Frequency-domain elastic full waveform inversion for VTI media

P>To describe subsurface structures in anisotropic media properly, particularly in transversely isotropic media with a vertical symmetry axis (VTI), which frequently appear in sedimentary basin environments, we develop a frequency-domain elastic full waveform inversion algorithm for 2-D VTI media. The inversion algorithm is based on the cell-based finite-difference modelling method and the adjoint state of the wave equation. Because the anisotropic inversion for VTI media deals with more elastic constants than the isotropic inversion, it is more prone to obtain local minimum solutions. For this reason, we may not succeed in properly describing the elastic constants of subsurface media if we only apply the standard inversion techniques to anisotropic waveform inversion. To compensate for the ill-posedness of the anisotropic waveform inversion, we couple elastic constants C-11 and C-33 based on Thomsen's relationship, which is also supported by the sensitivity analysis with respect to the parameters. To enhance the inversion results, we apply the frequency-selection strategy, moving from lower to higher frequencies and we carry out the inversion process over two stages. In both stages, all of the elastic constants are simultaneously optimized, as is done in the conventional waveform inversion. However, we only accept the inversion results for C-11, C-33 and C-44 at the first stage, which will be used as the starting models for the second stage and C-13 is reinitialized as a linearly increasing model. We apply our waveform inversion algorithm to a simple 3-layered model and a part of the overthrust model. For the 3-layered model, the first inversion stage is enough to yield reasonable inversion results for all of the elastic constants. For the overthrust model, the second stage is needed to enhance the inversion results for C-13.