Pavel Golikov

Accuracy comparison of nonhyperbolic moveout approximations for qP-waves in VTI media

There are many non-hyperbolic moveout approximations for VTI media with various accuracy claims. We perform an analytical and numerical comparison of the 11 moveout approximations developed for a homogeneous transversely isotropic medium with vertical symmetry axis (VTI). The comparison is based on evaluating their long-offset asymptotes and higher-order Taylor series coefficients computed for a VTI medium. To make the different approximations comparable we select approximation coefficients to preserve the fourth-order coefficient in Taylor series for traveltime squared. To make the comparison simpler, we define the traveltime as a function of normalized offset and one parameter which is the anelliptical parameter. We select the six best approximations and perform comparative analysis by plotting the asymptotic traveltime parameters and high-order Taylor coefficients versus anelliptical parameter. We also compute the relative error in traveltime for selected approximations for homogeneous and horizontally layered VTI models.

New weak-contrast approximation for reflection coefficients in transversely isotropic media

Using the qP-wave processing parameters and standard interpretation parameters, we derive a new weak-contrast approximation for qPqP- and qPqSV-reflection coefficients in a VTI medium. Being tested on few numerical models, the proposed approximation results in better accuracy compared with the standard weak-contrast approximation.

Moveout-based Geometrical Spreading Approximation in TTI Media

We derive moveout-based geometrical spreading approximations in TTI media and demonstrate their applicability with few numerical experiments. We propose a simple polynomial approximation and a rational one similar to well-known traveltime approximation. The accuracy tests show that the rational approximation provides significantly better accuracy especially for the large offsets. The proposed traveltime approximations can be easily extended for the multilayered TTI model with horizontal interfaces.

Asymptotical Comparison of Non-hyperbolic Moveout Approximations in a VTI Medium

In this paper, we perform the analytical and numerical comparison of the 11 moveout approximations for a homogeneous transversely isotropic medium with vertical symmetry axis (VTI) medium based on their long-offset asymptotes and high-order Taylor coefficients computed for VTI medium. To make different approximations comparable we select the approximation coefficients such that to preserve the fourth-order coefficient in Taylor series for traveltime squared. To make the comparison simpler, we define the traveltime as a function of normalized offset and one parameter which is the anelliptical parameter. We select six best approximations and perform comparative analysis by plotting the asymptotic traveltime parameters and high-order Taylor coefficients versus anelliptical parameter. We also compute the relative error in traveltime for selected approximations.

Traveltime Parameters for Vertically Heterogeneous 2D TTI Media

In this paper, we derive the traveltime parameters for 2D vertically heterogeneous transverse isotropic model with tilted axis of symmetry (TTI) model. We show that in case of one-way propagation there are two more traveltime parameters in additional to the standard ones (the vertical traveltime, the normal moveout velocity and the heterogeneity coefficient) such as reflection point sideslip and anti-symmetrical parameter. The comparison performed for synthetic multilayered TTI model shows that the effective TTI traveltime parameters are strongly affected by the tilt value. To illustrate the effect of tilt we compare the effective traveltime parameters for the VTI and TTI multilayered models. The most dramatical difference is observed for heterogeneity coefficient. We also compute the traveltimes for these models and denote significant difference due to the presence of tilt.

Application of Perturbation Theory to TTI Media

Using an elliptical tilted TI medium as a background we apply the perturbation method to compute both the eikonal and the slowness surface equations in a general TTI medium.

Inversion of traveltime parameters in tilted TI media

We derive the exact expressions for traveltime parameters in tilted transversely isotropic media. It is shown that weak‐anisotropy approximation gives sufficient accuracy for small values of the tilt. The inversion of traveltime parameters suffers from ambiquity problem that is linked to certain tilt intervals.