Elastic full waveform inversion for tilted transverse isotropic media: A multi-step strategy accounting for a symmetry axis tilt angle

Transversely isotropic media with a tilted symmetry axis (TTI) exits widely underground due to tectonic movement and mineral orientation. Traditional full waveform inversion (FWI) based on isotropic media or transversely isotropic media with a vertical symmetry axis (VTI) cannot deal with such situations. To address this limitation, TTI–based FWI was developed. However, its practical application faces challenges in estimating the symmetry axis tilt angle ${\theta }_t$. Previous studies have generally assumed that ${\theta }_t$ is equal to the strata dip angle, which is incorrect in complex structures such as salt domes and magmatic intrusion zones. Another theoretically robust way to estimate ${\theta }_t$ is to treat it as the parameter to be inverted, but there are still some problems unresolved. First, the parameter ${\theta }_t$ increases the nonlinearity of the inversion process, and its impact mechanism on inversion is not yet clear. Second, there is severe crosstalk (also known as trade-off or coupling) between parameters, but the current parameter decoupling technique for TTI–based FWI is not mature. To address the first problem, we assess the interaction between ${\theta }_t$ and other parameters by analysing the radiation patterns in the TTI background. Our analysis reveals that ${\theta }_t$ is most coupled by S-wave vertical velocity $v_{s0}$, and ${\theta }_t$ substantially affects anisotropic parameters $\epsilon$ and $\delta$. Therefore, we conclude that a good inversion of velocity parameters is a prerequisite for recovering ${\theta }_t$, and only after ${\theta }_t$ recovers can $\epsilon$ and $\delta$ be recovered. This conclusion provides a natural perspective for solving the second problem. We therefore propose a multi-step and multi-parameter joint inversion strategy to gradually improve the quality of parameter inversion and weaken their coupling. Numerical experiments demonstrate that our strategy achieves more accurate inversion results compared to previously proposed multi-parameter inversion strategies. Finally, the application to the field OBN dataset acquired from the South China Sea verifies the practicality of our method.