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The oversampling of wavefields in the vertical direction is effectively resolved by converting the vertical axis from depth to vertical time. Depending on lateral variation of the chosen vertical time, the resulting coordinate system can be made orthogonal or nonorthogonal. We derived wave equations for time extrapolation of both isotropic and anisotropic wavefields in the vertical time coordinate frame. Extrapolation in the vertical time domain features reduced computation cost due to elimination of oversampling in vertical direction. Using the $ \tau $ domain extrapolators, over $ 30\%$ speedup are observed for both isotropic and anisotropic RTMs.