Non-linear Rayleigh waves are investigated theoretically in materials having inhomogeneous third order and homogeneous second order elastic properties. Compared to the complete homogeneous case, the constants coupling the harmonics turn out to depend on frequency. The sensitivity and selectivity to the three Murnaghan's constants is discussed considering mono- and bi-chromatic inputs in the mark of the quasi-linear approximation. Numerical examples are given for depth profiles characteristic of dislocation densities in shot-peened metals. The predicted low-frequency scales are consistent with observation recently reported.