P-wave propagation in transversely isotropic media: I. Finite-frequency theory

We generalize the theory of 3D Fréchet kernels for P-wave traveltimes in isotropic media to the case of transversely isotropic media. Using the first-order Born approximation and the far-field approximation of the Green’s tensor, we show that three anisotropic perturbations of the stiffness tensor, in addition to the perturbation of the isotropic phase velocity, are required to describe the effects of hexagonal perturbations of the stiffness tensor. We derive the expressions of the scattering tensors and of the sensitivity kernels corresponding to the three anisotropic parameters.