Estimating Anisotropic Parameters in Vertically Transversely Isotropic Media Using Long-Offset Traveltime Approximations

Accurate estimation of anisotropic parameters in vertically transversely isotropic media is essential for reliable velocity modelling and seismic imaging in modern seismic exploration. However, long-offset seismic data often exhibit pronounced nonhyperbolic moveout, which leads to strong coupling between background velocity and anisotropic parameters and reduces the stability of conventional estimation approaches. To address this issue, we implemented a user-guided sequential parameter-estimation workflow within the framework of the classical two-step parameter-decoupling strategy. Specifically, a high-accuracy traveltime operator designed for long-offset data is employed in place of conventional low-order or fourth-order nonhyperbolic moveout approximations and is integrated with a semi-automatic moveout-flattening and parameter-selection procedure. Once the target reflection event, zero-offset time, offset windows, vertical P-wave velocity and candidate parameter ranges are specified, an objective-function-based grid search is used to select the optimal moveout parameters from the corrected reflection events. The resulting estimates of $V_{\mathrm{NMO}}$ and $\eta$ are subsequently used to recover the Thomsen anisotropic parameters $\delta$ and $\epsilon$. Numerical experiments on undulating layered models and applications to marine field reflection data demonstrate that the proposed approach effectively improves the reliability of anisotropic parameter estimation. The results indicate that the method provides an efficient and robust framework for estimating the anisotropic parameters of vertically transversely isotropic media and can offer reliable initial models for velocity model building and anisotropic seismic imaging under complex geological conditions.