Elastic full-waveform inversion for VTI media: A synthetic parameterization study

One of the main challenges for full-waveform inversion (FWI) is taking into account both anisotropy and elasticity. Here, we perform elastic FWI for a synthetic 2D VTI (transversely isotropic with a vertical symmetry axis) model based on the geologic section at Valhall field in the North Sea. Multicomponent surface data are generated by a finite-difference code. We apply FWI in the time domain using a multiscale approach with three frequency bands. An approximate inverse Hessian matrix, computed using the L-BFGS-B algorithm, is employed to scale the gradients of the objective function and improve the convergence. In the absence of significant diving-wave energy in the deeper part of the section, the model is updated primarily with reflection data. An oblique displacement source, which excites sufficiently intensive shear waves in the conventional offset range, helps provide more accurate updates in the Shear-wave vertical velocity, especially in the shallow layers. We test three model parameterizations, which exhibit different radiation patterns and, therefore, create different parameter trade-offs. Whereas most examples are for a constant-density model, we also generate a density field using Gardner's relationship and invert for the density along with the velocity parameters. The parameterizations that combine velocities and anisotropy coefficients generally yield superior results to the one that includes only velocities, provided that a reasonably accurate initial model is available.