Using well information to verify and improve waveform inversion results in transversely isotropic media

There is a fundamental problem with trade-offs between parameters in multiparameter full waveform inversion (FWI), including in transversely isotropic media with vertical axis of symmetry (VTI). In the parameterization using normal moveout (NMO) velocity $v_n$ and anisotropic parameters $\delta$ and $\eta$, the trade-off between $\delta$ (which relates the NMO velocity to depth) and the depth may cause shifts in the inverted NMO velocity. With the availability of well check-shot velocities, which often represent the vertical velocity, we develop a method to estimate the shifts at the well location and calculate a background $\delta$ model for additional iterations of FWI using this $\delta$ model. We apply the method to the VTI Marmousi II model and invert simultaneously for $v_{n}$, $\delta$ and $\eta$ parameters. Results show that we can use the assumed well velocities to estimate the required vertical shift and calculate a good background $\delta$ model. Using the background $\delta$ model, we can get a reliable NMO velocity model.