Explicit Fréchet Derivatives for 3-D Frequency-Domain Seismic Full-Waveform Inversion in Viscoelastic Tilted Transversely Isotropic Media and Fully Parallel Implementations

The Fréchet derivatives or sensitivity kernels of the observed seismograms are fundamental to seismic full-waveform inversion (FWI). They quantitatively measure the seismogram variations caused by any physical parameter perturbation of the Earth's subsurface. The 3-D viscoelastic tilted transversely isotropic (TTI) media are often encountered in practices due to the presence of dip thin layers, joints, fractures or cracks, orientated grains or crystallization, and water or gas saturation. To image such subsurface, we have derived explicit 3-D frequency-domain Fréchet derivatives of the seismogram spectrum with respect to 13 independent physical parameters of TTI rock, which include density, five elastic moduli, five Q-factors, and inclination and declination angles of the symmetric axis of rock structure. We have demonstrated a fully parallel implementation to compute the Fréchet derivatives and conduct synthetic subsurface imaging experiments, in which the 13 independent parameters of the subsurface targets are successfully reconstructed. The experimental results have verified the correctness and validity of the derived 3-D Fréchet derivatives for imaging viscoelastic TTI media.