method

Abstract This study introduces a new impedance matrix method for calculating surface wave dispersion in stratified layered media, with particular attention to high-frequency scenarios of higher modes in the existence of a low-velocity layer where the missing root problem is most severe. The key innovation of the method is the introduction of depth-dependent dispersion equations, specifically designed to address and mitigate the issue of missing roots for the trapped modes. This method provides flexibility in the dispersion equation, enabling easier root detection and improving the resolution of certain roots. Extensive comparative analysis with other methods, including the compound matrix method and the generalized reflection and transmission coefficients method, highlights the practicality of our approach. Graphical Abstract