Tilted transverse isotropy (TT!) is increasingly recognized as a more geologically plausible description of anisotropy in sedimentary formations than vertical transverse isotropy (VTI). Although model-building approaches for VTI media are well understood, similar approaches for VTI media are in their infancy, even when the symmetry-axis direction is assumed known. We describe a tomographic approach that builds localized an isotropic models by jointly inverting surface-seismic and well data. We present a synthetic data example of anisotropic tomography applied to a layered TTI model with a symmetry-axis tilt of 45 degrees. We demonstrate three scenarios for constraining the solution. In the first scenario, velocity along the symmetry axis is known and tomography inverts for Thomsen's epsilon and delta parameters. In the second scenario, tomography inverts for epsilon, delta, and velocity, using surface-seismic data and vertical check-shot travel-times. In contrast to the VTI case, both these inversions are nonunique. To combat nonuniqueness, in the third scenario, we supplement check-shot and seismic data with the delta profile from an offset well. This allows recovery of the correct profiles for velocity along the symmetry axis and E. We conclude that TTI is more ambiguous than VTI for model building. Additional well data or rock-physics assumptions may be required to constrain the tomography and arrive at geologically plausible TTI models. Furthermore, we demonstrate that VTI models with atypical Thomsen parameters can also fit the same joint seismic and check-shot data set. In this case, although imaging with VTI models can focus the TTI data and match vertical event depths, it leads to substantial lateral mispositioning of the reflections.
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