Dispersion Equations of Scholte Waves for Inclined Multi-layered Seabed

Scholte waves are surface waves that propagate along a fluid-solid interface and arise from the interference of P- and SV-waves. The conventional dispersion equations for surface waves are typically derived under the assumption of horizontal interfaces, and cannot be applied to inclined strata. The presence of inclined multi-layered seabed introduces substantial mathematical challenges in deriving dispersion equations for Scholte waves. To address this, a natural stratum coordinate system and a seismic wave propagation coordinate system are established. Coordinate rotation transformation matrices are derived to convert the seismic wave equations and boundary conditions between these two coordinates. In this natural stratum coordinate system, the dispersion equations of Scholte waves are derived with the presence of inclined multi-layered seabed. In addition, the dispersion curves and wavefields of Scholte waves are calculated for theoretical models with several inclined interfaces. The numerical results demonstrate that both the dipping angles and azimuths substantially influence the dispersion characteristics of Scholte waves. The effects of dipping angles on the dispersion curves are larger than those of azimuths. These derived equations can be further applied to high precision inversion of dispersion curves and to predict the S-wave velocities, dipping angles, and azimuths of shallow seabed with complex fluid-solid interfaces.