Abstract
While velocity contrasts are responsible for most of the events recorded in our data, the long wavelength behavior of the velocity model is responsible for the geometrical shape of these events. For isotropic acoustic materials, the wave dependency on the long (wave propagation) and short (scattering) wavelength velocity components is stationary with the propagation angle. On the other hand, in representing a transversely isotropic with a vertical symmetry axis medium with the normal moveout velocity, the anellepticity parameter eta, the vertical scaling parameter delta, and the sensitivity of waves vary with the polar angle for both the long and short wavelength features of the anisotropic dimensionless medium parameters (delta and eta). For horizontal reflectors at reasonable depths, the long wavelength features of the eta model is reasonably constrained by the long offsets, whereas the short wavelength features produce very week reflections at even reasonable offsets. Thus, for surface acquired seismic data, we could mainly invert for smooth eta responsible for the geometrical shape of reflections. On the other hand, while the delta long wavelength components mildly affects the recorded data, its short wavelength variations can produce reflections at even zero offset, with a behavior pattern synonymous to density. The lack of the long wavelength delta information will mildly effect focusing but will cause misplacement of events in depth. With low enough frequencies (very low), we may be able to recover the long wavelength delta using full waveform inversion. However, unlike velocity, the frequencies needed for that should be ultra-low to produce long-wavelength scattering-based model information as delta perturbations do not exert scattering at large offsets. For a combination given by the horizontal velocity, eta, and epsilon, the diving wave influence of eta is absorbed by the horizontal velocity, severely limiting the eta influence on the data and full waveform inversion. As a result, with a good smooth eta estimation, for example, from tomography, we can focus the full waveform inversion to invert for only the horizontal velocity and maybe epsilon as a parameter to fit the amplitude. This is possibly the most practical parametrization for inversion of surface seismic data in transversely isotropic with vertical symmetry axis media.