Triplications for the converted wave in transversely isotropic media with a tilted symmetry axis

In seismic data processing, serious problems could be caused by the existence of triplication and need to be treated properly for tomography and other inversion methods. The triplication in transversely isotropic medium with a vertical symmetry axis has been well studied and concluded that the triplicated traveltime only occurs for S wave and there is no triplication for P and converted PS waves since the P wave convexity slowness always compensates the S wave slowness concavity. Compared with the vertical symmetry axis model, the research of the triplication in transversely isotropic medium with a tilted symmetry axis is still keeping blank. In order to analyse the triplication for the converted wave in the tilted symmetry axis model, we examine the traveltime of the triplication from the curvature of averaged P and S wave slowness. Three models are defined and tested in the numerical examples to illustrate the behaviour of the tilted symmetry axis model for the triplicated traveltime with the change of the rotation angle. Since the orientation of an interface is related to the orientation of the symmetry axis, the triplicated traveltime is encountered for the converted wave in the tilted symmetry axis model assuming interfaces to be planar and horizontal. The triplicated region is influenced by the place and level of the concave curvature of the P and S wave slowness.