The Thomsen-Haskell method was used to determine sensitivities of the Rayleigh-wave phase velocities and spectral amplitude of vertical ground motion to insertion of a single velocity-anomaly layer into overburden underlain by a basement. The reference model comprised a 9-m thick overburden with shear-wave velocity (${ u}_s$ of 300 m/s above a half-space with ${ u}_s$ = 1000 m/s. The inserted layer, with a velocity of 150, 225, 375, or 450 m/s and a thickness of 1, 2, or 3 m, was placed at depths increasing from the surface in increments of 1 m. Phase velocities were computed for frequencies of 4 to 30 Hz. For inserted layer models, we placed an anomalous layer with thickness of 1 ~ 3 m, shear-wave velocity of 150 ~ 450 m/s, and at depths of 0 ~ 8 m in the overburden. The frequency range of 8 ~ 20 Hz were the most sensitive to the difference of $C_R$ between the inserted and reference models (${Delta}C_R$) for h = 1 m and the frequency range got wide as h increased. For all of the models, the spectral amplitudes of the fundamental mode exceeded those of the $1^{st}$-higher mode except at frequencies just above the low-frequency cutoff of the $1^{st}$-higher mode.