In the seismic analysis of high-altitude earth-rockfill dams built on deep overburden layers, directly using surface ground motion records as bedrock input often leads to a systematic overestimation of the structural dynamic response due to the neglect of nonlinear site filtering effects. To solve this ill-posed inverse problem, we develop a ground motion inversion framework using the adjoint-state method with a 1D nonlinear wave equation. The key improvement is a nonlinear constitutive model with an internal state variable (accumulated equivalent strain ψ) and relaxation rate β, capturing strain-history-dependent stiffness degradation and hysteretic damping under large strains. The weighting parameter α (0≤α≤1) continuously blends instantaneous nonlinear response (α→0) and historical memory effects (α→1), thus enabling accurate representation of pre-failure hysteretic behavior typical of deep overburden soils under seismic loading. We also include a wave velocity correction for altitude-dependent freeze-thaw effects, calibrated from borehole temperature data at the dam site. Synthetic data tests (160m profile) show that the method converges reliably: reconstructed bedrock waveforms match targets with >95% ISO fit (median 97.2%), and peak acceleration errors are below 0.5% (mean 0.3%, σ 0.1%). We then applied the method to a 3D dam model with 132m and 264m overburden at Pangduo, Tibet. The inverted bedrock input removes artificial high-frequency resonances from the dam-foundation interaction. Compared to using surface records directly as bedrock input, our method cuts errors at key dam nodes from about ±30% (IQR 33%) to within ±5% (IQR 5.5%). This could reduce seismic design margins by 40-50%. This provides more reliable ground motion inputs for seismic design of high-altitude dams.