We present measurements of $ u_{mu}$ charged-current cross section ratios on carbon, iron, and lead relative to a scintillator (CH) using the fine-grained MINERvA detector exposed to the NuMI neutrino beam at Fermilab. The measurements utilize events
of energies $2<E_{ u}<20~GeV$, with $left< E_{ u}right>=8~GeV$, which have a reconstructed $mu^{-}$ scattering angle less than $17^circ$ to extract ratios of inclusive total cross sections as a function of neutrino energy $E_{ u}$ and flux-integrated differential cross sections with respect to the Bjorken scaling variable $x$. These results provide the first high-statistics direct measurements of nuclear effects in neutrino scattering using different targets in the same neutrino beam. Measured cross section ratios exhibit a relative depletion at low $x$ and enhancement at large $x$. Both become more pronounced as the nucleon number of the target nucleus increases. The data are not reproduced by GENIE, a conventional neutrino-nucleus scattering simulation, or by the alternative models for the nuclear dependence of inelastic scattering that are considered.
