New traveltime approximations for VTI media and estimation of the Thomsen parameters

Conventional velocity analysis estimates the normal moveout velocity which corresponds to a combination of the P-wave vertical velocity and the anisotropy parameter δ for a transversely isotropic medium with a vertical axis of symmetry. We propose in this study a joint estimation of (pseudo-acoustic) P-wave velocity and Thomsen parameters with new traveltime approximations and a deterministic inversion algorithm with regularization by derivative matrices. The new traveltime expressions are based on rational approximations, with analytical expressions that are simple to use. Therefore, the new approximations improved the joint inversion performance by reducing algebraic complexity. Computationally, the algorithm is efficient due to the use of small matrices; it simplifies calculations without losing precision. The experiments with synthetic models validated the approach and the numerical simulations indicated that the proposed approximations have in average an accuracy similar to the expressions available in the literature. The tested model considered lateral velocity variation, increasing the challenge in relation to a flat-layered model. In particular, the phase and group velocity approximations presented better accuracy between 40 and 60 degrees. For traveltime computation the proposed approach presented better accuracy for offsets greater than 4 km.