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One-way Riemannian wavefield extrapolation (RWE) on computational<br>meshes conforming to the direction of turning-wave<br>propagation is presented as an alternative forward modeling<br>procedure for waveform inversion. Forward modeling tests<br>demonstrate that the RWE approach may be a sufficiently accurate<br>approximation for calculating the wavefield phases important<br>for early-arrival waveform inversion. Initial results indicate<br>that RWE waveforms are well matched at wide offsets to<br>finite-difference data, and can be used in a waveform inversion<br>scheme to invert synthetic data for 1D velocity perturbations.