CWP-752 Gradient computation for elastic full-waveform inversion in 2D VTI media

Full-waveform inversion (FWI) has proved effective in significantly improving the spa-tial resolution of seismic models. However, it is implemented mostly for isotropic me-dia and the applications to anisotropic models are often limited to acoustic approxima-tions. In a previous publication, we introduced a methodology for performing FWI of multicomponent (PP and PS) reflection data from a stack of horizontal, homogeneous VTI (transversely isotropic with a vertical symmetry axis) layers. Taking into account both anisotropy and elasticity in the description of the reflected wavefield makes it possible to resolve the interval Thomsen parameters and constrain the depth scale of the model. Here, we develop a foundation for extending elastic FWI to laterally het-erogeneous VTI media using the adjoint state method. The main focus is on deriving the gradients of the objective function with respect to the model parameters. To test the algorithm, we introduce Gaussian anomalies in the Thomsen parameters of a homo-geneous VTI medium and study the influence of the size of the anomaly, the source-receiver configuration, and the source polarization on the gradients. The model update for FWI can be produced by an appropriate scaling of the gradient using the steepest descent or similar methods.