<p>The mechanical properties of natural geological media often evolve continuously with depth, leading to a strong spatial dependence of the wave equation coefficients, which poses a formidable theoretical challenge for the analytical solution of wave fields. Breaking through the limitations of traditional uniform or simply layered models, this study innovatively constructs an inhomogeneous medium model in which the shear modulus varies continuously in a logarithmic form along the vertical direction. By introducing complex variable functions and conformal mapping techniques, this research successfully overcomes the bottleneck of solving the variable-coefficient Helmholtz governing equation by equivalently transforming it into a solvable standard form. Consequently, an explicit series analytical solution for the scattered wave field of a shallow circular tunnel subjected to incident SH waves is derived. Theoretical and numerical analyses reveal that, compared with homogeneous media, vertical inhomogeneity significantly reshapes the wave propagation paths and scattering patterns, and profoundly modulates the dynamic stress concentration behavior around the cavity. Based on the established analytical framework, the complex coupled modulation mechanisms among multiple factors including the medium’s inhomogeneity gradient, incident wavenumber, and tunnel depth—are systematically quantified. This study not only provides a novel theoretical perspective on the wave field distortion mechanisms in continuously inhomogeneous media but also offers solid theoretical support for the seismic design of underground structures and the accurate identification of dynamic weak zones under complex geological conditions.</p>