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Certain degree of smoothness of velocity models is required for most ray-based migration and tomography. Applying conventional smoothing in model parameters results in offset-dependent travel-time errors for reflected events, which can be large even for small contrasts in model parameters between the layers. This causes the shift in both the depth and residual moveout of the migrated images. To overcome this problem in transversely isotropic medium with a vertical symmetry axis, the preserved travel-time smoothing method was proposed earlier. We extend this method for orthorhombic media with and without azimuthal variation between the layers. We illustrate this method for a single interface between two orthorhombic layers and show that the smoothing-driven errors in travel time are very small for practical application.