<p>This study investigates the propagation characteristics of Rayleigh-type surface waves in layered viscoelastic media, with a particular focus on the role of impedance boundary conditions. The effects of material gradation, viscoelastic damping, and geometric configuration on wave speed and dispersion behavior are comprehensively analyzed, providing insights into the complexities of wave dynamics in heterogeneous media. A combination of analytical formulations and robust numerical techniques is employed to investigate the dispersive and damping characteristics of Rayleigh-type waves. The analysis systematically examines the effects of affecting parameters, including layer thickness, material gradation profiles, and viscoelastic properties, under impedance boundary conditions, thereby assessing their individual and combined influence on wave propagation behavior. The study demonstrates a pronounced sensitivity of Rayleigh-type wave characteristics to both impedance contrasts and material gradation parameters, highlighting the complex interplay between structural inhomogeneity and viscoelastic dissipation. These results provide valuable insights into the behavior of surface waves in engineered layered systems as well as in heterogeneous natural media. This work presents a novel framework for analyzing Rayleigh-type wave behavior under realistic boundary conditions and heterogeneous media. The findings have significant implications for geophysical exploration, structural health monitoring, and the design of advanced materials. Moreover, the results provide a solid foundation for future investigations in applied mechanics and wave-based diagnostics in layered viscoelastic systems.</p>